- #1

JJBladester

Gold Member

- 286

- 2

## Homework Statement

I'm trying to understand how Twin-T notch filters work. I get that they are made of two passive RC filters, one low-pass and one high-pass in parallel. The trouble I'm having is how to determine the corner frequencies (where V

_{out}= 0.707V

_{in}). The gain of the corner frequencies is 0.707... or so I thought... If the low-pass and high-pass filters are both 2nd-order then the corner frequencies would reside at a gain of 0.5 but I can't seem to see how the low-pass and high-pass parts of the circuit are 2nd-order.

## Homework Equations

Here is the circuit:

Page 7 of "www.niu.edu/~mfortner/labelec/lect/p575_07a.pdf" gives the gain of the low-pass filter as [itex]V_{out(LP)}=\left ( \frac{1/j\omega C}{R+1/j\omega C} \right )^{2}V_{in}[/itex].

## The Attempt at a Solution

I redrew the low-pass part of the circuit as:

which does not give the same output voltage as the 2nd-order low-pass filter in this diagram:

I get a low-pass filter gain of [itex]\frac{2X_{c}}{R+2X_{c}}[/itex] due to the parallel capacitors being the same as one capacitor with value 2C and the fact that the top-left resistor and the capacitor(s) form a voltage divider network. The output voltage is the voltage across the capacitor(s).

Why do I get a different gain equation for the "2nd order" low-pass filter part of the Twin-T circuit than the one listed above?

Last edited by a moderator: