Combined True Time Delay System Based on Inductor- less CMOS True-Time-Delay Cell

Combined True Time Delay System Based on Inductor- less CMOS True-Time-Delay Cell | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Combined True Time Delay System Based on Inductor- less CMOS True-Time-Delay Cell Ahmad Yarahmadi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5728795/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A novel true-time delay (TTD) system for 1-5GHz applications is presented in this paper. Conventional TTD systems must be better optimized in low frequencies. Most existing structures use transmission lines (TLs), artificial transmission lines (ATLs), or LC ladder structures, which result in large chip areas due to the size of the inductors. Some systems employ two different delay cells in their topologies, which is not desired for integration purposes. To address these issues, a combined true-time delay cell system (CTTDS) is proposed. This system consists of N-semi-identical building blocks, which can be cascaded to provide sufficient delay. Each block includes nearly identical TTD cells. A 4-bit resolution delay system with a 14 ps delay step and a total delay of 210 ps demonstrates the concept. The delay cells are inverter-based, inductor-less designs with resistive feedback to ensure wideband operation. Single pole dual throw (SPDT) switches are used to select the proper path for each cell in the system. This design is designed in TSMC 180nm CMOS technology. CMOS true-time delay cell timed array receiver true time delay system CMOS delay line all-pass-filter based Delay system Wideband CMOS all-pass-filter Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction There are several topologies in the literature for True time-delay systems. The ‘Trombone’ structure is a fundamental design where the signal encounters delay as it goes through the delay line, similar to a physical trombone [ 1 ]. This design is suitable for high-frequency applications, as the trombone can be easily implemented with a TL. For lower frequencies, LC ladders or ATLs are employed, but the large size of inductors at these frequencies creates area challenges [ 2 , 3 , 4 , 5 ]. The ‘fine and coarse tuning’ TTD system provides high delay resolution but requires separate blocks for fine and coarse delay steps [ 6 ]. Consequently, this design is unsuitable for integration or mass production due to the need for two separate delay lines. Several approaches have been proposed to address these limitations. Some designs employ ATLs or LC ladder structures for both blocks [ 7 , 8 ], which are effective at higher frequencies. However, these methods face area constraints at frequencies below 5GHz. Active delay cells offer potential solutions but cannot be easily cascaded in such designs due to the use of differing delay blocks. Switch-based TTD systems inspired by the ‘Trombone’ structure offer another alternative. These systems use cascaded, identical or semi-identical delay cells to form the delay line [ 9 ]. However, achieving high-resolution delay requires too many delay cells, leading to increased power consumption in active designs and area challenges in passive ones. Using fewer delay cells reduces resolution, while employing different delay cells introduces inconsistencies in performance across the delay line [ 10 , 11 , 12 , 13 ]. This paper presents a novel topology to address the mentioned issues. As shown in Fig. 1 , the Combined True Time Delay System achieves high delay with the required resolution while maintaining compactness and consistency in delay cell design. 2. The proposed structure As discussed above, TTD systems are typically designed for wideband and high-frequency applications. While TL-based TTD systems are used in these applications. As frequency decreases, ATL or LC ladder-based structures are applicable, too. However, these methods are not promising for low frequencies (below 5GHz, for example). So, another structure must be developed and optimized for low-frequency delay systems. As shown in Fig. 1 , the proposed CTTDS addresses this issue by reducing the number of delay cells and employing inductor-less designs. For instance, in a timed array system with four antennas spaced 3 cm apart, the required delay ranges from 14 ps to 210 ps, corresponding to phase shifts of 8° to 45°. [ 15 ]. Traditional approaches, such as TL-based or ATL-based TTD systems, are impractical due to area constraints. The proposed system achieves the desired delay using inductor-less TTD cells, significantly reducing area and power consumption. The multiplex switch-based structure needs 21 steps for this delay amount and resolution. This issue can be done with active delay cells to avoid area issues. Inductor-less TTD cells are used in the TTD systems to ensure the structure’s compactness. However, 21 delay cells consume too much power. The number of delay calls can be reduced if the switch-based structure is used. Since the lowest delay is 14ps and the largest one is 210ps (*15 times difference), the TTD system may need two types of delay cells. This matter is inappropriate for mass production and integration purposes of the TTD system. The fine and coarse delay cells can provide this resolution and delay with much fewer delay cells. However, unfortunately, the above issue is still present here, too. The CTTDS requires only four blocks to achieve a 210 ps delay. This design reduces the number of delay cells by half while maintaining the necessary resolution. Each block contains almost identical TTD cells, ensuring compactness and suitability for integration. Table 1 compares the proposed system with other TTD structuresFinally, with a 3x times difference between delay amounts, the similarity of the cells is ensured. Table 1 summarizes the power consumption, chip area, and required delay cells for the mentioned application of the TTD system. As shown in this table, the proposed topology consumes more power than the fine and coarse structure, but since it has similar delay cells, it will be better for integration. Table 1 The performance of the five TTD system structures for 1-5GHz applications TTD system Number of TTD cells Occupied chip area ability for Integration Power consumption The ‘trombone’ structure [ 2 ] 21 cells (if ATL or LC ladder is used) VERY HIGH (with TL-based passive cells) HIGH (with ATL or LC passive TTD cells) BAD (very bulky because of TL or ATL-based TTD cell ) LOW (passive structure) The ‘switch-based’ structure [ 10 ] 6 cells (steps: 12.5ps, 25ps, 50ps, 100ps, 200ps, 262.5ps ) LOW (with inductor-less active cells) Median (with inductor-based active cells) Median (different delay cells for the system) Almost LOW (acceptable number of delay cells) The multiplex structure [ 9 ] 21 identical cells Median (with inductor-less active cells) Almost High (inductor-based active cells) GOOD (all TTD cells are identical) HIGH (active TTD cells) The ‘fine and coarse tunning’ structure [ 6 ] 5 cells (Fine part:12.5ps, 25ps, 50ps Coarse part: 87.5ps, 175ps) LOW (with inductor-less active cells) Median (with inductor-based active cells) Median (different delay cells ) Almost LOW (acceptable number of delay cells) The proposed CTTDS 3 blocks with overall 9 cells (steps:12.5ps, 25ps, 50ps) VERY LOW (with inductor-less active cells) Median (with inductor-based active cells) GOOD (Almost identical cells) Median (active cells) 3. Proof of concept To validate the proposed system, four inductor-less TTD cells were redesigned based on [ 16 ] and [ 24 ]. The ideal transfer function (TF) of the TTD cell can be approximated with the Pade approximation. The TTD cells utilize CMOS inverters with resistive feedback, forming an all-pass filter. The delay can be tuned by adjusting the capacitor (C) and resistor (R). For this study, delays of 14, 28, 56, and 112 ps were achieved. However, delays above 28 ps exhibited variations exceeding 10%. To address this, a forward body bias technique was applied to ensure a flat delay response across the 1-5GHz bandwidth. Figure 2 illustrates the inverter-based TTD cell, while Fig. 3 shows the linearity of the delay response. To investigate the reason for this matter, it is worth finding out the maximum available delay with acceptable delay variations (max 5% delay variations over the frequency band of interest). As mentioned before, the Pade approximation is used to create the TF of the all-pass filter and then it will be used as a delay cell. In this case, if the true time delay is equal to the group delay, it can be said that the delay response will be linear. As a consequence, the delay variations will be limited [ 17 ]. For this fact, the relationship between true time delay \(\:\left({\tau\:}_{T}\right)\:\) and group delay ( \(\:{\tau\:}_{g}\) ) can be calculated as follows: From (1), it is evident that a linear phase relationship with frequency is required for equal true time delay and group delay. This equation is the exact purpose and characteristic of an ideal TTD cell. So, it is necessary to find a proper range for the linear phase