[Part 1 reviews a brief history of op amps and then looks at various op amp properties from a perspective of audio design.]
Bipolar input op-amps
Figure 4.4 shows the distortion from a 5532 working in shunt mode with low-value resistors of 1 kΩ and 2k2 setting a gain of 2.2 times, at an output level of 5 Vrms. This is the circuit of Figure 4.3(a) with RS set to zero; there is no CM voltage. The distortion is well below 0.0005% up to 20 kHz; this underlines what a superlative bargain the 5532 is.
Figure 4.3: Op-amp test circuits with added source resistance RS. (a) Shunt. (b) Series. (c) Voltage-follower. (d) Voltage-follower with cancellation resistor in feedback path
Figure 4.4: 5532 distortion in a shunt-feedback circuit at 5 Vrms out. This shows the AP SYS- 2702 output (lower trace) and the op-amp output (upper trace). Supply ±18 V
Figure 4.5 shows the same situation but with the output increased to 10 Vrms (the clipping level on ±18 V rails is about 12 Vrms) and there is now significant distortion above 10 kHz, though it only exceeds 0.001% at 18 kHz.
Figure 4.5: 5532 distortion in the shunt-feedback circuit of Figure 4.3(b). Adding extra resistances of 10 kΩ and 47 kΩ in series with the inverting input does not degrade the distortion at all, but does bring up the noise floor a bit. Test level 10 Vrms out, supply ±18 V
This remains the case when RS in Figure 4.3(a) is increased to 10 kΩ and 47 kΩ – the noise floor is higher but there is no real change in the audio-band distortion behavior. The significance of this will be seen in a moment.
We will now connect the 5532 in the series-feedback configuration, as in Figure 4.3(b); note that the stage gain is greater at 3.2 times but the op-amp is working at the same noise gain. The CM voltage is 3.1 Vrms. With a 10 Vrms output we can see in Figure 4.6 that even with no added source resistance the distortion starts to rise from 2 kHz, though it does not exceed 0.001% until 12 kHz.
Figure 4.6: 5532 distortion in a series-feedback stage with 2k2 and 1k feedback resistors, and varying source resistances. Output 10 Vrms
But when we add some source resistance RS, the picture is radically worse, with serious mid-band distortion rising at 6 dB/octave, and roughly proportional to the amount of resistance added. We will note it is 0.0085% at 10 kHz with RS = 47 kΩ.
The worst case for CM distortion is the voltage-follower configuration, as in Figure 4.3(c), where the CM voltage is equal to the output voltage. Figure 4.7 shows that even with a CM voltage of 10 Vrms, the distortion is no greater than for the shunt mode. However, when source resistance is inserted in series with the input, the distortion mixture of second, third, and other low-order harmonics increases markedly. It increases with output level, approximately quadrupling as level doubles. The THD is now 0.018% at 10 kHz with RS = 47 kΩ, more than twice that of the series-feedback amplifier above, due to the increased CM voltage.
Figure 4.7: 5532 distortion in a voltage-follower circuit with a selection of source resistances. Test level 10 Vrms, supply ±18 V. The lowest trace is the analyzer output measured directly, as a reference
It would be highly inconvenient to have to stick to the shunt-feedback mode, because of the phase inversion and relatively low input impedance that comes with it, so we need to find out how much source resistance we can live with. Figure 4.8 zooms in on the situation with resistance of 10 kΩ and below; when the source resistance is below 2k2, the distortion is barely distinguishable from the zero source resistance trace. This is why the low-pass Sallen-and-Key filters in Chapter 5 have been given series resistors that do not in total exceed this figure.
Figure 4.8: A closer look at 5532 distortion in a voltage-follower with relatively low source resistances; note that a 1 kΩ source resistance actually gives less distortion than none. Test level 10 Vrms, supply ±18 V
Close examination reveals the intriguing fact that a 1 kΩ source actually gives less distortion than no source resistance at all, reducing THD from 0.00065% to 0.00055% at 10 kHz. Minor resistance variations around 1 kΩ make no difference. This must be due to the cancellation of distortion from two different mechanisms. It is hard to say whether it is repeatable enough to be exploited in practice.
So, what's going on here? Is it simply due to non-linear currents being drawn by the op-amp inputs? Audio power amplifiers have discrete input stages that are very simple compared with those of most op-amps, and draw relatively large input currents. These currents show appreciable non-linearity even when the output voltage of the amplifier is virtually distortion free, and, if they flow through significant source resistances, will introduce added distortion .
