CHAPTER 2 REALIZATION OF SOME NOVEL TRANSCONDUCTANCE FILTERS

Transcription

1 CHAPTE EALZATON OF SOME NOEL TANSCONDUCTANCE FLTES This chapter is devoted to the realization of some novel active circuits by using transconductance amplifiers. The transconductance amplifier can be realized by the widely used device Op-Amp and specially designed operational transconductance amplifier (OTA). By using single Op-Amp in one circuit itself we can get two filter responses. The first circuit realizes first order low pass high pass response and the second one realizes second order high pass-band pass filter response. The quality factor Q of the second filter realization is low. The low value of Q is used in systems for which damping is important such as image frequency rejection and for lower bass in audio systems. t can also be used at the first stage of a cascaded filter. All the proposed realizations have low sensitivity to parameter variations. Applications of Op-Amps as transconductance amplifier are limited. Electronically controlled applications, variable frequency oscillators, filters and variable gain amplifier stages, are more difficult to implement with standard Op-Amps. n view of inherent tuning capability, the operational transconductance amplifier (OTA) is extensively used as a basic active device in many applications as compared to conventional Op-Amps. The internal circuit diagram of OTA is simpler than operational amplifier and therefore higher bandwidth can be obtained. Subsequently the chapter presents the basic operation of OTA along with its CMOS model, realization of the waveform generator and low-pass elliptical filter circuits using OTA.. APPLCATON OF OP-AMPS FO FLTE EALZATON As discussed in Section.4 several contributions have been reported for realization of active - C filters employing Op-Amps. Notable amongst them are Sallen- Key [5], Deliyannis-Friend [7-9], Moschytz [0], KHN [], Tow-Thomas [-4], Ackerberg-Moserberg [5], Tarmy- Ghausi [6], etc. Since the early stage of technological development the components and C could not be realized with precision, the active-c circuits were therefore not found suitable for precision 6

2 monolithic design at voice frequencies. To overcome this problem biquad active- circuits were proposed. These realizations were found to be suitable for the monolithic implementation due to elimination of external capacitors. A simple active- biquad realized by ao and Srinivasan [0] is shown in Figure.. in out Figure.: Active- biquad realized by ao and Srinivasan The single pole model of the operational amplifier can be expressed as : A ( s ) A ω c s ω 0 c (.) where,ω c is the cutoff frequency and A 0 is the DC open-loop gain of the operational amplifier. f the frequency range of interest is connected to the region where s >> ω equation reduces to c A( s) A0ω c s B s (.) where B is gain-bandwidth product of an operational amplifier. 7

3 The transfer function of circuit shown in Figure. can be obtained as out in s K K s A0 B K K s B B A0 (.) Assuming the parameter K of the circuit given by the transfer function (.) can be expressed as follows: K with the constraint A 0 << K, out in s K B K s B s B (.4) The transfer function thus obtained realizes bandpass filter. The center frequency ω 0 and the quality factor Q of the realization depend on the gain-bandwidth product B and K. Several active- filter realizations using Op-Amps have been reported in the literature. However, these circuits suffered from the following limitations: Temperature dependence of ω 0 : The gain bandwidth product of the Op-Amps B is given by B, where g m is the transconductance of the first input stage of the Op- g m CC Amp and C C is the internal compensated capacitance. Since g m is inversely proportional to the temperature, the cutoff frequency of the filter ω 0 depends on the temperature. Dynamic range limitation: The maximum distortion less output signal is determined by the slew rate of the Op-Amp. Since the transfer characteristics of an Op-Amp is nonlinear before the onset of saturation, the output of the amplifier shows distortions at the level well below the one determined by the slew rate value. Parasitic pole: The parasitic capacitance within the Op-Amp causes additional phase shift in the circuit response. Schaumann and Brand [] have shown the effect of additional parasitic capacitance on ω 0 and Q. 8

4 With the advent of MOS technology, a new approach was adopted to design filters by replacing altogether integrators and resistors by the only passive components capacitors. One such filter realization, proposed by Schaumann and Band [] employing only ratioed capacitors as passive components is shown in Figure.. They employed extra resistance of high value in parallel with C for DC biasing. The circuit realizes bandpass and lowpass filter responses simultaneously with outputs 0 and 0. The transfer function of the bandpass and lowpass filters realized with this circuit are respectively given by equations (.5) and (.6) 0 in (.5) C C s sb C C C C sb C C C B C C C 0 in (.6) C C s B sb C C C C C C C B C C C C C C in o o Figure.: Band pass and low pass filters proposed by Schaumann and Band The cutoff frequency and the quality factor are same for equation (.5) and (.6) and expressed as follows: 9

