rffilter

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Creates Butterworth RF filters, Chebyshev RF filters, and Chebyshev reverse filters.

Library

EngeeRF

Description

Use the function rffilter to create a Butterworth RF filter, Chebyshev RF filter, or Chebyshev reverse filter. An RF filter is a two-port circuit object that can be included as a circuit element. For more information about design, see Filter definition parameters and design tips.

You can also transform an object rffilter into the ladder LC filter using the function lcladder.

Syntax

Function call

rffiltobj = rffilter() — creates a two-port filter, the properties of which are set by default.

rffiltobj = rffilter(Name=Value) — sets properties specified by one or more name-value arguments. Unspecified properties retain their default values.

Arguments

Name-value input arguments

Specify optional argument pairs as Name=Value, where Name — the name of the argument, and Value — the appropriate value.

Example: rffiltobj = rffilter(FilterType = "Chebyshev") creates a two-port Chebyshev RF filter. You can specify multiple name-value pairs.

# filterType — filter type

+ "Butterworth" (by default) | "Chebyshev" | "InverseChebyshev"

Details

The filter type specified as "Butterworth", "Chebyshev" or "InverseChebyshev".

Типы данных

String

# responseType — type of filter characteristic

+ "Lowpass" (by default) | "Highpass" | "Bandpass" | "Bandstop"

Details

The type of filter characteristic, set as "Lowpass", "Highpass", "Bandpass" or "Bandstop". For more information, see Frequency characteristics.

Типы данных

String

# Implementation — filter implementation

+ "LC Tee" (by default) | "LC Pi" | "Transfer function"

Details

The filter implementation, specified as "LC Tee", "LC Pi" or "Transfer function".

Dependencies

For a filter like "InverseChebyshev" you can only use the implementation "Transfer function".

Типы данных

String

# FilterOrder — filter order

+ 3 (by default) | scalar

Details

The filter order, given as a real finite non-negative integer scalar. In a low-pass or high-pass filter, the order determines the number of elements with a concentrated amount of memory. In a bandpass or notch filter, the number of elements with a concentrated amount of memory is twice the value of the order.

Property FilterOrder it has the highest priority among all pairs of arguments of the "name-value" type in the filter design. Using this property sets for the property UseFilterOrder, read-only, value true.

Типы данных

Int64

# PassbandFrequency — bandwidth frequency

+ scalar | vector

Details

The bandwidth frequency, set as follows:

Scalar in Hz for low- and high-pass filters.
Two-element vector in Hz for bandpass or notch filters.

By default, the values are 1e9 for a low-pass filter, 2e9 for the high-pass filter, [2e9 3e9] for the bandpass filter and [1e9 4e9] for the notch filter.

Типы данных

Float64

# StopbandFrequency — frequency of the delay band
scalar | vector

Details

The frequency of the delay band, set as follows:

Scalar in Hz for low- and high-pass filters.
Two-element vector in Hz for bandpass or notch filters.

By default, the values are 2e9 for a low-pass filter, 1e9 for the high-pass filter, [1.5e9 3.5e9] for band-pass filters and [2.1e9 2.9e9] for notch filters.

Типы данных

Float64

# PassbandAttenuation — bandwidth attenuation

+ 10*log10(2) (by default) | scalar

Details

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

Типы данных

Float64

# StopbandAttenuation — attenuation in the delay band

+ 40 (by default) | scalar

Details

The attenuation in the delay band, set as a scalar in dB. For notch filters, this value is applied equally to both edges of the delay band.

Типы данных

Float64

# Zin — source impedance

+ 50 (by default) | scalar

Details

The impedance of the source, given as the positive real part of a finite scalar in ohms.

Типы данных

Float64

# Zout — load impedance

+ 50 (by default) | scalar

Details

The load impedance, given as the positive real part of a finite scalar in ohms.