If this was the case with the 5532 then the extra distortion would manifest itself whenever the op-amp was fed from a significant source resistance, no matter what the circuit configuration. But we have just seen that it only occurs in series-feedback situations; increasing the source resistance in a shunt-feedback does not perceptibly increase distortion. The effect may be present but if so it is very small, no doubt because op-amp signal input currents are also very small, and it is lost in the noise.
The only difference is that the series circuit has a CM voltage of about 3 Vrms, while the shunt circuit does not, and the conclusion is that with a bipolar input op-amp you must have both a CM voltage and a significant source resistance to see extra distortion. The input stage of a 5532 is a straightforward long-tailed pair (see Figure 4.21 below) with a simple tail-current source, and no fancy cascoding, and I suspect that the Early effect operates on it when there is a large CM voltage, modulating the quite high input bias currents, and this is what causes the distortion. The signal input currents are much smaller, due to the high open-loop gain of the op-amp, and as we have seen appear to have a negligible effect.
FET-input op-amps behave differently from bipolar-input op-amps. Take a look at Figure 4.9, taken from a TL072 working in shunt and in series configuration with a 5 Vrms output.
Figure 4.9: A TL072 shunt-feedback stage using 10 and 22 kΩ resistors shows low distortion. The series version is much worse due to the impedance of the NFB network, but it can be made the same as the shunt case by adding cancellation source resistance in the input path. No external loading, test level 5 Vrms, supply ±18 V
The circuits are as in Figure 4.3(a) and (b), except that the resistor values have to be scaled up to 10 and 22 kΩ because the TL072 is nothing like so good at driving loads as the 5532. This unfortunately means that the inverting input is seeing a source resistance of 10k||22k = 6.9k, which introduces a lot of CM distortion in the series case – five times as much at 20 kHz as for the shunt case. Adding a similar resistance in the input path cancels out this distortion, and the trace then is the same as the 'Shunt' trace in Figure 4.9. Disconcertingly, the value that achieved this was not 6.9k, but 9k1. That means adding -113 dBu of Johnson noise, so it's not always appropriate.
It's worth mentioning that the flat part of the 'Shunt' trace below 10 kHz is not noise, as it would be for the 5532; it is distortion.
A voltage-follower has no inconvenient medium-impedance feedback network, but it does have a much larger CM voltage. Figure 4.10 shows a voltage-follower working at 5 Vrms. With no source resistance the distortion is quite low, due to the 100% NFB, but as soon as a 10 kΩ source resistance is added we are looking at 0.015% at 10 kHz.
Figure 4.10: A TL072 voltage-follower working at 5 Vrms with a low source resistance produces little distortion (RS = 0R), but adding a 10 kΩ source resistance makes things much worse (RS = 10k). Putting a 10 kΩ resistance in the feedback path as well gives complete cancellation of this extra distortion (Cancel). Supply ±18 V
Once again, this can be cured by inserting an equal resistance in the feedback path of the voltage-follower, as in Figure 4.3(d) above. This gives the 'Cancel' trace in Figure 4.10. Adding resistances for distortion cancellation in this way has the obvious disadvantage that they introduce extra Johnson noise into the circuit.
Another point is that stages of this kind are often driven from pot wipers, so the source impedance is variable, ranging between zero and one-quarter of the pot track resistance. Setting a balancing impedance in the other op-amp input to a mid-value, i.e. one-eighth of the track resistance, should reduce the average amount of input distortion, but it is inevitably a compromise.
With JFET inputs the problem is not the operating currents of the input devices themselves, which are negligible, but the currents drawn by the non-linear junction capacitances inherent in field-effect devices. These capacitances are effectively connected to one of the supply rails. For P-channel JFETs, as used in the input stages of most JFET op-amps, the important capacitances are between the input JFETs and the substrate, which is normally connected to the V- rail (see Jung ).
According to the Burr-Brown data sheet for the OPA2134, 'The P-channel JFETs in the input stage exhibit a varying input capacitance with applied CM voltage.' It goes on to recommend that the input impedances should be matched if they are above 2 kΩ.
Common-mode distortion can be minimized by running the op-amp off the highest supply rails permitted, though the differences are not large. In one test on a TL072, going from ±15 to ±18 V rails reduced the distortion from 0.0045% to 0.0035% at 10 kHz.
