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dxt78

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input impedance of RLC tank, and characteristic impedance
Jul 14^th, 2011, 8:42am

Hello,
I have an RLC tank as shown in attachment (2R in parallel with an L and a C). I have two questions about it:
1) Why is the characteristic impedance of this LC tank sqrt(L/C) and what meaning does it have?
2) When computing the input resistance of this tank, what role should the characteristic impedance play?
Thanks.

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RLC.PNG

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buddypoor

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Re: input impedance of RLC tank, and characteristic impedance
Reply #1 - Jul 14^th, 2011, 8:57am

There is one single frequency wo=1/sqrt(LC) for which the reactive conductance of the capacitor and of the inductor (wC and 1/wL), respectively, are equal.
That means, at w=wo the input impedance of the whole circuit is zero.

Now the answer to your question:
If woC=1/woL you can insert the above expression for wo and you get:
woC=sqrt(C/L) and woL=sqrt(L/C).

In words: The characteristic impedance is the impedance of both reactive elements for w=wo (resonant frequency).

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LvW (buddypoor: In memory of the great late Buddy Rich)

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RFICDUDE

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Re: input impedance of RLC tank, and characteristic impedance
Reply #2 - Jul 14^th, 2011, 7:08pm

Your tank circuit is not 100% realistic. It is not physical to have two ideal reactive components in series and then a loss in parallel with the series LC; although, maybe this is a practical equivalent that I have not considered before.

A tank is usually a parallel RLC or a completely series RLC. The circuit you present is a perfect short at f = 2*pi/sqrt(LC).

The characteristic impedance represents the lossless energy exchange between C and L while R should represent the power dissipation.

The characteristic impedance should not necessarily be tied directly to the resistance, but it may be indirectly related if the source of the resistance is the series resistance in the inductor.

Others can correct me if my interpretation is not the best for your question.

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raja.cedt

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Re: input impedance of RLC tank, and characteristic impedance
Reply #3 - Jul 14^th, 2011, 9:03pm

hello dxt78,
as RF id said it's not a tank circuit. General meaning of tank is LC parallel circuit which can give pure sinusoidal osculations @ 1/sqrt(LC). i guess here you drawn ckt wrongly i guess. When you wish to add loss into tank generally series with inductor and seris with capacitor is good model. but here you have drawn LC seris circuit and then it has 2k // res. This ckt don't have any practical usage.

If you just want to know whats the characteristic impedance of your circuit, it is the frequency at which you will see 0 volts impedance

Thanks.

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rfcooltools.com

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Re: input impedance of RLC tank, and characteristic impedance
Reply #4 - Jul 18^th, 2011, 12:12pm

dxt78,

By use of the term "characteristic impedance" I �assume that you mean "transmission line characteristic impedance". �For simplicity �ignore the 2R in your circuit because when connected the impedance is not sqrt(L/C) Im going to ignore it and show how a lossless t-line will result in the sqrt(L/C). �For this tline picture that you place a port at the left hand side L and another connected to the node that ties the L and C together. �

For an ideal transmission line with ideal source/load impedance Zout=Zin = Z0

Vin/(sL+Z0||1/sC) = �Vout/(sL+Z0)

Iin*((1/sC)||Z0)=Iout*((1/sC)||(sL+Zo))

Vin/In = Vout/iout = Z0

Solve for Z0 and it will equal sqrt(L/C)

http://rfcooltools.com

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Larry_80

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Re: input impedance of RLC tank, and characteristic impedance
Reply #5 - Jul 19^th, 2011, 10:20pm

This is in response to people suggesting the circuit is not a "realistic" tank circuit in RF. I completely disagree with this. A monolithic inductor can have a series parasitic capacitor associated with it and a parallel parasitic resistor depending on how the parasitic cap and resistors are modeled.

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purplewolf Senior Member Offline Posts: 103	Re: input impedance of RLC tank, and characteristic impedance Reply #6 - Jul 21^st, 2011, 6:15am infact the series LC structures are claaed harmonic traps rather than harmonic tanks.
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harpoon Senior Member Offline Posts: 112 Hampshire	Re: input impedance of RLC tank, and characteristic impedance Reply #7 - Jul 25^th, 2011, 3:51pm dxt78, What are you trying to achieve with this circuit of yours ? I presume it is a RF trap with some matching/loading ?
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