Gain of the Thorsten/Peter Daniels gainclone?

[andy_c]

But Selfs results show that the CMRR is not constant during the signal cycle, much as the open loop gain is not constant during a signal cycle. (If it were, there would be no non-linear distortion). Especially around the zero crossing. open loop gain can vary by as much as a factor two. IF CMMM would also exhibit a similar non-linearity (which I am not sure, but Selfs results are convincing), that 0.09dB would vary during the signal cycle, which if it were symmetrical would give rise to 3rd order harmonics.

So however you cook it, CM distortion seems to be real, at least in some devices.

It's also possible to have CM distortion even if the CMRR is linear. Consider an input diff amp with resistive bias instead of a current source. For simplicity, assume the diff amp has no emitter degeneration, so that its behavior is characterized by:

Iout = I0 * tanh(Vdm/(2 * VT))

where VT = k * T / q, I0 is the "tail current" and Vdm is the difference-mode voltage.

This equation is still valid when the tail current is a function of time - which is exactly what happens in the non-inverting configuration when a resistor is used to bias the diff amp instead of a current source. The total I0 is approximately the DC value plus the common-mode input voltage divided by the tail current bias setting resistor. Assuming Vdm is small enough to not cause TIM distortion, tanh(x) ~= x. So now we have multiplication in the time domain!

Because cos(x) * cos = 1/2(cos(x+y) + cos(x-y)), and the frequencies are equal, we get the second harmonic generated by this mechanism. In other words, the diff amp is acting like a Gilbert cell mixer to the common-mode voltage, mixing a scaled version of it with the difference-mode voltage.

Some amp designers claim that amps sound better with resistive bias than with a current source. My opinion is that this may be due to a pleasant-sounding second harmonic effect.