# Calculating for a Gyrator Notch Filter

#### BarryBozeman

Joined Apr 1, 2016
41
Hi there -
I'm attempting to build my own calculator for a gyrator notch filter, but I don't know how the equation works exactly.
On the Elliot Sound Products website (http://sound.whsites.net/articles/gyrator-filters.htm), the equation is explained as :

f = 1 / ( 2 × π × √( L × C ))

I am uncertain, though, given the schematic, how to calculate for L, when there are no inductors. There is a step I'm missing.

Can anyone walk me through this equation? Thank you.

#### LvW

Joined Jun 13, 2013
1,056
The operational amplifier - together with R1,R2 and C1 form a so-called "active lossy inductor".
The input impedance of this part of the circuit is
Zin= sC1R1R2 + R1 +R2.

Hence, this active circuit simulates an inductor Ls=C1R1R2 iin series with a resistive loss (R1+R2).
As you know - a series resonant circuit Ls_Cs has a minimal impedance at w=wo.
Therefore, we can realize a (non-ideal) notch filter as shown in the diagram using an additional resistor Rs. Now, we have a voltage divider consisting of Rs and a lossy series resonant block.

#### LvW

Joined Jun 13, 2013
1,056
Dana - it is an 80-page paper.
It would be helpful if you would give some hints on which page the question is answered.

#### AnalogKid

Joined Aug 1, 2013
8,487
• ericgibbs

#### BarryBozeman

Joined Apr 1, 2016
41
The operational amplifier - together with R1,R2 and C1 form a so-called "active lossy inductor".
The input impedance of this part of the circuit is
Zin= sC1R1R2 + R1 +R2.

Hence, this active circuit simulates an inductor Ls=C1R1R2 iin series with a resistive loss (R1+R2).
As you know - a series resonant circuit Ls_Cs has a minimal impedance at w=wo.
Therefore, we can realize a (non-ideal) notch filter as shown in the diagram using an additional resistor Rs. Now, we have a voltage divider consisting of Rs and a lossy series resonant block.

I'm sorry, but I'm failing to understand something here. The goal, if I didn't manage to state it correctly: I'd like to make a simple equation, wehre if I enter values for R1, R2, C1, and C2, I can calculate the resonant frequency and the Q of a gyrator.

I'm not sure if I can get figure out how to get the value "L" (as used in "f = 1 / ( 2 × π × √( L × C ))") from the above information.

#### LvW

Joined Jun 13, 2013
1,056
I'm sorry, but I'm failing to understand something here. The goal, if I didn't manage to state it correctly: I'd like to make a simple equation, wehre if I enter values for R1, R2, C1, and C2, I can calculate the resonant frequency and the Q of a gyrator.
I'm not sure if I can get figure out how to get the value "L" (as used in "f = 1 / ( 2 × π × √( L × C ))") from the above information.
Didn`t I gave you the equation for the active-L ?
Do you realize that a series connection of L-C has a minimum for a (well-known) resonant frequency?
What else do you need?

You were asking "how the equation works". I have tried to explain how the circuit works.

#### ericgibbs

Joined Jan 29, 2010
10,188
hi Barry,
A couple of LTSpice plot images of your circuit, for reference only.
E