Implement first-order filter

Control and Measurements/Filters

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

Low-pass filter:

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

High-pass filter:

$$\begin{array}{c}H(s)=\frac{Ts}{1+Ts}\\ s=\text{Laplaceoperator}\\ T=\text{timeconstant}\end{array}$$

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.

**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.

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 |

The `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
at the MATLAB^{®} command prompt before you start.

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