# Application Report SLVA051

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1 Application Report November 998 Mixed-Signal Products SLVA05

2 ltage Feedback Vs Current Feedback Op Amps Application Report James Karki Literature Number: SLVA05 November 998 Printed on Recycled Paper

4 Contents Introduction Ideal Models Ideal Models with Feedback Frequency Dependant Gain Model Feedback with Frequency Dependant Models Summary Appendix A Derivation of Models A List of Figures Ideal Op Amp Model Noninverting Amplifr Frequency Model Feedback with Frequency Dependant Models Bode Plot ltage Feedback vs. Current Feedback Op Amps iii

5 iv SLVA05

6 ltage Feedback Vs Current Feedback Op Amps ABSTRACT This application report contrasts and compares the characteristics and capabilits of voltage and current feedback operational amplifrs. The report also points out the many similarits between the two versions. Introduction The voltage feedback (VF) operational amplifr (op amp) is the most common type of op amp. The less well known current feedback (CF) op amp has been commercially available for about 20 years, but many designers are still uncertain about how to use them. Terminology is a confusing factor for many people. The CF op amp is a transimpedance op amp and so has a different vocabulary associated with it. This report attempts to show that there are more similarits than differences between CF and VF op amps when considering basic circuit operation.

7 Ideal Models 2 Ideal Models The ideal VF op amp model is a powerful tool that aids in understanding basic VF op amp operation. There is also an ideal model for the CF op amp. Figure (a) shows the VF ideal model and Figure (b) shows the CF ideal model. Ve ave x Zt (a) VF Ideal Op Amp Model (b) CF Ideal Op Amp Model In a VF op amp, Figure. Ideal Op Amp Model a Ve () where Ve = is called the error voltage and a is the open loop voltage gain of the amplifr. In a CF op amp, Zt (2) where is called the error current and Zt is the open loop transimpedance gain of the amplifr. An amplifr where the output is a voltage that depends on the input current is called a transimpedance amplifr because the transfer function equates to an impedance i.e., Zt. 2 SLVA05

8 Ideal Models with Feedback 3 Ideal Models with Feedback Applying negative feedback around the ideal models, as shown in Figure 2 (a) and Figure 2 (b), results in noninverting amplifrs. In a VF op amp, when negative feedback is appld, the action of the op amp is to drive the error voltage to zero; thus the name voltage feedback. In a CF op amp, when negative feedback is appld, the action of the op amp is to drive the error current to zero; thus the name current feedback. Vi Ve ave Vi x Zt R R2 R R2 (a) VF Ideal Noninverting Amp (b) CF Ideal Noninverting Amp Figure 2. Noninverting Amplifr For each circuit, solving for in relation to Vi gives the transfer function of the circuit. In the VF circuit, Equation still holds true so that, = a Ve where Ve =. Now = Vi and R. Substituting and solving for R R2 Vi ; Vi a a R RR2 where b R R R2 R R2 R a RR2 R b ab In the CF circuit, Equation 2 still holds true so that, = Zt Zt. Also, = = Vi. Summing currents at node, ( ) R R2 0. Substituting and solving for Vi ; Vi R R2 R R2 Zt b R2 Zt (3) where b R (4) R R2 ltage Feedback Vs Current Feedback Op Amps 3

9 Ideal Models with Feedback In either circuit (VF or CF noninverting amplifr), it is desired to set the gain by the ratio of R to R2. The second term on the right hand side of Equations 3 and 4 is seen as an error term. In the VF case, if ab is large (ideally equal to infinity), then the error is negligible. In the CF case, if Zt is large (ideally equal to infinity) in comparison to R2, then the error is negligible. Comparing the ideal behavior of VF and CF amplifrs shows very little difference. 4 SLVA05

10 4 Frequency Dependant Gain Model Frequency Dependant Gain Model The open loop gain, a for VF or Zt for CF, is frequency dependant in real op amps. In Figure 3, components are added to the ideal models (of Figure ), which model the dominant bandwidth limitations. See Appendix A for the derivation of these models. Ve _ gm i = Ve gm Rc Cc VC x x Rt Cc VC x Zc (a) VF Zt (b) CF Figure 3. Frequency Model To solve the input to output transfer function is the same as above. For the VF op amp: Vc i Zc Ve gm Rc Cc. Rearranging and substituting Rc Cc Rc j2frccc gm Ve Rc j2frccc. This is the same as Equation with a gm Rc j2frccc. The term gm Rc is the open loop gain of the op amp, usually j2frccc denoted as a(f) in the literature. The VF op amp s open loop gain has a dc response, a break frequency, and a 20dB/dec roll-off. At low frequencs, 2fRcCc, and gm Rc, which is extremely high at dc. As Ve frequency increases, eventually 2fRcCc, and (gm Rc) Ve. 2 This is the dominant pole frequency, f D. At frequencs above f D, Cc begins to dominate the response so that gm, and the gain rolls off at Ve 2fCc 20dB/dec. Cc is usually chosen so that the amplification falls to unity [noted as Fu in Figure 5(a)] before upper frequency poles cause excessive phase shift. (5) (6) ltage Feedback Vs Current Feedback Op Amps 5

