# Differential amplifier

1. Jun 17, 2014

### etf

Hi!
Current sources Iss which are used for differential amplifier in photo c) are shown in photos a) and b). DC voltages VB1 and VB2 provide saturation for all MOSFETS. Calculate ratio of CMRR of differential amplifier with current source from image a) and CMRR of differential amplifier from image b). gm1, gm2, rds1 and rds2 are known.

So here I have to analyse two differential amplifiers:
1. I have to find CMRR1 for differential amplifier c) with current source a)
2. I have to find CMRR2 for differential amplifier c) with current source b)

Final result would be CMRR1/CMRR2. My question is, is there better approach in solving this problem? There would be a lot of work in previous steps. Is it possible, for example, to analyse differential amplifier c) with current source b) , calculate CMRR2 and use CMRR2 to calculate CMRR1 (putting gm2=0, rds2=∞ in CMRR2) ?

2. Jun 17, 2014

### rude man

It's instructive for you to start with circuit (a), compute CMRR, then repeat for circuit (b). You will gain insight into MOS diff amp design by doing that. It is not a lot of extra work.

3. Jun 17, 2014

### rude man

Actually, all you're asked to do is compute the ratio of CMRR's for current sinks (a) and (b). Which means don't spend a lot of time analyzing the differential input pair.

4. Jun 18, 2014

### The Electrician

You say that "gm1, gm2, rds1 and rds2 are known. " Does that mean that you have numerical values for them, or are you supposed to give symbolic answers?

Must you treat gm1 as different from gm2? And rds1 as different from rds2? It makes the answers more complicated if you do.

You will need to calculate the impedance of the two current sources, a) and b). Have you done that?

This problem's differential amplifier is not much different from the one in your other thread. Did you ever solve that one?

Can you assume that the characteristics of all the MOSFETs in the diff amp are the same?

5. Jun 18, 2014

### rude man

Question to you: how do changes in ISS affect the output for a single-ended output diff. amp. with an ISS "tail" which can vary with the CM input voltage?

Then, use your equivalent circuits for M1 and M2 to derive ∂ISS/∂V to (a) and (b) circuits, where V is the dc voltage at drain1 for (a) and drain2 for (b), then take the ratio. (a) is straight-forward. For (b) you get 2 simple equations in 2 unknowns: iSS and vd1. There are no significant complications in retaining separate gm1, gm2, rds1 and rds2. Note that I use lower case for variational and upper case for dc parameters.

BTW the differential-mode gain of this circuit → ∞, another reason not to get bogged down analyzing it. It's really a comparator, not an amplifier.

6. Jun 18, 2014

### etf

Are you sure that it wouldn't be a lot of work with separate analysis of diff. amp. with source a) and diff. amp. with source b) ? I already did analysis of one simillar diff. amp. (my previous thread) and there was a lot of work. This example is even more complicated.

I don't have numerical values so I have to give symbolic answers. I don't know how should I consider them :(

7. Jun 18, 2014

### etf

I didn't know this could be solved on that way. I will try to do it.

8. Jun 18, 2014

### rude man

As I said before, you should not be analyzing the entire amplifier. You should be looking only at the two I_SS networks, after understanding why.

9. Jun 18, 2014

### rude man

Good. This is a good exercise, showing you quantitatively that CM gain can depend on the type of "tail" chosen for your diff. amp. By "tail" I mean the networks (a) and (b).

10. Jun 18, 2014

### etf

I'm definitely not able to solve this problem on way you suggested me Could you please post solution? I would be very grateful :)

11. Jun 18, 2014

### rude man

We are no allowed to do that.

Draw a differential pair of MOSFETS, n-channel, with a resistor R1 in each drain going to +VDD. Connect the sources together and run a resistor R2 from the sources to -VDD.

Tie the two gates together and compute one of the drain voltages as you apply 0V, -1V and +1V respectively to the gates. What is the drain voltage in each case? (Assume same gm and Vth, and ignore rds (rds = infinite).)

Last edited: Jun 18, 2014
12. Jun 18, 2014

### etf

I know that it's prohibited by the rules of forum but I always gave my best in solving problems... You probably seen that, this is not first time you're helping me :)

13. Jun 18, 2014

### rude man

Respond to post 11.
You won't learn anything if you're handed the solution on a silver platter.