Типы данных

Float64

# Name — the name of the RF filter object

+ "Filter" (by default) | line

Details

The name of the RF filter object, set as a string. Two elements in the same schema cannot have the same names.

Типы данных

String

# NumPorts — number of ports

+ 2 (by default) | scalar

Details

The number of ports, set as a positive scalar.

This argument is read-only.

Типы данных

Int64

# Terminals — terminal names

+ ("p1+", "p2+", "p1−", "p2−") (default) | tuple of strings

Details

Terminal names specified as a tuple of strings from 4 elements.

This argument is read-only.

# DesignData — filter design data

+ structure

Details

Data about the filter design, specified as a structure.

This argument is read-only.

For more information, see Design data for LC Tee and LC Pi topologies and Design data for the implementation of the transfer function.

Типы данных

struct

# UseFilterOrder — using filter order during design

+ true (by default) | false

Details

Using the filter order in the design, defined as true or false.

This argument is read-only.

Типы данных

Bool

Output arguments

# rffiltobj is a two— port filter object

+ object

Details

A two-port filter object containing the following properties:

FilterType — the type of filter, for example "Butterworth";
ResponseType — filter characteristics, for example "Lowpass";
Zin — source impedance;
Zout — load impedance;
FilterOrder — filter order;
PassbandFrequency — bandwidth frequency;
StopbandFrequency — frequency of the delay band;
StopbandAttenuation — attenuation in the delay band;
PassbandAttenuation — bandwidth attenuation;
Implementation — filter implementation, for example "LC Tee";
UseFilterOrder — flag for using the filter order in the design;
DesignData — information about the filter structure:
- FilterType;
- ResponseType;
- Topology;
- FilterOrder;
- PassbandFrequency;
- StopbandFrequency;
- PassbandAttenuation;
- StopbandAttenuation;
- Inductors;
- Capacitors;
- Zeros21;
- Poles;
- AuxNum;
- Numerator11;
- Numerator21;
- Numerator22;
- Denominator;
- Auxiliary;
Name — the name of the filter, for example "Filter";
Ports — port names as a tuple of strings;
Terminals — terminal names in the form of a tuple of strings;
ParentNodes — nodes of the parent schema in the form of an array of integers, displayed only after adding the child schema to the parent schema;
ParentPath — the full path to the parent schema as a string, displayed only after adding the child schema to the parent schema.;
NumPorts — number of ports.

Examples

Default RF filter

Details

Let’s create and view the properties of the default RF filter object.

using EngeeRF

rfobj = rffilter()

println("FilterType: ", rfobj.FilterType,
        "\nResponseType: ", rfobj.ResponseType,
        "\nZin: ", rfobj.Zin,
        "\nZout: ", rfobj.Zout,
        "\nFilterOrder: ", rfobj.FilterOrder,
        "\nPassbandFrequency: ", rfobj.PassbandFrequency,
        "\nPassbandAttenuation: ", rfobj.PassbandAttenuation,
        "\nImplementation: ", rfobj.Implementation,
        "\nUseFilterOrder: ", rfobj.UseFilterOrder,
        "\nDesignData: ", rfobj.DesignData,
        "\nName: ", rfobj.Name,
        "\nTerminals: ", rfobj.Terminals,
        "\nNumPorts: ", rfobj.NumPorts)

FilterType: Butterworth
ResponseType: Lowpass
Zin: 50.0 + 0.0im
Zout: 50.0 + 0.0im
FilterOrder: 3
PassbandFrequency: 1.0e9
PassbandAttenuation: 3.010299956639812
Implementation: LC Tee
UseFilterOrder: true
DesignData: EngeeRF.RFFilterDesignData("Butterworth", "Lowpass", "lowpasstee", 3, 1.0e9, nothing, 3.010299956639812, nothing, [7.957747154594765e-9, 7.957747154594765e-9], [6.3661977236758135e-12], nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing)
Name: Filter
Terminals: ("p1+", "p2+", "p1-", "p2-")
NumPorts: 2

