Single Operational Current Amplifier Based Sinusoidal Oscillators 

Single Operational Current Amplifier Based Sinusoidal Oscillators | 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 Single Operational Current Amplifier Based Sinusoidal Oscillators Hussain Alzaher, IBRAHIM ALKHALIFA This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5325115/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 This paper presents important missing sinusoidal oscillators. There are numerous sinusoidal oscillators versions based on the three fundamental amplifiers namely the operational amplifier (OpAmp), the operational transconductance amplifier (OTA), and the operational transresistance amplifier (OTRA) but their counterparts based on the fourth type that is the operational current amplifier (OCA) are to be reported. Traditional applications use voltage-mode oscillators, however, several modern applications such as electrical impedance spectroscopy (EIS) require current-mode oscillators. In the literature, many current-mode oscillators have been proposed; however, they use active building blocks which operate in both voltage and current modes. In this paper, we propose two novel oscillators using the pure current-mode active element namely the OCA. Simulation results obtained from a standard 180nm CMOS process are provided. It is shown that the proposed oscillators consume approximately 120µW while working in the MHz range. Also, experimental results using prototypes implemented using commercially available ICs show the validity of the proposed designs. Sinusoidal oscillators current-mode circuits and systems current amplifier Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1 Introduction Sinusoidal oscillators are essential elements in many signal processing systems. They are used for carrier generation in communication circuits, as well as a test signal to characterize circuits. Although traditional applications utilize voltage-mode sinusoidal oscillators, modern biomedical applications such as electrical impedance tomography (EIT) need fully differential (FD) current signals, due to safety concerns, to interrogate body tissue [ 1 ]. Furthermore, charge-controlled mem-elements require a current sinusoidal input to measure the pinched hysteresis loop (PHL) of the device [ 2 ]. Considering the four basic amplifiers types, namely the operational voltage amplifier (OpAmp), the operational transresistance amplifier (OTRA), the operational transconductance amplifier (OTA), and operational current amplifier (OCA), it is obvious that the first two amplifier types cannot be used to provide output currents since their outputs are associated with low output impedance (ideally zero). In principle, current-mode sinusoidal oscillators (traditionally defined as oscillators with explicit output currents) can be obtained from available voltage-mode sinusoidal oscillators. However, this requires an additional active element(s) for converting voltage signal to current signal(s). On the other hand, there are enormous number of voltage-mode and current-mode oscillators based on operational transconductance amplifier (OTA). In fact, voltage-mode oscillators based on OTA can be converted to oscillators with explicit output current(s) by replacing single output OTA(s) by dual- or multi-output OTA(s). On the other hand, OCA based key sinusoidal oscillator topologies are still not available in literature. In this paper, this gap is minimized by presenting two new and fundamental sinusoidal oscillators using OCA. They are current mode counterparts of the famous Wein bridge and the phase shift oscillators. These sinusoidal oscillators are fundamental in the sense that their counterparts designed using OpAmps have been popularly available for the majority of the past century. At this leading stage, this manuscript concentrates on presenting the mathematical foundation/the systematic approach used to develop these new circuits and verifying their workability. The performance characteristics of the proposed circuits can always be optimized according to the desired system-level specifications. The paper is organized as follows. Section 2 explains the contributions of this work through critical study of the available solutions. Section 3 provides a brief background of the OCA and its applications. Section 4 presents the proposed oscillator circuits and derives the key equations required for their design. Section 5 provides simulation and experimental results of the proposed oscillators. Section 6 discusses the obtained results and compares them to recent designs in literature. Finally, section 7 offers a summary and a conclusion for the paper. 2 Available Solutions In general, sinusoidal oscillator circuits can be classified based on the number of available outputs as single output, quadrature output and multioutput oscillators. The latter two types have their own applications but require two or more amplifiers, active elements, or active building blocks. Here we would like to clarify a very important issue that an active building block may consist of two or more active elements whereas an active element may employ two or more amplifiers. This paper focuses on single output current mode oscillators which can often be realized using a single amplifier and hence truly canonic. Using minimum number of amplifiers and hence possibly the minimum power consumption in oscillator’s designs is crucial for modern low power applications. As explained in the introduction, that current mode oscillator based on a single amplifier could logically be obtained only from the OTA and the OCA. As for the OTA solutions, one can use OTA-based RC oscillators [ 3 ]-[ 8 ], which may employ one OTA along with a number of resistors and capacitors. In these kinds of circuits, it is difficult to control or optimize the oscillators’ characteristics because they involve two different types of resistances namely the passive resistors and the active resistors (gm of the OTAs). Also, when an OTA-RC oscillator is transformed into an OTA-C oscillator, by simulating the passive resistors with OTAs, the resulting oscillator would employ an excessive number of OTAs and hence will not be practically viable. Clearly, single output oscillator based on OTA-C approach would require at least two OTAs and hence naturally is not canonic. Over the years, many current-mode sinusoidal oscillators based on active elements and active building blocks have been proposed. A comprehensive review of such designs can be found in [ 9 ] that cites 249 works. They are mainly using Current Difference Transconductor Amplifier (CDTA), Voltage Difference Transconductor Amplifier (VDTA), Current Conveyor Transconductance Amplifier (CCTA), Differential-Input Buffered Transconductance Amplifier (DBTA), Current-Controlled Current Difference Transconductance Amplifier (CCCDTA), Current Follower Transconductance Amplifier (CFTA), Current Differencing Cascaded Transconductance Amplifier (CDCTA), Current-Backward Transconductance Amplifier (CBTA), Current Conveyors, Current-Feedback Operational Amplifier (CFOA), Operational Floating Amplifier (OFA), and Current Difference Buffered Amplifier (CDBA). More recent works published during the last three years, present sinusoidal oscillators based on, for examples, OTA, VDTA, voltage difference differential difference amplifier (VDDDA), second-generation voltage conveyor (VCII), CCCCTA, and the CFOA, respectively [ 10 ]-[ 15 ]. Such designs may employ a single active element or a single active building block; and may meet the usual basic requirements for sinusoidal oscillators of independent tuning of condition of oscillation (CO) and frequency of oscillation (FO). But it is unfair to compare them to their single amplifier counterparts. For example, a CCTA consists of a second generation current conveyor (CCII) and two OTAs. A CCII by itself can be decomposed to a voltage buffer (a unity gain voltage amplifier) and a current follower (a unity gain current amplifier). Therefore, these oscillators are less attractive for low power applications. Another problem is that these oscillators are associated with low form factor and hence they neither enforce uniformity nor allow optimization of performance. But the main issue is that although these oscillators provide explicit current outputs and hence traditionally defined as current mode oscillators, all of these oscillators are using active elements which are not purely current-mode; therefore, voltage-mode limitations such as limited swings at lower power supplies are inevitable. Therefore, the definitive solution to have true current mode oscillators is to design them utilizing the OCA. Consequently, these oscillators would truly have the well-known advantages of current mode signal processing such as low power consumption at high working frequencies and output swing independent of the supply voltage [ 16 ] and [ 17 ]. 