rfmodel.rational

Perform rational fit using pole-residue representation of the component

Description

Use the rational class to represent RF components using a rational function object of the form:

$$F(s)=\left({\displaystyle \sum _{k=1}^n\frac{C_k}{s-A_k}+D}\right)e^{-s\tau }\begin{array}{cc},& s=j2\pi f\end{array}$$

There are two ways to construct an rational function object:

• You can fit a rational function object to the component data using the rational function.

• You can use the rfmodel.rational constructor to specify the pole-residue representation of the component directly.

Creation

Syntax

h = rfmodel.rational

h = rfmodel.rational('Property1',value1,'Property2',value2,...)

Description

h = rfmodel.rational returns a rational function object whose properties are set to their default values.

h = rfmodel.rational('Property1',value1,'Property2',value2,...) sets properties using one or more name-value pairs. You can specify multiple name-value pairs. Enclose each property name in a quote

Properties

A — Poles of rational function object

complex vector

Poles of rational function object, specified as a complex vector in radians/second. The property length is shown in:

$$F(s)=\left({\displaystyle \sum _{k=1}^n\frac{C_k}{s-A_k}+D}\right)e^{-s\tau }\begin{array}{cc},& s=j2\pi f\end{array}$$

where, n must be equal to the length of the vector you provide for 'C'. n is the number of poles in the rational function object. By default, this property is empty.

Data Types: double

C — Residues of rational function object

complex vector

Residues of the rational function object, specified as a complex vector in radians/second. The property length is shown in

$$F(s)=\left({\displaystyle \sum _{k=1}^n\frac{C_k}{s-A_k}+D}\right)e^{-s\tau }\begin{array}{cc},& s=j2\pi f\end{array}$$

as n, must be equal to the length of the vector you provide for 'A'. n is the number of residues in the rational function object. By default, this property is empty.

Data Types: double

D — Frequency response offset

scalar

Frequency response offset, specified as a scalar. The default value is 0.

Data Types: double

Delay — Frequency response time delay

scalar

Frequency response time delay, specified as a scalar. The default value is 0.

Data Types: double

Name — Object name

'Rational Function' (default) | 1-by-N character array

Object name, specified as a 1-by-N character array. This is a read-only property.

Data Types: char

Object Functions

timeresp	Time response for rational objects
stepresp	Step-signal response for rational object and rationalfit function object
freqresp	Frequency response of rational object and rationalfit function object
impulse	Impulse response for rational function object
ispassive	Return true if rational fit output is passive at all frequencies
makepassive	Enforce passivity of rational fit
passivity	Plot passivity of N-by-N rational fit output
pwlresp	Calculate time response of piecewise linear input signal
generateSPICE	Generate SPICE file from rationalfit of S-parameters
writeva	Generate Verilog-A description of rational object
abcd	Construct state-space matrices from rational object
zpk	Compute zeros, poles, and gain of rational object

Examples

Fit Rational Function to Data

Fit a rational function to data from an rfdata.data object.

S = sparameters('defaultbandpass.s2p');
freq = S.Frequencies;
data = rfparam(S,2,1);
fit = rational(freq,data)

fit = 
  rational with properties:

      NumPorts: 1
      NumPoles: 10
         Poles: [10×1 double]
      Residues: [1×1×10 double]
    DirectTerm: 0
         ErrDB: -172.2180

Define, Evaluate and Visualize a Rational Function

Construct a rational function object, rat, with poles at -4 Mrad/s, -3 Grad/s,and -5 Grad/s and residues of 600 Mrad/s,2 Grad/s and 4 Grad/s.

rat=rfmodel.rational('A',[-5e9,-3e9,-4e6],'C',[6e8,2e9,4e9]);

Perform frequency-domain analysis from 1.0 MHz to 3.0 GHz.

f = [1e6:1.0e7:3e9];

Plot the resulting frequency response in decibels on the X-Y plane.

[resp,freq]=freqresp(rat,f);   
figure
plot(freq/1e9,20*log10(abs(resp)));      
xlabel('Frequency (GHz)')
ylabel('Magnitude (dB)')

Generate SPICE File of 2-by-2 S-parameters

Read a file named passive.s2p and fit the 2-by-2 S-parameters. Generate a SPICE file of these S-parameters.

S = sparameters('passive.s2p');
fit = rational(S);
generateSPICE(fit,'passive.ckt')

The circuit is saved in your current folder.

Version History

Introduced in R2009a