Help Measured vs Calculated - Frequency Response

In summary, the conversation discusses a discrepancy between the calculated, simulated, and measured results of a circuit's transfer function for the voltage over a capacitor. The transfer function is given and it is noted that the maximum output voltage occurs at 9254Hz for the function, but ~1400Hz for the measured results. The setup for the pSpice system is also provided, but the reason for the difference in gain between the measured and calculated/simulated results remains unclear. The relationship between ω and f is discussed and it is concluded that the angular frequency is the correct value to use. The conversation ends with the expert summarizer receiving an internet award for their help.
  • #1
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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:
sClpH.png

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!

tNMAR.png

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
 
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  • #2
Don't confuse ω with f. What's the relationship between ω and f?
 
  • #3
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
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
Weird, I suppose I'll just have to include that in my report, thanks for your help.
Here's your internet!
 

FAQ: Help Measured vs Calculated - Frequency Response

1. What is the difference between measured and calculated frequency response?

The measured frequency response is obtained by physically measuring the output of a system in response to different input signals. On the other hand, the calculated frequency response is obtained by using mathematical models or simulations to predict the response of a system to different input signals.

2. Which one is more accurate, measured or calculated frequency response?

In general, the measured frequency response is considered to be more accurate as it takes into account any external factors that could affect the system's response. However, the accuracy of the calculated frequency response depends on the accuracy of the mathematical models and simulations used.

3. What are the advantages of using measured frequency response?

One advantage of using measured frequency response is that it provides a more realistic representation of the system's behavior in real-world conditions. It also allows for the identification of any unexpected or non-linear behaviors that may not be captured by mathematical models.

4. When is it appropriate to use calculated frequency response?

Calculated frequency response is often used in situations where it is not possible or feasible to physically measure the response, such as in theoretical analyses or when studying complex systems. It can also be used as a preliminary step before conducting physical measurements.

5. Can measured and calculated frequency response be used interchangeably?

No, measured and calculated frequency response should not be used interchangeably as they represent different methods of obtaining the system's response. However, they can be compared to identify any discrepancies and improve the accuracy of the calculated response.

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