# Filter

Model RF Filter

• Library:
• RF Blockset / Circuit Envelope / Elements

## Description

The Filter block models RF filters of three 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 ripples of equal magnitude in the passband and monotonic in the stopband.

• Inverse Chebyshev: Chebyshev Type II filters have ripples of equal magnitude in the stopband and monotonic in the passband.

• Ideal: Ideal filters perfectly allow frequencies in the passband and completely reject frequencies in the stopband.

## Parameters

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### Main

Simulation type, specified as one of the following:

• `Ideal`

Simulates an ideal filter of the type specified in Filter type and the model specified in Implementation.

• `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.

• `Inverse Chebyshev`

Simulates a inverse Chebyshev filter of the type specified in Filter type and the `Transfer function` model specified in Implementation.

Filter type, specified as one of the following:

• `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.

Implementation, specified as one of the following:

• `LC Tee`: Model an analog filter with an LC lumped Tee structure when the Design method is Butterworth or Chebyshev.

• `LC Pi`: Model an analog filter with an LC lumped Pi structure when the Design method is Butterworth or Chebyshev.

• `Transfer Function`: Model an analog filter using two-port S-parameters when the Design method is Butterworth or Chebyshev.

• `Constant per carrier`: Model a filter with either full transmission or full reflection set as constant throughout the entire envelope band around each carrier.The Design method is specified as ideal.

• `Frequency Domain`: Model a filter using convolution with an impulse response. The Design method is specified as ideal. The impulse response is computed independently for each carrier frequency to capture the ideal filtering response. When a transition between full transmission and full reflection of the ideal filter occurs within the envelope band around a carrier, the frequency-domain implementation captures this transition correctly up to a frequency resolution specified in Impulse response duration.

By default, the Implementation is `Constant per carrier` for an ideal filter and `LC Tee` for Butterworth or Chebyshev.

### Note

Due to causality, a delay of half the impulse response duration is included for both reflected and transmitted signals. This delay will impair the filter performance when the source and load resistances differ from the values specified as filter parameters.

Passband edge frequency, specified as a scalar in Hz, kHz, MHz, or GHz.

#### Dependencies

To enable this parameter, set Design method to `Ideal`.

Select this parameter to implement the filter order manually.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Filter order, specified as a scalar. This order is the number of lumped storage elements in `lowpass` or `highpass`. In `bandpass` or `bandstop`, the number of lumped storage elements are twice the value.

### Note

For even order Chebyshev filters, the resistance ratio $\frac{{R}_{\text{load}}}{{R}_{\text{source}}}>{R}_{\text{ratio}}$ for Tee network implementation and $\frac{{R}_{\text{load}}}{{R}_{\text{source}}}<\frac{1}{{R}_{\text{ratio}}}$ for Pi network implementation.

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

where:

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

• Rp is the passband ripple in dB.

#### Dependencies

To enable this parameter, select Implement using filter order.

Passband frequency for lowpass and highpass filters, specified as a scalar in Hz, kHz, MHz, or GHz. The default value is ```1 GHz``` for `Lowpass` filters and `2 GHz` for `Highpass` filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Lowpass` or `Highpass`.

Passband frequencies for bandpass filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for bandstop filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandpass`.

Passband attenuation, specified as a scalar dB. For bandpass filters, this value is applied equally to both edges of the passband.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Stopband frequencies for bandstop filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for bandpass filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandstop`.

Stopband attenuation, specified as a scalar dB. For bandstop filters, this value is applied equally to both edges of the stopband.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandstop`.

Input source resistance, specified as a scalar in ohms.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Output load resistance, specified as a scalar in ohms.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Select to internally ground and hide the negative terminals. Clear to expose the negative terminals. When the terminals are exposed, you can connect them to other parts of your model.

Use this button to save filter design to a file. Valid file types are `.mat` and `.txt`.

### Visualization

Type of plots, specified as ```Voltage transfer```, `Phase delay`, or `Group delay`.

Type of plots, specified as `None`, `Voltage transfer`, ```Phase delay```, or ```Group delay```.

Scaling of y-axis, specified as,

• `Magnitude(decibels)`, `Magnitude(linear)` or `Angle(degrees)`, `Real`, or `Imaginary` for ```Voltage transfer``` parameters.

• `Magnitude(decibels)` or `Magnitude(linear)` for ```Phase delay``` or `Group delay` parameters.

Scaling of y-axis, specified as,

• `Magnitude(decibels)`, `Magnitude(linear)` or `Angle(degrees)`, `Real`, or `Imaginary` for ```Voltage transfer``` parameters.

• `Magnitude(decibels)` or `Magnitude(linear)` for ```Phase delay``` or `Group delay` parameters.

Frequency points to plot on x-axis, specified as a vector with each element units in Hz, kHz, MHz, or GHz.

X-axis scale, specified as `Linear` or `Logarithmic`.

Y-axis scale, specified as `Linear` or `Logarithmic`.

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## 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.