response of a TTD cell. The proposed TTD cell’s TF comes from first-order Pade approximation. With this in mind, the phase response of this TF can be calculated as follows: from (2), the phase response has a linear relation with frequency. This equation is arctangent-based. As shown in Fig. 3 , this equation is linear up to 0.4 Radian (23 degrees). It means that until the phase argument reaches this amount, the output of the TTD cell will remain linear. From the above equations, the maximum delay at 5GHz (which is used for this paper`s application) will be around 28ps. For the first order Pade approximation, 28ps delay is the maximum available wideband delay. So for larger delays, it is necessary to use some circuit-level or system-level approaches (like delay lock loop, master-slave circuit, and so on) for having a flat wideband delay [ 17 , 18 ]. So, it shows why other TTD cells in the literature have more than 10% delay variations for over 28ps delays in this frequency band [ 19 , 20 , 21 , 22 ]. So, to overcome this issue, [ 24 ] provides a forward body bias technique, which is used here for redesigning the last two delay cells. The design of the proposed system requires four cascaded delay cells, as shown in the Fig. 4 , where the delay cells provide delays of 14, 28, 56, and 112 picoseconds, respectively. As a result, the system can offer delays ranging from 0 to 210 picoseconds. The design of this delay system requires two key elements: delay cells and switches. For the first two delay stages (14 and 28 picoseconds), the CMOS inverter-based delay cell concept which is reported in [ 16 ] is used. For the third and fourth delay stages (56 and 112 picoseconds), an improved delay cell concept was employed [ 24 ]. The CTTDS and so the delay cells are simulated in 180nm CMOS technology. The delay/frequency response of these four cells, individually and not as part of a delay system, is shown in the Fig. 5 . This paper uses forward body bias to manipulate the threshold voltage of the TTD cell’s devices to optimize the delay cells. So flat wideband delay response is achieved with this technique As shown in the Fig. 5 , the desired smooth and wideband delay across the frequency band of interest has been achieved. The 14-picosecond delay cell shows a 2% variation over the bandwidth, with a maximum delay of approximately 14.15 picoseconds. The 28-picosecond cell exhibits a 5% variation, with a maximum delay of 27.15 picoseconds. Similarly, the 56-picosecond cell shows a 5% variation with a maximum delay of 56.10 picoseconds, and the 112-picosecond cell demonstrates a 5% variation, with a maximum delay of 113.11 picoseconds. Each delay cell, however, has slight losses, suggesting that for designing a complete receiver, it is necessary to include an amplifier at the beginning and end of the line. For the switch section of the delay system, this study used SPDT switches, presented in [ 23 ]. With these switches, delay steps from 0 to 210 picoseconds can be achieved with a single output channel, eliminating the need for multiple outputs for this structure. For the proposed system, we need eight switches, which can be programmed using 4 bits, enabling us to achieve all desired delays. This system has 16 states. First state is 0000, where the input signal experiences no delay. And the last state is 1111, where all delay cells are included in the line leading to maximum delay to the signal. These simulation results are summarized in Table 2 . In this table, switches S1 to S8 are opened and closed according to the settings in the table. Switches 1 and 2 control the first delay cell (14 ps), switches 3 and 4 control the second delay cell (28 ps), switches 5 and 6 control the third delay cell (56 ps), and switches 7 and 8 control the fourth delay cell (112 ps). These 16 states create the desired time-delay steps. One key point that stands out in Table 2 is that our switches introduce a total of 32ps of delay, making this the minimum delay for the entire system. In the absence of any delay cells, the input signal still experiences this amount of delay. The maximum delay is 248ps, and our system can provide delays between these two values with 16 steps. As a result, the total achievable delay is approximately 217ps (248.1ps − 30.88ps = 217.22ps), and for the 16 states, the average delay step is 13.5ps (217.22ps / 16 = 13.57ps), which is close to the target of 14 ps. This step size corresponds to a delay resolution of approximately 3.86 bits (the initial target was a 4-bit delay resolution). Table 2 Performance of the proposed time-delay system S7, S8 S5, S6 S3, S4 S1, S2 state Nominal delay (pS) Delay step is 14pS Delay (pS) Delay step (pS) Delay step variation D.V. S21 (dB) 0 0 0 0 0 0 (av 32pS for SPDT) 30.88–32.75 7% 5% -5.5 - -4.6 14.2–15 0 0 0 1 1 14 (46) 45.08–47.75 9% 5% -6.2 - -5.3 15.3–14.9 0 0 1 0 2 28 (60) 60.42–62.68 10% 3% -7.5 - -5.3 12.6-14.37 0 0 1 1 3 42 (74) 73.01–77.05 8% 5% -8.5 - -6 12.8–15.3 0 1 0 0 4 56 (88) 85.81–92.36 9% 7% -6 - -4.8 13.3–15.7 0 1 0 1 5 70 (102) 99.16–108.1 12% 8% -6.5 - -5.6 12.7-14.04 0 1 1 0 6 84 (116) 113.2-120.8 9% 6% -7.5 - -5.5 12.6–14.2 0 1 1 1 7 98 (130) 125.8–135.0 10% 6% -8.5 - -6.2 15-13.2 1 0 0 0 8 112 (144) 140.8-148.2 7% 5% -5.5 - -4.8 14.2–13 1 0 0 1 9 126 (158) 155.0-161.2 7% 4% -6.2 - -5.5 12.1–15.8 1 0 1 0 10 140 (172) 167.1–177.0 13% 5% -7.5 - -5.5 15.9–12.5 1 0 1 1 11 154 (186) 183.0-189.5 12% 4% -8.5 - -6.2 15.7–12.5 1 1 0 0 12 168 (200) 198.7–202.0 15% 2% -5.9 - -4.9 13.1–16.1 1 1 0 1 13 182 (214) 211.8-218.1 13% 3% -6.4 - -5.7 12.1–15.8 1 1 1 0 14 196 (228) 223.9-233.9 4% 3% -7.6 - -5.6 13.4–14.2 1 1 1 1 15 210 (242) 237.3-248.1 - 4% -8.6 - -6.4 Another evident point in the table is that the maximum absolute error is 8%, which is below the 10% tolerance limit. This is due to the use of body-biasing for the larger delay cells and the optimized design of the smaller delay cells. Furthermore, the smooth delay behavior for larger delay values is achieved through the adjustable body-biasing voltage of the two larger delay cells. As shown in the table, the smoothness of the gain improves for these states compared to the initial cases. Although, it is expected to start with a zero delay, and reach a final delay of 210 ps. However, with the given minimum delay, introduced by the switches ( it is approximately 32ps), a nominal delay column is shown, versus the actual delay provided by the structure. In all cases, the desired delay for the input signal is provided at the output node.The delay step differences are one of the critical factors in this system. In the worst case, our system exhibits less than 15% step error, indicating acceptable accuracy of the proposed structure. Figure 6 shows the delay response of the proposed delay system for different delay line configurations, ranging from the 0000 to the 1111 state. The figure demonstrates that the system provides a smooth delay from the minimum to the maximum delay with acceptable accuracy. The proposed structure exhibits relatively flat insertion loss. The worst-case insertion loss is less than 8.5dB. So, for designing a phased-array receiver based on this system, it is necessary to include a signal amplifier to the structure. In Fig. 7 , the insertion losses for different time-delay system configurations can be observed. Since the proposed system is intended to be as a part of a phased-array receiver, impedance matching at the input across different delay settings is essential. The S 11 parameter of the system has been evaluated for this purpose. As shown in Fig. 8 , the system provides the required minimum impedance matching in almost all cases. The proposed system was simulated for temperature variations from − 40°C to 125°C and for supply voltages ranging from 1.6V to 2V for the delay cells and switches. These simulations were performed for fast, typical, and slow corners, and the results are summarized in Table 3 . Table 3 Various simulation corners for the proposed delay cell Typical temperature (T) corner 27 o C Typical supply voltage (T) corner 1.8V Fast temperature (F) corner 125 o C Fast supply voltage (F) corner 2V Slow temperature (S) corner -40 o C Slow supply voltage (S) corner 1.6V FF: Fast - Fast SF: Slow - Fast SS: Slow - Slow FS: Fast - Slow TT: Typical - Typical The unconditional stability of the structure is ensured by the Rollet stability factor (K) where K is being greater than one, and the stability measure is always positive. Additionally, if the load stability factor (mu) is always greater than one, it is sufficient to guarantee stability. Similarly, if the source stability factor (mu_prime) is greater than one, the structure will be stable without any conditions. These four factors were observed, and stability was guaranteed based on these criteria. comprehensive simulations were conducted for all corners, and the results are shown in the Table 4 . The table presents the worst performance for each of the 16 time-delay system configurations among the (FF, FS, SF, SS, TT) corners. According to the table, the worst-case output for the source