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Design a circuit w/1 Ohm impedance

  • Engineering
  • Thread starter hogrampage
  • Start date
  • #1
108
1

Homework Statement


Design a suitable combination of resistors, capacitors, and/or inductors which has an equivalent impedance at ω=100 rad/s of 1Ω using at least one inductor.

Homework Equations


Zeq=ZR+ZL+ZC
ZR=R
ZL=jωL
ZC=-j/ωC

The Attempt at a Solution


I really am not sure how to start. I can see this being a fairly simple problem, but I just can't seem to wrap my head around it. I have read through the chapter numerous times, and I don't see anything else that could help at all.
 

Answers and Replies

  • #2
maybe
1= R + jwL +j/wC

1= R + j(wL+1/wC)

1= R + j(100L+1/100C)

easy one can be R =1, L=.01, C= -0.01
which equals 1 = 1+ j(0)
 
  • #3
gneill
Mentor
20,793
2,773

Homework Statement


Design a suitable combination of resistors, capacitors, and/or inductors which has an equivalent impedance at ω=100 rad/s of 1Ω using at least one inductor.

Homework Equations


Zeq=ZR+ZL+ZC
ZR=R
ZL=jωL
ZC=-j/ωC

The Attempt at a Solution


I really am not sure how to start. I can see this being a fairly simple problem, but I just can't seem to wrap my head around it. I have read through the chapter numerous times, and I don't see anything else that could help at all.
What do you know about LC or RLC circuits? Any special properties come to mind?
 
  • #4
108
1
ω0=[itex]\frac{1}{\sqrt{LC}}[/itex]

and

[itex]\alpha[/itex]=[itex]\frac{1}{2RC}[/itex]

Underdamped when [itex]\alpha[/itex]<ω0, which has imaginary components.
 
Last edited:
  • #5
gneill
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What conditions exist when a series RLC circuit are at resonance (ω = ωo)?
 
  • #6
108
1
At resonance, XL=XC, but that would just make them cancel out so I'm not sure what to do.
 
Last edited:
  • #7
gneill
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At resonance, XL=XC, but that would just make them cancel out so I'm not sure what to do.
Well, if they cancel out, what remains?...
 
  • #8
108
1
R, but I'm supposed to use at least one inductor. I must be over-analyzing this (I think about these things too much lol).
 
  • #9
gneill
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20,793
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R, but I'm supposed to use at least one inductor. I must be over-analyzing this (I think about these things too much lol).
Hmm, doesn't the "L" in "LC" count as an inductor?
 
  • #10
108
1
Yes, but I'm lost as to how to find the value(s). It isn't making sense to me. I don't even know which equation(s) to use. I have looked at the equations in the book and examples, and they aren't helping at all. No matter what, they always know at least one of the impedance values.

EDIT: Am I going anywhere with the below equation?

Zeq=jω[itex]\frac{1}{4\pi^{2}f^{2}C}[/itex]-[itex]\frac{j}{ωC}[/itex]

where Zeq=1.
 
Last edited:
  • #11
gneill
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I'm not sure what's confusing you :confused: Choose any L and a corresponding C that cancels it for the given frequency of operation --- then bang in a 1 Ohm resistor and you're home free.
 

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