Rail bootstrapping to reduce CM distortion
So what do you do if you need a really high-impedance low-distortion voltage-follower and you have a significant source resistance, but you don't want the added noise that would come from adding a cancellation resistor? We noted above that the non-linear input capacitances that cause the trouble with JFET op-amp voltage-followers are effectively connected to the V- supply rail or substrate. This suggests a way to remove the problem: if the supply rails are bootstrapped so they go up and down with the inputs, the signal voltage across the non-linear input capacitances is zero, no current can flow through them, and no extra distortion is generated.
Figure 4.11(a) shows the idea. The resistor–Zener chain R4, D1, D2, R5 creates ±5 V rails that are moved up and down by op-amp A4, and buffered by A2, A3. A1 expects reasonably low supply-rail impedances at HF, and attempting to run it directly from the outputs of A2, A3 does not work – the signal disappears in a fog of HF oscillation. The two resistors R2, R3 prevent this by isolating C1 from A2, A3 outputs, while capacitor C1 across A1 supply pins keeps the HF rail impedance low.
Figure 4.11: Bootstrapping the supply rails of voltage-follower A1 by moving them up and down with the input signal: (a) using op-amps; (b) using transistors
Since the ±5 V rails of A1 have to remain inside the fixed ±15 V supply rails, the possible swing of the supplies is limited and the maximum output is reduced compared with a basic voltage-follower. The circuit of Figure 4.11(a) clips at 6.7 Vrms (1 kHz). This could be increased somewhat by using ±17 or ±18 V fixed rails.
Figure 4.12 shows the result of basic bootstrapping while handling a 5 Vrms signal, which as we saw earlier, is enough to cause serious CM distortion. The increase in linearity is encouraging; the distortion is promptly halved.
Figure 4.12: TL072 voltage-follower distortion with (Y) and without (N) rail bootstrapping. Test level 5 Vrms, supply ±15 V
Figure 4.13, however, shows that we can do better by adding C2, C3. These are in parallel with the effective slope resistance of the Zeners, and improve the accuracy of the rail bootstrapping. The lower trace marked 'WITH' is once again indistinguishable from that of the test-gear alone.
Figure 4.13: Rail bootstrapping is much enhanced by adding capacitors C2, C3. TL072, test level 5 Vrms, supply ±15 V. The 'WITH' trace is essentially the distortion of the test-gear alone
Figures 4.12 and 4.13 were taken with near-zero source resistance, and show that internal CM distortion has been dealt with. But what happens when a 10 kΩ source resistance is reintroduced?
Figure 4.14 gives the answer: adding a 10 kΩ source resistance now makes almost no difference. Note that no cancellation resistor has been put in the feedback path.
Figure 4.14: TL072 Voltage-follower distortion with 10 kΩ and 50 Ω source resistances, and no cancellation. Test level 3 Vrms, supply ±15 V
Simpler rail bootstrapping
On contemplating Figure 4.11(a), it may occur to you that using three op-amps to make a friendly environment for one is a bit over-complex. You are quite right. It is always good to simplicate and add lightness when you can, and A2 and A3 can in fact be replaced by simple emitter-followers with no detectable loss in performance, as in Figure 4.11(b).
The two 47 Ω resistors have been removed, but C1 is retained. This seems to be reliably stable. The total supply voltage to A1 has been reduced by two Vbe drops, or 1.2 V; it could be restored by increasing the Zener voltages if required. The simpler version also uses less power as we no longer need to supply the quiescent currents of A2 and A3.
The attentive reader will recall that the troublesome non-linear capacitances are effectively connected to the substrate, which is usually the V- supply rail. Would it not be possible to bootstrap just that rail, and leave V+ connected to a fixed +15 V rail? It would – it works, but the results with an OPA2134, while more linear than with a conventional voltage-follower, are worse than bootstrapping both rails. Before we were keeping the magnitude of the A1 supply 0.0002 voltage substantially constant, although it was sailing up and down. If only one rail is bootstrapped the actual supply voltage is being modulated, so it is hardly surprising that linearity suffers.
The rail bootstrapping concept was also tested with the TL052 and the OPA2134 at 5 Vrms, and similar dramatic reductions in CM distortion were found.
