Transfer function and magintude known, unsure how to appoarch

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Discussion Overview

The discussion revolves around a problem involving electrical impedance, specifically finding the capacitive reactance needed to make a load appear purely resistive when placed in parallel with a given load impedance. The context includes theoretical aspects of circuit analysis and impedance calculations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a problem involving a voltage source, line impedance, load impedance, and an unknown capacitive reactance, seeking guidance on how to approach it.
  • Another participant suggests that the goal is simply to convert the complex load impedance into a purely resistive form, questioning the relevance of maximum power transfer considerations.
  • A participant raises a question about the nature of the line impedance, asking whether it represents the characteristic impedance or a series impedance, noting that the value seems unusual for a characteristic impedance.
  • There is a clarification about the notation used, with one participant correcting another regarding the meaning of "Ω" and "ω".
  • One participant shares their extensive efforts in solving the problem and references a similar question found on Yahoo Answers, presenting their calculated Thevenin impedance and expressing frustration over a specific angle in the resulting impedance.
  • Another participant highlights the need for additional parameters such as electrical length and phase constant to fully understand the problem, indicating that these cannot be deduced from the characteristic impedance alone.
  • A later reply challenges the approach taken by a participant, pointing out that the capacitor should not be connected in parallel with only part of the Thevenin impedance, emphasizing the importance of the complete impedance in the analysis.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of maximum power transfer, the interpretation of the line impedance, and the correct approach to connecting the capacitor. The discussion remains unresolved with multiple competing perspectives on how to proceed with the problem.

Contextual Notes

There are limitations regarding the assumptions made about the parameters involved, such as the unspecified frequency and the implications of the line impedance's nature. The discussion also reflects uncertainty about the correct method for analyzing the circuit.

cybhunter
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Homework Statement



Vs=7200V 0 degrees
ZLine=2Ω+20jΩ
ZLoad=138Ω+460jΩ
XC=unknown capacitance

(omega not given)

Find the capacitive reactance when, place in parallel with ZLoad will make the load appear purely resistive


Homework Equations


conj(Zline) =2Ω-20jΩ (for max power transfer to the load)

Zparallel=[(Zload)(XC)]/[Zload+XC] =Zline


The Attempt at a Solution



I multiply the numberator and denomator by the conjugate of (138+j460-jXC) to get

[[(460XC-j138XC)*(138-i(460-XC)]/(138^2+(460-XC)^2)]=2-20j

when I rearrange, I end up with:
68XC^2+240XC^2-9800XCj+980XC+210447i=230644
as you can see, I end up with a complex number as a solution, which does not make sense

How should I approach these kinds of problems where the transfer function (sans a component value) and the resulting vector is known?
 
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cybhunter said:
ZLoad=138Ω+460jΩ
XC=unknown capacitance

(omega not given)

Find the capacitive reactance when, place in parallel with ZLoad will make the load appear purely resistive
I don't think maximum power transfer need be brought into this. You are just asked to change 138Ω+460jΩ into 138+j0

If your examiner intended you do more than this, then the question fails to show it, as far as I can see.
 
Is Zline the characteristic impedance Z0 of the line, or is it a series impedance at the source? It's a very strange value to be Z0 of the line. Typical Z0 of a line is 50 + j0 ohms all the way to 300 + j0 ohms.

BTW Ω is not a parameter, it stands for "Ohms"!
 
rude man said:
BTW Ω is not a parameter, it stands for "Ohms"!
I believe OP is saying ω is not specified.
 
NascentOxygen said:
I believe OP is saying ω is not specified.

I believe you're right!
 
after racking my brain, going through practically a ream of paper and almost pulling my hair out for a couple days, apparently someone placed the problem on yahoo answers over a year ago:

http://answers.yahoo.com/question/index?qid=20110523124504AA7phCg

When I product over sum the impedance values (by theoretically shorting the independent voltage source), I end with an interesting conundrum: the Zth value is
2.06816Ω+19.1948jΩ (from (2+20j)*(138+460j)/(140+480j)). By plugging in XC= -19.1948j into the load resistance I end up with a j value that equals:
(-19.1948j)(138+460j)/(138+440.8052j) equals 0.2383-19.95j. When added to the the 2+20j (Line impedance), the resulting value is 2.2383+0.044j (2.239∠1.13) . I may be splitting hairs here but that 1.13 is driving me nuts
 
Something strange here. You need to know the electrical length θ = βx where β = phase constant and x = actual line length.

β = ω/v = ωT = 2π/λ

so you need to know ω and also delay time/unit length T, or just wavelength λ. Or L and C, inductance & capacitance per unit length.

These parameters cannot be deduced from Z0 alone.
 
cybhunter said:
after racking my brain, going through practically a ream of paper and almost pulling my hair out for a couple days, apparently someone placed the problem on yahoo answers over a year ago:

http://answers.yahoo.com/question/index?qid=20110523124504AA7phCg
That's handy. :smile:
When I product over sum the impedance values (by theoretically shorting the independent voltage source), I end with an interesting conundrum: the Zth value is
2.06816Ω+19.1948jΩ (from (2+20j)*(138+460j)/(140+480j)).
I'm with you there.
By plugging in XC= -19.1948j into the load resistance I end up with a j value that equals:
(-19.1948j)(138+460j)/(138+440.8052j)
That's where you are going wrong. You have determined what XC must be connected in parallel with the Thevenin impedance, but now you have decided to connect that XC in parallel with only part of what comprises the Thevenin impedance. Connecting a capacitor in parallel with the load (viz., 138+j460) is not equivalent to connecting that same capacitor in parallel with the Thevenin impedance.