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OTA-C osilatörlerinde ideal olmama problemi

OTA-C osilatörlerinde ideal olmama problemi

##### Dosyalar

##### Tarih

1996

##### Yazarlar

Çam, Uğur

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

İşemsel geçiş iletkenliği kuvvetlendiricisi(OTA) ve kapasite elemanları kullanılarak gerçkleştirilen devreler yüksek frekanslarda iyi bir performansa sahiptirler. OTA'mn eğiminin geniş bir frekans bölgesinde ayarlanabilmesi ve CMOS tümdevre teknolojisiyle tek bir VLSI cipinin üzerine yerleştirilebilmeleri bu devrelerin önemli avantajlanndandır. Bu çalışmada minumum sayıda OTA ve topraklanmış kapasite elamanı içeren bir filtre topolojisinden hareket edilerek yeni osilatör topolojileri elde edilmiştir. Bu osilatör yapılan, geçiş iletkenliği kuvvetlendiricisinin eğimi ile osilasyon frekansının osilasyon şartım etkilemeksizin kontrolü, yüksek frekanslarda çalışma, yapıda endüktans bulunmaması sebebiyle çok geniş ölçekli tümleştirmeye(VLSI) uygunluk, özelliklerini sağlar, önerilen yapılar için OTA'mn idealsizlik etkileri incelenmiş ve bu etkileri gidermek için, tasarım aşamasında topolojilere OTA ile gerçekleştirilen negatif ve pozitif direnç ilave edilmiştir. Bütün topolojiler sadece topraklanmış kapasite elamanı içerdiklerinden önerilen devreler hem monolitik tümdevre teknolojisi için hem de ince film fabrikasyonu için önemli bir özelliği sağlamaktadır. Ayrıca parazitik kapasiteler topraklanmış kapasitelere paralel geldiklerinden kolaylıkla hesaplanıp ayarlanabilirler. önerilen devreler OTA idealsizliklerini içeren bir makromodel yardımıyla analiz edilmiş ve idealsizliklerin osilasyon şartına ve osilasyon frekansına etkisi gösterilmiştir. Ayrıca osilasyon koşulu ve osilasyon frekansının devre parametrelerine olan duyarlılık analizi yapılmıştır. Osilatör devreleri kaskod akım aynalı simetrik OTA kullanılarak SPICE bilgisayar programı yardımıyla simüle edilmiştir. Simülasyonlarda TÜBİTAK MAM YİTAL 3u CMOS proses parametreleri kullanılmıştır. Bu devrelerden yükselme eğimi ve kırpılma problemi olmaksızın elde edilebilecek maksimum osilasyon genliği basit bir method yardımıyla belMenmiştir. önerilen devrelerden biri CA3080 bipolar tümdevre yapısı kullanılarak bord üzerinde denenmiştir. Deney sonunda bu devrenin frekansı ve genliği ayarlanabilir bir yüksek frekans osilatörü olarak çalışabileceği gösterilmiştir.

