In the equation below the functioning of the circuit is explained in a more mathematical way, leading to the transfer function of a first order low pass filter. The impedance of the resistor is written as Z1 and the impedance of the capacitor is written as Z2.
The corner frequency of this RC low pass filter is inversely proportional to the RC value:
Note that the dimension of w is in radians per second; if the frequency in Hertz is desired one should divide it by 2π:
Given the properties of the components, R = 5 kΩ and C = 0.1 µF, a corner frequency of 318 Hertz is obtained. This corresponds to the bode plot of the low pass filter transfer function:
In the filter above, all the power delivered to the load has to travel through the resistor. As is known a resistor is a dissipating component. In low power filters like signal filters this might not be a drawback, but in high power filters energy dissipation is undesirable because of the efficiency aspect and the accompanying heat production.
The associated transfer function of this RL low pass filter is given by:
The resistor and inductor values of the components can be chosen in such a way that the same corner frequency is obtained as in the resistor-capacitor filter. The bode plot is then equal to the one shown before.
The first mentioned filter type is called a RC low pass filter, while the second type is known as a RL low pass filter. Component values like the resistance, capacitance and inductance can be chosen in such a way that both filter types have the same transfer function.