What Capacitance is Needed to Tune an LC Circuit to 100 MHz?

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SUMMARY

The discussion focuses on calculating the capacitance required to tune an LC circuit, specifically for an FM radio operating at 100 MHz with an inductor value of 4 microhenries (µH). The relevant equation used is w = 2πf = 1/√(LC), where 'w' represents angular frequency, 'f' is frequency, 'L' is inductance, and 'C' is capacitance. The user encountered difficulties due to the presence of multiple unknowns and the need to convert units appropriately for accurate calculations.

PREREQUISITES
  • Understanding of LC circuit theory
  • Familiarity with the relationship between frequency, inductance, and capacitance
  • Knowledge of unit conversions between microhenries and megahertz
  • Proficiency in using the formula w = 2πf = 1/√(LC)
NEXT STEPS
  • Calculate the required capacitance using the formula C = 1/(L(2πf)²)
  • Study unit conversion techniques between inductance (µH) and frequency (MHz)
  • Explore practical applications of LC circuits in radio tuning
  • Learn about the effects of component tolerances on circuit performance
USEFUL FOR

Electronics students, radio frequency engineers, and hobbyists interested in tuning circuits for FM radio applications.

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Homework Statement


An LC circuit with an inductor of 4 microH is used as tuner for an FM radio. The capacitance required to tune into a radio stations of 100 MHz is most nearly what?

Homework Equations


w= 2pif = 1/sqrt LC



The Attempt at a Solution



I plugged in 4 microH into equation for f but I realized I have too many unknowns. I also tired 100 MHz for f but same problem. I am lost, please help!
 
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My advice is to figure out what quantity microH goes with and which quantity MHz goes with. They can't both be f unless microH and MHz are the same unit, which they aren't.
 

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