rffilter

Create Butterworth, Chebyshev, and inverse Chebyshev RF filter

Description

Use the rffilter object to create a Butterworth, Chebyshev or an Inverse Chebyshev RF filter. The RF filter is a two-port circuit object, and you can include this object as an element of a circuit. For more design information see, Parameters to Define Filter and Design Tips.

You can also convert the rffilter object to a LC ladder filter by using the lcladder object. For example, LCLad = lcladdder(rffiltobj) where rffiltobj is an rffilter object.

Creation

Syntax

rffiltobj = rffilter

rffiltobj = rffilter(Name=Value)

Description

rffiltobj = rffilter creates a two-port filter with default properties.

rffiltobj = rffilter(Name=Value) sets properties using one or more name-value pairs. For example, rffiltobj = rffilter(FilterType='Chebyshev') creates a two-port Chebyshev RF filter.

Properties

FilterType — Filter type

'Butterworth' (default) | 'Chebyshev' | 'InverseChebyshev'

Filter type, specified as 'Butterworth', 'Chebyshev', or 'InverseChebyshev'.

Example: 'FilterType','Chebyshev'

Example: rfobj.FilterType = 'Chebyshev'

Data Types: char | string

ResponseType — Filter response type

'Lowpass' (default) | 'Highpass' | 'Bandpass' | 'Bandstop'

Filter response type, specified as 'Lowpass', 'Highpass', 'Bandpass', or 'Bandstop'. For more information, see Frequency Responses.

Example: 'ResponseType','Highpass'

Example: rfobj.ResponseType = 'Highpass'

Data Types: char | string

Implementation — Filter implementation

'LC Tee' (default) | 'LC Pi' | 'Transfer function'

Filter implementation, specified as 'LC Tee', 'LC Pi', or 'Transfer function'.

Example: 'Implementation','Transfer function'

Example: rfobj.Implementation = 'Transfer function'

Dependencies

For 'Inverse Chebyshev' type filter, you can only use 'Transfer function' implementation.

Data Types: char | string

FilterOrder — Filter order

3 (default) | real finite non-negative integer

Filter order, specified as a real finite non-negative integer. In a lowpass or highpass filter, the order specifies the number of lumped storage elements. In a bandpass or bandstop filter, the number of lumped storage elements is twice the value of the order.

Note

FilterOrder has the highest precedence among all the name-value pairs in the filter design. Using this property sets the UseFilterOrder read-only property to true.

Example: 'FilterOrder',4

Example: rfobj.FilterOrder = 4

Data Types: double

PassbandFrequency — Passband frequency

scalar | two-element vector

Passband frequency, specified as:

• A scalar in hertz for lowpass and highpass filters.

• A two-element vector in hertz for bandpass or bandstop filters.

By default, the values are 1e9 for lowpass filter, 2e9 for highpass filter, and [2e9 3e9] for bandpass and [[1e9 4e9] for bandstop filters.

Example: 'PassbandFrequency',[3e6 5e6]

Example: rfobj.PassbandFrequency = [3e6 5e6]

Data Types: double

StopbandFrequency — Stopband frequency

scalar | two-element vector

Stopband frequency, specified as:

• A scalar in hertz for lowpass and highpass filters.

• A two-element vector in hertz for bandpass or bandstop filters.

By default, the values are 2e9 for lowpass filter, 1e9 for highpass filter, [1.5e9 3.5e9] for bandpass filters, and [2.1e9 2.9e9] bandstop filters.

Example: rffilter('ResponseType','lowpass','StopbandFrequency',[3e6 5e6])

Example: rfobj.StopbandFrequency = [3e6 5e6]

Data Types: double

PassbandAttenuation — Passband attenuation

10*log10(2) (default) | scalar

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

Example: 'PassbandAttenuation',5

Example: rfobj.PassbandAttenuation = 5

Data Types: double

StopbandAttenuation — Stopband attenuation

40 (default) | scalar

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

Example: 'StopbandAttenuation',30

Example: rfobj.StopbandAttenuation = 30

Data Types: double

Zin — Source impedance

50 (default) | positive real part finite scalar

Source impedance, specified as a positive real part finite scalar in ohms.

