# Homework Help: Help! Measured vs Calculated - Frequency Response

1. May 23, 2012

### Evales

I have a huge difference between what I'm measuring and what I'm calculating, since I can no longer check the circuit (and everyone in the class seems to be having the same problem as me) I'm going to assume it's the calculations.

I'm trying to calculate the response of the voltage over a capacitor, see the below diagram:

R = 500Ω;
L = 100mH;
C = 0.1μF.

The voltage source is an AC 1V source whose frequency is changed from 10Hz to 10kHz in steps.

For the transfer function:
V2= 1/(jωC) * I
V1= (R+jωL+(1/(jωC)) * I

Which gives the transfer function:
H(jω) = 1/ (1-ω2LC+jωRC)

Apparently this function get the highest output voltage (ie. the functions maximum) at 9254Hz.
My measured results show that the the highest output is at ~1400Hz.

When I simulate this circuit in pSpice and do an AC Sweep, I get the maximum appearing at the same point (~1400Hz), which leads me to believe that my measured results are correct.
However the results obtained from pSpice only have a gain of about 2, whereas the gain for the measured results was just under 17.

I need to compare the results I obtained with some system, be it pSpice or equations and both of them aren't working for me. Below is the setup of the pSpice system.

Please help! If you can figure out where I'm going wrong, I'll try my hardest to award you an internet!

R2 = 0.5k
L2 = 100mH
C2 = 0.1uF
V11:
VOFF=VAMPL=TD=TR=PHASE = 0
AC = 1V
FREQ=10

Simulation settings: Linear
Total Pts: 1000
Start Freq = 10
End Freq = 10k

2. May 23, 2012

### Staff: Mentor

Don't confuse ω with f. What's the relationship between ω and f?

3. May 23, 2012

### Evales

So it is the angular frequency, that clears up what was wrong with my assumption about my equation being wrong, do you know anything about pSpice and why my gain might be different?

4. May 23, 2012

### Staff: Mentor

I don't know why your measured gain would be different from the calculated or simulated ones. I calculate a gain of about 2 (in the neighborhood of 6 and a bit dB) when the circuit is at its resonant frequency.

5. May 23, 2012

### Evales

Weird, I suppose I'll just have to include that in my report, thanks for your help.