Op-amp circuit analysis using a transfer function

In summary, the student is trying to correct a circuit with a gain that is not correct. They need to calculate the gain of the correction transfer function and eliminate one pole and one zero to get the correct response.
  • #1
evol_w10lv
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Homework Statement


I have got transfer functions W(s) and Wk(s), where Wk(s) is correction transfer function.
mze1n52gh4shducqu6ss.png

So I calculate W(s) and Wk(s) in series.
Magnitude graph before correction:
325tqtj68jjtfve4xax4.png

Magnitude graph after correction:
w0u4vt6j0l6dx7gy0zb.png


The task is to make whole circuit and simulate it.

Homework Equations



The Attempt at a Solution


First of all, I tried to make it by parts:
xhzrr15rampgus2k6yn.png

e9n83phl8ipa03rslcp.png

d8kevj1wadhpmwwf5b8.png


What about 70/s?
And am I on the right way with otherones?
 
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  • #2
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.
.
 
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  • #3
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:
3iecivaigdiobzfrpbfp.png


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
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.

What about your pole at the origin?
 
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  • #5
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):
ifvdxt4h1auq0tf5kz13.png

on5jgaoq27ucoh6ewnju.png


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
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.
 
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  • #7
Thanks for the hint. Task already done.
 

1. What is an op-amp and how does it work?

An operational amplifier, or op-amp, is an electronic circuit component that amplifies the difference between two input signals. It typically has a very high gain and is used in a variety of electronic applications. In simple terms, an op-amp works by taking the difference between its two input signals and multiplying it by a very large number, thus amplifying the output signal.

2. What is a transfer function and why is it important in op-amp circuit analysis?

A transfer function is a mathematical representation of the relationship between the input and output signals of an electronic circuit. In op-amp circuit analysis, the transfer function is used to analyze the behavior and performance of the circuit. It allows us to predict how the circuit will respond to different input signals and make adjustments as needed.

3. How do I calculate the transfer function for an op-amp circuit?

The transfer function for an op-amp circuit can be calculated by taking the ratio of the output signal to the input signal. This can be done using the circuit's circuit diagram and applying basic circuit analysis techniques, such as Kirchhoff's laws and Ohm's law. Alternatively, there are online tools and software available that can help calculate the transfer function for more complex op-amp circuits.

4. What are some common applications of op-amp circuits?

Op-amp circuits have a wide range of applications in electronics, including audio amplifiers, voltage regulators, filters, and oscillators. They are also commonly used in instrumentation and control systems, such as in sensors and feedback loops. In general, op-amp circuits are used whenever precise amplification, filtering, or signal processing is required.

5. What are some common challenges in op-amp circuit analysis?

One common challenge in op-amp circuit analysis is understanding the behavior of non-ideal op-amps, which may have limitations and imperfections that affect their performance. Another challenge is dealing with feedback in op-amp circuits, which can sometimes lead to instability or oscillations. Additionally, understanding the effects of noise, temperature, and other environmental factors on op-amp circuits can be important for accurate analysis and design.

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