High pass filter and low pass filter question?

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Discussion Overview

The discussion revolves around the calculation of frequencies in a low pass filter circuit consisting of a resistor and a capacitor. Participants are attempting to determine the frequency that results in a specific gain and are also inquiring about the formula for a high pass filter. The conversation includes calculations, formula verification, and conceptual clarifications.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a formula for gain in a low pass filter and attempts to calculate the frequency corresponding to a gain of 0.25.
  • Another participant requests to see the calculations for finding ω and points out a potential error in the gain expression.
  • A participant provides an alternative gain expression for a high pass filter, suggesting that the initial formula may be incorrect.
  • Multiple participants express confusion regarding the frequency being asked for and the relationship between ω and f, with one confirming that f in Hz equals ω/2π.
  • There is a suggestion to derive the transfer function and sketch the circuit diagram to better understand the problem rather than relying on provided formulas.
  • One participant claims to have recalculated ω and arrived at a different frequency, but expresses uncertainty about the correctness of their answer.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct formula for the low pass filter gain, with some asserting it is incorrect while others defend it. There is also uncertainty regarding the calculations and the interpretation of the frequency being sought.

Contextual Notes

Participants mention potential calculation mistakes and the importance of deriving formulas rather than accepting them without verification. There are unresolved questions about the correct approach to the problem and the definitions of terms used.

Who May Find This Useful

This discussion may be useful for individuals studying electrical engineering, specifically those interested in filter circuits and frequency response analysis.

Grendelle
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You have a series circuit consisting of a ac power supply, a 1150.0 ohm resistor and a 144.0 nF capacitor. If the circuit is configured as a low pass filter, what frequency will cause the gain to be 0.25?
Formula
Gain = Vout / Vin = R / [R^2 + (1/ωC)^2]^1/2Solution
Plugging in R=1150 ohms
C=144*10^-9 F

to find a value for ω

And then using ω=2 π f
I got f= 0.05223Hz which is wrong.

Also what will be the formula for high pass filter?
Please help!
 
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Show your calculations for finding ##\omega##.
 
Grendelle;3785438[b said:
Formula[/b]
Gain = Vout / Vin = R / [R^2 + (1/ωC)^2]^1/2
Also what will be the formula for high pass filter?
Please help!

1. Formula for gain is wrong.

2. Gain expression for high-pass would be ωRC/√(1 + ω2R2C2)
 
Calculations for ω

ω=2∏f

The formula by prof has given me is Gain = Vout / Vin = R / [R^2 + (1/ωC)^2]^1/2 for a low pass filter.

0.25 = 1150 / [1150^2 + (1/ω*144*10^-9)^2]^1/2

My bad. I had a calculation mistake previously. I did it again and this time I solved it to get ω=1.5592*10^3
Using ω=2∏f, f=248.15 Hz.

Which is still wrong... :(I'm confused as to what frequency they are asking me for. Is the this frequency just plain ω? Am I making a mistake by calculating f=ω/2∏?
 
Grendelle said:
The formula by prof has given me is Gain = Vout / Vin = R / [R^2 + (1/ωC)^2]^1/2 for a low pass filter.
That is not a low pass filter. You seem to have dived into this problem without even sketching the circuit you are dealing with. Can you draw the circuit diagram for the low pass filter using the 2 specified components? Can you derive the transfer function Vout / Vin for it, rather than placing your faith in something without knowing whether it's the right formula or not?

I'm confused as to what frequency they are asking me for. Is the this frequency just plain ω? Am I making a mistake by calculating f=ω/2∏?
They are one and the same. But if in doubt, you can always write both.
 
Grendelle said:
Also what will be the formula for high pass filter?
You are asking the wrong question. What you should be asking of yourself at this point is, "What is the circuit for my high pass filter?"[/color]

Then determine for yourself its transfer function, and sketch it. That way, you can't go wrong.
 
Grendelle said:
Calculations for ω

ω=2∏f

The formula by prof has given me is Gain = Vout / Vin = R / [R^2 + (1/ωC)^2]^1/2 for a low pass filter.

0.25 = 1150 / [1150^2 + (1/ω*144*10^-9)^2]^1/2

My bad. I had a calculation mistake previously. I did it again and this time I solved it to get ω=1.5592*10^3
Using ω=2∏f, f=248.15 Hz.

Which is still wrong... :(


I'm confused as to what frequency they are asking me for. Is the this frequency just plain ω? Am I making a mistake by calculating f=ω/2∏?

No, you're right, f in Hz = ω/2π.

But the formula your prof gave you, if he really did, is still wrong.

Sketch the diagram for the low-pass circuit, write a summation of currents into the node at the capacitor. Then you can determine the right formula yourself. Don't just accept a formula from someone else, derive it for yourself, or you really won't learn what you need to.

BTW my answer is about 3724 Hz, is that what your prof got?
 

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