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# Second-Order Filter

Implement second-order filter

## Library

Control and Measurements/Filters

## Description

Based on the Filter type selected in the block menu, the Second-Order Filter block implements the following transfer function:

Low-pass filter:

High-pass filter:

Band-pass filter:

Band-stop (notch) filter:

The key characteristics of the Second-Order Filter block are:

• Input accepts a vectorized input of N signals, implementing N filters. This feature is particularly useful for designing controllers in three-phase systems (N = 3).

• Filter states can be initialized for specified DC and AC inputs.

• It enables you to compute and plot filter response.

## Dialog Box and Parameters

Filter type

Specify the type of filter: Lowpass, Highpass, Bandpass, or Bandstop (notch).

Natural frequency fn (Hz)

Specify the natural frequency of the filter, in hertz. This value must be a scalar or a vector.

Damping ratio Zeta (Q = 1/(2*Zeta))

Specify the damping ratio of the filter. The damping ratio is typically a value between 0 and 1.

The damping ratio is related to the filter quality factor Q:

For a bandpass or a bandstop filter, the 3 dB bandwidth is given by

Sample time

Specify the sample time of the block, in seconds. Set to 0 to implement a continuous block.

Initialize filter states

When this check box is selected, filter states are initialized according to the AC initial input and DC initial input parameters.

AC initial input: [ Mag, Phase (degrees), Freq (Hz) ]

Specify the magnitude of the initial AC component of the input signal, its phase, in degrees, and its frequency, in hertz.

When the input is vectorized (N signals), specify an N-by-3 matrix, where each row of the matrix corresponds to a particular input.

The AC initial input parameter is visible only when the Initialize filter states parameter is selected.

DC initial input

Specify the value of the initial DC component of the input signal. When the input signal is vectorized, specify a 1-by-N vector, where each value corresponds to a particular input.

The DC initial input parameter is visible only when the Initialize filter states parameter is selected.

Plot filter response

When this check box is selected, the filter step response and its Bode diagram (magnitude and phase of transfer function as a function of frequency) are plotted in a figure.

Frequency range (Hz): [Start, End, Inc.]

Specify the frequency range for plotting the filter Bode diagram. Specify a vector containing the starting frequency, the end frequency, and the incremental frequency, in hertz.

The Frequency range parameter is visible only when the Plot filter response parameter is selected.

## Characteristics

 Direct Feedthrough Yes Sample Time Specified in the Sample Time parameterContinuous if Sample Time = 0 Scalar Expansion Yes, of the parameters States Two states per filter Dimensionalized Yes

## Example

The power_SecondOrderFilterpower_SecondOrderFilter example shows the Second-Order Filter block using two Filter type parameter settings (Lowpass and Bandstop).

The model sample time is parameterized with variable Ts (default value Ts = 50e-6). To simulate continuous filters, specify Ts = 0 in the MATLAB® Command Window before starting the simulation.