Amplifiers and Feedback

Transcription

1 6 A Textbook of Operational Transconductance Aplifier and AIC Chapter Aplifiers and Feedback. INTRODUCTION Practically all circuits using Operational Transconductance Aplifiers are based around one of a few fundaental configurations. In this chapter, you will learn about these building blocks. The basic building blocks [] are realized using Operational Transconductance Aplifiers (OTA). It is shown that circuits provide iproveents in design siplicity and prograability when copared with Op-ap based structures as well as reduced coponent count.. BASIC INERTING AMPLIFIER The basic inverting aplifier is shown in Fig... The input voltage is applied to the inverting terinal of OTA and non-inverting terinal is grounded. The load resistance R L is connected at the output of OTA. Assuing OTA to be ideal, the output current of OTA is The current flowing through the load R L is also I o I o = g (.) I o = o RL (.) I B g I o o R L Fig.. Inverting aplifier

2 Aplifiers and Feedback 9 buffer is used at the output; it is useful for reducing the output ipedance (Z o ) of the OTA.The analysis of the circuit of Fig..4, gives and Z o = 0 o i = g R L (.0) I B g I o I o A o R L Fig..4 Inverting feedback aplifier In the inverting feedback aplifier of Fig..4, the effects of parasitics are due to output parasitic capacitance of the OTA along with instruentation parasitics, parallel the resistor R L in discrete coponent structures, thus causing a roll-off in the frequency response of the circuits..6 NON-INERTING FEEDBACK AMPLIFIER The circuit for non-inverting feedback aplifier is shown in Fig..5. The input is applied at the non-inverting terinal of OTA and the inverting terinal is grounded. oltage buffer is connected at the output of OTA. Analysis of the circuit of Fig..5 gives o = g R L (.) i and Z o = 0 I B R L g I o A o Fig..5 Non-inverting feedback aplifier

3 0 A Textbook of Operational Transconductance Aplifier and AIC The gain characteristics of the circuit of Fig..4 and Fig..5 are ideally sae, but the perforance of the two circuits is different due to difference in the effects of parasitics in the circuits. For non-inverting aplifier, the output parasitic capacitance of OTA is connected across the null port of an Op-ap and thus has negligible effects when the Op-ap works properly. For the inverting and non-inverting feedback aplifiers of Fig..4 and Fig..5, the ajor factor liiting the bandwidth is generally the finite gain-bandwidth product GB, of Op-ap. If the Op-aps are odeled by the single-pole roll-off odel, A(s) = GB/s, and OTAs are assued to be ideal, then bandwidth of these circuit is GB, which is independent of the voltage gain of the aplifier, while for single Op-ap base non-inverting and inverting aplifiers of gain K and K, the bandwidth is GB/K and GB/+K, respectively, which depends on gains..7 BUFFERED AMPLIFIERS The circuit for a feedback aplifier is shown in Fig..6. Input current (I i ) flowing through R is I i = ( - ) (.) R The output current of OTA, I o is I o = g (.3) KCL at gives I i = I o (.4) The current flowing through R is I o = ( 0 - ) R Equating equations (.3) and (.5) gives = o - g R (.5) (.6) R I i R g I o o I B Fig..6 Buffered aplifier

4 Aplifiers and Feedback Fro equations (.), (.3) and (.4), we have g = - R Solving this equation for, gives = ( + g R ) (.7) Substituting fro equation (.6) in equation (.7) gives ( + gr ) = o ( - gr ) or o = ( - gr ) (.8) i ( + gr ) and thus R+ R Z o = + g R Fro equation (.8), it is evident that the voltage gain can be continuously adjusted between positive and negative values with the paraeter g. Consider the circuit of Fig..7. The input signal is applied at the non-inverting terinal. The output current (I o ) of OTA is I o = g ( ) (.9) R R g I o o I B Fig..7 Buffered aplifier Also KCL at node gives I o = o - R (.0) o - = (.) R R