5 0 0 C C C C B ω (.7) ) ( C C C C BC Q (.8) The orthogonality between the cutoff frequency and the quality factor could not be achieved with the active- and active-c filter realizations reported in the literature. The second order lowpass filter realized by Xiao [] with one pole model of Op-Amp provides orthogonality between cutoff frequency and quality factor. Xiao s lowpass filter having low sensitivity to parameter variation is shown in Figure.. Figure.: Xiao s low pass filter The transfer function, the quality factor Q and cutoff frequency ω 0 of the filter are respectively given by the following expressions: B B s B C s i (.9) 4 C i o

6 4 4 0 C B ω (.0) BC Q (.) The expression (.0) and (.) exhibit orthogonality and hence the quality factor can be tuned independently of cutoff frequency by varying. The circuits discussed so far realized voltage mode transfer functions. Several other voltage mode transfer function realizations using Op-Amp pole have been published [4-6]. Higashimura first proposed current mode realization of transfer function using one pole model of the Op-Amp [7-8]. His circuit [7], shown in Figure.4, realizes highpass and bandpass filters with transfer function respectively given by equation (.) and (.). Figure.4: Higashimura s proposed current mode high pass and band pass filters C B C C s s s N HP (.) C N BP HP

7 BP N s C B s s C C C (.) As evident from the expression given in equations (.4) and (.5) for the quality factor Q and ω o for the quality factor can be tuned independently of cutoff / central frequency. B ω 0 (.4) C Q BC (.5) As stated earlier several voltage mode filters and current mode filters have been published. A number of filter realizations using one pole model of operational amplifier operating in the voltage mode (M) and current mode (CM) have also been proposed in the literature [5-8]. oltage mode filter are not suitable for small impedance load. A current mode filter circuit is suitable for all types of load. Since it offers low input impedance, a current mode filter is not suitable in many applications. oltage-current converters, which overcome the difficulties which arise in voltage-mode and current- mode circuits, can therefore be employed in most applications. Further, these transconductance filters meet the demanding specifications in several signal processing applications in different bands such as given in [6]. A notable contribution of realizations of lowpass and bandpass transconductance filter using single pole model of Op-Amp is due to Shah et al. [9]. The proposed circuit also offers less sensitivity to parameter variation as well as orthogonality between the cutoff frequency and the quality factor. The realizations of the circuits using one-pole Op-Amp model suffer from the limitation due to absolute value of gain-bandwidth product that is likely to vary with process tolerances and as a result change in the cutoff frequency can take place []. n the following section realization of two transconductance filters are proposed using zero-pole model of Op-Amp. These circuits offer high input impedance and low sensitivity figures. Nonlinear analysis of the proposed transconductance filters is also presented.

8 . POPOSED TANSCONDUCTANCE FLTE EALZATONS USNG OP-AMP Two proposed transconductance active filters employing single operational amplifier have been proposed in this section. The first circuit configuration realizes a first-order lowpass-highpass filter, whereas a second-order highpass-bandpass filter responses is realized using another configuration. Both the circuits employ passive and C components with spread not more than :0... EALZATON OF FST ODE TANSCONDUCTANCE LOW PASS AND HGH PASS FLTES Considering the zero-pole model of operational amplifier a first order transconductance low pass and high pass filter can be realized as shown in Figure.5. in LP - HP C Figure.5: Proposed low pass-high pass transconductance filter Two transfer functions of the filter circuit of Figure (.5) are given by equation (.6) and (.7) LP in A s C A) ( ) (.6) ( A HP in sc A s C A) ( A) (.7) ( where A is the open loop gain of the operational amplifier. These equations respectively represent the transconductance functions for LP and HP responses with same denominator. The cutoff frequency ω 0 of the responses is given by:

9 ( A) ω 0 (.8) C ( A) C( A) C C The cutoff frequency can therefore be controlled by either or C. The sensitivities of ω 0 due to variation in active gain-bandwidth product A and passive components are given by ω S 0 A 0 (.9) ω0 S (.0) ω0 S 0 (.) ω0 S (.) C These sensitivities are small and not more than one. The magnitude and phase responses of the LP and HP filters are shown in Figure.6. These match with the designed specifications. Figure.6(a): High pass filter magnitude response of proposed filter 4