Consider the values of some of the properties of the argument DesignData.

println("FilterType: ", rfobj.DesignData.FilterType,
        "\nResponseType: ", rfobj.DesignData.ResponseType,
        "\nTopology: ", rfobj.DesignData.Topology,
        "\nFilterOrder: ", rfobj.DesignData.FilterOrder,
        "\nPassbandFrequency: ", rfobj.DesignData.PassbandFrequency,
        "\nPassbandAttenuation: ", rfobj.DesignData.PassbandAttenuation,
        "\nInductors: ", rfobj.DesignData.Inductors,
        "\nCapacitors: ", rfobj.DesignData.Capacitors)

FilterType: Butterworth
ResponseType: Lowpass
Topology: lowpasstee
FilterOrder: 3
PassbandFrequency: 1.0e9
PassbandAttenuation: 3.010299956639812
Inductors: [7.957747154594765e-9, 7.957747154594765e-9]
Capacitors: [6.3661977236758135e-12]

S-Butterworth bandpass filter parameters (LC Tee implementation type)

Details

Creating a Butterworth bandpass filter object with the name BFCG_162W with bandwidth frequencies from 950 before 2200 MHz, delay bands from 770 before 3000 MHz, bandwidth attenuation 3.0 dB and attenuation in the delay band 40 dB, using the implementation type "LC Tee". Calculate the S-parameters of the filter at the frequency 2.1 GHz.

using EngeeRF

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

println("FilterType: ", rfobj.FilterType,
        "\nResponseType: ", rfobj.ResponseType,
        "\nImplementation: ", rfobj.Implementation,
        "\nPassbandFrequency: ", rfobj.PassbandFrequency,
        "\nStopbandFrequency: ", rfobj.StopbandFrequency,
        "\nPassbandAttenuation: ", rfobj.PassbandAttenuation,
        "\nStopbandAttenuation: ", rfobj.StopbandAttenuation,
        "\nZin: ", rfobj.Zin,
        "\nZout: ", rfobj.Zout,
        "\nFilterOrder: ", rfobj.FilterOrder,
        "\nUseFilterOrder: ", rfobj.UseFilterOrder,
        "\nDesignData: ", rfobj.DesignData,
        "\nName: ", rfobj.Name)

FilterType: Butterworth
ResponseType: Bandpass
Implementation: LC Tee
PassbandFrequency: [9.5e8, 2.2e9]
StopbandFrequency: [7.7e8, 3.0e9]
PassbandAttenuation: 3.0
StopbandAttenuation: 40.0
Zin: 50.0 + 0.0im
Zout: 50.0 + 0.0im
FilterOrder: 3
UseFilterOrder: true
DesignData: EngeeRF.RFFilterDesignData("Butterworth", "Bandpass", "bandpasstee", 3, [9.5e8, 2.2e9], [7.7e8, 3.0e9], 3.0, 40.0, [6.366197723675813e-9, 2.3797090773309714e-9, 6.366197723675813e-9], [1.903767261864777e-12, 5.0929581789406516e-12, 1.903767261864777e-12], nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing)
Name: BFCG_162W

Calculate the S-parameters at the frequency 2.1 GHz.

s = sparameters(rfobj, [2.1e9])

println("Impedance: ", s.Impedance,
        "\nNumPorts: ", s.NumPorts,
        "\nFrequencies: ", s.Frequencies,
        "\nParameters: ", s.Parameters)

Impedance: 50.0
NumPorts: 2
Frequencies: [2.1e9]
Parameters: ComplexF64[-0.5036556283329914 + 0.26286600429645146im -0.3807662021320426 - 0.7295543647649324im; -0.38076620213204276 - 0.7295543647649329im -0.5036556283330005 + 0.2628660042964558im;;;]

Creating an object lcladder based on the object rffilter. This object lcladder It can be used directly in the circuit, as well as for parametric analysis of inductance and capacitance values.

