# Designing a Circuit from a Transfer Function

#### SyntaxErrors

Joined Dec 3, 2015
2
So I was working on an Assignment where my transfer function of a LTI circuit is H(s) = Vout(s)/Vin(s) = (s+4) / ((s+1)^2 * (s+2) * (s+3))

I would like some clarification on a few parts.

http://i.imgur.com/Uv6KkXn.jpg

in part b) To get the step response we bring Vin(s) to the other side of the function then find the inverse laplace as Vin(s) = 1/s to get our step response?
part d) how do I get started on tackling this problem?

#### MrAl

Joined Jun 17, 2014
10,587
Hi,

Yes the unit step is 1/s, and that is convolved with the transfer function.

What have you done up to this point, like are you allowed to use op amps?
Have you used any types of passive filters yet?

For example, could you design a circuit from:
Vout/Vin=1/(s+1)

One way to design the circuit is to first discover how many integrations are required. Do you know how to find the integrations required, and if so, how to arrange them in order to get the desired response?

Last edited:

#### SyntaxErrors

Joined Dec 3, 2015
2
We are allowed to use op-amps and any LTI circuit elements.

I have not used any passive filters yet, we learned it in one day (Bode plots). At this point, we (group) are putting over cascading op amps.

#### Cyrenaica —

Joined Jun 7, 2015
17
So I was working on an Assignment where my transfer function of a LTI circuit is H(s) = Vout(s)/Vin(s) = (s+4) / ((s+1)^2 * (s+2) * (s+3))

I would like some clarification on a few parts.

http://i.imgur.com/Uv6KkXn.jpg

in part b) To get the step response we bring Vin(s) to the other side of the function then find the inverse laplace as Vin(s) = 1/s to get our step response?
part d) how do I get started on tackling this problem?
1) About b). I didn't understand your on-forum-statement fully, but for in-picture-statement, I think that all what you need here is to expand given function in Mathcad and then put it to Matlab. In Matlab you should build step responce plot. It's easy.
2) About d). When you will expand your given (initial) function in Mathcad, you should "separate" your derived fraction (for making and electrical design), for few elementary fractions. By multiplying them together you of course can obtain the initial function. Sorry, broken English. For example, you have transfer function: s/[(2+s)*(s^2)]. So, there are three dynamic blocks, which your system consist of: s (or s/1), 1/(2+s) and 1/(s^2). So just put blocks together! Watch my pictures for realisation of regulators — it might help.
Sorry, broken English.

#### Cyrenaica —

Joined Jun 7, 2015
17
Here are some results.

#### MrAl

Joined Jun 17, 2014
10,587
We are allowed to use op-amps and any LTI circuit elements.

I have not used any passive filters yet, we learned it in one day (Bode plots). At this point, we (group) are putting over cascading op amps.
Hi,

Ok, very good. Using op amps makes it much simpler.

Do you know how to approach the problem i suggested trying first:
Hs=1/(s+1)
?

You should start with that one if you never did this before.
I could show you the procedure if you like, but that's if you really dont know how to do it yet. In the Homework section here the idea is to let the original poster try to solve it first.
This one might seem a little harder than usual if you havent done it before, but once you do a couple it comes easy and fast. I am hoping you were taught at least a little already though.

Also, do you know how to read and/or make a block diagram? That is a diagram that is drawn with 'blocks' that are either gains or integrators, and one or more inputs and one or more outputs.
For example:

Vin o----A----o Vout

That's a simple block diagram with only one gain A. Normally that 'A' is enclosed in a rectangle which is usually just called a 'block'.