# How can I draw a circuit from its transfer function?

I am new in automation electronics and in this forum.

I have this transfer function: $G(s) = \dfrac{10}{(s+1) (s+5)}$ and I was asked to create the circuit with 5 op-amps and the correct resistors and capacitors.

I don't know much about these kinds of electronics and any help would appreciated.

• Do you have any ideas about how to get started? Do you know any ways to make a circuit that implements part of the solution? Sep 25 '15 at 16:55

Here's a fairly straightforward hint or two....

Split the function into simpler parts like: -

$G(s) = \dfrac{1}{s+1}\times \dfrac{1}{s+5}\times 10$

Each simpler part is a functional block and when functional blocks are placed in series they multiply to give $G(s)$.

So, the easy one is a gain of ten block but how do you implement $\dfrac{1}{s+1}$.

Take a look at what a simple low pass filter does formed by a resistor and capacitor: -

Now I'm mentioning the RC LPF because I recognized it has a transfer function similar to $\dfrac{1}{s+1}$. You can go and derive it if you want but there is enough info on the web to tell you that it is: -

$\dfrac{V_O}{V_I} = \dfrac{\frac{1}{CR}}{s+\frac{1}{CR}}$ if CR = 1 then you have one of the parts.

Hints over.

BTW, as an addition I think it can be done with two op-amps but if you want to use 5 there's nothing stopping you except the shame of it!