Filter

Model RF Filter

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Libraries:
RF Blockset / Circuit Envelope / Elements

Description

The Filter block models RF filters of four 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.

To filter RF complex baseband signals in Simulink, use the Idealized Baseband Filter block.

Examples

Frequency Response of Lowpass Chebyshev Filter

Example for Filter; lowpass Chebyshev.

• Open Script

Parameters

Main

Design method — Simulation type

Butterworth (default) | Chebyshev | Inverse Chebyshev | Ideal

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 — Filter type

Lowpass (default) | Highpass | Bandpass | Bandstop

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 — Implementation

LC Tee | LC Pi | Transfer function | Constant per carrier | Frequency Domain

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 — Passband edge frequency

1 GHz (default) | scalar

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

Dependencies

To enable this parameter, set Design method to Ideal.

Implement using filter order — Implement using filter order

off (default) | on

Select this parameter to implement the filter order manually.

Dependencies

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

Filter order — Filter order

3 (default) | scalar

Filter order, specified as a scalar within the range between [2, 60]. This order is the number of lumped storage elements in lowpass or highpass. In bandpass or bandstop, the number of lumped storage (L and C) 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.

$$R_{\text{ratio}}=\frac{\sqrt{1+{\epsilon }^2}+\epsilon }{\sqrt{1+{\epsilon }^2}-\epsilon }$$

where:

• $$\epsilon =\sqrt{{10}^{(0.1R_{\text{p}})}-1}$$

• R_p is the passband ripple in dB.

Dependencies

To enable this parameter, select Implement using filter order.

Passband frequency — Passband frequency for lowpass and highpass filters

scalar

Passband frequency for low[pass and highpass filters specified as a scalar in Hz, kHz, MHz, or GHz. Based on the Filter type you select, the default value of this parameter varies. The default values are listed in this table.

Filter Type	Default value of passband frequency
Lowpass	1 GHz
Highpass	2 GHz

Dependencies

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

Passband frequencies — Passband frequencies for bandpass filters

[2 3] GHz (default) | 2-tuple vector

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 (dB) — Passband attenuation

10*log10(2) (default) | scalar

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 — Stopband frequencies for bandstop filters

[2.1 2.9] GHz (default) | 2-tuple vector

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 (dB) — Stopband attenuation

40 (default) | scalar

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.

Source impedance (Ohm) — Input source resistance

50 (default) | scalar

Input source resistance, specified as a scalar in ohms.

Note

The source and load impedances must be equal when Implementation is set to Transfer function.

Dependencies

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

Load impedance (Ohm) — Output load resistance

50 (default) | scalar

Output load resistance, specified as a scalar in ohms.

Note

The source and load impedances must be equal when Implementation is set to Transfer function.

Dependencies

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

Ground and hide negative terminals — Ground RF circuit terminals

on (default) | off

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.

Export — Save filter design to a file

button

Use this button to save filter design to a MAT or TXT file. For more information, see Export Your Filter Design.

Visualization

Parameter 1 — Type of plots on y-axis

Voltage transfer (default) | Phase delay | Group delay

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

Parameter 2 — Type of plots

None (default) | Voltage transfer | Phase delay | Group delay

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

Format 1 — Scaling of y-axis

Magnitude (decibels) (default) | Magnitude (linear) | Angle (degrees) | Real | Imaginary

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.

Format 2 — Scaling of y-axis

Magnitude (decibels) (default) | Magnitude (linear) | Angle (degrees) | Real | Imaginary

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 — Frequency points to plot on x-axis

logspace(0,10,101) Hz (default) | vector

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

X-axis scale — X-axis scale

Linear (default) | Logarithmic

X-axis scale, specified as Linear or Logarithmic.

Y-axis scale — Y-axis scale

Linear (default) | Logarithmic

Y-axis scale, specified as Linear or Logarithmic.

More About

Export Your Filter Design

By clicking the Export button, you can export your filter design to a MAT or TXT file. You can then load this file and view the block parameters, as well as the resulting capacitor and inductor element values, which are stored as variables.

You can also view the resulting element values connected in an LC Tee or LC Pi ladder network topology. To view the element values, right-click the Filter block and select Mask, and then Look Under Mask. Pause on or click the element to see its label. You can map the resulting element values, stored in the MAT file as Capacitors and Inductors variables, to the elements connected in this ladder network using the labels.

To design an LC Tee or LC Pi ladder network, use the Implementation parameter.

Frequency Responses

Filter Type	Frequency Response
Lowpass
Highpass
Bandpass
Bandstop

Parameters To Define Filter and Design Tips

This table shows all the parameters required to design each filter correctly:

Additional Design Tips

Some additional design tips:

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.

Version History

Introduced in R2016b