# First-Order Filter

Implement first-order filter

## Library

Control and Measurements/Filters

## Description

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

Low-pass filter:

$H\left(s\right)=\frac{1}{1+Ts}$

High-pass filter:

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

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

• You can initialize filter states 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` or `Highpass`.

Time constant (s)

Specify the filter time constant, in seconds.

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, the 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.]

The frequency range used 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 One state per filter Dimensionalized Yes

## Example

The `power_FirstOrderFilter``power_FirstOrderFilter` example shows various uses of the First-Order Filter block using two Filter type parameter settings (`Lowpass` and `Highpass`).

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 you start.