stability factor (mu_prime) was found in the SF corner for most cases. For the load stability factor (mu), the worst output occurred in the SS corner in most cases. For the Rollet stability factor, the worst output was also in the SS corner. In terms of the stability measure, the worst output was observed in the TT corner in most cases. However, in all these cases, the minimum requirements for unconditional stability were met, with exact values for the worst-case scenario provided in the table. Regarding the S 11 parameter, the worst performance occurred in the SF corner, but even in this case, the system maintained the necessary impedance matching, with S 11 being less than − 8.3dB. For the S 21 parameter, the worst performance was observed in the FF corner, where the system still maintained the required matching, with S 21 being less than − 5.5dB. Concerning delay variations across the desired bandwidth, the SF and FF corners exhibited the worst performance, with a delay variation of up to 11% in the worst case. Table 4 The corner analysis results for the proposed delay cell S7, S8 S5, S6 S3, S4 S1, S2 state Mu stability factor Mu_prime stability factor K (Rollett) stability factor stability measure S 11 (dB) S 21 (dB) Delay Variation 0 0 0 0 0 1.864 2.355 2.41 1.15 <-8.3 <-5.5 7% 0 0 0 1 1 1.842 2.493 2.21 1.05 <-8.4 <-5.9 6% 0 0 1 0 2 1.723 2.225 1.87 0.89 <-8.3 <-5.9 5% 0 0 1 1 3 1.962 2.013 1.94 0.98 <-8.5 <-6.8 7% 0 1 0 0 4 1.912 1.912 2.01 1.12 <-8.4 <-5.7 9% 0 1 0 1 5 1.825 1.963 1.64 1.09 <-8.9 <-6.2 11% 0 1 1 0 6 1.726 1.712 1.95 1.02 <-8.5 <-6.2 9% 0 1 1 1 7 1.698 1.842 1.74 0.94 <-8.5 <-7.2 8% 1 0 0 0 8 1.626 1.926 1.62 0.87 <-8.4 <-6.9 7% 1 0 0 1 9 1.701 1.954 1.81 0.75 <-9.1 <-5.6 7% 1 0 1 0 10 1.759 1.859 1.75 0.92 <-8.3 <-6 7% 1 0 1 1 11 1.958 1.665 1.85 0.81 <-8.5 <-6 6% 1 1 0 0 12 1.678 1.965 1.49 0.79 <-8.6 <-7.1 4% 1 1 0 1 13 1.546 1.695 1.44 0.86 <-8.4 <-5.7 4% 1 1 1 0 14 1.523 1.561 1.45 0.82 <-8.3 <-7.3 5% 1 1 1 1 15 1.474 1.584 1.36 0.79 <-8.9 <-6.2 7% To evaluate the impact of device mismatches in the structure, Monte Carlo simulations were performed, assuming a mismatch in all available circuit components for 250 instances. For one of the worst cases (state 5), the maximum acceptable delay variation was analyzed, revealing that in 96% of cases (240 instances), the delay variations remained below 10%, indicating that the structure can achieve the desired delay with good resistance to variation. Examining other delay states also demonstrated that they have good resistance to variations within an acceptable 10% range. Analysis of the insertion loss showed that in 94% of cases, the maximum insertion loss was better than − 4.5dB. Input and output impedance matching simulations indicated that in 93% of cases, the maximum S 11 was less than − 10dB. Figure 9 presents the results of Monte Carlo simulations for 250 instances, showing the histogram of the maximum S 11 values at the input of the desired time-delay system. The stability factor (K) was always greater than one, and the stability measure was always positive in all cases. The load and source stability factors were also checked, confirming that both remained above one in all cases, indicating that the structure is unconditionally stable. Based on these simulations, it can be confidently stated that the proposed delay system is resistant to PVT (Process, Voltage, Temperature) variations, mismatches, and other parasitic effects. The 1dB compression point (P1dB) of this structure was also simulated, and the maximum P1dB, when all delay cells are engaged and at 3 GHz, was found to be -26.8dBm. The P1dB for other delay configurations is listed in the Table 5 . Additionally, the DC power consumption of this delay system, with a 1.8V power supply, was measured at 101mW. Table 5 P1dB values for different delay configurations of the proposed time-delay system S7, S8 S5, S6 S3, S4 S1,S2 state P1dB (dBm) 0 0 0 0 0 11.5 0 0 0 1 1 -3 0 0 1 0 2 -5.6 0 0 1 1 3 -7.3 0 1 0 0 4 11.9 0 1 0 1 5 -9.1 0 1 1 0 6 -12.2 0 1 1 1 7 -15.8 1 0 0 0 8 11.5 1 0 0 1 9 -14.7 1 0 1 0 10 -16.8 1 0 1 1 11 -17.4 1 1 0 1 13 -20.4 1 1 1 0 14 -23.4 1 1 1 1 15 -26.8 In Table 6 , the performance of the proposed structure is compared against other delay systems presented in recent years. This comparison shows that the performance of the proposed system, along with its inductor less delay cells, is acceptable. It should be noted that the compared structures include auxiliary amplifiers, while the proposed system does not utilize such an amplifier. However, considering its intended application, an amplifier can be added either at the input or output of the structure as needed. Table 6 Performance comparison of the proposed delay system against other recent delay structures [ 25 ] * [ 26 ] ^ [ 4 ] ^ This Work Process (CMOS) 0.18 0.18 0.14 0.18 Supply (V) 1.8 1.8 1.8 1.8 Frequency (GHz) 3–5 3–5 1-2.5 1–5 Delay Range (ps) 385–540 0-250 14–250 32–248 Delay Resolution (ps) 6 8 14 14 Average Gain (dB) 2–7 14–22 12–15 -7.2 - -5.5 $ Average P1dB (dBm) -27 N/A -28 -26 Power (mW) 106 151 250 101 Size (mm2) 2 N/A 1 1.5 *simulation, ^Measurement, $Without auxiliary amplifier 4. Conclusion This paper introduces a novel Combined True Time Delay System optimized for applications below 5GHz. The system features semi identical blocks of inductor-less TTD cells, making it compact and suitable for integration. Compared to existing designs, the proposed system demonstrates superior performance in terms of area efficiency, delay resolution, and power consumption. 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IEEE, 2014. Yarahmadi, Ahmad, and Abumoslem Jannesari. "A PVT resilient true‐time delay cell." IET Circuits, Devices & Systems 17, no. 2 (2023): 95-110. Aghazadeh, S. R., Herminio Martinez-Garcia, Enrique Barajas-Ojeda, and Alireza Saberkari. "A 3–5-GHz, 385–540-ps CMOS true time delay element for ultra-wideband antenna arrays." AEU-International Journal of Electronics and Communications 149 (2022): 154175. Qiu, Lei, Supeng Liu, Zhongyuan Fang, and Yuanjin Zheng. "An adaptive beamforming technique for UWB impulse transceiver." IEEE Transactions on Circuits and Systems II: Express Briefs 66, no. 3 (2018): 417-421. Garakoui, Seyed Kasra, Eric AM Klumperink, Bram Nauta, and Frank E. van Vliet. "Compact cascadable gm-C all-pass true time delay cell with reduced delay variation over frequency." IEEE journal of solid-state circuits 50, no. 3 (2015): 693-703. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5728795","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":398302102,"identity":"03f6a6a7-44ce-46f8-8825-df647eb89203","order_by":0,"name":"Ahmad Yarahmadi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVRIiWNgGAWjYDACCSDmAbNAJJuEHFgEBNiI1WJMshaGxAYJXEqhgH92d+KHNwyH5c3bzx7d8KPMIr1/du8zCYYaOwY+6QPYLblzdrPkHIbDhnPO5KXd7DknkTvjznEzCYZjyQxsfAnYrbmRu0Gah+Ew4wyGHLMbvG0SuQ030tgkGNgOMLDxYNchfyN382+gFvsZ/G/Mbv5tk0iXB2v5h1uLwY3cbSBbEmdI5JjdBtqSYADSwtiGW4shUIvlHIP05BkSb8xuy5yTMNx45xizRWJfMg8uLXJAh914U2FtO4M/x+zmm7I6ebnbbYw3Pnyzk5Pvwa4F6rxmNIEEWGThBnUE5EfBKBgFo2BEAwA8k1dPZvDoggAAAABJRU5ErkJggg==","orcid":"","institution":"Ayatollah Boroujerdi University","correspondingAuthor":true,"prefix":"","firstName":"Ahmad","middleName":"","lastName":"Yarahmadi","suffix":""}],"badges":[],"createdAt":"2024-12-29 07:23:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5728795/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5728795/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":73282075,"identity":"58153d30-0ce9-4332-9ecc-b688cf185e49","added_by":"auto","created_at":"2025-01-08 12:44:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":68256,"visible":true,"origin":"","legend":"\u003cp\u003eThe proposed Combined True Time Delay System\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/63db6c0ead06940b4145c2b2.png"},{"id":73282083,"identity":"e3153ea1-3b9a-4bff-b949-82acd4679dcd","added_by":"auto","created_at":"2025-01-08 12:44:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":252149,"visible":true,"origin":"","legend":"\u003cp\u003eThe inverter-based TTD cell and its layout proposed in [16] and used in this paper to create the CTTDS\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/ec17d9656bb0c79ff9a2250a.png"},{"id":73282076,"identity":"0790dbff-4cd5-4303-96f2-5ea97180bfde","added_by":"auto","created_at":"2025-01-08 12:44:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":29208,"visible":true,"origin":"","legend":"\u003cp\u003eThe plot of y=arctan(x) VS y=x\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/01e4ea99f4504167aae2a346.png"},{"id":73282081,"identity":"7cb3cc64-184d-4352-ad53-227a7d9e08ec","added_by":"auto","created_at":"2025-01-08 12:44:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":60822,"visible":true,"origin":"","legend":"\u003cp\u003eProposed delay system for achieving a 210-picosecond delay\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/5448075ba5acd534cd2b5222.png"},{"id":73282082,"identity":"9e4f3c6a-fe49-485f-95f9-f2a733ced59f","added_by":"auto","created_at":"2025-01-08 