# Low Pass Filter Gain

Discussion in 'Homework Help' started by onqun, Jun 11, 2010.

1. ### onqun Thread Starter Member

Feb 17, 2009
15
0
Hello guys, I need to create db vs frequency graph of a low pass filter. I have capcitor and resistor values. How am I going to find the gain ? R1 is connected to - side of the op amp, + side is grounded. Rf and C is connected in paralel from r1 to vout.

2. ### Ghar Active Member

Mar 8, 2010
655
73
Use circuit theory?

It works the same as if you just had resistors. You need to use either differential equations or Laplace. Probably Laplace...

It just becomes Zf/Zin instead of Rf/Rin for the gain.

3. ### onqun Thread Starter Member

Feb 17, 2009
15
0
I forgot it :/ i took the class 3 years ago :/ thats why I asked. For gain I have (Rf+Xc1)/R1, but i forgot what does Xc1mean and where should I plug the freguency:/

4. ### Ghar Active Member

Mar 8, 2010
655
73
How did you manage to get that?

It's close but wrong if Rf and C are in parallel.

Xc is the reactance of the capacitor. It's the frequency dependent term:
$X_c = \frac{1}{2\pi fC}$

However your equation won't have Xc, it'll have Zc (the impedance):

$Z_c = -jX_c$

Feb 17, 2009
15
0
6. ### onqun Thread Starter Member

Feb 17, 2009
15
0
How am i going to find the gain after this? (r2+xc)/r1?

7. ### Ghar Active Member

Mar 8, 2010
655
73
Do you remember how to solve op-amp circuits?

I recommend you use the Laplace transform:

$Z_c = \frac{1}{sC}$

$s = jw=j2\pi f$

Zc is parallel with Rf. You treat it the same as a resistor when you write equations.

8. ### onqun Thread Starter Member

Feb 17, 2009
15
0
all i remember is current does not go inside of the op amp :/

9. ### onqun Thread Starter Member

Feb 17, 2009
15
0
can matlab plot imaginary numbers?

Mar 8, 2010
655
73
11. ### onqun Thread Starter Member

Feb 17, 2009
15
0
I have one more question, in my book it says that, K = -z2/z1 , Can i write z2 as (rf+c) , so the gain would be - (rf +c)/r1?

12. ### Ghar Active Member

Mar 8, 2010
655
73
They're in parallel, not series:

$Z_2 = R_f || Z_c = \frac{1}{\frac{1}{R_f} + sC}$

13. ### onqun Thread Starter Member

Feb 17, 2009
15
0
I apologize i did correct on the paper , lol =)and yes i added the negative sign as well thank you. so is that final ( Zc//Rf)/R1 = gain is correct ?

14. ### Ghar Active Member

Mar 8, 2010
655
73
Yep that's all it is.

There's standard form to put it into which is good practice to follow:

$H(s) = \frac{K}{\frac{s}{w_o} + 1}$

This way you can set s = 0 and see the low frequency gain instantly (K), as well as the cut off frequency (wo).

15. ### onqun Thread Starter Member

Feb 17, 2009
15
0
thank you very much my friend have a good night =)