bandwidth

Frequency response bandwidth

Description

example

fb = bandwidth(sys) returns the bandwidth of the SISO dynamic system model 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 rad/TimeUnit, where TimeUnit is the TimeUnit property of sys.

This command requires a Control System Toolbox™ license.

example

fb = bandwidth(sys,dbdrop) returns the bandwidth for a specified gain drop.

Examples

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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.

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 sys.

dbdrop = -3.5;
fb = bandwidth(sys,dbdrop)
fb = 0.8348

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(:,:,2) is fb(2).

Input Arguments

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Dynamic system, specified as a SISO dynamic system model or an array of SISO dynamic system models. Dynamic systems that you can use include:

• Continuous-time or discrete-time numeric LTI models such as tf (Control System Toolbox), zpk (Control System Toolbox), or ss (Control System Toolbox) models.

• Frequency-response data models such as frd models. For such models, bandwidth uses the first frequency point to approximate the DC gain.

If 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).

Gain drop in dB, specified as a real negative scalar.

Output Arguments

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Frequency response bandwidth, returned as a scalar or an array. If sys is:

• A single model, then fb is the bandwidth of sys.

• A model array, then fb is an array of the same size as the model array sys. Each entry is the bandwidth of the corresponding entry in sys.

fb is expressed in rad/TimeUnit, where TimeUnit is the TimeUnit property of sys. 