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What is the resonant frequency of this??


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aryajur



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


Post21 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
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Location: Italy


Post21 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


Post21 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.
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