How to find C and L in maximum current?

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SUMMARY

In an RLC circuit, to achieve maximum current at a frequency of 90 MHz, the inductance (L) and capacitance (C) must be calculated such that the reactance of the inductor (Xl) equals the reactance of the capacitor (Xc). Given a resistance (R) of 1000 ohms, the resonance condition is met when Xl = -Xc. The Q factor, which determines the width of the resonance peak, must be calculated for a 10% current drop at 90.3 MHz to find the necessary reactance. This information is crucial for designing a resonating circuit that accounts for parasitic effects.

PREREQUISITES
  • Understanding of RLC circuit theory
  • Familiarity with resonance and Q factor calculations
  • Knowledge of reactance formulas: Xl = 2πfL, Xc = -1/(2πfC)
  • Basic circuit design principles
NEXT STEPS
  • Calculate the Q factor for a 10% current drop at 90.3 MHz
  • Determine the required reactance for resonance at 90 MHz
  • Use the formulas for Xl and Xc to solve for L and C
  • Research parasitic effects in RLC circuits and their impact on performance
USEFUL FOR

Electrical engineers, circuit designers, and hobbyists working with RLC circuits and radio frequency applications will benefit from this discussion.

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In a RLC circuit, radio waves with different frequency, f, hit the antenna and exert oscillating electric forces on the electrons on the antenna . Thus they act via antenna as individual batteries, each oscillating at their particular frequency f. Suppose R=1000 ohm. What should L and C be so we get the largest current in the circuits at frequency in 90 MHz.However, at frequency 90.3 current is only 1/10 as large.

Now I know that at Imax, Xl=Xc, but I don't know how to use the other given frequency to find C and L.

Any help please?
 
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Welcome to PF.

I assume the R is in parallel with the L and C.
Xl = 2*Pi*f*L, Xc = -1/ (2*Pi*f*C), when Xc + Xl = 0 you have resonance.

The width of the resonance peak is determined by the Q which is the ratio of reactance to resistance. See https://en.wikipedia.org/wiki/Q_factor

So find the Q required for 10% at 90.3MHz. Then calculate the reactance needed.
Then solve for the L and C at 90MHz that have that reactance.
 
Then, if you want to build a suitable resonating circuit, you find that, at 90MHz, nothing behaves quite as you'd expect, because of parasitic effects. There can be a lot of 'suck it and see', when you bolt it into a circuit.
 

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