12:44:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":80331,"visible":true,"origin":"","legend":"\u003cp\u003eThe output of the designed delay cells for achieving the desired 210-picosecond delay\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/744ae33f3961eff70fbe2b00.png"},{"id":73282095,"identity":"3cde14c6-f72c-4183-a348-bc4c6aafdee5","added_by":"auto","created_at":"2025-01-08 12:44:45","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":89491,"visible":true,"origin":"","legend":"\u003cp\u003eThe delay of the proposed time-delay system for various configurations, from the 0000 to the 1111 state\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/9f54fe212b1b1582b8cba4ca.png"},{"id":73282080,"identity":"91ab17b9-82a4-46b8-b1b5-7150bdfae1d5","added_by":"auto","created_at":"2025-01-08 12:44:44","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":132813,"visible":true,"origin":"","legend":"\u003cp\u003eThe insertion loss of the proposed time-delay system for various delay line configurations, from the 0000 to the 1111 state\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/e4e5b523e79f8ea83d503ab8.png"},{"id":73282482,"identity":"6b5ffbce-24ef-4d36-8d51-469bb4bedcf1","added_by":"auto","created_at":"2025-01-08 12:52:44","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":111119,"visible":true,"origin":"","legend":"\u003cp\u003eThe input impedance matching (S11) of the proposed system for 16 configurations\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/c35279c59649a79b3d8ac6aa.png"},{"id":73282090,"identity":"4b8e0139-552c-4029-92e6-b8f6a2d76471","added_by":"auto","created_at":"2025-01-08 12:44:45","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":23674,"visible":true,"origin":"","legend":"\u003cp\u003eThe Monte Carlo simulation histogram for 250 instances\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/9fc10d2a2abc19a9f07f23f2.png"},{"id":76235709,"identity":"bb0ac10c-72d0-4184-8708-2ea9fd2bf20d","added_by":"auto","created_at":"2025-02-13 20:08:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1616800,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5728795/v1/7a4f80b1-c5a5-4841-b56c-a96609ce06e2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Combined True Time Delay System Based on Inductor- less CMOS True-Time-Delay Cell","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThere are several topologies in the literature for True time-delay systems. The \u0026lsquo;Trombone\u0026rsquo; structure is a fundamental design where the signal encounters delay as it goes through the delay line, similar to a physical trombone [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This design is suitable for high-frequency applications, as the trombone can be easily implemented with a TL. For lower frequencies, LC ladders or ATLs are employed, but the large size of inductors at these frequencies creates area challenges [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe \u0026lsquo;fine and coarse tuning\u0026rsquo; TTD system provides high delay resolution but requires separate blocks for fine and coarse delay steps [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Consequently, this design is unsuitable for integration or mass production due to the need for two separate delay lines.\u003c/p\u003e \u003cp\u003eSeveral approaches have been proposed to address these limitations. Some designs employ ATLs or LC ladder structures for both blocks [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], which are effective at higher frequencies. However, these methods face area constraints at frequencies below 5GHz. Active delay cells offer potential solutions but cannot be easily cascaded in such designs due to the use of differing delay blocks.\u003c/p\u003e \u003cp\u003eSwitch-based TTD systems inspired by the \u0026lsquo;Trombone\u0026rsquo; structure offer another alternative. These systems use cascaded, identical or semi-identical delay cells to form the delay line [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. However, achieving high-resolution delay requires too many delay cells, leading to increased power consumption in active designs and area challenges in passive ones. Using fewer delay cells reduces resolution, while employing different delay cells introduces inconsistencies in performance across the delay line [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis paper presents a novel topology to address the mentioned issues. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the Combined True Time Delay System achieves high delay with the required resolution while maintaining compactness and consistency in delay cell design.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. The proposed structure","content":"\u003cp\u003eAs discussed above, TTD systems are typically designed for wideband and high-frequency applications. While TL-based TTD systems are used in these applications. As frequency decreases, ATL or LC ladder-based structures are applicable, too. However, these methods are not promising for low frequencies (below 5GHz, for example). So, another structure must be developed and optimized for low-frequency delay systems.\u003c/p\u003e\n\u003cp\u003eAs shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, the proposed CTTDS addresses this issue by reducing the number of delay cells and employing inductor-less designs. For instance, in a timed array system with four antennas spaced 3 cm apart, the required delay ranges from 14 ps to 210 ps, corresponding to phase shifts of 8\u0026deg; to 45\u0026deg;. [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e]. Traditional approaches, such as TL-based or ATL-based TTD systems, are impractical due to area constraints. The proposed system achieves the desired delay using inductor-less TTD cells, significantly reducing area and power consumption. The multiplex switch-based structure needs 21 steps for this delay amount and resolution. This issue can be done with active delay cells to avoid area issues. Inductor-less TTD cells are used in the TTD systems to ensure the structure\u0026rsquo;s compactness. However, 21 delay cells consume too much power. The number of delay calls can be reduced if the switch-based structure is used. Since the lowest delay is 14ps and the largest one is 210ps (*15 times difference), the TTD system may need two types of delay cells. This matter is inappropriate for mass production and integration purposes of the TTD system. The fine and coarse delay cells can provide this resolution and delay with much fewer delay cells. However, unfortunately, the above issue is still present here, too.\u003c/p\u003e\n\u003cp\u003eThe CTTDS requires only four blocks to achieve a 210 ps delay. This design reduces the number of delay cells by half while maintaining the necessary resolution. Each block contains almost identical TTD cells, ensuring compactness and suitability for integration. Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e compares the proposed system with other TTD structuresFinally, with a 3x times difference between delay amounts, the similarity of the cells is ensured. Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the power consumption, chip area, and required delay cells for the mentioned application of the TTD system. As shown in this table, the proposed topology consumes more power than the fine and coarse structure, but since it has similar delay cells, it will be better for integration.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe performance of the five TTD system structures for 1-5GHz applications\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTTD system\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNumber of TTD cells\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOccupied chip area\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eability for Integration\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePower consumption\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe \u0026lsquo;trombone\u0026rsquo; structure [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21 cells\u003c/p\u003e\n \u003cp\u003e(if ATL or LC ladder is used)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVERY HIGH (with TL-based passive cells)\u003c/p\u003e\n \u003cp\u003eHIGH (with ATL or LC passive TTD cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBAD (very bulky because of TL or ATL-based TTD cell )\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLOW (passive structure)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe \u0026lsquo;switch-based\u0026rsquo; structure [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6 cells (steps: 12.5ps, 25ps, 50ps, 100ps, 200ps, 262.5ps )\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLOW (with inductor-less active cells)\u003c/p\u003e\n \u003cp\u003eMedian (with inductor-based active cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedian (different delay cells for the system)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAlmost LOW (acceptable number of delay cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe multiplex structure [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21 identical cells\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedian (with inductor-less active cells)\u003c/p\u003e\n \u003cp\u003eAlmost High (inductor-based active cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGOOD (all TTD cells are identical)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHIGH (active TTD cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe \u0026lsquo;fine and coarse tunning\u0026rsquo; structure [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5 cells (Fine part:12.5ps, 25ps, 50ps Coarse part: 87.5ps, 175ps)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLOW (with inductor-less active cells)\u003c/p\u003e\n \u003cp\u003eMedian (with inductor-based active cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedian (different delay cells )\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAlmost LOW (acceptable number of delay cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe proposed CTTDS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3 blocks with overall 9 cells (steps:12.5ps, 25ps, 50ps)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVERY LOW (with inductor-less active cells)\u003c/p\u003e\n \u003cp\u003eMedian (with inductor-based active cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGOOD (Almost identical cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedian (active cells)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"3. Proof of concept","content":"\u003cp\u003eTo validate the proposed system, four inductor-less TTD cells were redesigned based on [\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e] and [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e]. The ideal transfer function (TF) of the TTD cell can be approximated with the Pade approximation. The TTD cells utilize CMOS inverters with resistive feedback, forming an all-pass filter. The delay can be tuned by adjusting the capacitor (C) and resistor (R).\u003c/p\u003e\n\u003cp\u003eFor this study, delays of 14, 28, 56, and 112 ps were achieved. However, delays above 28 ps exhibited variations exceeding 10%. To address this, a forward body bias technique was applied to ensure a flat delay response across the 1-5GHz bandwidth. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the inverter-based TTD cell, while Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows the linearity of the delay response.\u003c/p\u003e\n\u003cp\u003eTo investigate the reason for this matter, it is worth finding out the maximum available delay with acceptable delay variations (max 5% delay variations over the frequency band of interest). As mentioned before, the Pade approximation is used to create the TF of the all-pass filter and then it will be used as a delay cell. In this case, if the true time delay is equal to the group delay, it can be said that the delay response will be linear. As a consequence, the delay variations will be limited [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eFor this fact, the relationship between true time delay \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\tau\\:}_{T}\\right)\\:\\)\u003c/span\u003e\u003c/span\u003eand group delay (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}_{g}\\)\u003c/span\u003e\u003c/span\u003e) can be calculated as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"EquationNumber\"\u003e\u003cimg 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\" width=\"1019\" height=\"111\"\u003e\u003cbr\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eFrom (1), it is evident that a linear phase relationship with frequency is required for equal true time delay and group delay. This equation is the exact purpose and characteristic of an ideal TTD cell. So, it is necessary to find a proper range for the linear phase response of a TTD cell. The proposed TTD cell\u0026rsquo;s TF comes from first-order Pade approximation. With this in mind, the phase response of this TF can be calculated as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"EquationNumber\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"944\" height=\"73\"\u003e\u003cbr\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003efrom (2), the phase response has a linear relation with frequency. This equation is arctangent-based. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, this equation is linear up to 0.4 Radian (23 degrees). It means that until the phase argument reaches this amount, the output of the TTD cell will remain linear.\u003c/p\u003e\n\u003cp\u003eFrom the above equations, the maximum delay at 5GHz (which is used for this paper`s application) will be around 28ps. For the first order Pade approximation, 28ps delay is the maximum available wideband delay. So for larger delays, it is necessary to use some circuit-level or system-level approaches (like delay lock loop, master-slave circuit, and so on) for having a flat wideband delay [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e]. So, it shows why other TTD cells in the literature have more than 10% delay variations for over 28ps delays in this frequency band [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eSo, to overcome this issue, [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e] provides a forward body bias technique, which is used here for redesigning the last two delay cells.\u003c/p\u003e\n\u003cp\u003eThe design of the proposed system requires four cascaded delay cells, as shown in the Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, where the delay cells provide delays of 14, 28, 56, and 112 picoseconds, respectively. As a result, the system can offer delays ranging from 0 to 210 picoseconds.\u003c/p\u003e\n\u003cp\u003eThe design of this delay system requires two key elements: delay cells and switches. For the first two delay stages (14 and 28 picoseconds), the CMOS inverter-based delay cell concept which is reported in [\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e] is used. For the third and fourth delay stages (56 and 112 picoseconds), an improved delay cell concept was employed [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e]. The CTTDS and so the delay cells are simulated in 180nm CMOS technology. The delay/frequency response of these four cells, individually and not as part of a delay system, is shown in the Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. This paper uses forward body bias to manipulate the threshold voltage of the TTD cell\u0026rsquo;s devices to optimize the delay cells. So flat wideband delay response is achieved with this technique\u003c/p\u003e\n\u003cp\u003eAs shown in the Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, the desired smooth and wideband delay across the frequency band of interest has been achieved. The 14-picosecond delay cell shows a 2% variation over the bandwidth, with a maximum delay of approximately 14.15 picoseconds. The 28-picosecond cell exhibits a 5% variation, with a maximum delay of 27.15 picoseconds. Similarly, the 56-picosecond cell shows a 5% variation with a maximum delay of 56.10 picoseconds, and the 112-picosecond cell demonstrates a 5% variation, with a maximum delay of 113.11 picoseconds. Each delay cell, however, has slight losses, suggesting that for designing a complete receiver, it is necessary to include an amplifier at the beginning and end of the line.\u003c/p\u003e\n\u003cp\u003eFor the switch section of the delay system, this study used SPDT switches, presented in [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. With these switches, delay steps from 0 to 210 picoseconds can be achieved with a single output channel, eliminating the need for multiple outputs for this structure. For the proposed system, we need eight switches, which can be programmed using 4 bits, enabling us to achieve all desired delays.\u003c/p\u003e\n\u003cp\u003eThis system has 16 states. First state is 0000, where the input signal experiences no delay. And the last state is 1111, where all delay cells are included in the line leading to maximum delay to the signal. These simulation results are summarized in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. In this table, switches S1 to S8 are opened and closed according to the settings in the table. Switches 1 and 2 control the first delay cell (14 ps), switches 3 and 4 control the second delay cell (28 ps), switches 5 and 6 control the third delay cell (56 ps), and switches 7 and 8 control the fourth delay cell (112 ps). These 16 states create the desired time-delay steps.\u003c/p\u003e\n\u003cp\u003eOne key point that stands out in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e is that our switches introduce a total of 32ps of delay, making this the minimum delay for the entire system. In the absence of any delay cells, the input signal still experiences this amount of delay. The maximum delay is 248ps, and our system can provide delays between these two values with 16 steps. As a result, the total achievable delay is approximately 217ps (248.1ps \u0026minus;\u0026thinsp;30.88ps\u0026thinsp;=\u0026thinsp;217.22ps), and for the 16 states, the average delay step is 13.5ps (217.22ps / 16\u0026thinsp;=\u0026thinsp;13.57ps), which is close to the target of 14 ps. This step size corresponds to a delay resolution of approximately 3.86 bits (the initial target was a 4-bit delay resolution).