# Help Designing Circuit from Transfer Function

#### aje35

Joined Aug 1, 2012
1
Hello,
I am an electrical engineering student and taking an advanced circuits class.
I have been tasked to design a circuit from a given H(s) transfer function. The guidelines I must operate within are using:
- an op-amp
- resistors ranging from 100Ω to 10MΩ
- capacitors ranging from 200pF to 10μF.

The given transfer functions are:

H1(s) = (0.1s + 6000)/(s + 1200)
H2(s) = 60000/(s+500)^2

Any insight or help in to this problem would be greatly appreciated.

#### bertus

Joined Apr 5, 2008
22,233
Hello,

I found this post in "the completed projects forum", where it will stay "moderated" (invisible to others).
As it says it is for completed projects and not for questions.
I moved it over here and made it visible, so others can reply on the post.

As it looks like homework, what have you done to get a solution?

Bertus

#### #12

Joined Nov 30, 2010
18,224
I only looked because I'm completely useless at this and hoped to learn from somebody else's answer.

#### Bill B

Joined Nov 29, 2009
61
Is this for the design of an active filter?

#### #12

Joined Nov 30, 2010
18,224
The "S" terms would seem to indicate that. Hoping aje35 responds.

#### mlog

Joined Feb 11, 2012
276
The first one looks like a lag filter, or more appropriately a lag-lead, which means the lag is dominant. The second one looks like a critically damped 2nd order low pass filter.

#### daviddeakin

Joined Aug 6, 2009
207
H1(s) = (0.1s + 6000)/(s + 1200)
Find the DC gain of the transfer function (when s$$\rightarrow$$0)
In this case that gives 6000/1200 = 5

You also have a pole at s = 1200 rad/sec
And a zero at 6000/0.1 = 60000 rad/sec
This is a low-pass shelving filter, so you could perhaps use the opamp to provide a gain of 5, and then follow it with this:

H2(s) = 60000/(s+500)^2
Here you have a DC gain of 0.24
And two poles at 500 rad/sec

You could perhaps use a filter like this:

which takes care of the DC gain and one pole, then follow it with a passive RC filter to give the second pole.