Frequency response bandwidth
returns the bandwidth of the SISO dynamic system
fb = bandwidth(
sys. The bandwidth is the first frequency where the gain drops
below 70.79% (-3 dB) of its DC value. The bandwidth is expressed in
TimeUnit is the
TimeUnit property of
This command requires a Control System Toolbox™ license.
Compute System Bandwidth
Compute the bandwidth of the transfer function
sys = 1/(s+1).
sys = tf(1,[1 1]); fb = bandwidth(sys)
fb = 0.9976
This result shows that the gain of
sys drops to 3 dB below its DC value at around 1 rad/s.
Find Bandwidth of System with Custom Gain Drop
Compute the frequency at which the gain of a system drops to 3.5 dB below its DC value. Create a state-space model.
A = [-2,-1;1,0]; B = [1;0]; C = [1,2]; D = 1; sys = ss(A,B,C,D);
Find the 3.5 dB bandwidth of
dbdrop = -3.5; fb = bandwidth(sys,dbdrop)
fb = 0.8348
Find Bandwidth of Model Array
Find the bandwidth of each entry in a 5-by-1 array of transfer function models. Use a
for loop to create the array, and confirm its dimensions.
sys = tf(zeros(1,1,5)); s = tf('s'); for m = 1:5 sys(:,:,m) = m/(s^2+s+m); end size(sys)
5x1 array of transfer functions. Each model has 1 outputs and 1 inputs.
Find the bandwidths.
fb = bandwidth(sys)
fb = 5×1 1.2712 1.9991 2.5298 2.9678 3.3493
bandwidth returns an array in which each entry is the bandwidth of the corresponding entry in
sys. For instance, the bandwidth of
sys — Dynamic system
dynamic system model | model array
Dynamic system, specified as a SISO dynamic system model or an array of SISO dynamic system models. Dynamic systems that you can use include:
sys is an array of models,
bandwidth returns an array of the same size, where
each entry is the bandwidth of the corresponding model in
sys. For more information on model arrays, see
Model Arrays (Control System Toolbox).
dbdrop — Gain drop
-3 (default) | negative scalar
Gain drop in dB, specified as a real negative scalar.
fb — Frequency response bandwidth
scalar | array
Frequency response bandwidth, returned as a scalar or an array. If
A single model, then
fbis the bandwidth of
A model array, then
fbis an array of the same size as the model array
sys. Each entry is the bandwidth of the corresponding entry in
fb is expressed in
TimeUnit is the
Introduced before R2006a