\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003ePerformance of the proposed time-delay system\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS7, S8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS5, S6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS3, S4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS1, S2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003estate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNominal delay (pS) Delay step is 14pS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDelay\u003c/p\u003e\n \u003cp\u003e(pS)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eDelay step (pS)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDelay step variation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eD.V.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS21 (dB)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0 (av 32pS for SPDT)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e30.88\u0026ndash;32.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-5.5 - -4.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e14.2\u0026ndash;15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e14 (46)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e45.08\u0026ndash;47.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e9%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-6.2 - -5.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e15.3\u0026ndash;14.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e28 (60)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e60.42\u0026ndash;62.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e3%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-7.5 - -5.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12.6-14.37\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e42 (74)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e73.01\u0026ndash;77.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-8.5 - -6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12.8\u0026ndash;15.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e56 (88)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e85.81\u0026ndash;92.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e9%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-6 - -4.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e13.3\u0026ndash;15.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e70 (102)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e99.16\u0026ndash;108.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-6.5 - -5.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12.7-14.04\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e84 (116)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e113.2-120.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e9%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-7.5 - -5.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12.6\u0026ndash;14.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e98 (130)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e125.8\u0026ndash;135.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-8.5 - -6.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e15-13.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e112 (144)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e140.8-148.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-5.5 - -4.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e14.2\u0026ndash;13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e126 (158)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e155.0-161.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e4%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-6.2 - -5.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12.1\u0026ndash;15.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e140 (172)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e167.1\u0026ndash;177.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e13%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-7.5 - -5.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e15.9\u0026ndash;12.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e154 (186)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e183.0-189.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e4%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-8.5 - -6.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e15.7\u0026ndash;12.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e168 (200)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e198.7\u0026ndash;202.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e15%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e2%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-5.9 - -4.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e13.1\u0026ndash;16.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e182 (214)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e211.8-218.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e13%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e3%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-6.4 - -5.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e12.1\u0026ndash;15.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e196 (228)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e223.9-233.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e4%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e3%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-7.6 - -5.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e13.4\u0026ndash;14.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e210 (242)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e237.3-248.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-8.6 - -6.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eAnother evident point in the table is that the maximum absolute error is 8%, which is below the 10% tolerance limit. This is due to the use of body-biasing for the larger delay cells and the optimized design of the smaller delay cells. Furthermore, the smooth delay behavior for larger delay values is achieved through the adjustable body-biasing voltage of the two larger delay cells. As shown in the table, the smoothness of the gain improves for these states compared to the initial cases. Although, it is expected to start with a zero delay, and reach a final delay of 210 ps. However, with the given minimum delay, introduced by the switches ( it is approximately 32ps), a nominal delay column is shown, versus the actual delay provided by the structure. In all cases, the desired delay for the input signal is provided at the output node.The delay step differences are one of the critical factors in this system. In the worst case, our system exhibits less than 15% step error, indicating acceptable accuracy of the proposed structure.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows the delay response of the proposed delay system for different delay line configurations, ranging from the 0000 to the 1111 state. The figure demonstrates that the system provides a smooth delay from the minimum to the maximum delay with acceptable accuracy.\u003c/p\u003e\n\u003cp\u003eThe proposed structure exhibits relatively flat insertion loss. The worst-case insertion loss is less than 8.5dB. So, for designing a phased-array receiver based on this system, it is necessary to include a signal amplifier to the structure. In Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, the insertion losses for different time-delay system configurations can be observed.\u003c/p\u003e\n\u003cp\u003eSince the proposed system is intended to be as a part of a phased-array receiver, impedance matching at the input across different delay settings is essential. The S\u003csub\u003e11\u003c/sub\u003e parameter of the system has been evaluated for this purpose. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, the system provides the required minimum impedance matching in almost all cases.