Instrumentation Amplifier question

[cyeokpeng]

Hi,

Just a little question.
The question wants me to obtain an expression for v0 as a function of v1, v2 and vcm, and show how the commom mode signal vcm can be canceled from the output by a proper adjustment of one of the resistors, R3, R4 or R5.

To find v0, I have to apply the theory of superposition.

Output voltage due to v2 alone (v1=0, vcm=0) is
--> The voltage at the output of the lower op amp is (-R4/R3)v2
--> The voltage at the output of the upper op amp is -(R2/R5)*voltage at
the output of the lower op amp.

My question is: Why is R1 not considered in the closed loop voltage gain of
the upper op amp?

Thanks

 

[s_a]

Because in the case of V1 = Vcm = 0, there is no potential difference across r1, hence no current through it. So whatever the value of r1, no current flows through it, so it has no effect on the output Vo.

Likewise, in the case of V2 = Vcm = 0, there is no potential difference across r3, r4 nor r5, so the output Vo will be independent of r3, r4 and r5.

 

[cyeokpeng]

Thanks,

Actually, I suspect that this is the answer.
When we consider the case V1 = Vcm = 0V,
the inverting input of the upper op amp is close to 0V due to virtual ground, so there is no pd across R1, so we can consider R1 as an open circuit right?
Similarly, for the case when V2 = Vcm = 0V.

Thanks for your help!