Analyze and Plot RF Components
Analyze Networks in Frequency Domain
RF Toolbox™ lets you analyze RF components and networks in the frequency domain.
You use the analyze
function 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);
Note
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
function page.
Visualize Component and Network Data
The RF 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
This table summarizes the available plots and charts, along with the functions you can use to create each one and a description of its contents.
Plot Type  Functions  Plot Contents 

Rectangular Plot  Parameters as a function of frequency or, where applicable, operating condition. The available parameters include:
 
Budget Plot  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 Plots and Smith Charts®  Polar plot: Magnitude and phase of Sparameters as a function of frequency. Smith plot: 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 RF 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.
Note
You can use the listparam
function to list the
parameters of a specified circuit object that are available for plotting. You
can use the listformat
function to list the
available formats for a specified circuit object parameter.
The following topics describe the available plots:
Rectangular Plot
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
.
This 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 
Budget Plot
You use the link budget or 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 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 3D budget plot for this cascade using the
plot
method with the second argument set to
'budget'
, as shown in the following
command:
analyze(casc,linspace(1e9,3e9,100)); plot(casc,'budget','s21')
Note that you have to analyze
your circuit before plotting the budget plot and by
default the budget plot is a 2D plot. If you specify the array of frequencies
in the analyze
function you can visualize the budget
results in 3D. A curve on the budget plot for each circuit index represents the
contributions to the parameter value of the RF components up to that index. This
figure shows the budget plot.
If you specify two or more parameters, the RF Toolbox puts the parameters in a single plot. You can only specify a single format for all the parameters.
Mixer Spur Plot
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 RF toolbox calculates the output power from the mixer intermodulation table (IMT). These tables are described in detail in the Visualize 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. This figure shows the mixer spur plot.
For more information on mixer spur plots, see the plot
reference page.
Polar Plots and Smith Charts^{®}
You can use the RF toolbox to generate Polar plots and Smith charts. If you specify two or more parameters, the RF toolbox puts the parameters in a single plot.
The following table describes the Polar plot and Smith charts options, as well as the available parameters.
Note
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 RF 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.
Note
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
function, see the circle
reference page or Designing Matching Networks for Low Noise Amplifiers example about designing matching
networks.
Compute and Plot TimeDomain Specifications
The RF toolbox lets you compute and plot timedomain characteristics for RF components.
This section contains the following topics:
Compute Network Transfer Function
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 a 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. Here 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);
Fit Model Object to Circuit Object Data
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 RF toolbox used to represent the data, look at
the length of the A
vector of the
RationalFunc
model object.
nPoles = length(RationalFunc.A)
Note
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 Circuit Object with Model Object.
Use the freqresp
function 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']);
Compute and Plot TimeDomain Response
You use the timeresp
function to compute the timedomain response of the
transfer function that RationalFunc
represents. This 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
function.