Differential Amplifier - Differential Mode

[EEM]

Hello, I am hoping someone could help me with part B of this problem. I am not sure of the effects the resistor would have on the differential output gain.
Also I have attached my solution to part A but I am uncertain if I derived it correctly.

Any help would be appreciated !

[T3sl4co1l]

b. A resistor between outputs acts in parallel with (Rc + Rc), so reduces gain by that amount.  No effect on CM.

Tim

[EEM]

Thanks Tim !

I've attached my proof for b. Does this look OK ?
Also, I thought the added resistor would affect Vo1, so why would there be no effect on CM gain ?

[Marco]

b. A resistor between outputs acts in parallel with (Rc + Rc), so reduces gain by that amount.  No effect on CM.

With common mode gain they mean the gain for a single ended output (not the differential gain with transistor mismatch as is common).  Because of Ree this will change.

[T3sl4co1l]

Hmm, it should be 3, not 4.

What is the definition of differential output voltage?  Common mode?

Tim

[TimFox]

delta[Vout(diff)] = delta [Vout(1) - Vout(2)]
delta[Vout(cm)] = (1/2) x delta[(Vout1 + Vout2)]

[LvW]

I've attached my proof for b. Does this look OK ?

No - it doesn`t.
You have forgotten that the third (new) resistor is not at signal ground at one leg.