1. Circuit
I am analysing the stability for a ciruit in cadence by breaking the feedback loop. For stability analysis we have to find the Loop gain which is A(s)B, where B is beta factor
A(s) = Adc/((s/po)+1) - single pole opamp system
The above circuit has a loog gain
AB = ((Adc*Cf*Ron*po)s + Adc*po)/ (s^2(Ron*(Cin+Cf)) + s((Ron*po)*(Cin+Cf) + 1) + po)
This has 2 poles and 1 zero
P1 = -po
P2 = - 1/(Ron) *(Cin+Cf))
Z = - 1/(Ron) *Cf)
These equations were verified in matlab and the simulations were matching with the calculation now
2. Modified Circuit
Now the same circuit is modified with a switch added with the resistor Ron.
The switching wave is given below.
Now during ton, the Loop gain (AB) is same as before (including Ron, since the switch is closed). But during toff, the Ron is inneffective and the loop gain is changed as shown below
AB = (Adc*Cf*po)/ s(Cin+Cf)) + (Cin+Cf) *po
There is only one pole now
P = -po
But how can I comeup with an overall transfer function considering the swtching waveform. That means for ton, I should have the same transfer function as case1 and during toff should have the transfer function as case2. Also, the switching wave is periodic with period = ton + toff.
If someone know this how to model the transfer function, it will be helpful. Because, the stability analysis shows diferent results for both cases. I assume that this is due to the two different transfer functions.