The resistor-capacitor (RC) low-pass filter circuit diagram is given below. The voltage across the resistor is given by Ohm's law and is VR = I x R. The voltage across the capacitor, Vout lags the current by 900 and is given by Vout = I x XC, where XC is the capacitive reactance.
Looking at the diagram, Pythagoras's Theorem can be used to obtain the expression Vin = (VR2 + Vout2) ^ 0.5.
The impedance (ie combination of resistance and reactance) looking from the supply into the circuit is given by Z = (R2 + XC2) ^ 0.5.
The current in the circuit, I, is equal to Vin / Z.
RC Low-Pass Filter Excel Spreadsheet
|MathML formula||Formula Image||Straight text formula|
||fc = 1 / 2πRC|
fc = cut off frequency, Hertz
= that frequency at which output power has fallen by half
= that frequency at which output voltage has fallen by 1/(2^0.5) = 0.707
R = resistance in Ohms
C = capacitance in Farads
The cut off frequency is defined as that frequency at which the output power has fallen by 50%, ie 1/(2^0.5) = 0.707 of the voltage.
I intend to build the circuit below to test my understanding of RC low-pass filters. The 1 Ohm resistor makes little difference to the operation of the circuit, but can be used as a convenient way to measure current (a high input impedance voltmeter connected across the 1 ohm resistor will give a reading in volts that corresponds 1:1 with the current in amps).