3 Current Amplifiers A current amplifier could be realized as either an open-loop amplifier or a negative feedback amplifier. The difference between the two being the gain ( \(\:{A}_{i}\) ) of the amplifier. If \(\:{A}_{i}\) is designed to be finite then it is traditionally called a CA it is usually used in open-loop configurations. In contrast, an ideal OCA has \(\:{A}_{i}\to\:\infty\:\) and consequently must be used with negative feedback. This paper proposes the use of the latter type. Another point of interest is how to define the input and output terminals of the OCA. The definition that will be followed in this work is obtained through adjoint networks [ 16 ], from which it can be shown that a OCA has one input terminal and two differential output terminals. Figure 1 presents the suggested OCA symbol. Ideally, the OCA has zero impedance at the input port and infinite output impedance at the output ports. Its current terminal characteristics adhere to the following relationships. $$\:{I}_{op}=-{I}_{on}={A}_{i}{I}_{in}\:\text{w}\text{h}\text{e}\text{r}\text{e}\:{A}_{i}\to\:\infty\:$$ 1 A real OCA typically has a large current gain, small input equivalent resistance, and a very large output resistance. Its CMOS realization typically consists of three stages: a common gate amplifier, differential amplifier, and a balanced current output stage as shown in Fig. 2 [ 18 ]. The first two stages are to provide a high transresistance gain while the latter is to offer a high differential transconductance gain. A negative closed-loop feedback configuration is then achieved by shorting the inverting output with the input. The remaining non-inverting output terminal is used to drive a load or another circuit. The use of this OCA with negative feedback to achieve a unity gain current follower can be found in [ 18 ] and [ 19 ]. Many OpAmp basic applications can be realized using the OCA. Figure 3 . shows how to implement an inverting and a non-inverting amplifier which are used in next sections to realize the proposed oscillator circuits. $$\:{I}_{o1}=-\frac{{R}_{1}}{{R}_{2}}{I}_{in}$$ 2 $$\:{I}_{o2}=\left(1+\frac{{R}_{1}}{{R}_{2}}\right){I}_{in}$$ 3 4 Proposed Sinusoidal Oscillators There are two fundamental single OpAmp based sinusoidal oscillator types: the Wein bridge oscillator and the phase shift oscillator. This section demonstrates the procedure for developing their OCA counterparts. This is accomplished by first providing mathematical analysis of the RC networks that will be used in synthesizing the oscillators. Then, it proceeds to present the oscillator circuits using these networks and the two basic amplifier types. The Barkhausen criterion is commonly used to predict the frequency and condition of oscillation of sinusoidal oscillators. According to this criterion, an oscillator circuit can be described by the characteristic equation given by $$\:\:{s}^{2}+\:(a-b)s+{c}^{2}=0$$ 4 Where s is the complex frequency. The circuit will oscillate if the condition a − b = 0 is satisfied, and the frequency of oscillation will be given by \(\:{\:{\omega\:}}_{o}=c\) . In (2) the parameters a , b and c are functions of the circuit passive components when the oscillators are realized using closed loop amplifiers (e.g. the OpAmp and OCA) whereas they additionally involve the parameters of the active elements when the oscillator circuits are based on open loop amplifiers, for example, the transconductance of the OTAs. In the following subsections, the oscillators’ synthesizing procedure is demonstrated and the frequency of oscillation (FO), and condition of oscillation (CO) are derived. 4.1 RC Networks RC networks are used to obtain the desired phase shift in oscillators in order to convert a negative feedback loop into a positive feedback loop at one frequency only. In general, these networks can have a high pass (HP) or low pass (LP) magnitude frequency response. LP RC networks provide negative phase shift, whereas HP RC networks provide positive phase shift. Without loss of generality, the remainder of this subsection will focus on LP RC networks. It can be shown that a three section RC network, shown in Fig. 4 , provides a -180 o phase shift and a loss of \(\:\frac{1}{29}\) at \(\:{\omega\:}=\frac{\sqrt{6}}{RC}\) . These results are derived from the transfer function (TF) given by (5). $$\:\frac{{I}_{out}}{{I}_{in}}=\frac{\frac{1}{{R}^{3}{C}^{3}}}{{s}^{3}+\frac{{5s}^{2}}{RC}+\frac{6s}{{R}^{2}{C}^{2}}+\frac{1}{{R}^{3}{C}^{3}}\:}$$ 5 The other RC network of interest is the bandpass (BP) RC network shown in Fig. 5 . It provides a \(\:0^\circ\:\) at \(\:\omega\:=\frac{1}{RC}\) with a loss of \(\:\:\frac{1}{3}\) . Its TF is given by (6). $$\:\frac{{I}_{out}}{{I}_{in}}=\frac{\frac{s}{RC}}{{s}^{2}+\frac{3s}{RC}+\frac{1}{{R}^{2}{C}^{2}}\:}$$ 6 4.2 Phase Shift Oscillator Using the LP RC network of Fig. 4 and a single OCA, a phase shift oscillator can be realized as shown in Fig. 6 . The OCA is configured as an inverting amplifier but as the output current which is supposed to flow through R 2 going to ground (Fig. 3 ) and hence cannot be used to feed the passive network. Therefore, another inverting (negative) current is needed. That is the phase shift oscillator requires two negative feedback currents: one to form the amplifier and one to feed the passive phase shift network. As in the case of OTA, a multi-output OCA may be used to provide explicit output current signals instead of using an additional amplifier. The additional output stage can simply be implemented using an extra balanced output stage [ 19 ]. This means that this oscillator can provide two identical currents signals (I o1 and I o2 ) from the two unused positive output terminals. It can be shown that FO and CO are given by (7) and (8), respectively. $$\:FO:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}_{o}=\frac{\sqrt{6}}{2\pi\:RC}$$ 7 $$\:CO:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{R}_{1}}{{R}_{2}}=28$$ 8 4.3 Wein Bridge Oscillator Using the BP RC network of Fig. 5 and an OCA, a Wein bridge oscillator can be built as shown in Fig. 7 . In this case, the OCA is configured as non-inverting amplifier. Therefore, this oscillator can provide two differential output signals. Routine analysis shows that FO and CO are given by (9) and (10), respectively. $$\:FO:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}_{o}=\frac{1}{2\pi\:RC}$$ 9 $$\:CO:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{R}_{1}}{{R}_{2}}=2$$ 10 5 Results This section verifies the presented theory through both simulation using CMOS OCA and prototyping using commercially available ICs. 5.1 Simulation results The proposed oscillator circuits were simulated in a standard 180 nm CMOS process using T-Spice. The CMOS realization of Fig. 2 is expanded to offer two additional output currents namely I o2p and I o2n . This is achieved by incorporating and an identical additional output stage formed by M4c, M4d, M5c, M5d, MB10, MB11, MCP, and MCN as shown in Fig. 8 [ 19 ]. The supply voltage and the biasing currents are set to ± 0.9V and 10µA, respectively. The phase shift oscillator was designed, for example, to produce an oscillation frequency of 1MHz. The capacitance C was selected to be 10pF and hence the required resistance R = 39kΩ. The resistance of R 2 = 10kΩ was chosen. It was found that oscillation starts and sustains when R 1 = 300kΩ the result is shown in Fig. 9 . This records oscillation frequency of approximately 970kHz which is in very good agreement with the theoretical value. The Wein bridge oscillator was realized with C = 15.5pF and R = 10kΩ to produce an oscillation frequency of 1MHz. A resistance of R 2 = 10kΩ was used and hence it was found that the oscillation starts and sustains when R 1 = 22kΩ. Figure 10 shows the differential output waveforms while oscillation grows whereas Fig. 11 shows the output wave forms at steady state. The recoded frequency is 974kHz which is very close to the theoretical value. 