l = lcladder(rfobj)

println("Name: ", l.Name,
        "\nTopology: ", l.Topology,
        "\nInductances: ", l.Inductances,
        "\nCapacitances: ", l.Capacitances)

Name: BFCG_162W
Topology: bandpasstee
Inductances: Union{Nothing, Float64}[6.366197723675813e-9, 2.3797090773309714e-9, 6.366197723675813e-9]
Capacitances: Union{Nothing, Float64}[1.903767261864777e-12, 5.0929581789406516e-12, 1.903767261864777e-12]

Alternatively, for direct access to inductors and capacitors from the filter facility, use:

L = rfobj.DesignData.Inductors
C = rfobj.DesignData.Capacitors

Details

Let’s create a Chebyshev low-pass filter with a bandwidth 2 GHz. Let’s set the filter order to 5, and the implementation — "LC Pi".

using EngeeRF

rfobj = rffilter(FilterType = "Chebyshev", PassbandFrequency = 2e9,
                 FilterOrder = 5, Implementation = "LC Pi")

Calculate the group delay of the filter at the frequency 1.9 GHz.

freqs = [1.9e9, 1.9e9 + 1e3]
groupdelay(rfobj, freqs)

2-element Vector{Float64}:
 1.4402890343137618e-9
 1.4402890343137618e-9

Additional Info

Design data for LC Tee and LC Pi topologies

Details

For LC Tee or Pi topologies, the property DesignData returns the values of inductors and capacitors. Besides, DesignData includes other design parameters related to the type of characteristic:

Low-frequency/high-frequency response: filter order, bandwidth frequency, bandwidth attenuation.
Band-pass characteristic: filter order, bandwidth frequency, bandwidth attenuation, auxiliary parameters (W_x).
Delay band characteristic: filter order, delay band frequency, bandwidth attenuation, auxiliary parameters (W_x).

To characterize the delay band, W_x is a correction for the first frequency at which the prototype low—pass filter corresponds to the specified delay band losses. For the band—pass characteristic, W_x is a correction of the attenuation specification in the bandwidth, not equal to 3 dB. For more information, see [1].

Design data for the implementation of the transfer function

Details

To implement the transfer function, the property DesignData returns coefficients of a polynomial decomposed into factors for S-parameters. These multipliers group complex conjugate terms to preserve accuracy. All S-parameters have a common denominator present in the property DesignData.Denominator. The terms of the numerator for S₁₁, S₂₂ and S₂₁ (S₂₁ = S₁₂) can be calculated using the factorized polynomial present in the numerators DesignData.Numerator11, DesignData.Numerator22 and DesignData.Numerator21 accordingly.

For example, consider the default low-pass filter on the frequency 1 GHz. Data S₂₁ on the frequency 1 The GHz for this filter can be found as follows:

using EngeeRF
using Polynomials

r = rffilter(Implementation = "Transfer function")
f = 1e9
s = 1im * 2π * f

num21_1 = Polynomial(reverse(r.DesignData.Numerator21[1, :]))
num21_2 = Polynomial(reverse(r.DesignData.Numerator21[2, :]))
den1 = Polynomial(reverse(r.DesignData.Denominator[1, :]))
den2 = Polynomial(reverse(r.DesignData.Denominator[2, :]))

num21 = [num21_1(s), num21_2(s)]
den = [den1(s), den2(s)]

s21_1GHz = prod(num21 ./ den)

-0.5 - 0.5im

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

using EngeeRF

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

-0.49999999999999994 - 0.49999999999999994im

Besides, DesignData includes other design parameters related to the type of characteristic:

Low-frequency/high-frequency response: filter order, bandwidth frequency, auxiliary parameters (numerator polynomial 21).

For the Butterworth filter, the bandwidth frequency is at 3 dB.
Band-pass characteristic: filter order, bandwidth frequency, auxiliary parameters (W_x, numerator polynomial 21).
Delay band characteristic: filter order, delay band frequency, auxiliary parameters (W_x, numerator polynomial 21).

