Filter
Model RF Filter
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 rolloff 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
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 theTransfer 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 twoport Sparameters 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 frequencydomain 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.
$${R}_{\text{ratio}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\sqrt{1+{\epsilon}^{2}}+\epsilon}{\sqrt{1+{\epsilon}^{2}}\epsilon}$$
where:
$$\epsilon \text{\hspace{0.17em}}=\text{\hspace{0.17em}}\sqrt{{10}^{(0.1{R}_{\text{p}})}1}$$
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)  2tuple vector
Passband frequencies for bandpass filters, specified as a 2tuple 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)  2tuple vector
Stopband frequencies for bandstop filters, specified as a 2tuple 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.
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.
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 yaxis
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 yaxis
Magnitude
(decibels)
(default)  Magnitude (linear)
 Angle (degrees)
 Real
 Imaginary
Scaling of yaxis, specified as,
Magnitude(decibels)
,Magnitude(linear)
orAngle(degrees)
,Real
, orImaginary
forVoltage transfer
parameters.Magnitude(decibels)
orMagnitude(linear)
forPhase delay
orGroup delay
parameters.
Format 2 — Scaling of yaxis
Magnitude
(decibels)
(default)  Magnitude (linear)
 Angle (degrees)
 Real
 Imaginary
Scaling of yaxis, specified as,
Magnitude(decibels)
,Magnitude(linear)
orAngle(degrees)
,Real
, orImaginary
forVoltage transfer
parameters.Magnitude(decibels)
orMagnitude(linear)
forPhase delay
orGroup delay
parameters.
Frequency points — Frequency points to plot on xaxis
logspace(0,10,101) Hz
(default)  vector
Frequency points to plot on xaxis, specified as a vector with each element units in Hz, kHz, MHz, or GHz.
Xaxis scale — Xaxis scale
Linear
(default)  Logarithmic
Xaxis scale, specified as Linear
or
Logarithmic
.
Yaxis scale — Yaxis scale
Linear
(default)  Logarithmic
Yaxis 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, rightclick 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
See Also
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