Linear time-invariant (LTI) systems can be represented by the transfer function.
It determines the output signal of an LTI system for a given input signal in the frequency domain.
An RC low-pass filter serves as example to examine amplitude and phase of this complex valued frequency response.
LTI system's output is related to the input by the transfer function
In this briefing and the subsequent experiment an RC low-pass filter serves as example for an LTI system. The transfer function, amplitude response and phase response are derived.
An RC low-pass filter is a potential divider circuit containing a resistor and a capacitor. It implements a first order low-pass.
Recalling the capacitor impedance the transfer function results to
is the cutoff frequency
The rearrangement in polar coordinates leads to:
Thus the absolute value yields the amplitude response, and the argument yields the phase response.
Amplitude response |H(f)| of RC low-pass with fc = 10MHz
Calculate the missing values in the table!
|f (frequency) [MHz]
(output amplitude) [V]
(phase shift) [
Example output amplitude and phase shift for fc =10MHz and