5.2 Experimental results The proposed oscillators were implemented using commercial chips such as AD844. Experimental results are provided in this section. A current gain is obtained using two AD844s as shown in Fig. 12 . It can be shown easily that again of I of /I i = -R 1 /R 2 is obtained. For non-inverting gain of R 1 /R 2 , the output current can be inverted by an additional AD844. The phase shift oscillator circuit was designed using \(\:{R}_{1}=32\:k{\Omega\:}\) , \(\:{R}_{2}=1\:k{\Omega\:}\) , \(\:R=3\:k{\Omega\:}\) , and \(\:C=10\:nF\) . Obtained result is shown in Fig. 13 . The obtained \(\:{f}_{o}\) is very close to theoretical value of \(\:{f}_{o}=\) 13kHz. A Wein bridge oscillator prototype was implemented using \(\:{R}_{1}=31\:k{\Omega\:}\) , \(\:{R}_{2}=10\:k{\Omega\:}\) , \(\:R=25\:k{\Omega\:}\) , and \(\:C=1.5\:nF\) . The result is shown in Fig. 14 . The oscillation frequency is in good agreement with the theoretical value of 4.244kHz. 6 Comparison and Discussion Table 1 provides comparison with several recent sinusoidal oscillators [ 10 ]-[ 15 ]. Without loss of generality, these samples represent various types of available solutions. These solutions are classified as oscillators with explicit output voltage [ 12 ] and [ 13 ], and with explicit output current [ 10 ], [ 11 ], [ 14 ], and [ 15 ]. The voltage mode oscillators require superfluous voltage to current converters to produce current signals. On the other hand, the current mode oscillators usually do not provide differential output signals [ 11 ], [ 13 ], and [ 14 ]. The oscillator in [ 10 ] produces differential current signals but employs two OTAs. The supply voltage of the proposed oscillators is less than the other solutions and its power consumption is expected to be optimum since the proposed approach employs a single amplifier. Similar to other solutions, the proposed oscillators support operating frequencies in kHz and MHz. In fact, only [ 11 ] and this work have verified the operation of the presented oscillators via both CMOS realizations and prototyping. Finally, it must be mentioned that the performance characteristics of the proposed oscillators can always be optimized according to the desired system-level specifications. Table 1 Comparison with several recent works. Ref Year Device Active elements Output Differential Signals CMOS Realization Supply Power (µW) Test Frequency Prototype [ 10 ] 2022 OTA 2 OTAs Current Yes 180 nm 1.8V NR 2.75 MHz No [ 11 ] 2022 VDTA 2 OTAs Current No 350 nm ± 2V NR 1 MHz Yes [ 12 ] 2023 VDDDA OTA + DDA Voltage No Macro models ± 2V NR 245.5kHz Yes [ 13 ] 2023 VCII 2 CCII Voltage No No NR NR 113kHZ Yes [ 14 ] 2024 CCCCTA CCII + 2 OTAs Current No 180 nm ± 1V NR 4.9MHz No [ 15 ] 2024 CFOA CCII + Buffer Current No No ± 12 NR 1.174kHz Yes This work 2024 OCA 1 OCA Current No Fig. 6 Yes Fig. 7 180 nm ± 0.9 126 1MHz Yes 7 Conclusion Voltage-mode OpAmp based sinusoidal oscillators are fundamental electronics building blocks. But they have limited output swings set by the power supplies just like all voltage mode circuits. Moreover, in applications that require current output signals rather than voltage signals, superfluous voltage-to-current converters are mandatory to convert the output from voltage signals to current signals; thus, increasing power consumption. This paper presented novel OCA based sinusoidal oscillators that provide explicit output current signals using a single OCA. Simulation and experimental results confirming the presented theory are provided. The maximum operating frequency is limited by the GBW of the OCA. The OCA used in this paper was designed to have a GBW close to 100 MHz, so that the negative feedback circuits implemented using the OCA would be able to operate at GBW/100 = 1 MHz with neglectable OCA’s non-idealities. Note that the 100 factor is a general rule used for a safety margin. Simulation results have shown that the proposed circuits can operate at frequencies more than 1 MHz but the error between the simulation an theoretical results would increase. Future works will investigate optimizations of the proposed oscillators according to certain system level specifications. Similar to the OCA based square wave oscillator presented in [ 20 ], the proposed sinusoidal oscillators are expected to have significant impact on future research directions. Declarations Author Contribution The authors jointly come up with the idea of the manuscript. Both designed the circuits and have written the paper. H.Z did the simulation whereas I.K. did the expermintal tests. References Kweon, S., et al. (2022). On-Chip Sinusoidal Signal Generators for Electrical Impedance Spectroscopy: Methodological Review. IEEE Transactions on Biomedical Circuits and Systems , 16 (3), 337–360. Zhao, Q., Wang, C., & Zhang, X. (2019). A universal emulator for memristor, memcapacitor, and meminductor and its chaotic circuit. Chaos (Woodbury, N.Y.) , 29 (1). 10.1063/1.5081076 Abuelma’atti, M., & Khan, M. (1996). Grounded Capacitor Oscillators Using a Single Operationl Transconductance Amplifier. Active and Passive Electronic Components , 19 (2), 91–98. Tao, Y., & Fidler, K. (1998). Generation of Second-Order Single-OTA RC Oscillators, IEE Proceedings of Circuits Devices Systems, 145(4), pp. 271–277. Tao, Y., & Fidler, K. (2000). Electronically Tunable Dual-OTA Second-Order Sinusoidal Oscillator/Filters with Non-interacting Controls: A Systematic Synthesis Approach. IEEE Transactions on Circuits Systems I , 47 (2), 117–129. Singh, V. (2006). Equivalent Forms of Dual-OTA RC Oscillators with Application to Grounded-Capacitor Oscillators. IEE Proceedings of Circuits Devices Systems, 153 (2), 95–99. Singh, V. (2010). Equivalent Forms of Single-Operational Transconductance Amplifier RC Oscillators with Application to Grounded-Capacitor Oscillators. IET Circuits Devices Systems , 4 (2), 123–130. Senani, R., Gupta, M., Bhaskar, D. R., & Singh, A. K. (2014). Generation of equivalent forms of operational trans-conductance amplifier-RC sinusoidal oscillators: the nullor. IET J Eng . 10.1049/joe.2013.0200 Abuelma’atti, M. T. (2017). Recent Developments in Current-Mode Sinusoidal Oscillators: Circuits and Active Elements. Arabian Journal for Science and Engineering , 42 (7), 2583–2614. Rubio, F. (2022). Current-Mode Electronically-Tunable Sinusoidal Oscillator Based on a Shadow Bandpass Filter, International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design (SMACD), 1–4. Tiwari, S., & Arora, T. S. (2022). Fully electronically tunable sinusoidal oscillator employing single VDTA and all grounded components. Analog Integr Circ Sig Process , 113 , 81–91. Jaikla, W. (2023). Single VDDDA-Based Lossy Inductance Simulator for Application to Sinusoidal Oscillator, International Conference on Power, Energy and Electrical Engineering (CPEEE), 112–115. Scarsella, M., et al. (2023). The Implementation of Single VCII-based RC Sinusoidal Oscillators: 28 Novel Configurations. IEEE Sensors Journal . 10.1109/JSEN.2023.3339641 Bisariya, S., & Afzal, N. (2024). Electronically Tunable Sinusoidal Oscillator Using Only Single Current-Controlled Current Conveyor Trans-Conductance Amplifier. International Journal of Electrical and Electronics Research , 12 (1), 119–125. Srivastava, D., Senani, R., Raj, A., & Bhaskar, D. (2024). New explicit-current-output SRCO using a single CFOA and all grounded capacitors. International Journal of Electronics and Communications , 178 . doi.org/10.1016/j.aeue.2024.155297 Roberts, G., & Sedra, A. (1989). All current-mode frequency selective circuits. Electronics Letters , 25 , 759–761. Toumazou, C., Lidgey, E. J., & Haigh, D. G. (1990). Analogue IC design: the current-mode approach (Vol. 2). Peter Peregrinus Ltd. IEE Circuits and Systems Series. Cataldoa, G., Mitaa, R., & Pennisi, S. (2006). High speed CMOS unity gain current amplifier. Microelectronics Journal , 37 , 1086–1091. Alzaher, H. (2015). Current follower based reconfigurable integrator/ differentiator circuits with passive and active components reuse. Microelectronics Journal , 46 (2), 35–142. Alzaher, H. (2019). Novel Schmitt trigger and square-wave generator using single current amplifier. Ieee Access : Practical Innovations, Open Solutions , 7 , 186175–186181. Additional Declarations No competing interests reported. Supplementary Files supplementary.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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12:00:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":25778,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA possible CMOS realization of the OCA.