Oscillators have a wide range of using area in telecommunications, control systems, signal processing and measurement systems. For design of voltage-controlled sinusoidal oscillator, a variety of active OPAMP-RC networks have been reported up to now. But, these network don't operate at high frequency, don't have frequency tuning parameter effectively. On the other hand, OTA-C oscillator networks have some superiorities such as, open loop tunability of OTA, compatibility to VLSI, adjustibikty of oscillation frequency by tranconductance of OTA Since tranconductance of OTA is function of its tail current, oscillation frequency can be easily adjusted via this current. A great variety of RC-active circuits have been developed for generating sinewaves, most of them based on the use of conventional operational amplifier (op amp) as active component. This circuit typically perform correctly in audio frequency range(<20kHz), but their performance becomes severely degraded as the frequency increases. Together with frequency limitations op-amp based voltage controlled oscillators also exhibit other problems further restricting their usefulness. Different variable frequency RC-active oscillator have been reported whose frequency of oscillation can be controlled by a single resistor without affecting oscillation condition. Some additional circuitry has to be added to achieve this operation. One possible method is obtained is obtained by substituting the controlling resistor by a FET working in ohmic region. This reduces the voltage swing across the simulated resistance. Besides, the tunable frequency range is somewhat reduces and switching among different resistors is needed what makes the design approach not readily compatible with monolithic integrated circuits. Most of these problems can be overcome by the use of operational tranconductance amplifiers(OTA) as the active building block. By interconnecting OTAs and capacitors, oscillating can be obtained whose frequency of oscillation is proportional to transconductance of OTA. Since the transconductance gain of OTA can be varied or programmed by an external power supply, the voltage controlled VIoscillator can be readily implemented. Thus fully integrated voltage controlled transconductance amplifiers-capacitors oscillator(TACO) can be obtained with frequency adjustable over wide ranges, avoiding the necessity of switching among several passive components as observed in opamp design. The use of circuits composed of operational transconductance amplifiers and capacitors has been demonstrated to be potentially advantageous for the synthesis of high frequency continuos-time monolithic analog operators either linear or nonlinear. One basic reason for high frequency potential of these circuits comes from the fact that the OTA is used in a open loop. It means that no additional constraints are imposed on the frequency response due to local feedback -induced pole displacement. Another advantage of open loop OTA-based circuit is that the transconductance of the OTA is used as a design parameter. In a typical OTA architecture this gain can be adjusted either by changing the tail current of a differential pair or by using digitally controlled current mirrors. Programmability is hence an inherent property of OTA-C circuits. In this study, three new voltage-controlled sinusoidal oscillator topologies are proposed using only CMOS operational transconductance amplifiers and grounded capacitors. The oscillator configurations have the properties of oscillation frequency control using the tranconductans gain without affecting oscillation condition, suitability to the very large scale integration (VLSI) for not having any inductors, and the capability of operation at high frequency.For the proposed topologies, the nonideality effect such as finite output conductance, finite bandwidth are investigated, and to compensate these effects in the design stages negative resistors implemented with OTA's are added. The oscillator topologies are simulated with SPICE computer program and resulting output voltage waveform are plotted. A general sinusoidal network, has two conjugate pole on the imaginary axes and can be described by a second order characteristic equation (s2+bs+n02).voat=° 0) where b=0 is oscillation condition and Qo is oscillation frequency. Parameters b controls both the oscillation condition and the amplitude of the oscillation. Similarly, the level of distortion can be also shown to depend on b. The basic goal of OTA-C oscillator design is to achieve noninteractive control of b and Q0 with minimum number of component. VIISeveral OTA-C filter structures have been reported various researchers over the past several years[16]. Based upon, constructed with a minimum number OTA and grounded capacitor filter topology, novel OTA-C oscillator topologies are generated by converting of filters into oscillators which is explained in literature[9,20,21]. The general biqudratic transfer function is given as follows, iA,\ V^ *2* + ***+*. n. There are two possible ways for obtaining sinusoidal oscillator from this transfer function. In one of them the characteristic equation of the oscillator is obtained by equating the input voltage of filter Vm(s) to zero. In this case the following oscillator characteristic equation is obtained (f+bls+b0).Vo(s) = 0 (3) The second way is connecting the output terminal of filter to the input terminal. By doing so, the resulting oscillator characteristic equation is expressed as, s+ f \ f Y\ \~a s+ 2 J bo~aa U-* ?Vo(S) = 0 (4) 2 'J If the oscillation condition satisfy by making b=0, this two equation yields undamped oscillations. All the proposed topologies are very attractive both monolithic integrated technology(IC) and thin film fabrication due to including only grounded capacitors. Furthermore, the parasitic capacitors can be easily accounted and tuned for they are in parallel with grounded capacitors[ 13,15]. A large majority study on the design of OTA-C oscillator network where the OTA is assumed an ideal voltage-controlled current source(VCCS) and can be described by following equation, vmT"=g",(V+-V) (5) where L, is output current of OTA and V,V are noninverting and inverting input voltage of OTA.In many designs, the transconductance go, is variable by setting a control bias current lb so that gm is proportional to lb or g,n=k.Ib. On the contrary, for extreme frequency OTA doesn't performs ideal so that even small parasitic can produce pole displacements large enough to cause the oscillation to vanish or to increase