10 Figure.6(b): High pass filter phase response of proposed filter Figure.6(c): Low pass filter magnitude response of proposed filter 5

11 Figure.6(d): Low pass filter phase pass filter phase response of proposed filter.. EALZATON OF SECOND ODE TANSCONDUCTANCE HGH PASS AND BAND PASS FLTES Considering the zero-pole model of the operational amplifier, the circuit configuration shown in Figure.7 can be used to realize the high pass (HP) and band pass (BP) filter responses. in BP HP C C Figure.7: Proposed high pass and band pass transconductance filter The following second order transconductance functions for HP and BP responses can be obtained for this realization: 6

12 HP in s CC A s α s α 0 (.) BP in s sc A α s α 0 (.4) where the parameters α and α 0 are given by: C ( A) C ( A) C α (.5) C C ( A) A α 0 (.6) C C ( A) The cutoff frequency (ω 0) and Q of the above circuit are: ω 0 (.7) C C Q C C (.8) C C The active and passive sensitivities of ω 0 and Q are small. By taking value of Q is found to be 0.5 and the sensitivities with respect to various parameters are obtained as follows: ω S 0 A 0 (.9) ω 0 ω0 ω0 ω0 S S S C S C (.0) Q Q Q Q S S S C S C (.) The magnitude and phase responses of the HP and BP filters are shown in Figure.8 match with the designed specifications. 7

13 Figure.8(a): High pass filter magnitude response of proposed filter Figure.8(b): High pass filter phase response of proposed filter 8

14 Figure.8(c): Band pass filter magnitude response of proposed filter Figure.8(d): Band pass filter phase response of proposed filter 9

15 ESPONSE CONSDENG ONE-POLE MODEL OF OP-AMP Practical Op-Amps have finite (but large) input impedance, non zero (but small) output impedance and finite (but large) differential gain. The dependence of the differential gain of the Op-Amps on frequency is considered in the AC circuit model of the Op-Amps. This approach is based on the first order approximation of the Op-Amp, which is reasonable to determine the frequency response. Using first-order model of the Op-Amp in place of zero-order model, the circuits shown in Figure.5 yield the following transfer function: LP in B (.) s C s( C B) B HP in sb C (.) s C s( CB) B With the first order model of the Op-Amp following transfer function can be realized for the circuit shown in Figure.7 HP in BP in s B C C (.4) ( sc )( sc )( s B) s C sbc (.5) ( sc )( sc )( s B) s C t is thus observed that equations (.6), (.7), (.) and (.4) obtained with zero-order model of the Op-Amp get transformed to equations (.), (.), (.4) and (.5) respectively for the first-order model. Comparing the above equations it is observed that the order of the denominator gets increased and in some cases both the orders of denominator and numerator increase in one pole model. The frequency responses of the filters using zero and first order models of the Op-Amp have been shown in Figure

16 Figure.9 (a): Low pass filter magnitude responses of circuit shown in Figure.5 Figure.9 (b): Low pass filter phase responses of circuit shown in Figure.5

17 Figure.9(c): Magnitude responses of high pass filter of circuit shown in Figure.5 Figure.9(d): Phase responses of high pass filter of circuit shown in Figure.5

18 Figure.0(a): Magnitude responses of high pass filter of circuit shown in Figure.7 Figure.0(b): Phase responses of high pass filter of circuit shown in Figure.7

19 Figure.0(c): Magnitude responses of band pass filter of circuit shown in Figure.7 Figure.0(d): Phase responses of band pass filter of circuit shown in Figure.7 4

