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Finding the transfer function for same circuit under two different situaton

Jaikrishnan

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.

Parents Reply Children
  • in reply to Andrew Beckett

    Dear Andrew,

    i actually want to come up with a mathematical model, i mean the overall transfer function when there is switching. Not really simulation in Cadence. Simulations has been performed and now I want to verify with the calculations to see the matching between simulation and calculations. 

    It would be really helpful if you have some information on how to approach it.

    Thanks in advance

  • in reply to Jaikrishnan

    Dear Jaikrishman,

    I happened to have taken a couple of courses many years ago taught by two pioneers in the switching converter analysis effort. I think the methodology they proposed is appropriate for your circuit. Basically, Dr. Cuk and Dr. Middlebrook proposed a method to create a state-space model for a circuit that has two distinct state space relationships. In summary, the effort involves, as you have done, modeling the transfer function of each mode of operation separately, and then combining the two in a manner proportional to the time over which the circuit state exists in each of the two modes. Dr. Cuk PhD thesis proposes this and is followed on with a more concise paper by Dr. Middlebrook and Dr. Cuk in 1976 entitled "A general unified approach to modelling switching-converter power stages".

    I might suggest you refer to this paper, available from IEEE, for the details. However, the method is rather straightforward and you may be able to understand enough of it from my description to proceed.

    Shawn

  • in reply to ShawnLogan

    Thanks Shawn for the information

  • in reply to Jaikrishnan

    Dear Jaikrishman,

    Absolutely - I hope it provides enough information to get started with your analysis....sounds like an interesting study! Good luck!

    Shawn

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