[SOLVED] Op-amp common mode response

[jmvalks]

Hello.

I am reading through the book Analog Circuit Techniques with Digital Interfacing, by T.H Wilmshurst, 2001, and have reached section 3.8, Common-mode response.

Here, he states for the ideal op-amp:
V₀ = A₀(V_i+ - V_i-)
and for the real op-amp:
V₀ = A₀₊V_i+ + A_0-V_i-

Then he applies this expression to the non-inverting feedback amplifier:
A_f = A₀₊/(1 - A_0- * beta)
And then he states that for the ideal op-amp, A₀ = infinity, and so
A_f = -A₀₊ / A_0- / beta

I cannot see how he gets to the last step from the previous one. Which A₀ is he taking to infinity? He only defines A₀₊ and A_0- in the discussion.

Any ideas would be appreciated.

Thanks

 

[goldsmith]

Dear friend
Hi
you should know that op amp wants to going identical its inputs(with feedback) and without feed back compare its inputs: if
V+<V- then the out put voltage will be -vcc. and if V-<V+ , thus it's out put voltage will be +vcc.
in simple word, the op amp , is a differential amplifier( its input) .
with negative feed back , it can work in linear region. and if you have not negative feedback it work in cut off and saturation region. its cut off is -vcc ind its saturation is +vcc.
i hope being helpful
Best wishes
Goldsmith

 

[keith1200rs]

1 - A0- * beta is approximately - A0- * beta if A0 is infinite and beta is not zero. A bit like saying one minus infinity is -infinity.

Keith

 

[jmvalks]

1 - A0- * beta is approximately - A0- * beta if A0 is infinite and beta is not zero. A bit like saying one minus infinity is -infinity.

Keith

Hi Keith

Thanks for the response.

Yes - I was thinking on a similar line. So what he is really saying is that A_0- is >> 1, rather than infinity, otherwise it causes complications with the maths. I can understand it from your viewpoint.

The other way I looked at it is to assume that as the input signal is applied to the non-inverting input, it is the open loop gain for this terminal that is assumed to be infinity. With a bit of rearranging it is possible to get his result, but I'm sure the pure mathematicians would cringe at some of the reasoning.

Jonathan

 

[keith1200rs]

It is fairly common to try to drop inconvenient parts of equations by assuming things are infinity or zero only to keep some of them in the equations for later use when you don't assume they are infinity or zero!

Keith