Transfer functions and cut off frequency

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Discussion Overview

The discussion revolves around finding the transfer function H(jω) for an RC parallel circuit configuration, specifically with a resistor followed by a capacitor. Participants explore different expressions for the transfer function and seek clarification on circuit descriptions and derivations.

Discussion Character

  • Homework-related, Technical explanation, Debate/contested

Main Points Raised

  • One participant attempts to derive the transfer function for the RC parallel circuit, suggesting H(jω) = jw/(jw + 1/RC).
  • Another participant provides an alternative expression for the transfer function, indicating H(jω) = jw[C/(Rs+c)]/{jw + Rsc/[(Rs+c)R]}.
  • A third expression is presented as H(jω) = {[1/(R1C1)] - ω^2}/{1/(R1C1) - ω^2 + jw/(R2C1)}.
  • One participant requests clarification on circuit descriptions and suggests that diagrams would enhance understanding.
  • Another participant interprets the output of the circuit and notes the importance of providing detailed derivations and intermediate steps for clarity.
  • There is mention of actual component values being provided, implying that final results may require specific numerical substitutions.

Areas of Agreement / Disagreement

Participants express differing views on the correct form of the transfer function and the interpretation of circuit outputs. The discussion remains unresolved with multiple competing expressions and interpretations presented.

Contextual Notes

The discussion highlights potential ambiguities in circuit descriptions and the need for clear derivations. Some expressions may depend on specific assumptions about component values and configurations.

nikki92
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Homework Statement


RC parallel circuit with the resistor first and the capacitor next.

find the transfer function H(jw)

resistor first then capacitor

transfer function of a circuit with resister serial then capacitor and resister parallel


I have absolutely no background in circuits but need to understand this material to take a communications course.

The Attempt at a Solution



RC parallel would it be H(jw) = jw/(jw + 1/RC)

the other
H(jw) = jw(c/(R_s +c))/(jw + R_sC /(R_S+c)R
 
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Your question is a bit vague in the way of the circuit descriptions. It would much better if you could upload a diagram or two.
 
IMG_1809.jpg


H(jw)=jw/(jw+1/RC)

IMG_1810.jpg


H(jw) = jw[C/(Rs+c)]/ {jw +Rsc/[(Rs+c)R ]}

IMG_1811.jpg


H(jw) = {[1/(R1C1)] - w^2 } / {1/(R1C1) - w^2 +jw/(R2C1)}
 
Okay, that's better.

In the first diagram I interpret the output to be the capacitor current Io(t), even though the diagram is missing the current arrow on that branch. Traditionally the "o" subscript indicates an output. Your H(jw) would be correct for taking i2 as the output though.

The others are a bit more complicated to evaluate since there are several ways to simplify the expressions, and I'm not keen on spending time to see if yours can proven as identities of my own results. So. Perhaps if you could provide a bit more detail about your derivations (show and explain some intermediate steps) that would be excellent.

One thing I notice is that they have provided actual component values, so for final results they may be expecting you to plug them in for final results.
 

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