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