In the previous section we saw that CM distortion is also generated by bipolar input op-amps, though by a different mechanism, so rail bootstrapping ought to work for these types of opamp as well. Figure 4.15 shows that it does. Adding a 10 kΩ source resistance now causes virtually no extra distortion.
Figure 4.15: Rail bootstrapping works for 5532 voltage-followers as well; 10 kΩ and 50 Ω source resistances, and no cancellation. Test level 5 Vrms, supply ±15 V
Bootstrapping series-feedback JFET op-amp stages
The voltage-follower is the worst case for CM distortion, as the full output voltage exists on both inputs. In contrast, it is the best case for output loading, as there is no resistive feedback network at all to drive – just a high-impedance input pin. Similarly, the shunt-feedback amplifier is the best case for CM distortion as there is no significant signal on the inputs.
Series-feedback amplifier stages fall between these two cases. For a +10 dB amplifier stage, the signal on the inputs is one-third that of the output, and so the input distortion is less, but still very definitely present, as we saw in Figures 4.6 and 4.9.
Amplifier stages like this can have a mixture of distortion mechanisms. The impedance of the NFB network, as seen from the inverting input of the amplifiers, is 22 kΩ in parallel with 10 kΩ, i.e. 6.87 kΩ. We have seen above that this is enough to cause serious non-linearity unless the other input sees the same impedance, and it might be thought that reducing the impedance level of the NFB network would be a good way to deal with this, not least because it would minimize the Johnson noise produced by the network. Figure 4.16 shows that this does not work for the TL072; if the feedback network impedance is reduced by a factor of 10 the distortion gets worse rather than better, due to the heavier loading on the output.
Figure 4.16: With the TL072, reducing the impedance of the negative-feedback network may reduce input distortion, but output distortion more than makes up for it because of the extra loading. Upper trace 2k2 – 1 kΩ, lower trace 22 kΩ – 10 kΩ in feedback network
Input distortion has been replaced by a larger amount of output distortion; this is not a good exchange. Lowering the NFB network impedance is, however, likely to be successful with JFET op-amps having better load-driving capability than the TL072.
Rail bootstrapping is once more a possible answer. We drive the op-amp supply rails up and down with the same signal as the input – not the output. The only modification required is to take the increased output swing into account by increasing the A1 supply voltage to ±10 V (see Figure 4.17). The Zeners have been replaced with simple resistive dividers. This works just as well, and is a good thing as Zeners are more expensive than resistors. Figure 4.18 shows the excellent results.
Figure 4.17: Bootstrapping the rails of a series-feedback amplifier from the input of A1. The Zeners have been replaced by resistors
Figure 4.18: The benefit of bootstrapping the rails of a series-feedback amplifier with a gain of 3.23. The lower trace is essentially that of the THD from the test equipment
Coming up in Part 3: Selecting the right op amp.
Printed with permission from Focal Press, a division of Elsevier. Copyright 2010. "Small Signal Audio Design" by Douglas Self. For more information about this title and other similar books, please visit www.elsevierdirect.com.
 A. Blumlein, UK patent 482,470, 1936.
 W. Jung (Ed.), Op-Amp Applications Handbook, Newnes, 2006 (Chapter 8).
 D. Self, Audio Power Amplifier Design Handbook, fifth ed, Focal Press, 2009, pp. 186–189.
 D. Self, Audio Power Amplifier Design Handbook, fifth ed, Focal Press, 2009, p. 96.
 W. Jung (Ed.), Op-Amp Applications Handbook, Newnes, 2006, p. 399 (Chapter 5).
 D. Self, Audio Power Amplifier Design Handbook, fifth ed, Focal Press, 2009, p. 380.
Op amps in small-signal audio design - Part 1: Op amp history, properties
PRODUCT HOW-TO: Differential line driver with excellent load drive
Using Op Amps with Data Converters - Part 1 | Part 3 | Part 4 | Part 5
Yet More On Decoupling, Part 4: Op amp macromodels: A cautionary tale
Discrete audio amplifier basics - Part 1: Bipolar junction transistor circuits | Part 2: JFETs, MOSFETs and other circuit configurations
Op amps: to dual or not to dual? Part 1 | Part 2
Are you violating your op amp’s input common-mode range?
Distortion in power amplifiers, Part I: the sources of distortion | Part II: The input stage | Part III: The voltage amplifier stage | Part VII: frequency compensation and real designs