Active Low Pass Filter Design: 1kHz, Gain 20, 22kΩ Input Impedance

[kimandrew20]

Homework Statement

Design this circuit to give a cut off (-3dB) frequency of 1kHz, a low frequency gain of 20, and an input impedance equal to 22kΩ

Homework Equations

The Attempt at a Solution

So, I started off with Vout/Vin = [-R2/R1]/[1 + sCR₂. I also know that the dc gain will be -R2/R1. I also know that frequency = 1/[2∏R₂C]

Im a little lost as to where to start!

http://upload.wikimedia.org/wikipedia/commons/thumb/5/59/Active_Lowpass_Filter_RC.svg/300px-Active_Lowpass_Filter_RC.svg.png

 

[NascentOxygen]

Hi kimandrew20! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

What is the input impedance of the op-amp filter you show? Start with that.

Are you going to use just a single stage?

 

[kimandrew20]

Is the input impedance just the value that the problem has specified? The 22kΩ value?

Yes, just a single stage.

 

[kimandrew20]

I tried it again and I got a value for the capacitance and the resistors. Does this look correct?

R₁ will equal the input impedence (The two inputs, V- and V+ are at approximately the same voltage, R₁ is at ground voltage, therefore R₁ = input impedence = 22 kΩ

Gain (A) = (R_f/ R₁) → R_f/22k = 20
Therefore, R_f = 440 kΩ.

f = 1/ [2∏ * R * C] therefore
C = 1/ [2∏ * R * f] → 1/[2∏ * (22*1000) * (1 * 1000))] = 7.234 x 10^-9 F

 

[rude man]

You got the right R_f but the wrong C. Reconsider the R you used to compute C ...