RF Toolbox™ software lets you analyze RF components and networks
in the frequency domain. You use the analyze
method
to analyze a circuit object over a specified set of frequencies.
For example, to analyze a coaxial transmission line from 1 GHz to 2.9 GHz in increments of 10 MHz:
ckt = rfckt.coaxial; f = [1.0e9:1e7:2.9e9]; analyze(ckt,f);
For all circuits objects except those that contain data from a file, you must
perform a frequencydomain analysis with the analyze
method before visualizing component and network data.
For circuits that contain data from a file, the toolbox performs a
frequencydomain analysis when you use the read
method to import the
data.
When you analyze a circuit object, the toolbox computes the
circuit network parameters, noise figure values, and output thirdorder
intercept point (OIP3) values at the specified frequencies and stores
the result of the analysis in the object's AnalyzedResult
property.
For more information, see the analyze
reference page or the circuit object reference page.
The toolbox lets you validate the behavior of circuit objects that represent RF components and networks by plotting the following data:
Large and smallsignal Sparameters
Noise figure
Output thirdorder intercept point
Power data
Phase noise
Voltage standingwave ratio
Power gain
Group delay
Reflection coefficients
Stability data
Transfer function
The following table summarizes the available plots and charts, along with the methods you can use to create each one and a description of its contents.
Plot Type  Methods  Plot Contents 

Rectangular Plot  Parameters as a function of frequency or, where applicable, operating condition. The available parameters include:
 
Budget Plot (3D)  Parameters as a function of frequency for each component in a cascade, where the curve for a given component represents the cumulative contribution of each RF component up to and including the parameter value of that component.  
Mixer Spur Plot  Mixer spur power as a function of frequency for an  
Polar Plot  Magnitude and phase of Sparameters as a function of frequency.  
Smith^{®} Chart  Real and imaginary parts of Sparameters as a function of frequency, used for analyzing the reflections caused by impedance mismatch. 
For each plot you create, you choose a parameter to plot and, optionally, a format in which to plot that parameter. The plot format defines how the toolbox displays the data on the plot. The available formats vary with the data you select to plot. The data you can plot depends on the type of plot you create.
You can use the listparam
method
to list the parameters of a specified circuit object that are available
for plotting. You can use the listformat
method
to list the available formats for a specified circuit object parameter.
The following topics describe the available plots:
You can plot any parameters that are relevant to your object
on a rectangular plot. You can plot parameters as a function of frequency
for any object. When you import object data from a .p2d
or .s2d
file,
you can also plot parameters as a function of any operating condition
from the file that has numeric values, such as bias. In addition,
when you import object data from a .p2d
file, you
can plot largesignal Sparameters as a function of input power or
as a function of frequency. These parameters are denoted LS11
, LS12
, LS21
,
and LS22
.
The following table summarizes the methods that are available in the toolbox for creating rectangular plots and describes the uses of each one. For more information on a particular type of plot, follow the link in the table to the documentation for that method.
Method  Description 

plot  Plot of one or more object parameters 
plotyy  Plot of one or more object parameters with yaxes on both the left and right sides 
semilogx  Plot of one or more object parameters using a log scale for the Xaxis 
semilogy  Plot of one or more object parameters using a log scale for the Yaxis 
loglog  Plot of one or more object parameters using a loglog scale 
You use the link budget plot to understand the individual contribution of each component to a plotted parameter value in a cascaded network with multiple components.
The budget plot is a threedimensional plot that shows one or more curves of parameter values as a function of frequency, ordered by the circuit index of the cascaded network.
Consider the following cascaded network:
casc = rfckt.cascade('Ckts',... {rfckt.amplifier,rfckt.lcbandpasspi,rfckt.txline})
You create a budget plot for this cascade using the plot
method
with the second argument set to 'budget'
, as shown
in the following command:
plot(casc,'budget','s21')
A curve on the link budget plot for each circuit index represents the contributions to the parameter value of the RF components up to that index. The following figure shows the budget plot.
Budget Plot
If you specify two or more parameters, the toolbox puts the parameters in a single plot. You can only specify a single format for all the parameters.
You use the mixer spur plot to understand how mixer nonlinearities affect output power at the desired mixer output frequency and at the intermodulation products that occur at the following frequencies:
$${f}_{out}=N\ast {f}_{in}+M\ast {f}_{LO}$$
where
$${f}_{in}$$ is the input frequency.
$${f}_{LO}$$ is the local oscillator frequency.
N and M are integers.
The toolbox calculates the output power from the mixer intermodulation table (IMT). These tables are described in detail in the Visualizing Mixer Spurs example.
The mixer spur plot shows power as a function of frequency for
an rfckt.mixer
object or an rfckt.cascade
object
that contains a mixer. By default, the plot is threedimensional and
shows a stem plot of power as a function of frequency, ordered by
the circuit index of the object. You can create a twodimensional
stem plot of power as a function of frequency for a single circuit
index by specifying the index in the mixer spur plot command.
Consider the following cascaded network:
FirstCkt = rfckt.amplifier('NetworkData', ... rfdata.network('Type', 'S', 'Freq', 2.1e9, ... 'Data', [0,0;10,0]), 'NoiseData', 0, 'NonlinearData', inf); SecondCkt = read(rfckt.mixer, 'samplespur1.s2d'); ThirdCkt = rfckt.lcbandpasstee('L', [97.21 3.66 97.21]*1e9, ... 'C', [1.63 43.25 1.63]*1.0e12); CascadedCkt = rfckt.cascade('Ckts', ... {FirstCkt, SecondCkt, ThirdCkt});
Circuit index 0 corresponds to the cascade input.
Circuit index 1 corresponds to the LNA output.
Circuit index 2 corresponds to the mixer output.
Circuit index 3 corresponds to the filter output.
You create a spur plot for this cascade using the plot
method
with the second argument set to 'mixerspur'
, as
shown in the following command:
plot(CascadedCkt,'mixerspur')
Within the three dimensional plot, the stem plot for each circuit index represents the power at that circuit index. The following figure shows the mixer spur plot.
Mixer Spur Plot
For more information on mixer spur plots, see the plot
reference page.
You can use the toolbox to generate Polar plots and Smith Charts. If you specify two or more parameters, the toolbox puts the parameters in a single plot.
The following table describes the Polar plot and Smith Chart options, as well as the available parameters.
LS11
, LS12
,
LS21
, and LS22
are
largesignal Sparameters. You can plot these parameters as a function
of input power or as a function of frequency.
Plot Type  Method  Parameter 

