## Tuesday, September 13, 2022

### High Precision Composite Op-Amps, Part 3 - More Loop Gain

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

As discussed in my previous post on this topic, the resistive voltage divider in John D. Yewen's composite amplifier (see his article "High-precision composite op-amps" in Electronics & Wireless World, February 1987):

adds a zero to the loop gain, which helps to achieve stability at the expense of the loop gain:

For audio applications, it is desirable to maximize the loop gain, at least in the audio band, but preserve the phase margin. One way to keep that zero and maximize the loop gain at audio frequencies is to make the voltage divider frequency dependent, for example:

Adding an inductor in parallel to R3 adds a pole-zero pair (disregarding the inductor's own series resistance, the pole is at $F_p={1 \over {2 \pi}} {{R_3 || R_4} \over L_1}$, the zero at $F_z={1 \over {2 \pi}} {R_3 \over L_1}$). With the values shown, we get about 12dB of extra loop gain at 20kHz with the same phase margin as without the inductor:

A 22mH inductor may not be very practical, but a similar effect can be achieved with a resistive-capacitive divider, for example:

Here, the pole is at $F_p={1 \over {2 \pi R_5 (C_1 + C_2)}}$, the zero at $F_z={1 \over {2 \pi R_5 C_1}}$. With the values shown, the loop gain is about the same as with the inductor above:

Not bad for one additional passive component. It works in hardware, too - I will show a practical example in my next post.

## Tuesday, September 6, 2022

### High Precision Composite Op-Amps, Part 2 - Divide and Conquer

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

My previous post on this topic was on composite opamps from by John D. Yewen's article "High-precision composite op-amps" (Electronics & Wireless World, February 1987):

Appropriately choosing the voltage divider R1R2 at the output of U1 allows to achieve stability (obtain sufficient gain and phase margins) of the composite at the expense of the loop gain. Here, orange traces are the loop gain of the composite from the schematic above, while blue are the maximum possible (whether stable or not) loop gain with the same two opamps:

How can a simple resistive divider make the composite stable? Let me look at the role of the voltage divider in Yewen's composite.

Referring to the schematic above, U2 sees a (differential) input signal that is a sum of (i) the signal at the non-inverting output, where Ri and Rf connect, and (ii) the same signal amplifier by U1 and divided by R1R2.

At low frequencies, U1's gain is large, and U2's input signal is effectively that at its non-inverting input. The loop gain is the product of that of U1 and U2 and falls with frequency at 40dB/decade. At high frequencies, U1's gain is small, and U2's input signal is effectively that at its inverting input. The loop gain is just that of U2, falling at 20dB/decade.

The transition from "low" to "high" frequencies is a zero in the composite's loop gain, located at the frequency where the signal magnitudes at the non-inverting and inverting inputs of U2 are equal - that is, when the gain of U2 followed by R1R2 is unity. For a single-pole U1, that frequency is a fraction of U1's Gain Bandwidth Product (GBW):$$F_{zero}=GBW_{U_1} \times {R_2 \over {R_1+R_2}}$$In the example above, GBW is 10MHz, the divider's attenuation is 22, so the zero is at ${{10 MHz}\over 22} = {455 kHz}$.

That is, Yewen's voltage divider sets the frequency of a zero in the composite's loop gain. The higher the attenuation in the divider, the lower is the zero, and vice versa.

By the way, it is possible and quite practical to replace the fixed divider with a trimpot and adjust the zero to one's liking, e.g. to obtain the necessary phase margin.

Can we make it still better? Yes we can! Stay tuned...