20 t is observed that there is no major difference in the frequency response of the filters for two models up to frequency of 00 khz (approx). The cutoff frequency of the lowpass and highpass and center frequency of the bandpass filters remain unaltered in both the models (zero order as well as first order) of Op-Amp. Thus, the zero-order model realizes the desired filter response. Due to high open loop gain of the operational amplifier, the first order model does not alter the response in terms of the standard definition of the filter. Since, the consideration of the pole of the Op-Amp does not play significant role in the low frequency response. The proposed circuit has been designed using zero-pole model of the Op- Amp.. PEFOMANCE OF THE POPOSED TANSCONDUCTANCE FLTES USNG OP-AMP The performance of the circuits shown in Figure.5 and.7 employing operational amplifier LM74, for realizing lowpass-highpass combination and highpass-bandpass combination respectively, have been verified experimentally as well as by PSPCE simulation. These realizations have been obtained with kω, kω and C 00nF. Figure.6 (a) and.6(c) show the magnitude response of the low pass and high pass filters, each having cutoff frequency.5 khz. The phase responses of these filters have been shown in Figure.6(b) and.6(d) respectively. The highpass and bandpass filter circuits employ kω, kω, C 00nF and C 00nF. The magnitude and phase responses of these filters have respectively been shown in Figure.8(a),.8(c),.8(b) and 8(d). Each of these filters has the same cutoff frequency and center frequency.5 khz..4 CHAACTESTCS OF OPEATONAL TANSCONDUCTANCE AMPLFE (OTA) Transconductance is defined as the ratio of the current change at the output port with respect to the change in voltage at the input port. t is normally denoted by g m and mathematically is defined as: 5

21 g Δ 0 m Δin (.6) A transconductance amplifier is an example of voltage controlled current source (CCS) that provides output current proportional to the input voltage. An ideal transconductance amplifier is characterized by: infinite input impedance, infinite output impedance and infinite bandwidth. A transistor can be used to provide the characteristics of a transconductance amplifier as its collector current is proportional to the input voltage applied at the base terminal. Further, the requirements of a transconductance amplifier are also met with the impedances of a transistor being high as seen at the base terminal, very high at the collector terminal, and low at the emitter terminal. A NPN or a PNP transistor does not provide both positive and negative currents. Since a transconductance amplifier can provide both positive and negative currents, it can be used as a current source as well as a current sink. Operational amplifier has one more input terminal to control the transconductance of the amplifier, externally. Transconductance amplifier is called an operational transconductance amplifier, if the output current is made proportional to the differential input voltage applied at the input port. The symbolic representation of the transconductance amplifier and its small signal equivalent circuit representation are respectively shown in Figure.(a) and (b). Figure.(a): deal model of OTA Figure.(b): Equivalent circuit of OTA 6

22 The output current 0 of the ideal OTA can be expressed by equation (.7). g ( ) (.7) 0 m P N where g m, the transconductance can be expressed in terms of bias current ( bias ), charge (q), Boltzmann constant (k) and temperature (T) in Kelvin, as follows: g m q bias (.8) kt Since the output of an OTA is derived as the current, the output impedance of the OTA is very high (ideally infinity). n view of low output conductance of the OTA, it is suitable as an ideal current generator. An OTA can be made to work as an operational amplifier, if a resistance is connected at its output terminals. Since g m of the OTA is dependent on the bias current, the output characteristics of the OTA may be controlled externally by the bias current ( bias ). t adds new dimension to design and applications of OTA circuit. Operational transconductance amplifier is a versatile building block that intrinsically offers wider bandwidth. The principal difference between OTA and Op-Amp are as follows: The output of OTA is current where as the output of the Op-Amp is voltage. n linear applications, OTA is mainly used in the open loop mode while the Op- Amp is used in close loop mode with negative feedback. The load impedance decides the output voltage of the OTA. Therefore the output voltage of the OTA is controllable by the load impedance. The first stage of the Op-Amp may be considered as a voltage to current convertor; hence OTA can be seen as an integral part of an Op-Amp. Thus the OTA can be realized by a differential pair followed by the current mirror load. n 969, single output OTA was made commercially available by CA. During many papers were reported for OTA design and its application. n 985 Gieger and Sanches reported the possible synthesis of biquad and controllable impedance circuits using OTA [5]. 7

23 The basic CMOS model of OTA consists of eight MOS transistors as shown in Figure.. The MOS transistors M and M constitute a differential input voltage pair with M 5 and M 6 transistors acting as active load of the differential pair. The differential transistors are biased by the current source ( bias ). emaining transistors M 8, M 7, M and M 4 act as current mirrors. Figure.: Circuit diagram of CMOS OTA Commercially available OTAs are CA080, CA080A, LM600, LM700 etc. Among them LM700 is more commonly used in view of its low leakage current and good control on tansconductance and wider input voltage range. The internal circuit diagram of LM700 is shown in Figure. [-]. 8

