Question

3) Low Pass Filter [diagram omitted] a) What is Vout for very low and very high frequencies? b) Derive an expression for the angular frequency ? at which the impedance of the capacitor |Zc| is equal to R. c) Using the voltage divider formula derive an expression for the ratio of Vout to Vin, put it in the form shown below. This is what is known as the transfer function of this circuit and it describes as a function of frequency how the amplitudes of sine waves at different frequencies are transferred from the input to the output. Vout/Vin = 1 / (1 + ?) d) What is the value of this ratio at the angular frequency found in part b? This special frequency is known as the cut-off frequency for the filter. Below this frequency the output stays fairly constant, above this frequency it drops like 1/?. We usually say that this frequency corresponds to the bandwidth of the low pass filter. A note for those who know more or are going on: the magnitude of this ratio is wrong here because we used the absolute value for the impedance of the capacitor; if you use the actual complex impedance you get a different numerical value, but conceptually this simplified case can help to understand what is going on.

          3) Low Pass Filter

[diagram omitted]

a) What is Vout for very low and very high frequencies?

b) Derive an expression for the angular frequency ? at which the impedance of the capacitor |Zc| is equal to R.

c) Using the voltage divider formula derive an expression for the ratio of Vout to Vin, put it in the form shown below. This is what is known as the transfer function of this circuit and it describes as a function of frequency how the amplitudes of sine waves at different frequencies are transferred from the input to the output.

Vout/Vin = 1 / (1 + ?)

d) What is the value of this ratio at the angular frequency found in part b? This special frequency is known as the cut-off frequency for the filter. Below this frequency the output stays fairly constant, above this frequency it drops like 1/?. We usually say that this frequency corresponds to the bandwidth of the low pass filter. A note for those who know more or are going on: the magnitude of this ratio is wrong here because we used the absolute value for the impedance of the capacitor; if you use the actual complex impedance you get a different numerical value, but conceptually this simplified case can help to understand what is going on.

3) Low Pass Filter

[diagram omitted]

a) What is Vout for very low and very high frequencies?

b) Derive an expression for the angular frequency ? at which the impedance of the capacitor |Zc| is equal to R.

c) Using the voltage divider formula derive an expression for the ratio of Vout to Vin, put it in the form shown below. This is what is known as the transfer function of this circuit and it describes as a function of frequency how the amplitudes of sine waves at different frequencies are transferred from the input to the output.

Vout/Vin = 1 / (1 + ?)

d) What is the value of this ratio at the angular frequency found in part b? This special frequency is known as the cut-off frequency for the filter. Below this frequency the output stays fairly constant, above this frequency it drops like 1/?. We usually say that this frequency corresponds to the bandwidth of the low pass filter. A note for those who know more or are going on: the magnitude of this ratio is wrong here because we used the absolute value for the impedance of the capacitor; if you use the actual complex impedance you get a different numerical value, but conceptually this simplified case can help to understand what is going on.

Added by Aurora D.

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