# Design of Op amp given transfer function

i want to create a circuit as a homework with Operational Amplifiers ,Resistors and Capacitors that has a transfer function :

Actually i have been given the following ciruit and its transfer function to help me :

Any ideas? How should i start this ? Thanks.

• What are your thoughts so far? – Null Feb 6 '15 at 18:44
• Well i am not that used to drawing circuits given the transfer function, but i think i need a system with no zeros but 3poles.I also need to use a summer, an inverter and an inverting integrator – george_t Feb 6 '15 at 18:52
• Actually i have to use those three parts i mentioned before but cannot figure how i will come up with three poles . – george_t Feb 6 '15 at 19:03
• Can you use more than 1 of the type you mentioned? I am not good at this. Can you rewrite the transfer function using partial fraction? Now you end up with 3 integrator low-pass amps. Which you then sum together. Correct the polarity with an inverter if necessary. – rioraxe Feb 7 '15 at 22:45
• You can write this TF as a product of three terms and each individual terms can be implemented as as a low pass filter and then can be cascaded. – nidhin Feb 12 '15 at 18:00

## 2 Answers

The given function belongs to a third-order lowpass. The circuit as shown realizes a first-order function only.

I recommend to do the following: Because the given function has only REAL poles, you can find a corresponding realization based on a simple series connection of first-order circuits (without any feedback, but with buffering between the three stages). Feedback is only required for realizing complex poles. Or are you forced to use three stages with overall feedback?

Well you have three poles in your equation and one reactive element in your circuit, so you need two more caps.

Also, I'd refer to Ron Mancini's "Op Amps for Everyone" for reference on op-amp circuit design. Available for free here:

http://www.siongboon.com/projects/2008-04-27_analog_electronics/op%20amps%20for%20everyone%20third%20edition%202009%20%28Texas%20Instrument%29.pdf