5 A Textbook of Operational Transconductance Aplifier and AIC or or and = R o R + R Equating equations (.9) and (.0) gives o = g R ( ) (.) o g R = ( g R ) (.3) Substituting fro equation (.) in equation (.3) gives o i Z o = = g ( R + R ) ( + g R ) R+ R + g R (.4) Hence, it is evident that voltage gain can be adjusted with the help of paraeter g. In the circuit Fig..7, if we interchange the positive and negative terinals of the OTA, then very large gains can be obtained as g R approaches to unity (as Z o approaches infinity). In that case voltage gain is given as o i = g ( R + R ) ( - g R ) Z o Æ (.5).8 SCALE CHANGER The circuit for scale changer is shown in Fig..8. It consists of two OTAs without any passive coponents. The input signal is applied at the inverting terinal of OTA. The output is taken at the output of OTA. I B g o I B I o OTA g I o o OTA Fig..8 Scale changer

6 4 A Textbook of Operational Transconductance Aplifier and AIC I B I B3 g I o I B I 3 g 3 3 I o3 I o g Fig..9 Suing aplifier or KCL at 3 gives I = I o3 = ( g 3 3 ) Fro equations (.3), (.3) and (.33), we get Equating equations (.35) and (.36) gives I = g 3 3 (.35) I = g + g (.36) g 3 3 = g + g 3 = g g 3 + g g 3 (.37) Fro equation (.37), it is evident that the output voltage 3 is the su of two scaled voltages, and it can be controlled either by g, g or g 3. This circuit can also be extended to ore than two signals. Interchanging the input terinal of any feed in OTA will change the sign of the corresponding suing coefficient..0 DIFFERENTIATOR The circuit for OTA-based differentiator can be obtained by loading the output of an OTA by an inductor.

7 Aplifiers and Feedback 5.0. Two OTA-Based Differentiator The circuit for differentiator using two OTAs is shown in Fig..0. It consists of two OTAs along with two passive coponents. The OTA with transconductance gain g is loaded with single OTA-based inductor. [3] The output current I o is I o = g (.38) Also I o = ( o - ) R (.39) The output current I o is, Also I o = g o (.40) I o = ( o )sc (.4) Equating equations (.38) and (.39) gives Rg = ( o ) or = ( o + g ) (.4) R C I i o g o g o I o Fig..0 Two OTA-based differentiator Equating equations (.40) and (.4) gives ( o )sc = g o or = o sc - g o (.43) sc Equating the equations (.4) and (.43) gives voltage gain differentiator as o i = -sg RC g F oi HG i K J of the (.44)

8 6 A Textbook of Operational Transconductance Aplifier and AIC Fro equation (.44), it is clear that, an ideal inverting differentiator is realized. The voltage gain of the realized differentiator can conveniently be controlled ore strongly with the bias current control of the OTAs, i.e., either by g or g. Inverting and non-inverting differentiator can be obtained by connecting inverting or non-inverting terinal of OTA to ground respectively..0. Three OTA-Based Differentiator The circuit for differentiator using three OTAs is shown in Fig... It consists of three OTAs along with a capacitor. The OTA with g is loaded by two OTAbased inductors []. The output current I o is KCL at o gives I o = g (.45) I o = I o3 (.46) I o = g o (.47a) Also I o = s C (.47b) I o3 = g 3 (.48) Fro equations (.45), (.46) and (.48), we get g = ( g 3 ) or = g g i (.49) 3 Equating the equations (.47a) and (.47b) gives g o = s C or = g o (.50) sc I o3 g 3 I o g I o g o C Fig.. Three OTA-based differentiator

9 Aplifiers and Feedback 9 The realized current ode differentiator is coposed of only active devices; hence, the circuit is suitable for onolithic ipleentation either with CMOS or bipolar technologies. In addition to this no realizability conditions are iposed for the circuit and all the active sensitivities are found to be low.. INTEGRATOR Integrators serves as the basic building block in any filter structures. The circuit for OTA based integrator can be obtained by loading the output of OTA by a capacitor... Ideal Integrator The voltage variable integrator with a differential input is shown in Fig..3(a). It is also known as prograable integrator (PI). Its sybolic representation is shown in Fig..3(b). In the circuit of Fig..3(a), the OTA is loaded by a capacitor. Since the output ipedance of OTA is ideally infinite, a very high input ipedance buffer is used to avoid undesirable loading. The output current (I o ) of OTA is given as I o = g (.6) Also I o = s o C o (.63) + cc I B g I o o C o cc (a) Prograable integrator I B o (b) The sybol for prograable integrator Fig..3