\u003c/p\u003e\n\u003cp\u003eThe proposed system was simulated for temperature variations from \u0026minus;\u0026thinsp;40\u0026deg;C to 125\u0026deg;C and for supply voltages ranging from 1.6V to 2V for the delay cells and switches. These simulations were performed for fast, typical, and slow corners, and the results are summarized in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eVarious simulation corners for the proposed delay cell\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTypical temperature (T) corner\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e27\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTypical supply voltage (T) corner\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e1.8V\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFast temperature (F) corner\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e125\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFast supply voltage (F) corner\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2V\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSlow temperature (S) corner\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-40\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSlow supply voltage (S) corner\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.6V\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFF: Fast - Fast\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSF: Slow - Fast\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSS: Slow - Slow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFS: Fast - Slow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTT: Typical - Typical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eThe unconditional stability of the structure is ensured by the Rollet stability factor (K) where K is being greater than one, and the stability measure is always positive. Additionally, if the load stability factor (mu) is always greater than one, it is sufficient to guarantee stability. Similarly, if the source stability factor (mu_prime) is greater than one, the structure will be stable without any conditions. These four factors were observed, and stability was guaranteed based on these criteria.\u003c/p\u003e\n\u003cp\u003ecomprehensive simulations were conducted for all corners, and the results are shown in the Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. The table presents the worst performance for each of the 16 time-delay system configurations among the (FF, FS, SF, SS, TT) corners. According to the table, the worst-case output for the source stability factor (mu_prime) was found in the SF corner for most cases. For the load stability factor (mu), the worst output occurred in the SS corner in most cases. For the Rollet stability factor, the worst output was also in the SS corner. In terms of the stability measure, the worst output was observed in the TT corner in most cases. However, in all these cases, the minimum requirements for unconditional stability were met, with exact values for the worst-case scenario provided in the table.\u003c/p\u003e\n\u003cp\u003eRegarding the S\u003csub\u003e11\u003c/sub\u003e parameter, the worst performance occurred in the SF corner, but even in this case, the system maintained the necessary impedance matching, with S\u003csub\u003e11\u003c/sub\u003e being less than \u0026minus;\u0026thinsp;8.3dB. For the S\u003csub\u003e21\u003c/sub\u003e parameter, the worst performance was observed in the FF corner, where the system still maintained the required matching, with S\u003csub\u003e21\u003c/sub\u003e being less than \u0026minus;\u0026thinsp;5.5dB. Concerning delay variations across the desired bandwidth, the SF and FF corners exhibited the worst performance, with a delay variation of up to 11% in the worst case.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe corner analysis results for the proposed delay cell\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS7, S8\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS5, S6\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS3, S4\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS1, S2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003estate\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMu stability factor\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMu_prime stability factor\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eK (Rollett) stability factor\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003estability measure\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS\u003csub\u003e11\u003c/sub\u003e(dB)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS\u003csub\u003e21\u003c/sub\u003e(dB)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDelay Variation\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.864\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.355\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-5.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.842\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.493\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-5.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.723\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.225\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-5.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.962\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.013\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-6.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.912\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.912\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-5.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.825\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.963\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-6.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.726\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.712\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-6.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.698\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.842\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-7.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.626\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.926\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-6.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.701\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.954\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-9.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-5.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.759\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.859\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.958\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.665\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.678\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.965\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-7.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.546\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.695\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-5.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.523\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.561\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-7.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.474\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.584\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-8.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;-6.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eTo evaluate the impact of device mismatches in the structure, Monte Carlo simulations were performed, assuming a mismatch in all available circuit components for 250 instances. For one of the worst cases (state 5), the maximum acceptable delay variation was analyzed, revealing that in 96% of cases (240 instances), the delay variations remained below 10%, indicating that the structure can achieve the desired delay with good resistance to variation. Examining other delay states also demonstrated that they have good resistance to variations within an acceptable 10% range.\u003c/p\u003e\n\u003cp\u003eAnalysis of the insertion loss showed that in 94% of cases, the maximum insertion loss was better than \u0026minus;\u0026thinsp;4.5dB. Input and output impedance matching simulations indicated that in 93% of cases, the maximum S\u003csub\u003e11\u003c/sub\u003e was less than \u0026minus;\u0026thinsp;10dB. Figure \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e presents the results of Monte Carlo simulations for 250 instances, showing the histogram of the maximum S\u003csub\u003e11\u003c/sub\u003e values at the input of the desired time-delay system. The stability factor (K) was always greater than one, and the stability measure was always positive in all cases. The load and source stability factors were also checked, confirming that both remained above one in all cases, indicating that the structure is unconditionally stable.\u003c/p\u003e\n\u003cp\u003eBased on these simulations, it can be confidently stated that the proposed delay system is resistant to PVT (Process, Voltage, Temperature) variations, mismatches, and other parasitic effects. The 1dB compression point (P1dB) of this structure was also simulated, and the maximum P1dB, when all delay cells are engaged and at 3 GHz, was found to be -26.8dBm. The P1dB for other delay configurations is listed in the Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. Additionally, the DC power consumption of this delay system, with a 1.8V power supply, was measured at 101mW.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eP1dB values for different delay configurations of the proposed time-delay system\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS7, S8\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS5, S6\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS3, S4\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eS1,S2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003estate\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eP1dB (dBm)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-5.