A sinusoid has just been fed into a system.
2 views (last 30 days)
Show older comments
The system in question has a frequency response given by H(w) = 1/(1+0004jw), where w represents frequency in rads/second.
The input sinusoid has an amplitude of 3, phase of 0 radians and a frequency of 33Hz.
How would I determine the amplitude and phase (between -pi and pi rads) of the sinusoidal output?
Many thanks.
(Keep in mind that an LTI system never changes the frequency of a sinusoid.)
8 Comments
Sam Chak
on 26 Mar 2022
No wonder, I almost use
s = tf('s');
sys = 1/(1 + 4*s);
bode(sys)
Hz is equivalent to rad/s.
The Bode plot can tell you whether a sinusoidal input signal in amplified or attenuated (in dB), or how much it is shifted in phase when passing through a linear dynamical system at a certain frequency. These info are generally useful when designing low-pass and high-pass filters.
Accepted Answer
Star Strider
on 26 Mar 2022
Using phasors —
syms omega
sympref('AbbreviateOutput',false); % Optional
omega = 2*pi*33; % Radian Frequency
H = 1/(1+0.004*j*omega) % System
phasorH = [abs(H), angle(H)] % Phasor = [Amplitude PhaseAngle]
phasorInput = [3, 0]
phasorOutput = [phasorH(1)*phasorInput(1), phasorH(2)+phasorInput(2)] % Multiply Amplitudes, Add Phases
So, the output has an amplitude of 2.3091 and a phase angle of -0.6924 radians.
I haven’t routinely worked with phasors in a while (since grad school, back in the Precambrian) so check this. However, I believe the approach is correct.
.
2 Comments
More Answers (1)
Sam Chak
on 26 Mar 2022
Edited: Sam Chak
on 26 Mar 2022
This is sort of the "control theorist's way", if you are interested to learn.
s = tf('s');
sys = 1/(1 + 0.004*s)
omega = 33*2*pi;
[mag, phase, wout] = bode(sys, omega)
Input_Amplitude = 3
Output_Amplitude = Input_Amplitude*mag
Output_phase_in_radian = (pi/180)*phase % the unit degree is commonly used
sys =
1
-----------
0.004 s + 1
Continuous-time transfer function.
mag =
0.7697
phase =
-39.6716
wout =
207.3451
Input_Amplitude =
3
Output_Amplitude =
2.3091
Output_phase_in_radian =
-0.6924
0 Comments
See Also
Categories
Find more on Get Started with Control System Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!