[SOLVED] calculation of input and output impedance using feedback technique

suppose any Voltage current feedback network is implemented and we have calculated its Aβ (loop gain) then how will i found its input /output impedance from this expression . Figure is given below for a reference


I have calculated Aβ as -gm1 ro1 {Rs gm / (1+ gm Rs)}

Have you looked at Blackman's impedance formula already? Otherwise just connect a test current source where A1 is and measure the voltage at the gate?

Rahul Sharma said:

suppose any Voltage current feedback network is implemented and we have calculated its Aβ (loop gain) then how will i found its input /output impedance from this expression . Figure is given below for a reference
I have calculated Aβ as -gm1 ro1 {Rs gm / (1+ gm Rs)}

Click to expand...

I can confirm your loop gain expression.
Here is my calculation:

Open loop gain: Ao=-gm1*ro1 (ro1 is the output resistance of M1).
Feedback factor (source follower M2): β=gm2*Rs/(1+gm2*Rs).
Loop gain: LG=Ao*β.
Output impedance: r,out=ro1/(1+LG)
Input impedance: Rs/(1+LG)

Correction: In the 3rd line from the bottom please read LG= -(Ao*β) because Ao is defined as negative.

LvW said:

I can confirm your loop gain expression.
Here is my calculation:

Open loop gain: Ao=-gm1*ro1 (ro1 is the output resistance of M1).
Feedback factor (source follower M2): β=gm2*Rs/(1+gm2*Rs).
Loop gain: LG=Ao*β.
Output impedance: r,out=ro1/(1+LG)
Input impedance: Rs/(1+LG)

Click to expand...

Shouldn't β involve ro2? And subsequently, shouldn't zin and zout also involve ro2?

The Electrician said:

Shouldn't β involve ro2? And subsequently, shouldn't zin and zout also involve ro2?

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Yes - ro2 was neglected for finding the feedback factor. (Also the transistors input impedances have been neglected).
But I think, this is a "normal" process since in electronics no formula is correct by 100%.
For example, it is common practice to also neglect all unwanted feedback effects (y12).
And - with respect to tolerances of all parameters - it makes no sense to include all effects and tiny parameters.

These are mosfets--unless the operating frequency is at radio frequencies, neglecting the input impedances makes perfect sense. At frequencies below RF, the gate impedances of mosfets are many orders of magnitude greater than the other circuit impedances. The impedance ro of a mosfet is not as many orders of magnitude different from the other typical circuit impedances. You didn't neglect ro1; why neglect ro2?

A good reason for not neglecting ro2 can be seen by considering a boundary case: if gm2 goes to zero, the expression for zin, Rs/(1+LG), becomes just Rs. This can only be the value of zin if the impedance at the gate of M1 is zero, but in reality that impedance would be the gate impedance of a mosfet, a value much larger than zero. This is not a small error.

If ro2 is taken into account, when gm2 goes to zero, zin becomes Rs + ro2 because then the impedance at the gate of M1 is ro2; M2 becomes just a resistor ro2 to AC ground.

An interesting thing to do for this circuit would be to substitute some actual values for a real mosfet and see what the error is when neglecting ro (1/y22), the mosfet input impedance (1/y11) and y12.

Yes - in principle, I agree to your considerations.
However, one should not forget what "neglect" means: It is always required to have a sum of several (at least two) values in order to see if it is acceptable to "forget" one or some values within this sum.
And this, for example, applies to ro2. At the output of M2 we have the sum of two conductances: 1/ro2 and the ideal source conductance (zero) of the current source.
As far as ro1 is concerned, one should consider the way how ro1 appears in the equation. I think, it appears in parallel to Rs (that means: The sum of both conductances).
And therefore, I think ro1 can be neglected.

LvW said:

Yes - in principle, I agree to your considerations.
However, one should not forget what "neglect" means: It is always required to have a sum of several (at least two) values in order to see if it is acceptable to "forget" one or some values within this sum.
And this, for example, applies to ro2. At the output of M2 we have the sum of two conductances: 1/ro2 and the ideal source conductance (zero) of the current source.
As far as ro1 is concerned, one should consider the way how ro1 appears in the equation. I think, it appears in parallel to Rs (that means: The sum of both conductances).
And therefore, I think ro1 can be neglected.

Click to expand...

Do you mean ro2 in the red part? ro1 isn't in parallel to Rs, and you didn't neglect it.

The Electrician said:

Do you mean ro2 in the red part? ro1 isn't in parallel to Rs, and you didn't neglect it.

Click to expand...

Thank you and sorry - yes, you are correct. I have mixed up M1 and M2. Without looking at the drawing I automatically have assumed that M1 is the most left and m2 the most right transistor.