24 Figure.: Circuit Diagram of LM700 The transistor Q 4 and Q 5 are the differential input pair of the OTA. The ratio of the collector current flowing through Q 4 and Q 5 is proportional to the differential input voltage in as shown in equation (.9) KT ln 5 in (.9) q 4 where KT/q is approximately 6m at 5 o C and 5 and 4 are the collector currents of the transistor Q 5 and Q 4 respectively. Transistors Q, Q and diode D form a current mirror for the externally applied bias current bias such that bias current is the summation of the collector current 4 and 5. bias 4 5 (.40) Q 6, Q 7 and D 4 form a current mirror for 4 which is again followed by a current mirror constituted with Q 8, Q 9 and D 5. Similarly Q 0, Q and D 6 form a current mirror for 5. The difference current is obtained from the output terminal. For DC analysis (no signal condition) 9

25 the currents supplied by the matched transistor Q 4 and Q 5 are equal and depend on the bias current as shown in equation (.4). bias 4 5 (.4) For small differential input voltage in, equation (.9) can be expressed as: KT q 4 KT q in ln (.4) 4 in 4q 4 (.4) KT 5 biasq in (.44) KT The transistor Q and Q are connected as Darlington pair, to work as voltage buffer. For very small input voltage (order of m) the equation (.9) may be considered to be linear and be approximated as equation (.4). The diodes D and D are used to increase the linear range of operation of the differential amplifier provided that the signal current s is less than diode current D /. OTA is versatile building block with on chip tuning capability. t can be employed for the realization of basic building blocks such as floating resistor, grounded resistor, negative resistance and inductor. Gieger and Sanchez [5] have reported various applications of OTA in the synthesis of first order and second order filters. OTA circuits employing capacitor as load (OTA-C) are employed for realization of various linear and non-linear circuits [6-57]. They can be also used for implementing voltage controlled oscillators (CO) and voltage controlled filters (CF) for analog synthesizer. Further, OTA can be used to operate as a two quadrant multiplier, driver circuit for light emitting diode (LED), for realization of automatic gain control (AGC) amplifier, pulse integrators, control loops for capacitive sensors, active filters and oscillators. n this chapter a new waveform generator using OTA has been proposed with special feature of generating three waveforms square, triangular and sinusoidal simultaneously. 40

26 .5 WAEFOM GENEATO CCUTS USNG OTA A waveform generator with current/voltage mode has wide range of application in the instrumentation, communication systems and signal processing. The sinusoidal, triangular and square waveforms can be realized by using Op-Amp or OTA. Op-Amps are very well known active device, which are mainly used with negative feedback for introducing some pole constraint in the design. Op-Amps are also not gain programmable and therefore can not be compensated for drift errors. The frequency of the circuit can not be changed without changing the passive components. Due to these limitations OTA is preferred over the Op- Amp as a basic active element. t works in open loop mode, which does not add any constraint on the frequency response to compensate for local feedback introduced pole [7] and the transconductance of the OTA is electrically tunable. The circuits realized with OTA have simple configuration and wide frequency sweep. Several circuits using OTA have been reported in the literature. Barranco et al. [8-40] have proposed the sinusoidal oscillator employing two OTA and three capacitors as shown in Figure.4. g m - C C C g m - Figure.4: Barranco s two OTA and three capacitor oscillator The frequency of oscillationω 0 of the circuit may be obtained as 4

27 g g m m ω 0 (.45) CC CC CC The transconductance g m and g m are used for the trimming of the waveform. n order to place the poles in the right half of s-plane nearer to origin, the transconductance g m is kept larger than g m. Subsequently a sinusoidal oscillator has been realized using three OTA with two capacitors. The circuit diagram is shown in Figure.5 g m C C g m - gm - Figure.5: Three OTA and two capacitor oscillator The frequency of this oscillator circuit is given by equation (.46). f o π g g C C m m (.46) The second OTA employed in the circuit, is used to keep the poles of characteristic equation in the right half of s-plane, close to the origin. Senani [4] proposed tunable OTA-C filter employing three OTA and two capacitors as shown in Figure.6. 4

28 - g m gm - - gm C C Figure.6: Sinusoidal oscillator proposed by Senani. Senani s circuit works as an oscillator under the constraint g g. The frequency of oscillation is given by equation (.47). m m f 0 π g g C C m m (.47) Abuelma atti [5] realized sinusoidal oscillator employing two OTAs and two capacitors as shown in Figure.7. C g m - C gm - Figure.7: Sinusoidal Oscillator proposed by Abuelma atti The frequency of oscillator is dependent on the condition equation (.48). g g and is given by m gm m 4

