rfckt.cascade

Cascaded network

Description

Use the cascade object to represent cascaded networks of RF objects that are characterized by the components that make up the individual network. The following figure shows the configuration of a pair of cascaded networks.

Note

rfbudget is recommend over rfckt.cascade because it enables you to:

• Create an RF budget chain and compute the RF budget results for a chain of two-port elements. You can include linear and nonlinear elements in your chain. For more information, see Elements.

• Compute gain, noise figure, IP2, and IP3 of cascaded RF elements using Friis and harmonic balance solvers and export to RF Blockset™ and rfsystem for circuit envelope analysis.

(since R2023b)

Creation

Syntax

h = rfckt.cascade

h = rfckt.cascade('Ckts',value)

Description

h = rfckt.cascade returns a cascaded network object whose properties all have their default values.

h = rfckt.cascade('Ckts',value) returns a cascaded network with elements specified in the name-value pair property Ckts.

Properties

AnalyzedResult — Computed S-parameters, noise figure, OIP3, and group delay values

rfdata.data object

This property is read-only.

Computed S-parameters, noise figure, OIP3, and group delay values. For more information, see Algorithms.

Data Types: function_handle

Ckts — Circuit objects in network

cell array of object handles

Circuit objects in network. All circuits must be 2-port. By default, this property is empty.

Data Types: char

Name — Name of cascaded network

1-by-N character array

This property is read-only.

Name of cascaded network.

Data Types: char

nport — Number of ports of cascaded network

positive integer

This property is read-only.

Number of ports of cascaded network. The default value is 2.

Data Types: double

Object Functions

analyze	Analyze RFCKT object in frequency domain
calculate	Calculate specified parameters for rfckt objects or rfdata objects
circle	Draw circles on Smith Chart
extract	Extract specified network parameters from rfckt object or data object
listformat	List valid formats for specified circuit object parameter
listparam	List valid parameters for specified circuit object
loglog	Plot specified circuit object parameters using log-log scale
plot	Plot circuit object parameters on X-Y plane
plotyy	Plot parameters of RF circuit or RF data on xy-plane with two Y-axes
getop	Display operating conditions
polar	Plot specified object parameters on polar coordinates
semilogx	Plot RF circuit object parameters using log scale for x-axis
semilogy	Plot RF circuit object parameters using log scale for y-axis
smith	Plot circuit object parameters on Smith Chart
write	Write RF data from circuit or data object to file
getz0	Calculate characteristic impedance of RFCKT transmission line object
read	Read RF data from file to new or existing circuit or data object
restore	Restore data to original frequencies
getop	Display operating conditions
groupdelay	Group delay of S-parameter object or RF filter object or RF Toolbox circuit object

Examples

Create RF Circuit Cascade Network

Create a cascade network using rfckt.cascade with amplifier and transmission lines as elements.

amp = rfckt.amplifier('IntpType','cubic');
tx1 = rfckt.txline;
tx2 = rfckt.txline;
casccircuit = rfckt.cascade('Ckts',{tx1,amp,tx2})

casccircuit = 
   rfckt.cascade with properties:

              Ckts: {[1x1 rfckt.txline]  [1x1 rfckt.amplifier]  [1x1 rfckt.txline]}
             nPort: 2
    AnalyzedResult: []
              Name: 'Cascaded Network'

Algorithms

The analyze method computes the AnalyzedResult property using the data stored in the Ckts property as follows:

• The analyze method starts calculating the ABCD-parameters of the cascaded network by converting each component network's parameters to an ABCD-parameters matrix. The figure shows a cascaded network consisting of two 2-port networks, each represented by its ABCD matrix.

  The analyze method then calculates the ABCD-parameters matrix for the cascaded network by calculating the product of the ABCD matrices of the individual networks.

  The following figure shows a cascaded network consisting of two 2-port networks, each represented by its ABCD-parameters.

  

  The following equation illustrates calculations of the ABCD-parameters for two 2-port networks.

  $$\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[\begin{array}{cc}A\prime & B\prime \\ C\prime & D\prime \end{array}\right]\left[\begin{array}{cc}A\prime \prime & B\prime \prime \\ C\prime \prime & D\prime \prime \end{array}\right]$$

  Finally, analyze converts the ABCD-parameters of the cascaded network to S-parameters at the frequencies specified in the analyze input argument freq.

• The analyze method calculates the noise figure for an N-element cascade. First, the method calculates noise correlation matrices C_A' and C_A”, corresponding to the first two matrices in the cascade, using the following equation:

  $$C_A=2kT\left[\begin{array}{cc}{R}_n& \frac{N{F}_{\min }-1}{2}-R_n{Y}_{opt}{}^{\ast }\\ \frac{N{F}_{\min }-1}{2}-R_n{Y}_{opt}& R_n{\left|Y_{opt}\right|}^2\end{array}\right]$$

  where k is Boltzmann's constant, and T is the noise temperature in Kelvin.

  The method combines C_A' and C_A” into a single correlation matrix C_A using the equation

  $$C_A=C_A^{\text{'}}+\left[\begin{array}{cc}A\text{'}& B\text{'}\\ C\text{'}& D\text{'}\end{array}\right]C_A^{\text{'}\text{'}}\left[\begin{array}{cc}A\text{'}& B\text{'}\\ C\text{'}& D\text{'}\end{array}\right]$$

  By applying this equation recursively, the method obtains a noise correlation matrix for the entire cascade. The method then calculates the noise factor, F, from the noise correlation matrix of as follows:

  $$\begin{array}{l}F=1+\frac{z^{+}{C}_{A}z}{2kT\mathrm{Re}\left\{Z_S\right\}}\\ z=\left[\begin{array}{c}1\\ Z_S{}^{*}\end{array}\right]\end{array}$$

  In the two preceding equations, Z_S is the nominal impedance, which is 50 ohms, and z⁺ is the Hermitian conjugation of z.

• The analyze method calculates the output power at the third-order intercept point (OIP3) for an N-element cascade using the following equation:

  $$OI{P}_3=\frac{1}{\frac{1}{OI{P}_{3,N}}+\frac{1}{G_N\cdot OI{P}_{3,N-1}}+\dots +\frac{1}{G_N\cdot G_{N-1}\cdot \dots \cdot G_2\cdot OI{P}_{3,1}}}$$

  where G_n is the gain of the nth element of the cascade and OIP_3,N is the OIP₃ of the n^th element.

• The analyze method uses the cascaded S-parameters to calculate the group delay values at the frequencies specified in the analyze input argument freq, as described in the analyze reference page.

References

[1] Ludwig, R. and P. Bretchko, RF Circuit Design: Theory and Applications, Prentice Hall, 2000.

Version History

Introduced before R2006a