# Design a circuit w/1 Ohm impedance

1. Sep 16, 2012

### hogrampage

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
Zeq=ZR+ZL+ZC
ZR=R
ZL=jωL
ZC=-j/ωC

3. 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.

2. Sep 16, 2012

### scootypuffsnr

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. Sep 16, 2012

### Staff: Mentor

What do you know about LC or RLC circuits? Any special properties come to mind?

4. Sep 16, 2012

### hogrampage

ω0=$\frac{1}{\sqrt{LC}}$

and

$\alpha$=$\frac{1}{2RC}$

Underdamped when $\alpha$<ω0, which has imaginary components.

Last edited: Sep 16, 2012
5. Sep 16, 2012

### Staff: Mentor

What conditions exist when a series RLC circuit are at resonance (ω = ωo)?

6. Sep 16, 2012

### hogrampage

At resonance, XL=XC, but that would just make them cancel out so I'm not sure what to do.

Last edited: Sep 16, 2012
7. Sep 16, 2012

### Staff: Mentor

Well, if they cancel out, what remains?...

8. Sep 16, 2012

### hogrampage

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. Sep 16, 2012

### Staff: Mentor

Hmm, doesn't the "L" in "LC" count as an inductor?

10. Sep 16, 2012

### hogrampage

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$\frac{1}{4\pi^{2}f^{2}C}$-$\frac{j}{ωC}$

where Zeq=1.

Last edited: Sep 16, 2012
11. Sep 16, 2012

### Staff: Mentor

I'm not sure what's confusing you 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.