distortion severely. There are three main OTA nûnidealities affecting the performance of OTA-C oscillator structure. These are finite input and output conductance, input and output capacitance, frequency dependent transconductance gain. In order to explain the effect of dominant OTA nonidealities a highly true model is used in the nodal analysis. In the so for studies the frequency dependence of transconductance gain of OTA is modeled and is used to search this nonideality effect to oscillator structure by making an assumption a time delay Tj trough each OTA, such that ga(s) = #moe~sT (6) which can be approximated g(s) by giving the two first terms of its Taylor expansion for frequency much over than T1 gmw=gjx-*rl) (?) where T=l/û>p. Although not particularly exact, does allow us to do rough analysis of the effect of high order poles without using the true gm response for simplicity. On the other hand this approach can be used up several megahertz, at high frequency it is insufficient and a more correct model is needed[12,22]. This model is formalized as, 1+ - where (ap is an effective pole at high frequency. In order to understand the effect of frequency dependence of transconductance gain to oscillator structure, in this study more correct model is used. The proposed topologies are simulated by using cascod OTA structure with SPICE computer program.. The workability of CMOS version of all the proposed oscillator circuit has been tested by SPICE simulations. In the simulations The KSPICE model parameters for NMOS and PMOS transistor are taken from taken from TÜBİTAK MAM YITAL 3ja process. It can be concluded that low-frequency deviations are due to the the finite output conductance, whereas high frequency deviations arise because of the OTA instrict reactive behavior. Hence, dependent on the intended TACO frequency range the designer should optimize carefully the OTA for minimum deviations to the ideal case. For high frequency, the target will be the minimization of the instrict OTA reactive behavior, which can be better achieved by using simplest possible OTA structure. For low frequency, cascoded structures can be used to niinimize the OTA output resistance[7,6]. Sensitivity study forms an important index of the performance of any active network. The parameter of interest in the oscillator circuit is the frequency of osculation. All the proposed topologies enjoy relatively low sensitivity. In practice OTAs do not operate linearly if their output signal exceeds certain values. If the output voltage of any OTA saturates, we get a clipped wave-form. If the output current saturates, we get saw-tooth wave-form, which is known as the slew-rate-limiting problem. In this study for the proposed OTA-C oscillator network the maximum output signal level is determined using a simple formula not causing clipping and slew-rate-limiting problem. The theoretical result is verified by SPICE simulation results. Furthermore the affect of transconductance nonlinearity of OTA to oscillation condition and oscillation frequency is investigated. It is observed that nonlinear saturation characteristic of OTA behaves as a simple form of amplitude control mechanism. Although the CA3080 has some imperfections, oscillations have been successfully generated and sustained with frequencies up to 3.6 MHz. For applications, where the dynamic range is not a stringent factor, low-cost noninteractive electronically tunable OTA-C oscillators can be built using the C A3 080 bipolar IC OTAs. For applications, where CA3080 is not adequate, better performance can be obtained by using improved CMOS OTA structure. It is worthy to mention that the relatively large amounts of distortion observed at high frequency and amplitude. In addition to any discrepancies between theotrical and experimental results, is attributed to the nonidealities of the OTAs, for example the input and output impedances, frequency dependent transconductance gain of the OTAs that where taken into consideration in the analysis presented in this study [13, 14].From a practical viewpoint, the high frequency performance of bipolar OTAs, such as the CA3080 is quite good. The transconductance gain, g",, can be varied over several decades by adjusting an external dc bias current lb. The major limitation of existing OTAs is linearity. For CA3080, it is limited to about 30mVp-p to maintain reasonable degree of linearity. In order to simulate the proposed oscillator structure the symmetrical OTA with cascoded current mirrors is used. The OTA has been building at TÜBİTAK MAM with 3u CMOS process. Compared to bipolar technology, MOS technology has both advantages and disadvantages in implementing analog functions. MOS transistor inherently display lower transconductance than bipolar devices, leading to higher dc offsets in differential amplifiers. However, the virtually infinite input resistance of the device when used an amplifier and zero offset when used as a switch allow a signal voltage to be stored on a monolithic capacitor and sensed continuously and nondestructively. This result in a precision on-chip analog sample/hold capability that does not exist in bipolar technology. This capability has been widely utilized to enhance the performance of MOS analog circuits, performing functions such as sample-data analog filtering, offset storage and cancellation, precision amplification and precision binary attention[19]. Prior to the mid-1970s, MOS technology was utilized primarily for memory and logic functions and the analog functions mat were required in a given system were typically implemented by using bipolar integrated circuits such as operational amplifiers. However, in more recent years, the steady increases in chip complexity brought about by continuing improvements in lithographic resolution have created the economic incentive to implement subsystems containing both analog and digital subcircuit. At present time, analog integrated circuits are designed and fabricated, in bipolar technology, in MOS technology, and in technology which combine both type of devices in one process. The necessity of combining complex digital functions on the same integrated circuit with analog functions has resulted in an increased use digital of MOS technologies for analog functions such as analog-digital conversion required for interfaces between analog signals and digital systems. However, bipolar technology is now used will continuo to be used in wide range of applications requiring high-current drive capability and the highest levels of precision analog performance.

