Engineering Diff gain of a push pull degenerated differential pair

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The discussion focuses on calculating the small signal differential gain of a push-pull degenerated differential pair circuit. The user has approached the problem by analyzing the core circuit separately and applying the half-circuit technique, leading to a derived transfer function. However, they encounter difficulties incorporating the push-pull stage into their analysis, particularly regarding the role of output capacitors and current cancellation in the output stage. Insights from previous discussions highlight the importance of balancing the circuit to avoid amplifying uncontrolled parameters, suggesting that adjustments in the design are necessary for achieving the desired output. The conversation emphasizes the need for careful consideration of circuit symmetry and the effects of asymmetrical components on overall performance.
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Homework Statement
Find the differential gain
Relevant Equations
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Hello; (this is going to be lengthy post)

So im trying to find the small signal differential gain of this circuit

punjabi.webp


The input is at the 2 NMOS's above the degeneration resistor and the output is where the capacitors are hanging (excuse that I didnt label them, the program where I drew the circuit doesnt have that option).
My approach was divide and conquer; I first wanted to look only at the "core" part of the circuit (excluding the Push-pull stage) and find the diff. gain of that part and than combine it all together;

This is the core part of the circuit
hehexd.webp


You notice that this has external biasing for the bottom two transistors that create a current mirror. This is not included in the original circuit since I wanted to preserve readibilty; but basically im biasing with an ideal current source with a diode connected NMOS. An equivalent, but simpler circuit is this
1750549275038.webp


The bottom two NMOS transistors are as ideal current sources. The reason I prefer the core circuit to look like this is since something rather similar can be found in the book of Razhavi (design of analog CMOS circuits) and I have been able to understand how he tackles problems similar to this.
My simulation of the circuit has shown that I have perfecty symmetry so I opted to use the half circuit technique described in the Razhavi book. I just look at one side of the circuit and calculate the gain; the total gain is just that times 2.

So thats what I did; The top diode connected PMOS active load will act as an resistor with an value 1/gm (we neglect gds since it is significantly smaller) the current source will go to a virtual ground (explained in Razhavi) and the degeneration resistor will be "split" to Rs/2 on both sides.

Than we do the small signal analysis (if needed I can post the circuit diagramm) and I get the following result;

$$ \frac{Vout}{Vin} = \frac{-gm_N}{gm_P(1+\frac{gm_NRS}{2})} $$

where ## gm_N ## is the gm of the NMOS in the middle and ## gm_P ## the transcondutance of the diode connected PMOS

Now this is where I get stuck; I cannot incorporate the push-pullstage. I am not sure if I should draw the push pull stage seperatly and simplify as much as possible and add to my existing core circuit or do I have to do it in one swoop so to say?

Any insights?

Also what do you think of my plan to do the small signal analysis? And how is this looking so far.

Excuse the lengthy post and thanks in advance!
 
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arhzz said:
Now this is where I get stuck; I cannot incorporate the push-pullstage.
The use of an output capacitor suggests you are building a low-pass filter or an integrator. Why does the value of C not show up in the transfer function?
arhzz said:
Any insights?
In an earlier thread, we discussed why the currents in each output stage exactly cancelled, appearing to be only nanoamps in an output load resistor.

By crossing over the mirror circuits above the input resistor, the circuit came to life and produced the expected output current and voltage. That cross-over is not implemented in the circuit you post here, so there will be no differential output current to integrate into the load capacitor.

I believe the book you are using is: "Design Of Analog CMOS Integrated Circuits". Behzad Razavi. McGraw Hill. 2003.

arhzz said:
Also what do you think of my plan to do the small signal analysis?
That is a sensible approach, however the cross-connection necessary between the sides will require a negative sign be introduced into part of the one-sided analysis.
 
Baluncore said:
The use of an output capacitor suggests you are building a low-pass filter or an integrator. Why does the value of C not show up in the transfer function?

In an earlier thread, we discussed why the currents in each output stage exactly cancelled, appearing to be only nanoamps in an output load resistor.

By crossing over the mirror circuits above the input resistor, the circuit came to life and produced the expected output current and voltage. That cross-over is not implemented in the circuit you post here, so there will be no differential output current to integrate into the load capacitor.

I believe the book you are using is: "Design Of Analog CMOS Integrated Circuits". Behzad Razavi. McGraw Hill. 2003.


That is a sensible approach, however the cross-connection necessary between the sides will require a negative sign be introduced into part of the one-sided analysis.
For the C; I first tried finding the transfer function without the push pull stage and since the caps are "hanging" at the output of the push pull stage I neglected them.

Now for the circuit itself; (I find it cool you remember my earlier post). I actually never crossed the mirror currents, the solution was adjusting the W/L ratio of the mirror currents in the push pull stage and implementing a degeneration resistor for the DC simulation.

In fact I have simulated the result I am looking for (the differential pair with push-pull stage and caps)
1750590780465.webp

Here it is for a certain value of C and Ibias.

So the circuit I posted (now with NMOS at the bottom instead of PMOS) is the one I am looking for.
 
arhzz said:
So im trying to find the small signal differential gain of this circuit

punjabi.webp
Circuits are designed to be balanced, so parameters that cannot be controlled, such as thermal effects, will largely cancel. Your circuit appears to amplify the uncontrolled parameters by unbalancing the channel parameters of the MOSFETs you use.

Where have you ever seen a circuit like the one you present, being analysed or operated ?
 
Baluncore said:
Circuits are designed to be balanced, so parameters that cannot be controlled, such as thermal effects, will largely cancel. Your circuit appears to amplify the uncontrolled parameters by unbalancing the channel parameters of the MOSFETs you use.

Where have you ever seen a circuit like the one you present, being analysed or operated ?
To be honest nowhere, this is a task I was given for my bachelor thesis.
 
The output of a transconductance amplifier will be the difference of two almost identical currents in the circuit output.

There will be an amplifier bias current, Iabc . The differential input voltage will cause a current, i = Vin / Rin , to flow through the input resistor.
The differential input stage will then offset Iabc by +i and -i, giving,
Iabc+i on one side, and Iabc-i on the other.

There are two ways to perform the subtraction that makes the output independent of Iabc.

1. Subtraction from Iabc; by using a wide, multiple output Iabc mirror.
giving outputs of;
Iabc - Iabc+i = -i .
Iabc - Iabc-i = +i .
See No-Cross circuit below.

2. Subtraction of the opposite side of the input, by using a crossover,
giving outputs of;
Iabc+i - Iabc-i = +2i ;
Iabc-i - Iabc+i = -2i ;
See Cross-Over circuit below.

By making the MOSFETs asymmetrical, you thought you had fixed the problem. But you are now taking Iabc+i,
then multiplying it by a MOSFET mirror asymmetry, A ;
before subtracting the original.
Iout = A*(Iabc+i) - (Iabc+i) = (A-1)*Iabc + (A-1)*i .
That has NOT eliminated Iabc from the outputs.
That is the problem with your crooked circuit at the moment.

If all the MOSFETs were identical, then A = 1, and Iout = 0.
That was your original thread's problem, perfect cancellation = 0.

1. No-Cross.
No-Cross.webp


2. Cross-Over.
Cross-over.webp
 
Okay I will look into it, thanks!
 

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