Example: 'Zin',70

Example: rfobj.Zin = 70

Data Types: double

Zout — Load impedance

50 (default) | positive real part finite scalar

Load impedance, specified as a positive real part finite scalar in ohms.

Example: 'Zout',70

Example: rfobj.Zout = 70

Data Types: double

Name — Name of RF filter object

'Filter' (default) | character vector

Name of RF filter object, specified as a character vector. Two elements in the same circuit cannot have the same name. All names must be valid MATLAB^® variable names.

Example: 'Name','filter1'

Example: rfobj.Name = 'filter1'

Data Types: char | string

NumPorts — Number of ports

2

Number of ports, specified as a 2. This property is read-only.

Data Types: double

Terminals — Names of terminals

{'p1+','p2+','p1-','p2-'}

Names of the terminals, specified as a {'p1+','p2+','p1-','p2-'}. This property is read-only.

Data Types: char

DesignData — Filter design data

structure

Filter design data, specified as a structure. This property is read-only. For more information, see Design Data for LC Tee and LC Pi Topologies and Design Data for Transfer Function Implementation.

Data Types: struct

UseFilterOrder — Use of filter order for filter design

true | false

Use of filter order for filter design, specified as a true or false. This property is a read-only.

Data Types: logical

Object Functions

groupdelay	Group delay of S-parameter object or RF filter object or RF Toolbox circuit object
sparameters	Calculate S-parameters for RF data, network, circuit, and matching network objects
set	Set rffilter object property values
zpk	Converts rffilter to zero-pole-gain representation
tf	Converts rffilter to transfer function
lcladder	Create LC ladder network
rfplot	Plot input reflection coefficient and transducer gain of matching network
clone	Create copy of existing circuit element or circuit object
circuit	Circuit object

Examples

Default RF Filter

Create and view the properties of a default RF filter object.

rfobj = rffilter

rfobj = 
  rffilter: Filter element

             FilterType: 'Butterworth'
           ResponseType: 'Lowpass'
         Implementation: 'LC Tee'
            FilterOrder: 3
      PassbandFrequency: 1.0000e+09
    PassbandAttenuation: 3.0103
                    Zin: 50
                   Zout: 50
             DesignData: [1x1 struct]
         UseFilterOrder: 1
                   Name: 'Filter'

rfobj.DesignData

ans = struct with fields:
            FilterOrder: 3
              Inductors: [7.9577e-09 7.9577e-09]
             Capacitors: 6.3662e-12
               Topology: 'lclowpasstee'
      PassbandFrequency: 1.0000e+09
    PassbandAttenuation: 3.0103

S-Parameters of Butterworth passband filter (LC Tee Implementation Type)

Create a Butterworth passband filter object named BFCG_162W with passband frequencies between 950 and 2200 MHz, stopband frequencies between 770 and 3000 MHz, passband attenuation of 3.0 dB, and stopband attenuation of 40 dB using 'LC Tee' implementation type. Calculate the S-parameters of the filter at 2.1 GHz.

robj = rffilter('ResponseType','Bandpass','Implementation','LC Tee','PassbandFrequency',[950e6 2200e6],                        ...
    'StopbandFrequency',[770e6 3000e6],'PassbandAttenuation',3,'StopbandAttenuation',40);
robj.Name = 'BFCG_162W'

robj = 
  rffilter: Filter element

             FilterType: 'Butterworth'
           ResponseType: 'Bandpass'
         Implementation: 'LC Tee'
      PassbandFrequency: [950000000 2.2000e+09]
    PassbandAttenuation: 3
      StopbandFrequency: [770000000 3.0000e+09]
    StopbandAttenuation: 40
                    Zin: 50
                   Zout: 50
             DesignData: [1x1 struct]
         UseFilterOrder: 0
                   Name: 'BFCG_162W'

Calculate the S-parameters at 2.1 GHz.

s = sparameters(robj,2.1e9)

s = 
  sparameters with properties:

      Impedance: 50
       NumPorts: 2
     Parameters: [2x2 double]
    Frequencies: 2.1000e+09

Build a lcladder object from the rffilter object. This lcladder object can be used in a circuit directly and could also be used for parametric analysis across inductor and capacitance values.

