LTI system example: RC lowpass filter
Linear timeinvariant (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 lowpass filter serves as example to examine amplitude and phase of this complex valued frequency response.
In this briefing and the subsequent experiment an RC lowpass filter serves as example for an LTI system. The transfer function, amplitude response and phase response are derived. An RC lowpass filter is a potential divider circuit containing a resistor and a capacitor. It implements a first order lowpass.
Recalling the capacitor impedance the transfer function results to
$H(f)=\frac{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$j2\pi C$}\right.}{R+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$j2\pi C$}\right.}=\frac{1}{1+j2\pi RC}$
or
$H(f)=\frac{1}{1+j(f/{f}_{C})}$ where ${f}_{C}$
is the cutoff frequency
${f}_{C}=\frac{1}{2\pi RC}$.
The rearrangement in polar coordinates leads to:
$H(f)=\frac{1}{\sqrt{1+(f/{f}_{C}{)}^{2}}}\cdot {e}^{j\cdot \mathrm{arctan}(f/{f}_{C})}$
Thus the absolute value $\leftH(f)\right$ yields the amplitude response, and the argument $\mathrm{arg}(H(f))$ yields the phase response.
$\leftH(f)\right=\frac{1}{\sqrt{1+(f/{f}_{C}{)}^{2}}}$
$\phi (f)=\mathrm{arctan}(f/{f}_{C})$
Calculate the missing values in the table!
f (frequency) [MHz]  5  10  15  20  40 

$\widehat{y}$ (output amplitude) [V]  0.707  0.447  
$\phi $ (phase shift) [ $\xb0$ ]  45.00  63.44 
In this laboratory experiment you will analyze the amplitude and phase response of a RC lowpass filter. In a sinewave analysis the amplitude and phase response is measured.
Start
The simulation starts with a sine input signal at amplitude 1V and frequency of 10MHz. The oscilloscope shows both the input and output signal.
Experiment
Adjust the input frequency and measure the respective amplitudes and phase delay times of the output signal. Compare the results with the values calculated in the tutorial.

Note that, with the input signal starting at zero, the phase delay time can be metered at the zero crossing of the output signal (black). The phase shift is the phase delay time divided by the cycle duration.
$\phi =\frac{t\cdot 360\xb0}{T}$Note
Stop the simulation after a complete oscilloscope sweep by pressing pause on your keypad and click on the point to measure. Ctrl + click yields the local maximum or zero crossing of the measured curve.
Next steps
 To change the filter itself, click on the block diagram to open the properties.
The cutofffrequency can be changed and the filter is reinitialized.  A rightclick on the filter offers to open the transfer function or the impulse response according to the cutoff frequency setting.
 Beyond the input properties frequency and amplitude, the waveform can be changed as well.