11 Frequency Dependant Gain Model For the CF op amp: Vc Zt Rc Cc. Rearranging and substituting Rc Cc Rc j2frtcc Rt j2frtcc. This is the same as Equation 2 with Zt Rt j2frtcc (7) The term Zt Rt is the open loop gain of the op amp, which is j2frtcc frequency dependent, and is more properly denoted Zt(f). The CF op amp s open loop gain has a dc response, a break frequency, and a 20dB/dec roll off. At low frequencs, 2fRtCc, and Rt, which is extremely high at dc. As frequency increases, eventually 2fRtCc, and Rt. This is the 2 dominant pole frequency, f D. At frequencs above f D, Cc begins to dominate the response so that, and the gain rolls off at 20dB/dec. Cc is usually 2fCc chosen so that Zt will roll off to the desired feedback resistor value before upper frequency poles cause excessive phase shift. 6 SLVA05

12 5 Feedback with Frequency Dependant Models Feedback with Frequency Dependant Models Applying a negative feedback network (as in Figure 2) to the op amp frequency models as shown in Figure 4 results in noninverting amplifrs. Vi Ve _ gm i = Ve gm Rc Cc VC x Vi x Rt Cc VC x R R2 Zc R R2 Zt (a) VF (b) CF Figure 4. Feedback with Frequency Dependant Models Solve the transfer function for the VF noninverting amplifr by substituting a gm Rc in Equation 3. Therefore : j2frccc Vi R R2 R gm Rc R j2frccc RR2 (8) The gain-bandwidth relationship of the VF noninverting amplifr can be seen clearly by expanding and collecting terms in the second term on the right hand side of Equation 8. gm Rc R j2frccc RR2 gmrc RR2 R RR2 R RR2j2fRcCc gmrcr j2fcc gm Usually gm Rc is very large so that R R2. Disregarding gm Rc R this term and substituting Equation 9 into Equation 8 results in (9) ltage Feedback Vs Current Feedback Op Amps 7

13 Feedback with Frequency Dependant Models Vi R R2 R R RR2 j2fcc gm The term R R2 is the desired closed loop gain of the amplifr. R At low frequency where R R2 j2fcc R gm j, R R2. Vi R As frequency increases, eventually R R R2 j2f c Cc gm j (0) () 8 SLVA05 and the gain of the circuit is reduced by 3 db: Vi frequency f c gm R 2Cc of the circuit. Rearranging, fc R R2 gm R R2 R. The 2 is the 3 db bandwidth, or cutoff frequency R R2 constant. Therefore, R 2Cc in a voltage feedback op amp, the product of the closed loop gain and the closed loop bandwidth is constant over most of the frequencs of operation. This is the gain bandwidth product, (GBP). The result is that if gain is multipld by 0, bandwidth is divided by 0. Solve the transfer function for the CF noninverting amplifr by substituting Zt Rt j2frtcc in Equation 4. Therefore: (2) Vi R R2 R R R2 R (R2) j2frtcc Rt R2 Rt j2fr2cc Normally R2 Rt and is disregarded resulting in: (3) Vi R R2 R j2fr2cc Equation 3 shows that the 3dB bandwidth or cutoff frequency, f c, can be set by selection of R2 so that f c, and gain can be set by selection of R. 2R2Cc Thus in a CF op amp gain and bandwidth are independent of each other.

14 Feedback with Frequency Dependant Models Figure 5 shows Bode plots of the gain vs. frequency characteristics of the VF and CF op amp models. gmrc Open Loop Gain Vi R R2 R Closed Loop Gain 20 db/dec Upper Frequency Poles fd 2 RcCc fc GBP R R R2 Frequency (a) VF Bode Plot fu GBP Rt Open Loop Gain 20 db/dec R2 fd 2 RtCc fc 2 R2Cc Frequency (b) CF Bode Plot Figure 5. Bode Plot Upper Frequency Poles ltage Feedback Vs Current Feedback Op Amps 9

