What is the resonant frequency of this??

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aryajur

Joined: 23 Oct 2004
Posts: 689
Helped: 73
Location: Sunnyvale, USA

21 Nov 2004 4:02 What is the resonant frequency of this??

What is the resonant frequency expression of this circuit?? That is for what value of ω will the transfer Impedance Vo / Is1 be maximum?

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sergio mariotti

Joined: 22 Dec 2003
Posts: 467
Helped: 42
Location: Italy

21 Nov 2004 9:10 Re: What is the resonant frequency of this??

The resonance is the power equilibrium between reactive elements (read components).
At resonating frequency , the generator supply active power only.
So, regardeless the dissipative elements (the resistors), the C1 is // to L1
so: F0= 1/(2*3.1415..*√L1*C1)

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aryajur

Joined: 23 Oct 2004
Posts: 689
Helped: 73
Location: Sunnyvale, USA

21 Nov 2004 13:53 Re: What is the resonant frequency of this??

I was able to solve for it. Actually if the series resistance would have been absent with the inductor the resonant frequency would have been:

Quote:

ω = 1/ √(LC)

But since the circuit has a series resistor with an inductor on solving we get the resonant frequency as:

ω = √[{-B+√(B²-4AK)}/{2A}]

where A = (R2²)(L²*L²)(C²)
B = 2(R2²)(R1²)(L²)(C²)
K = (R1²*R1²)(R2²)(C²) - 2(R1²)(R2²)LC - L²(R2²) - 2(L²)(R1)(R2)

Pretty complex ! But when R1 = 0 the expression reduces to the former.