10 30 A Textbook of Operational Transconductance Aplifier and AIC and Equating equations (.6) and (.63) gives g = s o C o T P = o i = g sc o = K s (.64) K = g I B = (.65) Co C T o where K = integration constant Fro equation (.64), it is clear that the circuit realizes an ideal integrator and its gain is directly proportional to OTA s bias current I B. Hence, gain can be controlled by varying the bias current I B. Inverting and non-inverting integrators can be obtained by connecting inverting or non-inverting terinal of OTA to ground respectively... Lossy Integrators The circuit for lossy integrator is shown in Fig..4(a). The input is applied at non-inverting terinal of OTA. The output current, I o is given as I B g I o o C R (a) Lossy integrator I B I B I o I o g C o g I o o (b) OTA-C lossy integrator Fig..4

11 or Also Equating equations (.66) and (.67) gives Aplifiers and Feedback 3 I o = g (.66) I o = o (G + sc ) (.67) g = o (G + sc) o i = gr + scr (.68) Equation (.68) shows that the circuit of Fig..4(a) has a loss that is fixed by the RC product and the gain is adjusted by g. This circuit also works as first order low-pass filter. Another circuit for lossy integrator is shown in Fig..4(b). It consists of two OTAs along with a capacitor. This circuit can be obtained by replacing the resistor R of circuit in Fig..4(a) by an OTA-based siulated resistor. Consider the analysis of circuit of Fig..4(b), the output current I o of first OTA is or KCL at o gives I o = g (.69) I o = I o (.70) The current flowing through capacitor is I o + I o is given as I o + I o = sc o (.7) o = I o + I sc o (.7) I o = g o (.73) Substituting the expressions of current I o fro equation (.69) and I o fro (.73) in equation (.7), we get o = g - g o sc After siplification, the voltage gain of the integrator is given by o g = (.74) i sc + g Equation (.74) shows that the pole frequency can be controlled by g and dc gain by g.

12 3 A Textbook of Operational Transconductance Aplifier and AIC..3 Active only Integrator The active only integrator with electronically tunable tie constants is described, which consists of two OTAs and one Op-ap, without using any passive coponent. The resulting current ode active only integrator is shown in Fig..5. The routine analysis of the circuit yields H int (s) = I I o in = g B 4 sg 3 = st (.75) where t = g 3 /Bg 4 (.76) I in g 3 I o A g4 I o Fig..5 Active only integrator It can be seen that the tie constant of the integrator of Fig..5 can be tuned electronically by changing g 3 and or g 4. The active sensitivities of the circuit are expresses as S g t 3 = S g t 4 = S B t = (.77) These sensitivities are all sall. It can be noted that t can be ade large siply by changing the ratio g 3 /g 4 without an increase in the active sensitivities. In addition to this the current ode integrator can be converted to a transipedance type by reoving the output OTA and taking signal fro the Op-ap output. Effects of non-idealities of the integrator The effects of the non-idealities of Op-ap and OTAs on the integrator transfer function are investigated. Considering the non-ideal odels of the Op-ap and OTA given by equations (.58) and (.59), the transfer function of differentiator is given by g Bw pbw s 04 p4 ( + w p ) 3 H int (s) = (.78) g w ss ( + ( w + w ) s+ w w p pb p pb p

13 Aplifiers and Feedback 35 I B I B g I o o g o I o R o I R o3 I B3 I o3 I B4 g 3 o3 g 4 I o4 o4 R 3 Fig..7 OTA-based teperature-insensitive instruentation aplifier with g and g 3, such as the coercially available dual variable OTAs CA380 or LM3600. If the circuit is designed such that g R >>, I B = I B3 or g = g 3, then the analysis of the circuit gives o = g g R R ( ) = I I B B R R ( ) (.87) o4 = g 4 R3 ( g R i ) = I B4 R3 ( 3 I B R i ) (.88) 3 It can be seen fro equations (.87) and (.88) that the voltage gains of instruentation aplifier are electronically tunable by the bias control currents I B and I B4 without disturbing the balance of the circuit. In addition to this the circuit obtains a coon-ode gain of zero without the need of any resistor atching.