15 Summary 6 Summary A VF op amp is a voltage amplifr a(f) and a CF op amp is a Ve transimpedance amplifr Zt(f). In each the effect of negative feedback is to drive the input to zero: Ve 0 and 0; thus the names VF and CF. When configured as noninverting amplifrs with negative feedback, both op amps provide a voltage gain that is determined by the feedback network. In each the open loop gains, a(f) and Zt(f), are frequency-dependent and limit the bandwidth of operation. In VF op amp circuits the gain bandwidth product is constant over the normal frequencs of operation. In CF op amp circuits the gain and bandwidth can be set independently of one another. The majority of VF op amps are unity-gain stable, so the designer is relved of the burden of compensating circuits for stable operation. This also limits bandwidth to the minimum capability of the op amp design. The impedance of the negative feedback component determines stability in a CF op amp circuit. There is a minimum value of R2 to maintain stability (conversely there is a maximum bandwidth for a given phase margin). For this reason, if a buffer amplifr is configured by shorting the output to the negative input, the circuit will oscillate. Also, care must be taken when using capacitance in the feedback loop as in the case of an integrator or low pass filter. Table. VF vs CF: Comparison of Major Parameters PARAMETER VF CF Open loop gain ltage a(f). Frequency dependant, Ve Transimpedance Zt(f). limits bandwidth. Frequency dependant, limits bandwidth. Closed loop gain Vi b ab Vi b R2 Zt Ideal closed loop gain Set by feedback factor b Set by feedback factor b Gain bandwidth product Gain and bandwidth interdependent. Constant over most frequencs of operation. Gain and bandwidth independent of each other. Normally unity gain stable. Minimum impedance in feedback component Stability required for stability Bandwidth Set by closed loop gain Set by impedance of feedback component 0 SLVA05

16 Appendix A Derivation of Models Figure A and Figure A2 show simplifd schematic diagrams of the THS400 and THS300, and their models. The following discussion provides an overvw of how the frequency dependent models are derived. A. THS400 VF Frequency Dependent Model (see Figure A ) Derivation of Models A.. A..2 A..3 Differential Pair Q and Q2 comprise the input differential pair. Three current sources, i, are used to bias the circuit for normal operation; i=ii2. When =, i=i2, and the collector currents of Q, Q2, Q3, and Q4 are equal. When VP>, Q2 turns on harder and i2 increases. The bottom current source insures that i=ii2. Therefore i decreases.. When <, Q turns on harder and i increases. The bottom current source insures that i=ii2. Therefore i2 decreases. Thus the differential voltage at the input and causes differential currents to be generated in Q3 and Q4. The differential input stage is modeled by the transconductance amplifr, gm. High Impedance The current, i2, develops voltage, Vc, at the high impedance node formed by the current mirror structure, D5 Q5 and D6 Q6, and capacitor Cc. The high impedance stage is modeled by the parallel impedance, Zc Rc Cc. Rc models the equivalent dc resistance to ground. Cc is actually two capacitors; one to the positive supply and one to the negative supply. Cc is the parallel combination and the supply pins are assumed to be ac grounds. Double Output Buffer Q7 through Q0 form a double buffer that is a class AB amplifr. The voltage Vc is buffered to the output so that =Vc. The double output buffer is modeled by the X buffer amplifr. ltage Feedback Vs Current Feedback Op Amps A-

17 Derivation of Models VCC Differential Pair High Impedance Double Output Buffer i i D7 i i2 i i2 D8 Q Q2 Q3 Q4 Q9 VC Q7 D5 Q6 CC Q8 i Q0 Q5 D6 VCC (a) THS400 Simplifd Schematic i = Ve gm Ve gm _ Rc Cc (b) VF Model Figure A. VF Model Derivation A.2 THS300 CF Frequency Dependent Model (see Figure A 2) A.2. A.2.2 Class AB Amplifr D Q and D2 Q2 comprise a class AB amplifr where the signal at is buffered with a gain of to. The input stage is modeled by the X buffer amplifr between and. Current Mirror The collector current of Q is drawn through D3. D3 Q3 form a current mirror so that the collector current of Q3 equals the collector current of Q. The same is true for the bottom side so that Q2 s current is mirrored by Q4. This is modeled as a current source equal to the input error current driving the high impedance. A-2 SLVA05

18 Derivation of Models A.2.3 A.2.4 High Impedance The current, i or i2, develops voltage, Vc, at the high impedance node, D5 D6, and Cc. The high impedance is modeled by parallel impedance, Zt Rt Cc. Rt models the equivalent dc resistance to ground. Cc is actually two capacitors; one to the positive supply and one to the negative supply. Cc is the parallel combination and the supply pins are assumed to be ac grounds. Triple Output Buffer Q5 through Q0 form a triple buffer that is a class AB amplifr. The voltage Vc is buffered to the output so that =Vc. The triple output buffer is modeled by the X buffer amplifr. VCC Class AB Amplifr Current Mirror High Impedance Triple Output Buffer i i D3 Q3 Q7 Q5 Q9 D Q D5 D9 Vc D2 Q2 D6 Cc D0 Q6 Q0 D4 Q4 Q8 i2 i2 VCC (a) THS300 Simplifd Schematic x Vc x Rt Cc (b) CF Model Zt Figure A 2. CF Model Derivation ltage Feedback Vs Current Feedback Op Amps A-3

19 A-4 SLVA05

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