You have already asked this question in Homework Help. Multiple posts are considered bad form, and you still need to show us your work because we don't do homework for you. You need to show us some effort towards a solution.now i have this equation
g(s)=4/(s^2+3*s+4)
and need to Design the equivalent electric circuit (using op-amps) describing open loop transfer function of this process G(s).
assuming ideal op-amp
I'm not sure that is a viable strategy. 1st order realizations have a pole on the real axis which this transfer function does not.I will not do homework for you, either. But I will offer an explanation of how to do this process: First, factor that polynomial term into a product of first order terms, then create the circuit with the response of each of those terms, snf then put the circuits in series. If you are not able to do that then you should have paid better attention to the lecture during class.
OK, then second order terms, with a resistor and either an inductor or a capacitor. We used that method back in my feedback systems class in 1972. I may have forgotten some of the details since then.I'm not sure that is a viable strategy. 1st order realizations have a pole on the real axis which this transfer function does not.
now because of covid-19 , the all lesson being self study and i can't understand this part.I will not do homework for you, either. But I will offer an explanation of how to do this process: First, factor that polynomial term into a product of first order terms, then create the circuit with the response of each of those terms, snf then put the circuits in series. If you are not able to do that then you should have paid better attention to the lecture during class.
Quadratic equations with real coefficients can have roots that areOK, then second order terms, with a resistor and either an inductor or a capacitor. We used that method back in my feedback systems class in 1972. I may have forgotten some of the details since then.
Hello AGAINnow i have this equation
g(s)=4/(s^2+3*s+4)
and need to Design the equivalent electric circuit (using op-amps) describing open loop transfer function of this process G(s).
assuming ideal op-amp
I'll be making book on the non-return of the TS. We didn't conform to his world view.Hello AGAIN
So you are saying that you have absolutely no idea whatsoever how to do this?
What have you been taught so far...anything related to this at least?
I defined a process, and without anybody factoring the expressson to see if it would work for that one, the attack hit hard and heavy. BUT not one person tried the evaluation to see if it would work.I'll be making book on the non-return of the TS. We didn't conform to his world view.
Since getting face time with an instructor could be problematical, maybe we could be bit bit more Socratic, and answer questions with one or more. Or as Yoda might say: "Question relentlessly we should".
Not quite true. Factoring the denominator is a good thing, and I did that. The factors are a complex conjugate pair. Knowing the pole locations as α ± jβ, there are any number of 2nd order circuits than can be implemented. This particular pair of poles is not on the unit circle, or the Chebyshev Ellipse, and it does not meet the criteria for a 2nd order Bessel, which still leaves many other biquad realizations. The only part you missed was not being able to implement complex poles as independent circuits. No biggie!I defined a process, and without anybody factoring the expressson to see if it would work for that one, the attack hit hard and heavy. BUT not one person tried the evaluation to see if it would work.
Given that it appears to have been a homework assignment my presumption was that the problem would have a solution. I only had one instructor at one college who would give non-solvable homework. That did teach us to examine the data of problems to verify that an answer could exist. Of course it may also be that the function is copied incorrectly.Not quite true. Factoring the denominator is a good thing, and I did that. The factors are a complex conjugate pair. Knowing the pole locations as α ± jβ, there are any number of 2nd order circuits than can be implemented. This particular pair of poles is not on the unit circle, or the Chebyshev Ellipse, and it does not meet the criteria for a 2nd order Bessel, which still leaves many other biquad realizations. The only part you missed was not being able to implement complex poles as independent circuits. No biggie!
The transfer function is in a standard form with ω₀ = 2, and Q= 2/3. So the implementation follows from those parameters, or you can get them from the pole locations. The existence of a solution was never even a question.Given that it appears to have been a homework assignment my presumption was that the problem would have a solution. I only had one instructor at one college who would give non-solvable homework. That did teach us to examine the data of problems to verify that an answer could exist. Of course it may also be that the function is copied incorrectly.
Hi,Given that it appears to have been a homework assignment my presumption was that the problem would have a solution. I only had one instructor at one college who would give non-solvable homework. That did teach us to examine the data of problems to verify that an answer could exist. Of course it may also be that the function is copied incorrectly.
There are well known and common implementations for 2nd order transfer functions with a complex conjugate pair of poles including Tow Thomas, Biquad, Sallen-Key and others. The implementations follow directly from the complex poles, or from the parameters ω₀. and Q, which are simple functions of the coefficients.Hi,
Sorry but i found it to be unfactorable too except in the form of complex poles.
I dont think there is a way to resolve this such that we can obtain two first order realizations. The reason for this is because complex poles always come from 2nd degree expressions which come only from circuits that can not be directly cascaded.
We can look at this though and see if we can find some augmentation that would allow us to proceed in that manner just with a slight modification. I have a feeling though that we might end up with the state space solution once again.
Yes i realize that, but he was looking for a piecewise circuit solution where we find part of the total solution and then another part, then combine them with simple interconnections. This could come from factoring in the completely real case, but i dont think there is a solution for the complex case. Of course there is a solution for the entire problem taken at once without trying to factor the transfer function, but the implementation goal was different for this approach.There are well known and common implementations for 2nd order transfer functions with a complex conjugate pair of poles including Tow Thomas, Biquad, Sallen-Key and others. The implementations follow directly from the complex poles, or from the parameters ω₀. and Q, which are simple functions of the coefficients.
Yes there is. It is called the Tow Thomas filter and it works by rewriting the transfer function to show the use of two integrators, exactly as you would do it if you were programming an analog computer to solve the problem. Just like we did 50 years ago.Yes i realize that, but he was looking for a piecewise circuit solution where we find part of the total solution and then another part, then combine them with simple interconnections. This could come from factoring in the completely real case, but i dont think there is a solution for the complex case. Of course there is a solution for the entire problem taken at once without trying to factor the transfer function, but the implementation goal was different for this approach.
The more general method is the state space, which TT is just one case of, and if you notice i mentioned that and that was the original method i posted in my first post in this thread.Yes there is. It is called the Tow Thomas filter and it works by rewriting the transfer function to show the use of two integrators, exactly as you would do it if you were programming an analog computer to solve the problem. Just like we did 50 years ago.
Here is a link
https://en.wikipedia.org/wiki/Electronic_filter_topology#Biquad_filter
No we are clear. I'm not that familiar wit the state space method. I guess I read your post too fast.The more general method is the state space, which TT is just one case of, and if you notice i mentioned that and that was the original method i posted in my first post in this thread.
But that's not the same as factoring, creating two completely separate circuits, then connecting them in cascade and winding up with the transfer function you were after all along.
I thought you were already familiar with this as you seemed to understand the difference in your previous posts.
To show the difference, simply start with a denominator that *is* factorable into real factors, create two first order filters, then simply tie them together in cascade without any other connections including no feedback. Compare that to TT and see the difference. However we both know that does not work with a factoring that turns out to be complex.
Did i make this clear yet? If not i guess i could show a circuit or two.
OK, there is a solution, probably I should have qualified that as a simple, or easy, or convenient solution. Typically homework problems get more complicated as one advances down the listing.The transfer function is in a standard form with ω₀ = 2, and Q= 2/3. So the implementation follows from those parameters, or you can get them from the pole locations. The existence of a solution was never even a question.