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/56195870a7f65a6c7310774a.png"},{"id":67654430,"identity":"3b712177-9c59-483b-872b-f495e6d4f64c","added_by":"auto","created_at":"2024-10-28 12:08:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":6883,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eClosed loop OCA based amplifiers.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/f83e72db64705d6d61aa15c5.png"},{"id":67654432,"identity":"3a90aa90-04e7-47c3-96a8-3d2374b87a54","added_by":"auto","created_at":"2024-10-28 12:08:25","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":5264,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLP RC networks.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/a07d0f8ae2cd4597e02bff58.png"},{"id":67653679,"identity":"18b4fbda-eb75-41e0-9048-aa0e5af0dce4","added_by":"auto","created_at":"2024-10-28 12:00:25","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":5552,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBP RC network.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/ca68f2edc4fdc2c4095e54d8.png"},{"id":67656128,"identity":"46c6d640-3f54-4767-b577-166651dfca89","added_by":"auto","created_at":"2024-10-28 12:16:25","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":10322,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProposed phase shift oscillator using OCA.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/8aa13c258b81829a91ce1fc3.png"},{"id":67656129,"identity":"b86bebe0-a0f8-4bbd-b76b-87102d8c4077","added_by":"auto","created_at":"2024-10-28 12:16:25","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":9329,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProposed Wein bridge oscillator using CA.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/d92e7cb2abb357602eb12033.png"},{"id":67654431,"identity":"5c9d7df9-7449-451f-ba33-ccdd54d0f055","added_by":"auto","created_at":"2024-10-28 12:08:25","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":31946,"visible":true,"origin":"","legend":"\u003cp\u003eA possible CMOS realization of the multi-output OCA.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/9cd331dfca606cef294a10b0.png"},{"id":67653678,"identity":"79491079-56d2-4716-b970-5fae9c70c81e","added_by":"auto","created_at":"2024-10-28 12:00:25","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":120338,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation results of the phase shift oscillator.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/94ff9aed7c4571ffc72b5a81.png"},{"id":67653685,"identity":"22fbeda9-918e-4070-ac23-ded4f451bd56","added_by":"auto","created_at":"2024-10-28 12:00:25","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":174842,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSimulation results of the Wein bridge oscillator producing differential signals at transient.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/4240f6eb609a265362e342a1.png"},{"id":67653683,"identity":"884252a2-110f-4c2a-befb-880b6edb2a76","added_by":"auto","created_at":"2024-10-28 12:00:25","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":184785,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSimulation results of the Wein bridge oscillator producing differential signals at steady state.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/f69d17f910f8f9c75f4f7d8e.png"},{"id":67653686,"identity":"ff77bbca-8740-4303-a4bc-66970d976156","added_by":"auto","created_at":"2024-10-28 12:00:26","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":19065,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA configuration of AD844 to mock a single output OCA.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/aba357b77a4827ede7de44e2.png"},{"id":67653681,"identity":"2bc43321-e5a7-46f9-88e4-b1b8cbf72f3e","added_by":"auto","created_at":"2024-10-28 12:00:25","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":36666,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePhase shift oscillator experimental result.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/ebb17a06e390de39fe123065.png"},{"id":67654427,"identity":"ef614b40-fe48-428d-ae12-43c7518886aa","added_by":"auto","created_at":"2024-10-28 12:08:25","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":67559,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMeasured output of Wein bridge oscillator.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/d54a053b5ae2853faaea0f84.png"},{"id":84308029,"identity":"720f3c18-8f74-4b28-9d93-536be35bb88b","added_by":"auto","created_at":"2025-06-10 11:47:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1608306,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/e97a1f4e-abb9-4856-8303-7f5fc23cce9a.pdf"},{"id":67654425,"identity":"1a8e7fc4-d515-4926-9cc3-42ff412cd065","added_by":"auto","created_at":"2024-10-28 12:08:25","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":44040,"visible":true,"origin":"","legend":"","description":"","filename":"supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-5325115/v1/3436135ba48444e27ed3afc1.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Single Operational Current Amplifier Based Sinusoidal Oscillators ","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eSinusoidal oscillators are essential elements in many signal processing systems. They are used for carrier generation in communication circuits, as well as a test signal to characterize circuits. Although traditional applications utilize voltage-mode sinusoidal oscillators, modern biomedical applications such as electrical impedance tomography (EIT) need fully differential (FD) current signals, due to safety concerns, to interrogate body tissue [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Furthermore, charge-controlled mem-elements require a current sinusoidal input to measure the pinched hysteresis loop (PHL) of the device [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eConsidering the four basic amplifiers types, namely the operational voltage amplifier (OpAmp), the operational transresistance amplifier (OTRA), the operational transconductance amplifier (OTA), and operational current amplifier (OCA), it is obvious that the first two amplifier types cannot be used to provide output currents since their outputs are associated with low output impedance (ideally zero). In principle, current-mode sinusoidal oscillators (traditionally defined as oscillators with explicit output currents) can be obtained from available voltage-mode sinusoidal oscillators. However, this requires an additional active element(s) for converting voltage signal to current signal(s). On the other hand, there are enormous number of voltage-mode and current-mode oscillators based on operational transconductance amplifier (OTA). In fact, voltage-mode oscillators based on OTA can be converted to oscillators with explicit output current(s) by replacing single output OTA(s) by dual- or multi-output OTA(s).\u003c/p\u003e \u003cp\u003eOn the other hand, OCA based key sinusoidal oscillator topologies are still not available in literature. In this paper, this gap is minimized by presenting two new and fundamental sinusoidal oscillators using OCA. They are current mode counterparts of the famous Wein bridge and the phase shift oscillators. These sinusoidal oscillators are fundamental in the sense that their counterparts designed using OpAmps have been popularly available for the majority of the past century. At this leading stage, this manuscript concentrates on presenting the mathematical foundation/the systematic approach used to develop these new circuits and verifying their workability. The performance characteristics of the proposed circuits can always be optimized according to the desired system-level specifications. The paper is organized as follows. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e explains the contributions of this work through critical study of the available solutions. Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e provides a brief background of the OCA and its applications. Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the proposed oscillator circuits and derives the key equations required for their design. Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e5\u003c/span\u003e provides simulation and experimental results of the proposed oscillators. Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e6\u003c/span\u003e discusses the obtained results and compares them to recent designs in literature. Finally, section \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003e7\u003c/span\u003e offers a summary and a conclusion for the paper.\u003c/p\u003e"},{"header":"2 Available Solutions","content":"\u003cp\u003eIn general, sinusoidal oscillator circuits can be classified based on the number of available outputs as single output, quadrature output and multioutput oscillators. The latter two types have their own applications but require two or more amplifiers, active elements, or active building blocks. Here we would like to clarify a very important issue that an active building block may consist of two or more active elements whereas an active element may employ two or more amplifiers. This paper focuses on single output current mode oscillators which can often be realized using a single amplifier and hence truly canonic. Using minimum number of amplifiers and hence possibly the minimum power consumption in oscillator\u0026rsquo;s designs is crucial for modern low power applications.\u003c/p\u003e \u003cp\u003eAs explained in the introduction, that current mode oscillator based on a single amplifier could logically be obtained only from the OTA and the OCA. As for the OTA solutions, one can use OTA-based RC oscillators [\u003cspan additionalcitationids=\"CR4 CR5 CR6 CR7\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]-[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], which may employ one OTA along with a number of resistors and capacitors. In these kinds of circuits, it is difficult to control or optimize the oscillators\u0026rsquo; characteristics because they involve two different types of resistances namely the passive resistors and the active resistors (gm of the OTAs). Also, when an OTA-RC oscillator is transformed into an OTA-C oscillator, by simulating the passive resistors with OTAs, the resulting oscillator would employ an excessive number of OTAs and hence will not be practically viable. Clearly, single output oscillator based on OTA-C approach would require at least two OTAs and hence naturally is not canonic.\u003c/p\u003e \u003cp\u003eOver the years, many current-mode sinusoidal oscillators based on active elements and active building blocks have been proposed. A comprehensive review of such designs can be found in [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] that cites 249 works. They are mainly using Current Difference Transconductor Amplifier (CDTA), Voltage Difference Transconductor Amplifier (VDTA), Current Conveyor Transconductance Amplifier (CCTA), Differential-Input Buffered Transconductance Amplifier (DBTA), Current-Controlled Current Difference Transconductance Amplifier (CCCDTA), Current Follower Transconductance Amplifier (CFTA), Current Differencing Cascaded Transconductance Amplifier (CDCTA), Current-Backward Transconductance Amplifier (CBTA), Current Conveyors, Current-Feedback Operational Amplifier (CFOA), Operational Floating Amplifier (OFA), and Current Difference Buffered Amplifier (CDBA). More recent works published during the last three years, present sinusoidal oscillators based on, for examples, OTA, VDTA, voltage difference differential difference amplifier (VDDDA), second-generation voltage conveyor (VCII), CCCCTA, and the CFOA, respectively [\u003cspan additionalcitationids=\"CR11 CR12 CR13 CR14\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]-[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Such designs may employ a single active element or a single active building block; and may meet the usual basic requirements for sinusoidal oscillators of independent tuning of condition of oscillation (CO) and frequency of oscillation (FO). But it is unfair to compare them to their single amplifier counterparts. For example, a CCTA consists of a second generation current conveyor (CCII) and two OTAs. A CCII by itself can be decomposed to a voltage buffer (a unity gain voltage amplifier) and a current follower (a unity gain current amplifier). Therefore, these oscillators are less attractive for low power applications. Another problem is that these oscillators are associated with low form factor and hence they neither enforce uniformity nor allow optimization of performance.\u003c/p\u003e \u003cp\u003eBut the main issue is that although these oscillators provide explicit current outputs and hence traditionally defined as current mode oscillators, all of these oscillators are using active elements which are not purely current-mode; therefore, voltage-mode limitations such as limited swings at lower power supplies are inevitable. Therefore, the definitive solution to have true current mode oscillators is to design them utilizing the OCA. Consequently, these oscillators would truly have the well-known advantages of current mode signal processing such as low power consumption at high working frequencies and output swing independent of the supply voltage [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] and [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e"},{"header":"3 Current Amplifiers","content":"\u003cp\u003eA current amplifier could be realized as either an open-loop amplifier or a negative feedback amplifier. The difference between the two being the gain (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{i}\\)\u003c/span\u003e\u003c/span\u003e) of the amplifier. If \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{i}\\)\u003c/span\u003e\u003c/span\u003e is designed to be finite then it is traditionally called a CA it is usually used in open-loop configurations. In contrast, an ideal OCA has \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{i}\\to\\:\\infty\\:\\)\u003c/span\u003e\u003c/span\u003e and consequently must be used with negative feedback. This paper proposes the use of the latter type. Another point of interest is how to define the input and output terminals of the OCA. The definition that will be followed in this work is obtained through adjoint networks [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], from which it can be shown that a OCA has one input terminal and two differential output terminals. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the suggested OCA symbol.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIdeally, the OCA has zero impedance at the input port and infinite output impedance at the output ports. Its current terminal characteristics adhere to the following relationships.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{I}_{op}=-{I}_{on}={A}_{i}{I}_{in}\\:\\text{w}\\text{h}\\text{e}\\text{r}\\text{e}\\:{A}_{i}\\to\\:\\infty\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eA real OCA typically has a large current gain, small input equivalent resistance, and a very large output resistance. Its CMOS realization typically consists of three stages: a common gate amplifier, differential amplifier, and a balanced current output stage as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The first two stages are to provide a high transresistance gain while the latter is to offer a high differential transconductance gain. A negative closed-loop feedback configuration is then achieved by shorting the inverting output with the input. The remaining non-inverting output terminal is used to drive a load or another circuit. The use of this OCA with negative feedback to achieve a unity gain current follower can be found in [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] and [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMany OpAmp basic applications can be realized using the OCA. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. shows how to implement an inverting and a non-inverting amplifier which are used in next sections to realize the proposed oscillator circuits.\u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{I}_{o1}=-\\frac{{R}_{1}}{{R}_{2}}{I}_{in}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{I}_{o2}=\\left(1+\\frac{{R}_{1}}{{R}_{2}}\\right){I}_{in}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4 Proposed Sinusoidal Oscillators","content":"\u003cp\u003eThere are two fundamental single OpAmp based sinusoidal oscillator types: the Wein bridge oscillator and the phase shift oscillator. This section demonstrates the procedure for developing their OCA counterparts. This is accomplished by first providing mathematical analysis of the RC networks that will be used in synthesizing the oscillators. Then, it proceeds to present the oscillator circuits using these networks and the two basic amplifier types.