14 36 A Textbook of Operational Transconductance Aplifier and AIC.4 COMPARATOR For an OTA to function as a coparator, it has to be worked in the non-linear region of its characteristic. The OTA will basically act as a coparator with current output. The circuit for OTA-based coparator [5] is shown in Fig CC g I o R R o CC Fig..8 OTA-based coparator A coparator is a circuit, which copares input signal with a reference voltage R. Usually, the reference voltage R is applied to non-inverting terinal with a proper load and buffer connected at the output, the OTA behaves like a DCS. With the buffered OTA, the output voltage will switch fro a positive () level to a negative (0) level, as the inverting signal is less than or greater than the reference level. o ( ) = i = R O i R( v) = i = R Fig..9 Transfer characteristic

15 Aplifiers and Feedback 37 For the proper operation, the output current (or voltage across load) should be of constant value I() or () for > R and another constant value I(0) or (0) for < R. The transfer characteristic is shown in Fig..9. The special features of an OTA-based coparator of Fig..9 is that the voltages (0) and () ay be varied siply by varying the bias current I B or the voltage B. Because I o is directly proportional to I B, the change in I B causes the OTA to saturate at different levels of voltages. Thus, different levels of output voltages ay be obtained through bias current control. The bias current liits are set by anufacturer s specifications. + cc g o z D R L R z D Fig..0 OTA-based coparator using claping diodes The zener diodes D and D are used to clap the output of the coparator as shown in Fig..0. As the Zener diodes reduce the switching speed, the technique of bias current control sees to be ore attractive fro the considerations of speed. Also it provides convenient and continuous control of output levels..5 ZERO-CROSSING DETECTORS In the circuit of OTA-based coparator of Fig..8, if R is equal to zero, then the output will change fro one state to another very rapidly, every tie the input passes through zero. Such a configuration is called a zero-crossing detector. In the OTA-based zero-crossing detector, the two extree levels of output can be controlled through the bias current. Soe of the applications of zero-crossing detectors are given below.

16 38 A Textbook of Operational Transconductance Aplifier and AIC.5. Square Wave fro a Sine Wave If the input to a coparator is a sine wave, then the output is a square wave. In case of a zero-crossing detector a syetrical square wave results. The circuit for square wave fro sine wave is shown in Fig..(a). At higher frequencies, the rising and falling edges of the square wave becoe slanted, as with the case of an Op-ap coparator, due to slew rate liitation. In the OTA-based circuit of square wave fro sine wave, the aplitude of square wave can be adjusted through bias control current of OTA. (a) Square wave fro sine wave generator Fig...5. Tiing Marker fro A Sine Wave The square wave output o of circuit of Fig..(b) is applied to the input of an R-C circuit, as shown in Fig... If the tie constant RC is very sall as

17 40 A Textbook of Operational Transconductance Aplifier and AIC I B I o g I B I o o T g R R Fig..3 New current controlled OTA-R Schitt trigger o IB R L ve ( + ) increasing IB R th I R B th IB R ( L ve) decreasing Fig..4 Transfer characteristic of Schitt trigger can note fro the circuit that there is no change until reaches a value equal to T. As begins to exceed this value, a negative voltage appears between the input terinals of first OTA. This voltage is aplified by the first aplifier, which is fored by first OTA and resistor R, and thus, output o goes negative. The second voltage aplifier, fored by second OTA and resistor R, in turn causes T to negative thereby increasing the negative input to first OTA and keeping the

18 4 A Textbook of Operational Transconductance Aplifier and AIC [4] W. Surakapontorn,. Riewruja, K. Kuwachara, C. Surawatpunya, K. Anuntahirunrat,. Teperature insensitive voltage-to-current converter and its applications, IEEE Transaction on Instruentation and Measureent, ol. 48, No. 6, pp , 999. [5] Z. Ansari, Realization and study of soe non-linear circuits using operational transconductance aplifier M.Sc. Engg. Dissertation, A.M.U. Aligarh, India, 984. [6] K. Ki, H.-W.Cha and W.-S. Chung, OTA-R Schitt trigger with independently controllable threshold and output voltage levels, Electronic Letters, ol. 33, No. 3, pp , 997.