29 g. g gm (.48) π C C m m ω 0 π CC.A number of sinusoidal oscillators employing other active devices such as Op-Amp, current conveyor, etc has been reported in the literature. The conventional circuit for generating square waveforms using operational amplifier is shown in Figure.8. C - out Figure.8: Square waveform generator using one Op-Amp This circuit suffers from slew rate limitation and the frequency of oscillation can be controlled by passive components only. Though square wave is obtainable at the output terminals, the triangular waveform across the capacitor is exponential in nature. The modified version of the above circuit is shown in Figure.9. C 4 Figure.9: Square and triangular wave generator using two Op-Amps 44

30 Haslett [4] proposed a square wave generator employing one OTA, one comparator and one Op-Amp as shown in Figure.0. The frequency of oscillation of the circuit proposed by him can be controlled by the externally applied voltage. B C in B CC Figure.0: Square waveform generator proposed by Haslett This circuit also suffers from slew rate limitation as it employs Op-Amp along with other active and passive components. Further, secondary source of error arises due to current imbalances between the positive and negative terminal of OTA. Chung et al. [4] proposed temperature-stable voltage controlled oscillator using two OTAs and operational amplifiers as shown in Figure.. 45

31 O C B O B B B Figure.: Temperature insensitive voltage controlled oscillator Their circuit employs more active and passive components and slew rate limitations are not overcome. Many square wave generator circuits have been reported in the literature [44-46]. Later, Chung et al. [46] realized square and triangular waveform generators using three OTA as shown in Figure.. 46

32 C Figure.: Triangular and square wave generator proposed by Chung et al The amplitude and frequency of the oscillation of this circuit can be controlled independently. All these circuits discussed above may be used to generate either the sinusoidal waveform or square and triangular waveforms. None of these circuits produce square, triangular and sinusoidal wave form simultaneously..5. POPOSED WAEFOM GENEATO CCUT The proposed circuit generates square, triangular and sinusoidal signal simultaneously. t employs three OTAs, two resistors and two capacitors as shown in Figure.. The amplifier bias current bias which may or may not be same in all three OTAs. 47

33 B B g m g m C B g m C Figure.: Circuit Diagram of proposed waveform generator The OTAs of the proposed circuit employs positive feedback. The output of the OTA is B /C. Since the positive feedback of the OTA makes it saturated, its output will be ± B. With the output of OTA being B, the output of OTA across the capacitor C tries linearly to build up the voltage and when it reaches this value the output of OTA drops to - B. As a result the capacitor C starts loosing the voltage linearly till it reaches to this negative voltage. When the voltage across the capacitor becomes - B, the voltage goes down and the output of OTA changes to B. This process repeats in generation of ramp output across C and square waveform across. The ramp signal is again integrated in the circuit to obtain the sinusoidal waveform. The time period T during which the output voltage of OTA changes from B to - B is given by equation (.49). B ( B) T C B (.49) earranging equation (.49), we obtain 48

34 B T C (.50) B Since the charging and discharging path for the capacitor is same, the frequency of the waveform generator may be expressed by equation (.5) f B (.5) T T 4C B The desired shape of the sinusoidal is obtained across by integrating the ramp signal in the circuit. The frequency of the waveform generator can be changed by changing the bias current of OTA and OTA for the given and C from the above equation. The Figure.4 shows the various waveform responses of the frequency 4.4 khz by selecting B 950.5μA, B μA, B 950.5μA and 0 kω, 0 kω, C 0nF and C 0nF. The main feature of the proposed circuit is its linearity. Figure.5 shows the graph between the bias current of the first OTA and frequency of the waveform generator. Figure.4(a): Sinusoidal, triangular and square waveform of proposed waveform generator 49

35 Figure.4(b): Waveforms in CO Figure.5: Graph between bias current B and oscillation frequency of the proposed waveform generator 50