Oscillators have a wide range of using area in telecommunications, control systems, signal processing and measurement systems. For design of voltage-controlled sinusoidal oscillator, a variety of active OPAMP-RC networks have been reported up to now. But, these network don't operate at high frequency, don't have frequency tuning parameter effectively. On the other hand, OTA-C oscillator networks have some superiorities such as, open loop tunability of OTA, compatibility to VLSI, adjustibikty of oscillation frequency by tranconductance of OTA Since tranconductance of OTA is function of its tail current, oscillation frequency can be easily adjusted via this current. A great variety of RC-active circuits have been developed for generating sinewaves, most of them based on the use of conventional operational amplifier (op amp) as active component. This circuit typically perform correctly in audio frequency range(<20kHz), but their performance becomes severely degraded as the frequency increases. Together with frequency limitations op-amp based voltage controlled oscillators also exhibit other problems further restricting their usefulness. Different variable frequency RC-active oscillator have been reported whose frequency of oscillation can be controlled by a single resistor without affecting oscillation condition. Some additional circuitry has to be added to achieve this operation. One possible method is obtained is obtained by substituting the controlling resistor by a FET working in ohmic region. This reduces the voltage swing across the simulated resistance. Besides, the tunable frequency range is somewhat reduces and switching among different resistors is needed what makes the design approach not readily compatible with monolithic integrated circuits. Most of these problems can be overcome by the use of operational tranconductance amplifiers(OTA) as the active building block. By interconnecting OTAs and capacitors, oscillating can be obtained whose frequency of oscillation is proportional to transconductance of OTA. Since the transconductance gain of OTA can be varied or programmed by an external power supply, the voltage controlled VIoscillator can be readily implemented. Thus fully integrated voltage controlled transconductance amplifiers-capacitors oscillator(TACO) can be obtained with frequency adjustable over wide ranges, avoiding the necessity of switching among several passive components as observed in opamp design. The use of circuits composed of operational transconductance amplifiers and capacitors has been demonstrated to be potentially advantageous for the synthesis of high frequency continuos-time monolithic analog operators either linear or nonlinear. One basic reason for high frequency potential of these circuits comes from the fact that the OTA is used in a open loop. It means that no additional constraints are imposed on the frequency response due to local feedback -induced pole displacement. Another advantage of open loop OTA-based circuit is that the transconductance of the OTA is used as a design parameter. In a typical OTA architecture this gain can be adjusted either by changing the tail current of a differential pair or by using digitally controlled current mirrors. Programmability is hence an inherent property of OTA-C circuits. In this study, three new voltage-controlled sinusoidal oscillator topologies are proposed using only CMOS operational transconductance amplifiers and grounded capacitors. The oscillator configurations have the properties of oscillation frequency control using the tranconductans gain without affecting oscillation condition, suitability to the very large scale integration (VLSI) for not having any inductors, and the capability of operation at high frequency.For the proposed topologies, the nonideality effect such as finite output conductance, finite bandwidth are investigated, and to compensate these effects in the design stages negative resistors implemented with OTA's are added. The oscillator topologies are simulated with SPICE computer program and resulting output voltage waveform are plotted. A general sinusoidal network, has two conjugate pole on the imaginary axes and can be described by a second order characteristic equation (s2+bs+n02).voat=° 0) where b=0 is oscillation condition and Qo is oscillation frequency. Parameters b controls both the oscillation condition and the amplitude of the