\u003c/p\u003e \u003cp\u003eThe Barkhausen criterion is commonly used to predict the frequency and condition of oscillation of sinusoidal oscillators. According to this criterion, an oscillator circuit can be described by the characteristic equation given by\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:\\:{s}^{2}+\\:(a-b)s+{c}^{2}=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003es\u003c/em\u003e is the complex frequency. The circuit will oscillate if the condition \u003cem\u003ea\u003c/em\u003e\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0 is satisfied, and the frequency of oscillation will be given by\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:{\\omega\\:}}_{o}=c\\)\u003c/span\u003e\u003c/span\u003e. In (2) the parameters \u003cem\u003ea\u003c/em\u003e, \u003cem\u003eb\u003c/em\u003e and \u003cem\u003ec\u003c/em\u003e are functions of the circuit passive components when the oscillators are realized using closed loop amplifiers (e.g. the OpAmp and OCA) whereas they additionally involve the parameters of the active elements when the oscillator circuits are based on open loop amplifiers, for example, the transconductance of the OTAs. In the following subsections, the oscillators\u0026rsquo; synthesizing procedure is demonstrated and the frequency of oscillation (FO), and condition of oscillation (CO) are derived.\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1 RC Networks\u003c/h2\u003e \u003cp\u003eRC networks are used to obtain the desired phase shift in oscillators in order to convert a negative feedback loop into a positive feedback loop at one frequency only. In general, these networks can have a high pass (HP) or low pass (LP) magnitude frequency response. LP RC networks provide negative phase shift, whereas HP RC networks provide positive phase shift. Without loss of generality, the remainder of this subsection will focus on LP RC networks. It can be shown that a three section RC network, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, provides a -180\u003csup\u003eo\u003c/sup\u003e phase shift and a loss of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{29}\\)\u003c/span\u003e\u003c/span\u003e at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\omega\\:}=\\frac{\\sqrt{6}}{RC}\\)\u003c/span\u003e\u003c/span\u003e. These results are derived from the transfer function (TF) given by (5).\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\frac{{I}_{out}}{{I}_{in}}=\\frac{\\frac{1}{{R}^{3}{C}^{3}}}{{s}^{3}+\\frac{{5s}^{2}}{RC}+\\frac{6s}{{R}^{2}{C}^{2}}+\\frac{1}{{R}^{3}{C}^{3}}\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe other RC network of interest is the bandpass (BP) RC network shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. It provides a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:0^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\omega\\:=\\frac{1}{RC}\\)\u003c/span\u003e\u003c/span\u003e with a loss of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\frac{1}{3}\\)\u003c/span\u003e\u003c/span\u003e. Its TF is given by (6).\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:\\frac{{I}_{out}}{{I}_{in}}=\\frac{\\frac{s}{RC}}{{s}^{2}+\\frac{3s}{RC}+\\frac{1}{{R}^{2}{C}^{2}}\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Phase Shift Oscillator\u003c/h2\u003e \u003cp\u003eUsing the LP RC network of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and a single OCA, a phase shift oscillator can be realized as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The OCA is configured as an inverting amplifier but as the output current which is supposed to flow through R\u003csub\u003e2\u003c/sub\u003e going to ground (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) and hence cannot be used to feed the passive network. Therefore, another inverting (negative) current is needed. That is the phase shift oscillator requires two negative feedback currents: one to form the amplifier and one to feed the passive phase shift network. As in the case of OTA, a multi-output OCA may be used to provide explicit output current signals instead of using an additional amplifier. The additional output stage can simply be implemented using an extra balanced output stage [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis means that this oscillator can provide two identical currents signals (I\u003csub\u003eo1\u003c/sub\u003e and I\u003csub\u003eo2\u003c/sub\u003e) from the two unused positive output terminals. It can be shown that FO and CO are given by (7) and (8), respectively.\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:FO:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:{f}_{o}=\\frac{\\sqrt{6}}{2\\pi\\:RC}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:CO:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\frac{{R}_{1}}{{R}_{2}}=28$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Wein Bridge Oscillator\u003c/h2\u003e \u003cp\u003eUsing the BP RC network of Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and an OCA, a Wein bridge oscillator can be built as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. In this case, the OCA is configured as non-inverting amplifier. Therefore, this oscillator can provide two differential output signals. Routine analysis shows that FO and CO are given by (9) and (10), respectively.\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:FO:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:{f}_{o}=\\frac{1}{2\\pi\\:RC}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:CO:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\frac{{R}_{1}}{{R}_{2}}=2$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5 Results","content":"\u003cp\u003eThis section verifies the presented theory through both simulation using CMOS OCA and prototyping using commercially available ICs.\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Simulation results\u003c/h2\u003e \u003cp\u003eThe proposed oscillator circuits were simulated in a standard 180 nm CMOS process using T-Spice. The CMOS realization of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e is expanded to offer two additional output currents namely I\u003csub\u003eo2p\u003c/sub\u003e and I\u003csub\u003eo2n\u003c/sub\u003e. This is achieved by incorporating and an identical additional output stage formed by M4c, M4d, M5c, M5d, MB10, MB11, MCP, and MCN as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The supply voltage and the biasing currents are set to \u0026plusmn;\u0026thinsp;0.9V and 10\u0026micro;A, respectively. The phase shift oscillator was designed, for example, to produce an oscillation frequency of 1MHz. The capacitance C was selected to be 10pF and hence the required resistance R\u0026thinsp;=\u0026thinsp;39kΩ. The resistance of R\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;10kΩ was chosen. It was found that oscillation starts and sustains when R\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;300kΩ the result is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. This records oscillation frequency of approximately 970kHz which is in very good agreement with the theoretical value.\u003c/p\u003e \u003cp\u003eThe Wein bridge oscillator was realized with C\u0026thinsp;=\u0026thinsp;15.5pF and R\u0026thinsp;=\u0026thinsp;10kΩ to produce an oscillation frequency of 1MHz. A resistance of R\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;10kΩ was used and hence it was found that the oscillation starts and sustains when R\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;22kΩ. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the differential output waveforms while oscillation grows whereas Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows the output wave forms at steady state. The recoded frequency is 974kHz which is very close to the theoretical value.\u003c/p\u003e\u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Experimental results\u003c/h2\u003e \u003cp\u003eThe proposed oscillators were implemented using commercial chips such as AD844. Experimental results are provided in this section. A current gain is obtained using two AD844s as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e. It can be shown easily that again of I\u003csub\u003eof\u003c/sub\u003e/I\u003csub\u003ei\u003c/sub\u003e = -R\u003csub\u003e1\u003c/sub\u003e/R\u003csub\u003e2\u003c/sub\u003e is obtained. For non-inverting gain of R\u003csub\u003e1\u003c/sub\u003e/R\u003csub\u003e2\u003c/sub\u003e, the output current can be inverted by an additional AD844.