Stability of the CSA amplifier

[tisheebird]

I can not see any ZD in the feedback circuit.
BETA= -1/Zf

By the way, starting with the closed loop transfer function showed by FvM in post #20, the circuit can not be unstable under no matter what circumstances. See below.

But when I have finding out the roots of the loop gain equation in post no#17, the roots are coming positive..I mean x=(-b±√(b^2-4ac))/2a.. b^2 is coming greater than 4ac term..What to do..??

 

[CataM]

But when I have finding out the roots of the loop gain equation in post no#17, the roots are coming positive..I mean x=(-b±√(b^2-4ac))/2a.. b^2 is coming greater than 4ac term..What to do..??

If b^2 > 4ac then Δ>0 which means your roots are real i.e. not complex BUT that does not mean they are positive.

 

[tisheebird]

If b^2 > 4ac then Δ>0 which means your roots are real i.e. not complex BUT that does not mean they are positive.

I agree with you...but (zeta) is greater than 1 which means system is overdamped...Right??

 

[CataM]

but (zeta) is greater than 1 which means system is overdamped...Right??

Yes. But in order to determine the dynamics of a system you have to watch the characteristic polynomial of the whole transfer function , not just the loop gain. In other words, you have to find ζ (zeta) watching the denominator of the whole transfer function Vout/Vin, not the loop gain.

 

[tisheebird]

Yes. But in order to determine the dynamics of a system you have to watch the characteristic polynomial of the whole transfer function , not just the loop gain. In other words, you have to find ζ (zeta) watching the denominator of the whole transfer function Vout/Vin, not the loop gain.

Thanks a lot...So you mean to say that I can only find ζ (zeta) watching the denominator of the whole transfer function Vout/Iin of my charge sensitive amplifier..??
So, I am still confused how to study the stability from the loop gain expression...Please could you tell me what next and how to study the stability from the loop gain expression (characteristic polynomial)..??

 

[CataM]

The absolute stability, which answers to the question : Is the whole system stable, YES or NOT ? is answered by looking to the denominator of the whole transfer function Vout/Vin showed in post #20 and talked about it in post #26. (the denominator of a transfer function is called the characteristic polynomial)

The relative stability of a system, which answers to the question: How stable is my system, what margins does it have, how much can I increase the gain without making it unstable etc... ? is answered by looking to the loop gain (Open loop gain * feedback).

Your system as already said in post #26, can not be unstable.

 

[FvM]

I didn't check your calculation, but apparently you have calculated that the close loop transfer function has only real poles when putting in reasonable circuit parameters. This answers the question about stability, what do you want else?

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Your system as already said in post #26, can not be unstable.

That's the case if the circuit has no additional poles. A real amplifier will become third order due to additional cascode poles, so it is at least potentially unstable. But it won't ever happen for the assumed component values.

 

[tisheebird]

Thanks a lot... Can you please factor this expression or tell me how to do factorization for this term...

s^2(RfCfro3C2+RfCdro3C2) + s(gm1ro3RfCf+ RfCf+ RfCd +ro3C2) +gm1ro3...

I am trying to get this in a form of (1+sw/wo) (1+sw/w1)...

 

[CataM]

factor this expression or tell me how to do factorization for this term...

s^2(RfCfro3C2+RfCdro3C2) + s(gm1ro3RfCf+ RfCf+ RfCd +ro3C2) +gm1ro3...

I am trying to get this in a form of (1+sw/wo) (1+sw/w1)...

Having only letters is impossible to know if b^2-4a*c is greater than 0 or not i.e. you will have real solutions or complex ones.

That could actually be a design constraint in order to design accordingly to what you really want.

 

[tisheebird]

Could anyone of you tell me how to calculate the DC offset voltage of this charge sensitive amplifier using folded cascode design..???

 

[Dominik Przyborowski]

The amplifier has not a diff pair, so you cannot talk about offset, but dc op point only (output dc level). The dc voltage at output is the same as input dc level (if feedback current is nil) and is equal to gate-source voltage of input transistor (related to a proper rail).