Accelerating the pace of engineering and science

# AnalyzedResult property

Package: rfckt

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

## Values

rfdata.data object

## Description

Handle to an rfdata.data object that contains the S-parameters, noise figure, OIP3, and group delay values computed over the specified frequency range using the analyze method. This property is empty by default.

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-parameter 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 CA' and CA", corresponding to the first two matrices in the cascade, using the following equation:

${C}_{A}=2kT\left[\begin{array}{cc}{R}_{n}& \frac{N{F}_{\mathrm{min}}-1}{2}-{R}_{n}{Y}_{opt}{}^{\ast }\\ \frac{N{F}_{\mathrm{min}}-1}{2}-{R}_{n}{Y}_{opt}& {R}_{n}{|{Y}_{opt}|}^{2}\end{array}\right]$

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

The method combines CA' and CA" into a single correlation matrix CA 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, ZS 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 Gn is the gain of the nth element of the cascade and OIP3,N is the OIP3 of the nth 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.

## Examples

Analyze a cascade of three circuit objects:

```amp = rfckt.amplifier('IntpType','cubic');
tx1 = rfckt.txline;
tx2 = rfckt.txline;