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe phase shift oscillator circuit was designed using \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{1}=32\\:k{\\Omega\\:}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{2}=1\\:k{\\Omega\\:}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R=3\\:k{\\Omega\\:}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C=10\\:nF\\)\u003c/span\u003e\u003c/span\u003e. Obtained result is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e. The obtained \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{o}\\)\u003c/span\u003e\u003c/span\u003e is very close to theoretical value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{o}=\\)\u003c/span\u003e\u003c/span\u003e13kHz.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA Wein bridge oscillator prototype was implemented using \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{1}=31\\:k{\\Omega\\:}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{2}=10\\:k{\\Omega\\:}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R=25\\:k{\\Omega\\:}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C=1.5\\:nF\\)\u003c/span\u003e\u003c/span\u003e. The result is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e. The oscillation frequency is in good agreement with the theoretical value of 4.244kHz.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6 Comparison and Discussion","content":"\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e provides comparison with several recent sinusoidal oscillators [\u003cspan additionalcitationids=\"CR11 CR12 CR13 CR14\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]-[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Without loss of generality, these samples represent various types of available solutions. These solutions are classified as oscillators with explicit output voltage [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] and [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], and with explicit output current [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], and [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. The voltage mode oscillators require superfluous voltage to current converters to produce current signals. On the other hand, the current mode oscillators usually do not provide differential output signals [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], and [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The oscillator in [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] produces differential current signals but employs two OTAs. The supply voltage of the proposed oscillators is less than the other solutions and its power consumption is expected to be optimum since the proposed approach employs a single amplifier. Similar to other solutions, the proposed oscillators support operating frequencies in kHz and MHz. In fact, only [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] and this work have verified the operation of the presented oscillators via both CMOS realizations and prototyping. Finally, it must be mentioned that the performance characteristics of the proposed oscillators can always be optimized according to the desired system-level specifications.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison with several recent works.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRef\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDevice\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eActive elements\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eOutput\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDifferential\u003c/p\u003e \u003cp\u003eSignals\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eCMOS\u003c/p\u003e \u003cp\u003eRealization\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSupply\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003ePower\u003c/p\u003e \u003cp\u003e(\u0026micro;W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003cp\u003eFrequency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003ePrototype\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOTA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2 OTAs\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCurrent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e180 nm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.8V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e2.75 MHz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVDTA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2 OTAs\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCurrent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e350 nm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;2V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1 MHz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVDDDA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOTA\u0026thinsp;+\u0026thinsp;DDA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVoltage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMacro models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;2V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e245.5kHz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVCII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2 CCII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVoltage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e113kHZ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCCCCTA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCCII\u0026thinsp;+\u0026thinsp;2 OTAs\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCurrent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e180 nm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;1V\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.9MHz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCFOA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCCII +\u003c/p\u003e \u003cp\u003eBuffer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCurrent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.174kHz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOCA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1 OCA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCurrent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e\u003c/p\u003e \u003cp\u003eYes Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e180 nm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;0.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1MHz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"7 Conclusion","content":"\u003cp\u003eVoltage-mode OpAmp based sinusoidal oscillators are fundamental electronics building blocks. But they have limited output swings set by the power supplies just like all voltage mode circuits. Moreover, in applications that require current output signals rather than voltage signals, superfluous voltage-to-current converters are mandatory to convert the output from voltage signals to current signals; thus, increasing power consumption. This paper presented novel OCA based sinusoidal oscillators that provide explicit output current signals using a single OCA. Simulation and experimental results confirming the presented theory are provided.\u003c/p\u003e \u003cp\u003eThe maximum operating frequency is limited by the GBW of the OCA. The OCA used in this paper was designed to have a GBW close to 100 MHz, so that the negative feedback circuits implemented using the OCA would be able to operate at GBW/100\u0026thinsp;=\u0026thinsp;1 MHz with neglectable OCA\u0026rsquo;s non-idealities. Note that the 100 factor is a general rule used for a safety margin. Simulation results have shown that the proposed circuits can operate at frequencies more than 1 MHz but the error between the simulation an theoretical results would increase. Future works will investigate optimizations of the proposed oscillators according to certain system level specifications. Similar to the OCA based square wave oscillator presented in [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], the proposed sinusoidal oscillators are expected to have significant impact on future research directions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eThe authors jointly come up with the idea of the manuscript. Both designed the circuits and have written the paper. H.Z did the simulation whereas I.K. did the expermintal tests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKweon, S., et al. (2022). On-Chip Sinusoidal Signal Generators for Electrical Impedance Spectroscopy: Methodological Review. \u003cem\u003eIEEE Transactions on Biomedical Circuits and Systems\u003c/em\u003e, \u003cem\u003e16\u003c/em\u003e(3), 337\u0026ndash;360.