36 .6 ELLPTCAL FLTE EALZATON USNG OTA Among the various filter approximations, the most generalized filters approximations are Butterworth, Chebyshev and Cauer. The Butterworth filter responses are also known as maximally flat response. t provides maximally flat band response in the pass band and stop band. The roll-off is smooth and monotonic with a rate of 0dB/ pole. The transition band of this filter response is much higher than others. Another approximation of the ideal filter is Chebyshev response or equal ripple response in the pass band. t has a steeper roll rate near the cutoff frequency as compared to the Butterworth filter and poorer transient response. Cauer filters are also called elliptical filters. The elliptical filter has ripples in both in the pass band and stop band. t has a very narrow transition band as compared to other approximations. t is also an optimal realization of ideal filter response. Higher order filters are needed in order to satisfy the selectivity requirement of the telecommunication systems and many other applications. These filters are realized by following approaches: i) Cascade second order stages without negative and with negative feedback. ii) Simulation of passive LC filters. Among these two approaches the first approach cascade second order stages without negative takes more area and active/passive components for the realizations. ts design is simple and easily tunable but it offers bad sensitivity. Cascade stages with negative feedback circuits have low sensitivity to parameter variations but their design is complex. The second approach based on the simulation of the passive LC filters is more attractive due to the simplicity in design and extremely low sensitivity. Earlier grounded and floating inductors were simulated using Op- Amps, Deboo s gyrator, iordan gyrators and other circuits. With the advent of OTA and other novel active devices it has been possible to realize filters by using second approach mentioned above. n this section 7 th order elliptical low pass filter is realized for the cutoff frequency MHz by employing OTA. The normalized 7 th order doubly terminated (for improved sensitivity) LC network is shown in Figure.6. 5

37 .99H 7.98mH 80.65mH L L 4 L 6 in Ω.76F C C 9.9mF C C 4 C F 7.mF.5F C 5.776F C mF Ω L Figure.6: Normalised 7 th order doubly terminated LC filter The ladder circuit designed for frequency and impedance denormalized for the cutoff frequency of MHz is shown in Figure.7. 9.µH 5.µH µh L L 4 L 6 KΩ 87.pF C C 4 C 6 KΩ in C 0pF C 60.9pF 40.5pF C 5.pF 0.pF C 7 pf Figure.7:7 th order LC filter for cutoff frequency MHz The state equation of the circuit shown in Figure by virtually eliminating C, C 4 and C 6 are given in the following Table.. Table.: The state equations for the circuit shown in Figure.7 i ( in ) sc sl sc 5

38 4 4 sl sc 6 6 sl sc out 7 out The circuit diagram shown in Figure.7 can be realized by using OTA-C filters with lossy integrators with finite poles describing the equations in Table.. The realized 7 th order elliptical filter using OTA and capacitors with component values is shown in Figure.8 in C L C L C L C C 4 C 6 out C C C5 C 7 - Figure.8: 7 th order elliptical filter using OTA C 87.pF, C 0pF, C 40.7pF, C pF, C 5 0.pF, C 6.pF, C 7 pf, C L 6pF, C L 0pF, C L 4.6pF 5

39 The frequency response of the OTA-C filter is shown in Figure.9. The response matches the one available with LC ladder circuit of the figure. Figure.9(a): Magnitude response of the 7 th order elliptical filter Figure.9(b): Phase response of the 7 th order elliptical filter 54

40 .7 CONCLUSON This chapter presents various developments in the realizations of the active filters employing Op-Amps, the performance of the filter realizations employing zero-pole model and one-pole model of Op-Amp. Next, the chapter focuses realization of two transconductance filters using single Op-Amp. One transconductance filter employing three passive components- one capacitor and two resistors simultaneously realizes low pass-high pass transconductance filter responses. Whereas another transconductance filter realizes high pass-band pass transconductance filter with two resistors and two capacitors. The cutoff /center frequency ω 0 is to be tunable by the changing the values of the passive components and is independent from the open loop gain of the operational amplifier. The realizations have low sensitivity to variable and sensitive parameter A 0 (gain bandwidth product) and employ minimum number of passive components. Subsequently the chapter is devoted to realization of waveform generators using OTA LM700. arious waveform generators employing OTA, reported in the literature, realize individual waveforms such as sinusoidal waveform, square and triangular waveforms. n the literature no single wave-shaping circuit appears to have been reported for realization of more than two different types of waveforms at a time. The proposed single waveform generator circuit realizes square, triangular and sinusoidal waveforms simultaneously. Further, the 7 th order elliptical filters realization based LM700 has been simulated using PSPCE and compared with LC network. t can be used for video signal processing in T. 55