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