 polar 

 smithplot with type argument
set to 'z' 

 smithplot with type argument
set to 'y' 

 smithplot with type argument
set to 'zy' 

By default, the toolbox plots the parameter as a function of
frequency. When you import block data from a .p2d
or .s2d
file,
you can also plot parameters as a function of any operating condition
from the file that has numeric values, such as bias.
The circle
method lets you place circles on a Smith Chart to depict stability regions and display constant gain, noise
figure, reflection and immittance circles. For more information about this
method, see the circle
reference page or the twopart RF Toolbox example about designing matching networks.
For more information on a particular type of plot, follow the link in the table to the documentation for that method.
The toolbox lets you compute and plot timedomain characteristics for RF components.
This section contains the following topics:
You use the s2tf
function to convert 2port
Sparameters to a transfer function. The function returns a vector
of transfer function values that represent the normalized voltage
gain of a 2port network.
The following code illustrates how to read file data into a
passive circuit object, extract the 2port Sparameters from the object
and compute the transfer function of the data at the frequencies for
which the data is specified. z0
is the reference
impedance of the Sparameters, zs
is the source
impedance, and zl
is the load impedance. See the s2tf
reference page for more information on
how these impedances are used to define the gain.
PassiveCkt = rfckt.passive('File','passive.s2p') z0=50; zs=50; zl=50; [SParams, Freq] = extract(PassiveCkt, 'S Parameters', z0); TransFunc = s2tf(SParams, z0, zs, zl);
You use the rationalfit
function to fit
a rational function to the transfer function of a passive component.
The rationalfit
function returns an rfmodel
object
that represents the transfer function analytically.
The following code illustrates how to use the rationalfit
function
to create an rfmodel.rational
object that contains
a rational function model of the transfer function that you created
in the previous example.
RationalFunc = rationalfit(Freq, TransFunc)
To find out how many poles the toolbox used to
represent the data, look at the length of the A
vector
of the RationalFunc
model object.
nPoles = length(RationalFunc.A)
The number of poles is important if you plan to use the RF model object to create a model for use in another simulator, because a large number of poles can increase simulation time. For information on how to represent a component accurately using a minimum number of poles, see Represent a Circuit Object with a Model Object.
See the rationalfit
reference
page for more information.
Use the freqresp
method
to compute the frequency response of the fitted data. To validate
the model fit, plot the transfer function of the original data and
the frequency response of the fitted data.
Resp = freqresp(RationalFunc, Freq); plot(Freq, 20*log10(abs(TransFunc)), 'r', ... Freq, 20*log10(abs(Resp)), 'b'); ylabel('Magnitude of H(s) (decibels)'); xlabel('Frequency (Hz)'); legend('Original', 'Fitting result'); title(['Rational fitting with ', int2str(nPoles), ' poles']);
You use the timeresp
method to compute the timedomain
response of the transfer function that RationalFunc
represents.
The following code illustrates how to create a random input signal, compute
the timedomain response of RationalFunc
to the input signal,
and plot the results.
SampleTime=1e11; NumberOfSamples=4750; OverSamplingFactor = 25; InputTime = double((1:NumberOfSamples)')*SampleTime; InputSignal = ... sign(randn(1, ceil(NumberOfSamples/OverSamplingFactor))); InputSignal = repmat(InputSignal, [OverSamplingFactor, 1]); InputSignal = InputSignal(:); [tresp,t]=timeresp(RationalFunc,InputSignal,SampleTime); plot(t*1e9,tresp); title('Fitting TimeDomain Response', 'fonts', 12); ylabel('Response to Random Input Signal'); xlabel('Time (ns)');
For more information about computing the time response of a model object, see
the timeresp
reference page.