Register to reply

Active Filter Derivation

by dillonmhudson
Tags: active, derivation, filter
Share this thread:
dillonmhudson
#1
Apr29-11, 04:29 PM
P: 50


Can I get some help with this? I don't even know where to begin.
Phys.Org News Partner Science news on Phys.org
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
jegues
#2
Apr29-11, 05:07 PM
jegues's Avatar
P: 1,089
Quote Quote by dillonmhudson View Post


Can I get some help with this? I don't even know where to begin.
Bandpass filters usually employ both inductors and capictors.

The inductor cuts off the high frequencies, while the capacitor cuts off the low frequencies, ideal for a bandpass filter.
jegues
#3
Apr29-11, 05:15 PM
jegues's Avatar
P: 1,089
Quote Quote by jegues View Post
Bandpass filters usually employ both inductors and capictors.

The inductor cuts off the high frequencies, while the capacitor cuts off the low frequencies, ideal for a bandpass filter.
Whoops, I just noticed that the the answer is given in the figure. I can see they did not use a capacitor!

I managed to derive the transfer function for this circuit and found the following,

[tex]T(jw) = \frac{-z}{(jwL + z)(jwL + R)}[/tex]

Now we simply need to select our Z such that the requirement for resonant frequency is obatined.

If we select,

[tex]z = R_{z}[/tex]

We rearrange the transfer function,

[tex]\frac{-\frac{1}{R}}{(1 + \frac{jwL}{R_{z}})(1 + \frac{jwL}{R})}[/tex]

This becomes,

[tex]\frac{-\frac{1}{R}}{(1 + \frac{jw}{w_{L}})(1 + \frac{jw}{w_{H}})}[/tex]

Now we know what wL and wH are we can solve for fL and fH since,

[tex]f = 2\pi w[/tex]

Then our desired resonant frequency,

[tex]f_{r} = \sqrt{f_{L} \cdot f_{H}}[/tex]

Simply solve for, [tex]R_{z}[/tex].

You should find that, [tex]R_{z} = \frac{100\pi^{2}L^{2}}{R}[/tex]


Register to reply

Related Discussions
First Order Active Low Pass Filter Engineering, Comp Sci, & Technology Homework 11
Design an active filter 2nd order Engineering, Comp Sci, & Technology Homework 3
Active Second-order low-pass Butterworth filter Electrical Engineering 1
3rd order low pass Butterworth active filter Electrical Engineering 3
Active band pass RC filter Introductory Physics Homework 0