# Differential Input Resistance - MOSFET Diff Amp

1. May 17, 2013

### 00iCon

So I've been lurking here for a while now, always checking other's solutions but this one has just got me stumped.

Skill level: 3rd year electronic circuit design (about the level expected in Sedra & Smith from chapter 3 onwards)

1. The problem statement, all variables and given/known data

For the MOSFET differential amplifier in the above figure(check attachments), draw the small
signal model. Determine the differential input resistance (Rid), output resistance (Ro) and
gain (Ad) of the circuit when v_1 = v_d/2 and v_2 = -v_d/2.

2. Relevant equations

For a BJT:
R_id = 2 r_pi

3. The attempt at a solution

There's only one bit that I'm trying to wrap my head around. The differential input resistance. As a MOSFET there's only a capacitance between the gate and the source. Despite whatever resistance we put in, the capacitance causes the entire v_1 to be at the gate, since no current flows out of the gate.

Using the formula for a BJT's R_id but substituting r_pi to be an open circuit (R= infinite) is R_id infinite? Is it a trick question? (The bit that has me hesitating is the lecturer underlined the word differential).

(attachments are my small signal model and the circuit from the question)

#### Attached Files:

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• ###### MOSFET differential amp.jpg
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2. May 17, 2013

### rude man

Well, Rid = infinity, that you can bank on.

V_d is undefined.

Are M3 and M4 p-channel?

I don't do small-signal models but I could determine Ad and Ro if I knew what Vd was.

3. May 18, 2013

### 00iCon

Thanks for the confirmation of what I suspected. That's all I needed. The other stuff was covered in lectures ant tutes. V_d was not given, I'm pretty sure we have to do it in terms of V_d.