# Op-amp circuit analysis using a transfer function

1. May 11, 2014

### evol_w10lv

1. The problem statement, all variables and given/known data
I have got transfer functions W(s) and Wk(s), where Wk(s) is correction transfer function.

So I calculate W(s) and Wk(s) in series.
Magnitude graph before correction:

Magnitude graph after correction:

The task is to make whole circuit and simulate it.
2. Relevant equations

3. The attempt at a solution
First of all, I tried to make it by parts:

And am I on the right way with otherones?

2. May 11, 2014

### rude man

first, you should cancel the identical pole & zero at s = -10.
then, the second ckt is incorrect. what is the high freq. gain of (0.01s+1)/(0.017s+1)? What components determine the high-freq. gain?
finally, suppose you have an inverter with gain = -Zf/Zi. Equate Zf/Zi to k/s to find your Zi and Zf components.
.

3. May 12, 2014

### evol_w10lv

It seems to me, I had a missunderstanding about the task. And there is mistake in the correction TF Wk(s), I guess.
I simulated W(s) - red colour, Wk(s) -green colour, W(s)*Wk(s) - blue colour.
Bode plot:

http://www.bildites.lv/images/5ltl503z567e84sgk3pk.png

The problem is gain of Wk(s) TF. After corner frequency W1, I expect the graphic like it is standart W(s) (red), but it isn't, because there is unexpected gain in Wk(s).

Here are calculations, how I get Wk(s) and simulation:

And the problem is not because 1/60 = 0.0166666.. = ~ 0.017
There's something wrong with gain. What can be reason for wrong result?

4. May 12, 2014

### rude man

I see nothing wrong with this. If Wk(s) = what you say, then your implementation is correct. The low freq. gain is 1.0, the high freq. gain is 1.47 and the time constants all check out.

5. May 12, 2014

### evol_w10lv

I calculated Wk(s) by myself, it wasn't given.
I have got standart W(s) and I have to implement Wk(s) to get graphic like this (red is correction):

But in the bode plot (in my previous post), after last corner frequency the new graphic isn't like the standart W(s), because there is this small gain. Maybe I don't understand something about it, but it suggests that there's mistake in my Wk(s) TF, because the high frequency gain is 1.47, but I want the gain to be 1.0 to get the same graphic after that corner frequency. What could be wrong there with Wk(s) in this case?

Corner frequencies: 1, 4, 10 60 rad/s were suggested by teacher.

6. May 12, 2014

### rude man

Well, you're confusing me a lot.

OK, if you want to correct per your latest frequency response (the bottom graph), you need to eliminate one pole and one zero. So figure out what your W_k(s) should be to cancel those. Your Bode plot (red) tells you what to do.

7. May 14, 2014