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-7.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-9.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-12.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-15.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-14.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-16.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-17.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-20.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-23.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-26.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eIn Table \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, the performance of the proposed structure is compared against other delay systems presented in recent years. This comparison shows that the performance of the proposed system, along with its inductor less delay cells, is acceptable. It should be noted that the compared structures include auxiliary amplifiers, while the proposed system does not utilize such an amplifier. However, considering its intended application, an amplifier can be added either at the input or output of the structure as needed.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003ctable id=\"Tab6\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003ePerformance comparison of the proposed delay system against other recent delay structures\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e] *\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e] ^\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e] ^\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThis Work\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eProcess (CMOS)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSupply (V)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFrequency (GHz)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u0026ndash;5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u0026ndash;5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1-2.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u0026ndash;5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDelay Range (ps)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e385\u0026ndash;540\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0-250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u0026ndash;250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32\u0026ndash;248\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDelay Resolution (ps)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAverage Gain (dB)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u0026ndash;7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u0026ndash;22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u0026ndash;15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-7.2 - -5.5 \u003cspan\u003e$\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAverage P1dB (dBm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN/A\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePower (mW)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e151\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e101\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSize (mm2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN/A\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"5\"\u003e*simulation, ^Measurement, $Without auxiliary amplifier\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n\u003c/table\u003e\n"},{"header":"4. Conclusion","content":"\u003cp\u003eThis paper introduces a novel Combined True Time Delay System optimized for applications below 5GHz. The system features semi identical blocks of inductor-less TTD cells, making it compact and suitable for integration. Compared to existing designs, the proposed system demonstrates superior performance in terms of area efficiency, delay resolution, and power consumption. To prove the system's feasibility, a TTD cell based on a CMOS inverter with an inductor-less structure is applied to the CTTDS. The TTD cell can deliver the required delay with good DV. The delay cell can provide 14, 28, 56, and 112ps delays by adjusting its R and C while other devices are unchanged. Although, a forward body bias technique is applied to flatten its delay over the frequency band of interest in the last two delay cells.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors reviewed the manuscript\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eSanggu Park A 15\u0026ndash;40 GHz CMOS True-Time Delay Circuit for UWB Multi-Antenna Systems2013\u003c/li\u003e\n\u003cli\u003eMa, Qian, Domine MW Leenaerts, and Peter GM Baltus. \u0026quot;Silicon-based true-time-delay phased-array front-ends at Ka-band.\u0026quot; IEEE Transactions on Microwave Theory and Techniques 63.9 (2015): 2942-2952.\u003c/li\u003e\n\u003cli\u003eGhazizadeh, Mohammad Hossein, and Ali Medi. \u0026quot;Novel trombone topology for wideband true-time-delay implementation.\u0026quot; IEEE Transactions on Microwave Theory and Techniques 68.4 (2019): 1542-1552.\u003c/li\u003e\n\u003cli\u003eLee, Wooram, and Alberto Valdes-Garcia. \u0026quot;Continuous true-time delay phase shifter using distributed inductive and capacitive miller effect.\u0026quot; IEEE Transactions on Microwave Theory and Techniques 67.7 (2019): 3053-3063.\u003c/li\u003e\n\u003cli\u003eMa, Ting, and Feng Hu. \u0026quot;Three‐bit 2\u0026ndash;18 GHz all‐pass network‐based trombone phase delay line with improved insertion loss variation.\u0026quot; IET Microwaves, Antennas \u0026amp; Propagation 13.12 (2019): 2032-2036.\u003c/li\u003e\n\u003cli\u003eMa, Qian, D. Leenaerts, and R. Mahmoudi. \u0026quot;A 10\u0026ndash;50GHz True-Time-Delay phase shifter with max 3.9% delay variation.\u0026quot; 2014 IEEE Radio Frequency Integrated Circuits Symposium. IEEE, 2014.\u003c/li\u003e\n\u003cli\u003eChen, Yang, and Wenyuan Li. \u0026quot;Compact and broadband variable true-time delay line with DLL-based delay-time control.\u0026quot; Circuits, Systems, and Signal Processing 37.3 (2018): 1007-1027.\u003c/li\u003e\n\u003cli\u003eWenyuan, Li, Wang Wan, and Chen Yang. \u0026quot;A 0.5\u0026ndash;3GHz true-time-delay phase shifter for multi-antenna systems.\u0026quot; 2017 IEEE 2nd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC). IEEE, 2017.\u003c/li\u003e\n\u003cli\u003eKim, Ki-Jin, et al. \u0026quot;Hybrid Beamforming Architecture and Wide Bandwidth True-Time Delay for Future High Speed Communications 5G and Beyond 5G Beamforming System.\u0026quot; 2018 IEEE 3rd International Conference on Integrated Circuits and Microsystems (ICICM). IEEE, 2018.\u003c/li\u003e\n\u003cli\u003eMoallemi, Soroush, Richard Welker, and Jennifer Kitchen. \u0026quot;Wide band programmable true time delay block for phased array antenna applications.\u0026quot; 2016 IEEE Dallas Circuits and Systems Conference (DCAS). IEEE, 2016.\u003c/li\u003e\n\u003cli\u003eJung, Minjae, Hong-Jib Yoon, and Byung-Wook Min. \u0026quot;A wideband true-time-delay phase shifter with 100% fractional bandwidth using 28 nm CMOS.\u0026quot; 2020 IEEE Radio Frequency Integrated Circuits Symposium (RFIC). 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Conventional TTD systems must be better optimized in low frequencies. Most existing structures use transmission lines (TLs), artificial transmission lines (ATLs), or LC ladder structures, which result in large chip areas due to the size of the inductors. Some systems employ two different delay cells in their topologies, which is not desired for integration purposes. To address these issues, a combined true-time delay cell system (CTTDS) is proposed. This system consists of N-semi-identical building blocks, which can be cascaded to provide sufficient delay. Each block includes nearly identical TTD cells. A 4-bit resolution delay system with a 14 ps delay step and a total delay of 210 ps demonstrates the concept. The delay cells are inverter-based, inductor-less designs with resistive feedback to ensure wideband operation. Single pole dual throw (SPDT) switches are used to select the proper path for each cell in the system. This design is designed in TSMC 180nm CMOS technology.\u003c/p\u003e","manuscriptTitle":"Combined True Time Delay System Based on Inductor- less CMOS True-Time-Delay Cell","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-08 12:44:39","doi":"10.21203/rs.3.rs-5728795/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"cf56a89e-7020-45e7-aa77-957ed95a1628","owner":[],"postedDate":"January 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-02-13T20:08:21+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-08 12:44:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5728795","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5728795","identity":"rs-5728795","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}