l = lcladder(robj)

l = 
  lcladder: LC Ladder element

        Topology: 'bandpasstee'
     Inductances: [1.8116e-09 5.7297e-09 8.3361e-09 2.8294e-09 1.2214e-08 2.3802e-09 1.2214e-08 2.8294e-09 8.3361e-09 5.7297e-09 1.8116e-09]
    Capacitances: [6.6900e-12 2.1152e-12 1.4539e-12 4.2835e-12 9.9228e-13 5.0919e-12 9.9228e-13 4.2835e-12 1.4539e-12 2.1152e-12 6.6900e-12]
            Name: 'lcfilt'

Alternatively, to access the inductors and capacitors directly from the filter object use:

L = robj.DesignData.Inductors;
C = robj.DesignData.Capacitors;

Group Delay of Chebyshev Lowpass Filter

Create a Chebyshev lowpass filter with a passband frequency of 2 GHz.

robj = rffilter('FilterType','Chebyshev','PassbandFrequency',2e9);

Set the filter order to 5 and the implementation to LC Pi.

set(robj,'FilterOrder',5,'Implementation','LC Pi');

Calculate the group delay of the filter at 1.9 GHz.

groupdelay(robj,1.9e9)

ans = 
1.4403e-09

Design Butterworth Filter and Determine Filter Order

This example shows how to design a low-pass Butterworth filter with passband frequency of 3 kHz, stopband frequency 7 kHz, passband attenuation of 2 dB, and stopband attenuation 60 dB. Display the filter order of such a designed filter and determine the passband frequency at 3.0103 dB. See [2] in rffilter object page.

Filter Parameters

Fp = 3e3;          % Passband frequency, Hz
Ap = 2;            % Passband attenuation, dB
Fs = 7e3;          % Stopband frequency, Hz
As = 60;           % Stopband attenuation, dB

Design Filter

r = rffilter("FilterType","Butterworth","ResponseType","Lowpass","Implementation","Transfer function","PassbandFrequency",Fp,     ...
    "PassbandAttenuation",Ap,"StopbandFrequency",Fs,"StopbandAttenuation",As);

Filter Order of Designed Filter

N = r.DesignData.FilterOrder;
sprintf('Calculated filter order is %d',N)

ans = 
'Calculated filter order is 9'

Frequency at 3.0103 dB

F_3dB = r.DesignData.PassbandFrequency/1e3;
sprintf('Frequency at 3.0103 dB is %d kHz',F_3dB)

ans = 
'Frequency at 3.0103 dB is 3.090733e+00 kHz'

Visualize Magnitude Response

frequencies = linspace(0,2*Fs,1001);
rfplot(r, frequencies)

Note: To use rfplot and plot on the same figure use setrfplot. Type 'help setrfplot' in command window for information.

Reference

1. Larry D. Paarmann, Design and Analysis of Analog Filters: A Signal Processing Perspective, Kluwer Academic Publishers

Design Chebyshev Filter and Determine Filter Order

Design a low-pass Chebyshev filter with 0.1 dB bandpass ripple, cut-off frequency of 1 rad/sec, and 50 dB attenuation at 1.1 rad/sec. Display the filter order of this designed filter [1].

Define Parameters

Fp = 1/(2*pi);          % Passband frequency, Hz
Rp = 0.1;               % Ripple in Passband, dB
Fs = 1.1/(2*pi);        % Stopband frequency, Hz
As = 50;                % Stopband attenuation, dB

Design Filter

r = rffilter("FilterType","Chebyshev","ResponseType","Lowpass","Implementation","Transfer function","PassbandFrequency",Fp,     ...
    "PassbandAttenuation",Rp,"StopbandFrequency",Fs,"StopbandAttenuation",As)

r = 
  rffilter: Filter element

             FilterType: 'Chebyshev'
           ResponseType: 'Lowpass'
         Implementation: 'Transfer function'
      PassbandFrequency: 0.1592
    PassbandAttenuation: 0.1000
      StopbandFrequency: 0.1751
    StopbandAttenuation: 50
                    Zin: 50
                   Zout: 50
             DesignData: [1x1 struct]
         UseFilterOrder: 0
                   Name: 'Filter'

Filter Order of Designed Filter

N = r.DesignData.FilterOrder;
sprintf('Calculated filter order is %d',N)

ans = 
'Calculated filter order is 19'

Reference

1. G.Ellis, Michael,Sr.Electronic Filter Analysis and Synthesis,Artech House, 1994

Frequency Response of Even Order Chebyshev Filter

Design even order Chebyshev filter and plot the filter's frequency response.