oscillation. Similarly, the level of distortion can be also shown to depend on b. The basic goal of OTA-C oscillator design is to achieve noninteractive control of b and Q0 with minimum number of component. VIISeveral OTA-C filter structures have been reported various researchers over the past several years[16]. Based upon, constructed with a minimum number OTA and grounded capacitor filter topology, novel OTA-C oscillator topologies are generated by converting of filters into oscillators which is explained in literature[9,20,21]. The general biqudratic transfer function is given as follows, iA,\ V^ *2* + ***+*. n. There are two possible ways for obtaining sinusoidal oscillator from this transfer function. In one of them the characteristic equation of the oscillator is obtained by equating the input voltage of filter Vm(s) to zero. In this case the following oscillator characteristic equation is obtained (f+bls+b0).Vo(s) = 0 (3) The second way is connecting the output terminal of filter to the input terminal. By doing so, the resulting oscillator characteristic equation is expressed as, s+ f \ f Y\ \~a s+ 2 J bo~aa U-* ?Vo(S) = 0 (4) 2 'J If the oscillation condition satisfy by making b=0, this two equation yields undamped oscillations. All the proposed topologies are very attractive both monolithic integrated technology(IC) and thin film fabrication due to including only grounded capacitors. Furthermore, the parasitic capacitors can be easily accounted and tuned for they are in parallel with grounded capacitors[ 13,15]. A large majority study on the design of OTA-C oscillator network where the OTA is assumed an ideal voltage-controlled current source(VCCS) and can be described by following equation, vmT"=g",(V+-V) (5) where L, is output current of OTA and V,V are noninverting and inverting input voltage of OTA.In many designs, the transconductance go, is variable by setting a control bias current lb so that gm is proportional to lb or g,n=k.Ib. On the contrary, for extreme frequency OTA doesn't performs ideal so that even small parasitic can produce pole displacements large enough to cause the oscillation to vanish or to increase distortion severely. There are three main OTA nûnidealities affecting the performance of OTA-C oscillator structure. These are finite input and output conductance, input and output capacitance, frequency dependent transconductance gain. In order to explain the effect of dominant OTA nonidealities a highly true model is used in the nodal analysis. In the so for studies the frequency dependence of transconductance gain of OTA is modeled and is used to search this nonideality effect to oscillator structure by making an assumption a time delay Tj trough each OTA, such that ga(s) = #moe~sT (6) which can be approximated g(s) by giving the two first terms of its Taylor expansion for frequency much over than T1 gmw=gjx-*rl) (?) where T=l/û>p. Although not particularly exact, does allow us to do rough analysis of the effect of high order poles without using the true gm response for simplicity. On the other hand this approach can be used up several megahertz, at high frequency it is insufficient and a more correct model is needed[12,22]. This model is formalized as, 1+ - where (ap is an effective pole at high frequency. In order to understand the effect of frequency dependence of transconductance gain to oscillator structure, in this study more correct model is used. The proposed topologies are simulated by using cascod OTA structure with SPICE computer program.. The workability of CMOS version of all the proposed oscillator circuit has been tested by SPICE simulations. In the simulations The KSPICE model parameters for NMOS and PMOS transistor are taken from taken from TÜBİTAK MAM YITAL 3ja process. It can be concluded that low-frequency deviations are due to the the finite output conductance, whereas high frequency deviations arise because of the OTA instrict reactive behavior. Hence, dependent on the intended TACO frequency range the designer should optimize carefully the OTA for minimum deviations to the ideal case. For high frequency, the target will be the minimization of the instrict OTA reactive behavior, which can be better achieved by using simplest possible OTA structure. For low frequency, cascoded structures can be used to niinimize the OTA output resistance[7,6]. Sensitivity study forms an important index of the performance of any