#### akbarza

##### Advanced Member level 4

Hi

I found the schematic(schematic1.pdf) in a file that I downloaded of net. but unfortunately, I deleted it and now I don't have access to it. The schematic is a capacitor feedback model of a circuit. I drew the schematic with ltspice software.

The problems are related to obtaining transfer function of it:

First method (node analysis): if I write node analysis in Vout then (I use Cl instead of Cload ):

Vout/vin = (Rout.cf.s -A.Rout)/(1+(cf+cl).Rout.s)

If I write node analysis in vin ( I assume input current to opamp is neglectable) then:

Vout/Vin = (1+(cf+cin).Rin.s) / (Rin.cf.s)

Obviously, two above TF's are not compatible.

In other side, we have three capacitor that one of them is not independent, so the denominator must be of order 2 namely we must have in denominator something like 1+b0.s +b1.s^2 .

But in above I had denominator of order 1.

What is my mistake?

Second method (zero value time constants or ZVT):

I uploaded file 7042.pdf (in this file the method ZVT has been described to obtain transfer function (TF)).

Problems:

I found the schematic(schematic1.pdf) in a file that I downloaded of net. but unfortunately, I deleted it and now I don't have access to it. The schematic is a capacitor feedback model of a circuit. I drew the schematic with ltspice software.

The problems are related to obtaining transfer function of it:

First method (node analysis): if I write node analysis in Vout then (I use Cl instead of Cload ):

Vout/vin = (Rout.cf.s -A.Rout)/(1+(cf+cl).Rout.s)

If I write node analysis in vin ( I assume input current to opamp is neglectable) then:

Vout/Vin = (1+(cf+cin).Rin.s) / (Rin.cf.s)

Obviously, two above TF's are not compatible.

In other side, we have three capacitor that one of them is not independent, so the denominator must be of order 2 namely we must have in denominator something like 1+b0.s +b1.s^2 .

But in above I had denominator of order 1.

What is my mistake?

Second method (zero value time constants or ZVT):

I uploaded file 7042.pdf (in this file the method ZVT has been described to obtain transfer function (TF)).

Problems:

- First in page 7/47, the word
__independen__t has been written. Can you explain about its meaning? - I wanted to obtain Tf with ZVT method.
- With a TF of the form H = (a0+a1.s+a2.s^2) / (1+b0.s+b1.s^2).
- To obtain a1 according page 23/47 a1 equals with sum of some Ti.Hi terms( I am writing this text in word and then will copy/paste to site, so I changed notation)
- Where Ti is characteristic time of i'th capacitor and it's value is ci.Ri. where Ri is total resistance seen from ci when for j<>i then cj=0. ( I used <> for is not the same).
- For Hi, in page 22/47 is written Hi=H (when ci tends to infinite and for j<>i cj=0).
- For cin capacitor in node Vin: Hi= H (when cin tends to infinite and cf , cl tend to zero)
- As cin-->infinite then 1/(cin.s) =0, so vin=0.
- As cf,cl -->0 then 1/(cf.s)-->inf , 1/(cl.s)-->inf. so capacitor feedback branch is broken and circuit is as vin-opamp(-A)-Rout-vout, so vin=0 leads to vout=0.
- Now Hi,cin= vout /vin = 0/0, what can I do now?
- Is true what I wrote in above lines? Guide me plz.

- Excuse me for
**lengthy**text. - Thanks