Frequency Response of Even Order Chebyshev Filter using Transfer Function Implementation

Design even order Chebyshev filter with specified parameters.

Fp = 3e9;          % Passband frequency, GHz
Rp = 10;           % Passband attenuation, dB
Fs = 7e9;          % Stopband frequency, GHz
As = 50;           % Stopband attenuation, dB
rffiltobj = rffilter("FilterType","Chebyshev","ResponseType","Lowpass","Implementation","Transfer function","PassbandFrequency",Fp,...
    "PassbandAttenuation",Rp,"StopbandAttenuation",As, "StopbandFrequency",Fs);

Plot the frequency response of even order Chebyshev filter using rfplot function.

rfplot(rffiltobj,linspace(0,7.5e9,1001))

Visualize the stopband and passband attenuation using plot function.

hold on;
plot([0 7.5], repmat([-rffiltobj.PassbandAttenuation -rffiltobj.StopbandAttenuation],2,1),'--')

Use DesignData parameter to verify the order of your filter.

N = rffiltobj.DesignData.FilterOrder;
sprintf('Calculated filter order is %d',N)

ans = 
'Calculated filter order is 4'

More About

Design Data for LC Tee and LC Pi Topologies

For LC Tee or Pi topologies, DesignData returns inductor and capacitor values. In addition, DesignData includes other design parameters relevant to response type.

• Lowpass/Highpass Response: Filter order, Passband Frequency, Passband Attenuation

• Bandpass Response: Filter order, Passband Frequency, Passband Attenuation, Auxiliary (W_x).

• Bandstop Response: Filter order, Stopband Frequency, Passband Attenuation, Auxiliary (W_x).

For bandstop response, W_x is an adjustment for the first frequency at which the lowpass prototype meets the prescribed bandstop loss. For bandpass response, W_x is an adjustment of specification of passband attenuation not equal to 3 dB. For more information, see [1].

Design Data for Transfer Function Implementation

For transfer function implementation, DesignData returns factored polynomial coefficients for S-parameters. These factors group the complex conjugate terms to preserve precision. All S-parameters have a common denominator present in Denominator. The numerator terms for S₁₁, S₂₂, and S₂₁ (S₂₁ = S₁₂) can be evaluated using the factored polynomial present in numerators Numerator11, Numerator22, and Numerator21, respectively.

For example, consider a default lowpass filter at 1 GHz. You can find the S₂₁ data at 1 GHz for the filter as follows:

r = rffilter('Implementation','Transfer function');
f = 1e9;
num21 = [polyval(r.DesignData.Numerator21(1,:),1i*2*pi*f) ...
        polyval(r.DesignData.Numerator21(2,:),1i*2*pi*f)];
den = [polyval(r.DesignData.Denominator(1,:),1i*2*pi*f) ...
      polyval(r.DesignData.Denominator(2,:),1i*2*pi*f)];
s21_1GHz = prod(num21./den,2)

s21_1GHz =

  -0.5000 - 0.5000i

Alternatively, you can use the sparameters function to calculate the example:

S = sparameters(r,1e9);
S.Parameters(2,1)

ans =

  -0.5000 - 0.5000i

In addition, DesignData includes other design parameters relevant to response type for:

• Lowpass/Highpass Response: Filter order, Passband Frequency, Auxiliary (Numerator21 Polynomial)

  Note

  Passband frequency is at 3 dB for Butterworth filter.

• Bandpass Response: Filter order, Passband Frequency, Auxiliary (W_x, Numerator21 Polynomial)

• Bandstop Response: Filter order, Stopband Frequency, Auxiliary (W_x, Numerator21 Polynomial)

For bandstop response, W_x is an adjustment for the first frequency at which the lowpass prototype meets the prescribed bandstop loss. For bandpass response, W_x is an adjustment of specification of passband attenuation not equal to 3 dB.

Some additional design tips:

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:

References

[1] G.Ellis, Michael,Sr.Electronic Filter Analysis and Synthesis,Artech House, 1994

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

Version History

Introduced in R2018b