# Documentation

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# Filter

Model RF filter

Elements

## Description

The Filter block models RF filters of two designs:

• Butterworth: Butterworth filters have a magnitude response that is maximally flat in the passband and monotonic overall. This smoothness comes at the price of decreased roll-off steepness.

• Chebyshev: Chebyshev Type I filters have equal ripple in the passband and monotonic in the stopband.

The frequency responses of the filter types are shown:

Filter TypeFrequency Response
Lowpass

Highpass

Bandpass

Bandstop

## Parameters

### Main

Design method
• `Butterworth`

Simulates a butterworth filter of the type specified in Filter type and the model specified in Implementation.

• `Chebyshev`

Simulates a chebyshev filter of the type specified in Filter type and the model specified in Implementation.

By default, the Design method is `Butterworth`.

Filter type
• `Lowpass`: Simulates a lowpass filter type of the design specified in Design method.

• `Highpass`: Simulates a highpass filter type of the design specified in Design method.

• `Bandpass`: Simulates a bandpass filter type of the design specified in Design method.

• `Bandstop`: Simulates a bandstop filter type of the design specified in Design method.

By default, the Filter Type is `Lowpass`.

Implementation
• `LC Tee`: Model an analog filter having a LC lumped Tee structure.

• `LC Pi`: Model an analog filter having a LC lumped Pi structure.

• `Transfer Function`: Model an analog filter using two-port S-parameters.

By default, the Implementation is ```LC Tee```.

Implement using filter order

Select this check box to specify the Filter order.

Filter order

Specify the order of the filter. This order is the number of lumped storage elements in `lowpass` or `highpass`. In case of `bandpass` or `bandstop`, the number of lumped storage elements will be twice the value. This option is available only when Implement using filter order is selected. The default value of filter order is 3.

### Note

For even order Chebyshev filters, the resistance ratio Rload/Rsrc > Rratio for Tee network implementation and Rload/Rsrc < 1/Rratio for Pi network implementation.

`${R}_{ratio}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\sqrt{1+{\in }^{2}}+\in }{\sqrt{1+{\in }^{2}}-\in }$`
where:

• `$\in \text{\hspace{0.17em}}=\text{\hspace{0.17em}}\sqrt{{10}^{\left(0.1{R}_{p}\right)}-1}$`

• Rp is the passband ripple in dB.

Passband frequency

When the Filter type is set to `Lowpass` or `Highpass`, specify the passband frequency as a scalar in `Hz`, `kHz`, `MHz`, `GHz`. The default value is 1 GHz.

Passband frequencies

When the Filter type is set to `Bandpass` , specify the passband edge frequencies as a 2–tuple vector in `Hz`, `kHz`, `MHz`, `GHz`. The default value is [2 3] GHz.

### Note

This tab is also available for `Bandstop` filters when Implement using filter order is not selected.

Passband attenuation (dB)

Specify the passband attenuation in `dB`. For bandpass filters this value is applied equally to both edges of the passband.

Stopband frequency

When the Filter type is set to `Lowpass` or `Highpass`, specify the stopband frequency as a scalar in `Hz`, `kHz`, `MHz`, `GHz`. The default value is 2 GHz.

Stopband frequencies

When the Filter type is set to `Bandstop`, specify the stopband edge frequencies as a 2–tuple vector in `Hz`, `kHz`, `MHz`, `GHz`. The default value is [2.1 2.9] GHz.

### Note

This tab is also available for `Bandpass` filters when Implement using filter order is not selected.

Stopband attenuation (dB)

Specify the stopband attenuation in `dB`. For bandstop filters, this value is applied equally to both edges of the stopband. The default value is 40 dB.

Source impedance (Ohm)

Specify the value of input source resistance in ohms. The default value is 50 ohms.

Specify the value of output load resistance in ohms. The default value is 50 ohms.

Ground and hide negative terminals

Select this option to internally ground and hide the negative terminals. Clear this to expose the negative terminals. By exposing these terminals, you can connect them to other parts of your model.

By default, this option is selected.

Save the filter design to a file. Valid file types are .mat and .txt .

Main Combination Options

LowpassHighpassBandpassBandstop
ButterworthOrder, ωp, Ap Order, ωp, ApOrder, ωpL, ωpH, ApOrder, ωsL, Ap, ωsH, As
ωp, Ap, ωs, Asωp, Ap, ωs, AspL, ωpH), Ap, (ωsL, ωsH), AspL, ωpH), Ap, (ωsL, ωsH), As
ChebyshevOrder, ωp, ApOrder, ωp, ApOrder, ωpL, ωpH, ApOrder, ωsL, Ap, ωsH, As
ωp, Ap, ωs, Asωp, Ap, ωs, AspL, ωpH), Ap, (ωsL, ωsH), AspL, ωpH), Ap, (ωsL, ωsH), As
Order = filter order, ωp = passband frequency, Ap = passband attenuation in dB, ωpL, ωpH = passband frequencies, ωsL, ωsH = stopband frequencies, As = stopband attenuation

### Visualization Tab

Parameter1, Parameter2

For Parameter1, specify the plots on left y-axis from : `Voltage transfer`, ```Phase delay``` or `Group delay`. The default value `Voltage transfer`.

For Parameter2, specify the plots on left y-axis from : `Voltage transfer`, ```Phase delay``` or `Group delay`. If the model has only one parameter specify the plots as `None`. The default value `None`.

The options in Parameter1 and Parameter2 are mutually exclusive.

Format1, Format2

Specify the scaling of the y-axis for Parameter1 and Parameter2.

• For `Voltage transfer` parameters, specify the format as `Magnitude(decibels)`, `Magnitude(linear)` or `Angle(degrees)`, `Real`, or `Imaginary`.

• For `Phase delay` or ```Group delay``` parameters, specify the format as `Magnitude(decibels)` or `Magnitude(linear)` .

The default value is ```Magnitude (decibels)```.

Frequency points

Specify frequency points to plot on the x-axis in `Hz`, `kHz`, `MHz`, `GHz`.

Y-axis scale

Specify the scale for the y-axis. The default value is `Linear`.

X-axis scale

Specify the scale for the x-axis. The default value is `Linear`.

## References

[1] Kendall Su, Analog Filters, Second Edition.

[2] Louis Weinberg, Network Analysis and Synthesis, Huntington, New York: Robert E. Krieger Publishing Company, 1975.

[3] Larry D. Paarmann, Design and Analysis of Analog Filters, A Signal Processing Perspective with MATLAB Examples, Kluwer Academic Publishers, 2001.

[4] Michael G. Ellis, SR., Electronic Filter Analysis and Synthesis, Norwood, MA: Artech House, 1994.

[5] Anatol I. Zverev, Handbook of Filter Synthesis, Hoboken, NJ: John Wiley & Sons, 2005.