Deriving Expression for Vout/Vi in Low Pass Filter

In summary, the conversation is discussing deriving an expression for the Vout/Vi ratio in a L-R-C circuit as a function of the angular frequency W of the source. The circuit diagram and the location of Vout are also mentioned. One person is struggling to understand and solve the problem and is asking for help from someone else. The other person suggests considering the individual components and their voltages, currents, and impedances.
  • #1
Pixter
30
0
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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  • #2
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 throught the individual components? The total impedance in terms of the impedances of the individual components?

Regards,
George
 

1. What is a Low Pass Filter?

A Low Pass Filter is an electronic circuit that allows low frequency signals to pass through while attenuating high frequency signals. It is commonly used to filter out noise and unwanted high frequency components from a signal.

2. How do you derive the expression for Vout/Vi in a Low Pass Filter?

The expression for Vout/Vi in a Low Pass Filter can be derived using the voltage divider rule. The output voltage, Vout, is equal to the input voltage, Vi, multiplied by the ratio of the impedance of the resistor, R, to the total impedance of the circuit. This can be expressed as Vout/Vi = R/(R + Xc), where Xc is the reactance of the capacitor in the circuit.

3. What is the significance of the cut-off frequency in a Low Pass Filter?

The cut-off frequency, also known as the -3dB frequency, is the frequency at which the output voltage of the Low Pass Filter drops to 70.7% of the input voltage. This frequency is important as it determines the range of frequencies that will be attenuated by the filter.

4. How does the value of the capacitor affect the output voltage in a Low Pass Filter?

The value of the capacitor in a Low Pass Filter affects the cut-off frequency. A larger capacitor will result in a lower cut-off frequency, allowing lower frequency signals to pass through. A smaller capacitor will result in a higher cut-off frequency, allowing higher frequency signals to pass through.

5. Can the expression for Vout/Vi be used for different types of Low Pass Filters?

Yes, the expression for Vout/Vi can be used for different types of Low Pass Filters as long as the circuit contains only one resistor and one capacitor. However, the specific values of the resistor and capacitor may differ depending on the type of filter.

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