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao, Q., Wang, C., \u0026amp; Zhang, X. (2019). A universal emulator for memristor, memcapacitor, and meminductor and its chaotic circuit. \u003cem\u003eChaos (Woodbury, N.Y.)\u003c/em\u003e, \u003cem\u003e29\u003c/em\u003e(1). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1063/1.5081076\u003c/span\u003e\u003cspan address=\"10.1063/1.5081076\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbuelma\u0026rsquo;atti, M., \u0026amp; Khan, M. (1996). Grounded Capacitor Oscillators Using a Single Operationl Transconductance Amplifier. \u003cem\u003eActive and Passive Electronic Components\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(2), 91\u0026ndash;98.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTao, Y., \u0026amp; Fidler, K. (1998). Generation of Second-Order Single-OTA RC Oscillators, IEE Proceedings of Circuits Devices Systems, 145(4), pp. 271\u0026ndash;277.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTao, Y., \u0026amp; Fidler, K. (2000). Electronically Tunable Dual-OTA Second-Order Sinusoidal Oscillator/Filters with Non-interacting Controls: A Systematic Synthesis Approach. \u003cem\u003eIEEE Transactions on Circuits Systems I\u003c/em\u003e, \u003cem\u003e47\u003c/em\u003e(2), 117\u0026ndash;129.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSingh, V. (2006). Equivalent Forms of Dual-OTA RC Oscillators with Application to Grounded-Capacitor Oscillators. IEE Proceedings of Circuits Devices Systems, 153 (2), 95\u0026ndash;99.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSingh, V. (2010). Equivalent Forms of Single-Operational Transconductance Amplifier RC Oscillators with Application to Grounded-Capacitor Oscillators. \u003cem\u003eIET Circuits Devices Systems\u003c/em\u003e, \u003cem\u003e4\u003c/em\u003e(2), 123\u0026ndash;130.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSenani, R., Gupta, M., Bhaskar, D. R., \u0026amp; Singh, A. K. (2014). Generation of equivalent forms of operational trans-conductance amplifier-RC sinusoidal oscillators: the nullor. \u003cem\u003eIET J Eng\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1049/joe.2013.0200\u003c/span\u003e\u003cspan address=\"10.1049/joe.2013.0200\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbuelma\u0026rsquo;atti, M. T. (2017). Recent Developments in Current-Mode Sinusoidal Oscillators: Circuits and Active Elements. \u003cem\u003eArabian Journal for Science and Engineering\u003c/em\u003e, \u003cem\u003e42\u003c/em\u003e(7), 2583\u0026ndash;2614.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRubio, F. (2022). Current-Mode Electronically-Tunable Sinusoidal Oscillator Based on a Shadow Bandpass Filter, International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design (SMACD), 1\u0026ndash;4.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTiwari, S., \u0026amp; Arora, T. S. (2022). Fully electronically tunable sinusoidal oscillator employing single VDTA and all grounded components. \u003cem\u003eAnalog Integr Circ Sig Process\u003c/em\u003e, \u003cem\u003e113\u003c/em\u003e, 81\u0026ndash;91.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJaikla, W. (2023). Single VDDDA-Based Lossy Inductance Simulator for Application to Sinusoidal Oscillator, International Conference on Power, Energy and Electrical Engineering (CPEEE), 112\u0026ndash;115.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScarsella, M., et al. (2023). The Implementation of Single VCII-based RC Sinusoidal Oscillators: 28 Novel Configurations. \u003cem\u003eIEEE Sensors Journal\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1109/JSEN.2023.3339641\u003c/span\u003e\u003cspan address=\"10.1109/JSEN.2023.3339641\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBisariya, S., \u0026amp; Afzal, N. (2024). Electronically Tunable Sinusoidal Oscillator Using Only Single Current-Controlled Current Conveyor Trans-Conductance Amplifier. \u003cem\u003eInternational Journal of Electrical and Electronics Research\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(1), 119\u0026ndash;125.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSrivastava, D., Senani, R., Raj, A., \u0026amp; Bhaskar, D. (2024). New explicit-current-output SRCO using a single CFOA and all grounded capacitors. \u003cem\u003eInternational Journal of Electronics and Communications\u003c/em\u003e, \u003cem\u003e178\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003edoi.org/10.1016/j.aeue.2024.155297\u003c/span\u003e\u003cspan address=\"10.1016/j.aeue.2024.155297\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRoberts, G., \u0026amp; Sedra, A. (1989). All current-mode frequency selective circuits. \u003cem\u003eElectronics Letters\u003c/em\u003e, \u003cem\u003e25\u003c/em\u003e, 759\u0026ndash;761.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eToumazou, C., Lidgey, E. J., \u0026amp; Haigh, D. G. (1990). \u003cem\u003eAnalogue IC design: the current-mode approach\u003c/em\u003e (Vol. 2). Peter Peregrinus Ltd. IEE Circuits and Systems Series.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCataldoa, G., Mitaa, R., \u0026amp; Pennisi, S. (2006). High speed CMOS unity gain current amplifier. \u003cem\u003eMicroelectronics Journal\u003c/em\u003e, \u003cem\u003e37\u003c/em\u003e, 1086\u0026ndash;1091.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlzaher, H. (2015). Current follower based reconfigurable integrator/ differentiator circuits with passive and active components reuse. \u003cem\u003eMicroelectronics Journal\u003c/em\u003e, \u003cem\u003e46\u003c/em\u003e(2), 35\u0026ndash;142.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlzaher, H. (2019). Novel Schmitt trigger and square-wave generator using single current amplifier. \u003cem\u003eIeee Access : Practical Innovations, Open Solutions\u003c/em\u003e, \u003cem\u003e7\u003c/em\u003e, 186175\u0026ndash;186181.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"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},"keywords":"Sinusoidal oscillators, current-mode circuits and systems, current amplifier","lastPublishedDoi":"10.21203/rs.3.rs-5325115/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5325115/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper presents important missing sinusoidal oscillators. There are numerous sinusoidal oscillators versions based on the three fundamental amplifiers namely the operational amplifier (OpAmp), the operational transconductance amplifier (OTA), and the operational transresistance amplifier (OTRA) but their counterparts based on the fourth type that is the operational current amplifier (OCA) are to be reported. Traditional applications use voltage-mode oscillators, however, several modern applications such as electrical impedance spectroscopy (EIS) require current-mode oscillators. In the literature, many current-mode oscillators have been proposed; however, they use active building blocks which operate in both voltage and current modes. In this paper, we propose two novel oscillators using the pure current-mode active element namely the OCA. Simulation results obtained from a standard 180nm CMOS process are provided. It is shown that the proposed oscillators consume approximately 120\u0026micro;W while working in the MHz range. Also, experimental results using prototypes implemented using commercially available ICs show the validity of the proposed designs.\u003c/p\u003e","manuscriptTitle":"Single Operational Current Amplifier Based Sinusoidal Oscillators ","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-28 12:00:20","doi":"10.21203/rs.3.rs-5325115/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":"73ea09c5-9402-4191-adc3-ae5792060565","owner":[],"postedDate":"October 28th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-10T11:39:06+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-28 12:00:20","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5325115","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5325115","identity":"rs-5325115","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}