active network. The parameter of interest in the oscillator circuit is the frequency of osculation. All the proposed topologies enjoy relatively low sensitivity. In practice OTAs do not operate linearly if their output signal exceeds certain values. If the output voltage of any OTA saturates, we get a clipped wave-form. If the output current saturates, we get saw-tooth wave-form, which is known as the slew-rate-limiting problem. In this study for the proposed OTA-C oscillator network the maximum output signal level is determined using a simple formula not causing clipping and slew-rate-limiting problem. The theoretical result is verified by SPICE simulation results. Furthermore the affect of transconductance nonlinearity of OTA to oscillation condition and oscillation frequency is investigated. It is observed that nonlinear saturation characteristic of OTA behaves as a simple form of amplitude control mechanism. Although the CA3080 has some imperfections, oscillations have been successfully generated and sustained with frequencies up to 3.6 MHz. For applications, where the dynamic range is not a stringent factor, low-cost noninteractive electronically tunable OTA-C oscillators can be built using the C A3 080 bipolar IC OTAs. For applications, where CA3080 is not adequate, better performance can be obtained by using improved CMOS OTA structure. It is worthy to mention that the relatively large amounts of distortion observed at high frequency and amplitude. In addition to any discrepancies between theotrical and experimental results, is attributed to the nonidealities of the OTAs, for example the input and output impedances, frequency dependent transconductance gain of the OTAs that where taken into consideration in the analysis presented in this study [13, 14].From a practical viewpoint, the high frequency performance of bipolar OTAs, such as the CA3080 is quite good. The transconductance gain, g",, can be varied over several decades by adjusting an external dc bias current lb. The major limitation of existing OTAs is linearity. For CA3080, it is limited to about 30mVp-p to maintain reasonable degree of linearity. In order to simulate the proposed oscillator structure the symmetrical OTA with cascoded current mirrors is used. The OTA has been building at TÜBİTAK MAM with 3u CMOS process. Compared to bipolar technology, MOS technology has both advantages and disadvantages in implementing analog functions. MOS transistor inherently display lower transconductance than bipolar devices, leading to higher dc offsets in differential amplifiers. However, the virtually infinite input resistance of the device when used an amplifier and zero offset when used as a switch allow a signal voltage to be stored on a monolithic capacitor and sensed continuously and nondestructively. This result in a precision on-chip analog sample/hold capability that does not exist in bipolar technology. This capability has been widely utilized to enhance the performance of MOS analog circuits, performing functions such as sample-data analog filtering, offset storage and cancellation, precision amplification and precision binary attention[19]. Prior to the mid-1970s, MOS technology was utilized primarily for memory and logic functions and the analog functions mat were required in a given system were typically implemented by using bipolar integrated circuits such as operational amplifiers. However, in more recent years, the steady increases in chip complexity brought about by continuing improvements in lithographic resolution have created the economic incentive to implement subsystems containing both analog and digital subcircuit. At present time, analog integrated circuits are designed and fabricated, in bipolar technology, in MOS technology, and in technology which combine both type of devices in one process. The necessity of combining complex digital functions on the same integrated circuit with analog functions has resulted in an increased use digital of MOS technologies for analog functions such as analog-digital conversion required for interfaces between analog signals and digital systems. However, bipolar technology is now used will continuo to be used in wide range of applications requiring high-current drive capability and the highest levels of precision analog performance.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996

##### Anahtar kelimeler

Osilatörler,
Oscillators