# 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; casc = rfckt.cascade('Ckts',{tx1,amp,tx2}); analyze(casc,[1e9:1e7:2e9]); casc.AnalyzedResult ```

## References

Hillbrand, H. and P.H. Russer, "An Efficient Method for Computer Aided Noise Analysis of Linear Amplifier Networks," IEEE Transactions on Circuits and Systems, Vol. CAS-23, Number 4, pp. 235–238, 1976.