Deriving Expression for Vout/Vi in Low Pass Filter

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SUMMARY

The discussion focuses on deriving the expression for the voltage ratio Vout/Vi in a low pass filter circuit consisting of a capacitor, inductor, and resistor in series. The output voltage Vout is measured across the capacitor, while the input voltage Vi is the source voltage. Key concepts include understanding the total impedance of the circuit and the individual voltages across the components. The response emphasizes the importance of recognizing the relationships between voltages and currents in series circuits to derive the required expression.

PREREQUISITES
  • Understanding of series circuits and their components: capacitor, inductor, and resistor.
  • Familiarity with voltage and current relationships in electrical circuits.
  • Knowledge of impedance in AC circuits.
  • Basic grasp of angular frequency (W) in relation to circuit behavior.
NEXT STEPS
  • Study the derivation of voltage ratios in RLC circuits.
  • Learn about calculating total impedance in series RLC circuits.
  • Explore the concept of phase angles in AC circuits.
  • Investigate the frequency response of low pass filters.
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in analyzing low pass filter behavior in RLC circuits.

Pixter
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Q: Derive an expression for the Vout/Vi, the ratio of the output and source voltage amplitudes, as a function of the angular frequencie W of the source.

The L-R-C circuits looks like this..



source(ac)----------capacitor-----inductor----resistor----(back to start)

Vout is taken "between" the source and resitor and between the capacitor and inductor.

A: Well i know som formula but I can't really identify anything or understand how to set-up the problem...

maybe someone could explain the problem in easier terms and maybe give me a push in the right direction.

Thanks
 
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So, this is a series circuit, with V_out = V_C, the voltage across the capacitor.

What do you know about the voltages across the individual components in a series circuit? The currents through the individual components? The total impedance in terms of the impedances of the individual components?

Regards,
George
 

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