[sdiy] Differential amps and noise cancellation in dsPIC 33FJ128GP802 uP's DAC

[Steve Lenham]

On 05/05/2021 20:25, Guy McCusker via Synth-diy wrote:
>> You mean the input impedances of the complete circuit with respect to ground? These are equal.
>> As long as the feedback works properly, both the inverting and the noninverting input of the opamp are at the same voltage. Since R5 and R7 are both 10k, a signal source connected to the left side of either R5 or R7 sees the same input impedance.
> 
> I don't think that is correct but happy to be put straight if I am
> mistaken. My take is as follows.
> 
> Ignoring the capacitor to make life easier, a signal connected at R7
> sees 20k to ground always.
> With the input at R7 grounded, a signal connected at R6 sees 10k to
> the virtual ground. I can't see any circumstances under which a signal
> at R5 sees 20k to ground.
> 
> What am I missing?
> Guy.

You're not mistaken - the input impedances of the single-opamp 
differential amplifier are not equal.

But for a balanced (differential) input signal, the inverting pin of the 
opamp isn't a virtual ground. Imagine feeding the R7 input with +1V and 
the R5 input with -1V. The non-inverting terminal of the opamp will be 
at +0.5V due to the divider action of R7 and R8. There is 0.5V across R7 
and a positive input current of 50uA. So the positive input impedance is 
indeed 1V/50uA = 20k.

However, due to feedback, the opamp keeps its input terminals at the 
same voltage, i.e. the voltage at the inverting terminal must also be 
+0.5V. The voltage across R5 = (-1) - 0.5 = -1.5V and so the negative 
input current is -150uA. That results in a negative input impedance of 
(-1)/(-150uA) = 6.7k.

So, in a nutshell, the difference in the two input impedances is even 
worse than it first appears. The degree will vary with different diffamp 
gains, but the principle stays the same.

It's worth bearing in mind that this doesn't actually matter if your 
source impedance is negligible, because in that case the different 
loadings will not affect the input voltages. But the common-mode 
rejection ('noise cancellation') gets degraded more and more as the 
source impedance increases.

One nifty answer to this is the so-called "Superbal" circuit, where you 
use a second opamp to invert the output signal. The bottom leg of the 
input network (R8 and C17 in the original circuit) is then attached to 
the output of that opamp instead of ground. The effect of this is to 
keep both input terminals of the first opamp at zero volts rather than 
half the positive input voltage. Since the balanced input voltages have 
the same magnitude with respect to ground, the input currents will be 
equal and hence the input impedances will also be equal. It's a great 
circuit and I use it all the time for balanced audio equipment.

Cheers,

Steve L.
Benden Sound Technology