# Determine the value of the resistor required to get a 12 kHz cut-off frequency.

Discussion in 'Homework Help' started by aaron0000934, Dec 15, 2010.

1. ### aaron0000934 Thread Starter New Member

Dec 14, 2010
7
0
Im stuck on the problem below

A low pass filter is to be made from a resistor and Capacitor shown. Determine the value of the resistor required to get a 12 kHz cut-off frequency.
Assuming you test this circuit with an input voltage of 10Vpk at 1.2kHz, 12kHz and 120kHz what is the expected output voltages?

I am unsure how the cut-off frequency affects the resistor. Where do I start?

• ###### P6.JPG
File size:
8.5 KB
Views:
39
Last edited: Dec 15, 2010
2. ### R!f@@ AAC Fanatic!

Apr 2, 2009
8,787
771
What is the formula use to calculate the output

3. ### aaron0000934 Thread Starter New Member

Dec 14, 2010
7
0
if the cutoff frequency formula is fc=1/(2∏RC) than I should be able to solve for resistance R=1/(2∏fcC) ?

4. ### aaron0000934 Thread Starter New Member

Dec 14, 2010
7
0
how do I solve the expected Vo for the frequencies given?

5. ### Fraser_Integration Member

Nov 28, 2009
142
5
you need to derive the transfer function or gain for this circuit, in other words Vo/Vi

Treat it as a voltage divider but use the impedances of both elements. I will get you started:

Vo = (Zc / Zr+Zc)Vi

rearrange this to get Vo/Vi = something, and then substitute in the values for impedance of the circuit elements.

Oh and the cut-off frequency formula is correct

6. ### Ron H AAC Fanatic!

Apr 14, 2005
7,050
657
Phase shift makes this more complex than you have indicated.

7. ### Fraser_Integration Member

Nov 28, 2009
142
5
It didn't ask for phase shift.

and it's still the same procedure, just leave the j's in! and phase shift = arctan {Im/Re}

8. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
I 'll agree with Fraser_Integration. Just treat it as a voltage divider with a variable impedance on the capacitor end. Make a universal formula and input the frequency values, or find the impedance for each frequency first and input that to the divider.

9. ### Ron H AAC Fanatic!

Apr 14, 2005
7,050
657
All I'm saying is this:
At 1.2kHz, the actual Vo/Vs=0.995
If you calculate Xc/(R+Xc), you get 0.909, which is the wrong answer.

As Fraser_Integration said, you have to include the j's.