Some additional design tips:

"Lowpass" "Highpass" "Bandpass" "Bandstop"

	`"Lowpass"`	`"Highpass"`	`"Bandpass"`	`"Bandstop"`
`"Butterworth"`	Order, , Auxiliary parameters (numerator polynomial 21)	Order, , Auxiliary parameters (numerator polynomial 21, W_x)	Order, , Auxiliary parameters (W_x)
`"Chebyshev"`	Order, , Auxiliary parameters (numerator polynomial 21)	Order, , Auxiliary parameters (fourth power of the numerator 21, W_x)
`"InverseChebyshev"`	Order, , Auxiliary parameters (W_x)	Order,

"Butterworth"

Order, , Auxiliary parameters (numerator polynomial 21)

Order, , Auxiliary parameters (numerator polynomial 21, W_x)

Order, , Auxiliary parameters (W_x)

"Chebyshev"

Order, , Auxiliary parameters (numerator polynomial 21)

Order, , Auxiliary parameters (fourth power of the numerator 21, W_x)

"InverseChebyshev"

Order, , Auxiliary parameters (W_x)

Order,

Frequency characteristics

Details

The value of the argument FilterType Frequency response Designations

The value of the argument `FilterType`	Frequency response	Designations
`"Lowpass"`		— bandwidth frequency — frequency of the delay band — bandwidth attenuation @ — attenuation in the delay band @
`"Highpass"`
`"Bandpass"`		— bandwidth frequencies — frequency of the delay band — attenuation in the bandwidth at specified bandwidth frequencies — attenuation in the delay band at the specified delay band frequencies
`"Bandstop"`

"Lowpass"

filter ce 1 en

— bandwidth frequency

— frequency of the delay band

— bandwidth attenuation @

— attenuation in the delay band @

"Highpass"

filter ce 2 en

"Bandpass"

filter ce 3 en

— bandwidth frequencies

— frequency of the delay band

— attenuation in the bandwidth at specified bandwidth frequencies

— attenuation in the delay band at the specified delay band frequencies

"Bandstop"

filter ce 4 en

filter ce 5 en

filter ce 6 en filter ce 7 en

Filter definition parameters and design tips

Details

The table shows all the parameters necessary for the correct design of each filter.

"Lowpass" "Highpass" "Bandpass" "Bandstop"

	`"Lowpass"`	`"Highpass"`	`"Bandpass"`	`"Bandstop"`
`"Butterworth"`	Order, ,	Order, ,	Order, ,	Order, ,
, , ,	, , ,	, , ,	, , ,
`"Chebyshev"`	Order, ,	Order, ,	Order, ,	Order, , ,
, , ,	, , ,	, , ,	, , ,
`"InverseChebyshev"`	Order, , ,	Order, , ,	Order, , ,	Order, ,
, , ,	, , ,	, , ,	, , ,
Order, ,	Order, ,	Order, ,

"Butterworth"

Order, ,

, , ,

"Chebyshev"

Order, ,

Order, , ,

, , ,

"InverseChebyshev"

Order, , ,

Order, ,

, , ,

Order, ,

The following designations are used in this table:

— bandwidth frequency;
— attenuation in the bandwidth / unevenness in the bandwidth;
— frequency of the delay band;
— attenuation in the delay band / unevenness in the delay band.

The unevenness (ripple) in the bandwidth or delay is analyzed as attenuation in the bandwidth or delay, respectively.

Literature

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

rffilter

Description

Syntax

Function call

Arguments

Name-value input arguments

Output arguments

Examples

Default RF filter

S-Butterworth bandpass filter parameters (LC Tee implementation type)

Low-pass Chebyshev filter group delay

Additional Info

Design data for LC Tee and LC Pi topologies

Design data for the implementation of the transfer function

Frequency characteristics

Filter definition parameters and design tips

Literature