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bharat

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loop gain of two stage of opamp
Aug 24^th, 2006, 11:20pm

For conventional two stage opamp
First stage is standard active current mirror as load, diff pair and tail current source
Second stage common source amplifier

Now for the stability analysis, I need to draw the bode's plot were X axis is logarithmic frequency and Y axis is MOD of loop gain [A(s)f(s)], where A(s) is open loop gain and f(s) is feedback factor.

I am not seeing any feedback from output to input, hence f(s) is zero or loop gain is zero.

My question statement is: if there is no visible output to input connection, how can I draw the bode's plot and arrive on the conclusion that there are two poles before unity gain frequency and one needs to connect miller capacitance between first stage to second stage to make it single pole before unity gain frequency.

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aaron_do Senior Fellow Offline Posts: 1398	Re: loop gain of two stage of opamp Reply #1 - Aug 25^th, 2006, 1:35am you should be plotting the open loop gain [A(s)]. You want to see the output phase and make sure it isn't 180 from input where the gain is more than unity. If gain > 1 when the phase is inverse then when you connect the feedback the amp will oscillate.
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sheldon

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Re: loop gain of two stage of opamp
Reply #2 - Aug 25^th, 2006, 2:21am

bharat,

It is a little hard to understand what is happening from your description,
could you post a copy of your testbench.

Aaron,

In general it is better to work with the loop gain whentrying to understand
stability. Putting an amplifier inside of a loop can change its characteristics as
illustrated in Ken's book.

Best Regards,

Sheldon

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aamar

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Germany

Re: loop gain of two stage of opamp
Reply #3 - Aug 25^th, 2006, 6:34am

Hallo,

Look, if you want to study the stability of your opamp you should not consider the feedback (at least at first), the opamp's stability should be tested alone. This means, you have to plot the open loop gain A(s) and the phase and using the calculator you can automatically calculate the GainBW product and your phase margin which should be at least 60 degree or more (also you can find these values form the Bode plots).

How can you know that there are two poles before the unity gain? the answer is using both your gain and phase diagram and it is more clear in the phase diagram where you will find your phase -45 from its initial state and -225 degrees. and then you will decide that you have to split your poles so as your gain will reach the unity level before the second pole and that's why you will use the compensation (miller) capacitance.

Second, the stability of your FB circuit depends on the transfer function of the circuit (amplifier) and it would be A(s)/(1+A(s)F(s)) and not the loop gain alone.

But in case of you want to plot the A(s)f(s) alone for any reason, asuming your FB circuit is frequency dependent, you can plot the A(s) alone by simulating the open loop amplifier alone, and simulating your FB circuit also in the same frequency range and in the same schematic. Then plot the 2 bode plots and again with the calculator you can plot their product.

in case of a resistive FB (frequency independent) you can plot the Bode plot of the open loop db20(A(s)) and add to it the db20(R) of the resistance and this would be the loop gain.

I hope it would help,

Best regards,

aamar

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bharat

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Re: loop gain of two stage of opamp
Reply #4 - Aug 27^th, 2006, 11:11pm

sheldon wrote on Aug 25^th, 2006, 2:21am:

bharat,

� It is a little hard to understand what is happening from your description,
could you post a copy of your testbench.

Aaron,

� In general it is better to work with the loop gain whentrying to understand
stability. Putting an amplifier inside of a loop can change its characteristics as
illustrated in Ken's book.

� �Best Regards,

Sheldon

I am partially answering the question what I have asked. It may help, to make my question more clear. Though there is no physical connection from output to input OR output to input is not shorted, but at higher frequencies the parasitic capacitances make virtual connection from output to input. For the analysis purpose, we take the worst case feedback factor, which is UNITY. So the loop gain A(s)f(s) turns out to be A(s) only
[f(s) = 1] and which is nothing but open loop gain.

Sheldon,
Does this explaination make sense? Therefore in text book analysis though we see openloop gain but due to specific value of f(s) it is equal to closed loop gain. I am not able to insert my testbench as image. Cry

thanks
-Bharat

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uncle_ezra

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Re: loop gain of two stage of opamp
Reply #5 - Aug 28^th, 2006, 12:34am

Testing using unity gain feedback is a safe design methodology. However this come at the expense of higher power consumption since the feedback factor is usually <1, so you are actually overdesigning by testing your circuit in unity feedback configuration. So if your feedback factor is fixed you can simulate the loop gain and tune your circuit accordingly. Just use the stb analysis and use iprobe or cmdmprobe if differential, to break the loop.

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