# Documentation

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## Modeling a High-Speed Backplane (Part 1: Measured 16-Port S-Parameters to 4-Port S-Parameters)

This example shows how to use RF Toolbox™ to import N-port S-parameters representing high-speed backplane channels, and converts 16-port S-parameters to 4-port S-parameters to model the channels and the crosstalk between the channels.

With the 4-port S-parameters, a rational function object can be built for a differential channel. The second part of the example -- Modeling a High-Speed Backplane (Part 2: 4-Port S-Parameters to a Rational Function) -- will show how to use rational functions to model a differential high-speed backplane channel.

With the rational function object, the Time-Domain Reflectometry and Time-Domain Transmission can be calculated for a differential channel. The third part of the example -- Modeling a High-Speed Backplane (Part 3: 4-Port S-Parameters to Differential TDR and TDT) -- will show how to use rational functions to calculate the Time-Domain Reflectometry and Time-Domain Transmission.

With the rational function object, a Simulink® model can be built for a differential channel. The fourth part of the example -- Modeling a High-Speed Backplane (Part 4: Rational Function to a Simulink Model) -- will show how to build a Simulink model from a rational function.

With the rational function object, a Verilog-A module can also be generated for a differential channel. The fifth part of the example -- Modeling a High-Speed Backplane (Part 5: Rational Function to a Verilog-A Module) -- will show how to generate a Verilog-A module from a rational function.

Figure 1: 16-Port differential backplane

### Read the Single-Ended 16-Port S-Parameters

Read a Touchstone® data file into an `sparameters` object. The data in this file are the 50-ohm S-parameters of a 16-port differential backplane designed for a 2-Gbps high-speed signal, shown in Figure 1, measured at 1496 frequencies ranging from 50 MHz to 15 GHz.

```filename = 'default.s16p'; backplane = sparameters(filename) freq = backplane.Frequencies; ```
```backplane = sparameters: S-parameters object NumPorts: 16 Frequencies: [1496x1 double] Parameters: [16x16x1496 double] Impedance: 50 rfparam(obj,i,j) returns S-parameter Sij ```

### Convert the 16-Port S-Parameters to 4-Port S-Parameters to Model a Differential Channel

Use the `snp2smp` function to convert 16-port S-parameters to 4-port S-parameters that represent the first differential channel. The port index of this differential channel, `N2M`, which specifies how the ports of the 16-port S-parameters map to the ports of the 4-port S-parameters, is `[1 16 2 15]`. (The port indices of the second, third and fourth channels are `[3 14 4 13]`, `[5 12 6 11]` and `[7 10 8 9]`, respectively). The other 12 ports, `[3 4 5 6 7 8 9 10 11 12 13 14]`, are terminated with the characteristic `Impedance` specified by the `sparameters` object. Then, create an `sparameters` object with 4-port S-parameters for the first differential channel.

``` (Port 1) (Port 16) Port 1 > ----->| |<----- < Port 2 | DUT | Port 3 > ----->| |<----- < Port 4 (Port 2) (Port 15)```
```n2m = [1 16 2 15]; z0 = backplane.Impedance; first4portdata = snp2smp(backplane.Parameters,z0,n2m,z0); first4portsparams = sparameters(first4portdata,freq,z0) ```
```first4portsparams = sparameters: S-parameters object NumPorts: 4 Frequencies: [1496x1 double] Parameters: [4x4x1496 double] Impedance: 50 rfparam(obj,i,j) returns S-parameter Sij ```

Plot `S21` and `S43` of the first differential channel.

```figure rfplot(first4portsparams,2,1) hold on rfplot(first4portsparams,4,3,'-r') % % If you want to write the 4-port S-parameters of the differential % % channel into a |.s4p| file, then uncomment the line below. % % rfwrite(first4portsparams,'firstchannel.s4p') ```

### Convert 16-Port S-Parameters to 4-Port S-Parameters to Model the Crosstalk Between Two Differential Channels

Use the `snp2smp` function to convert 16-port S-parameters to 4-port S-parameters that represent the crosstalk between port `[3 4]` and port `[16 15]`. As shown in Figure 1, these ports are on different channels. The other 12 ports, `[1 2 5 6 7 8 9 10 11 12 13 14]`, are terminated with the characteristic `Impedance` specified by the `sparameters` object. Then, create an `sparameters` object with 4-port S-parameters for the crosstalk.

``` (Port 3) (Port 16) Port 1 > ----->| |<----- < Port 2 | DUT | Port 3 > ----->| |<----- < Port 4 (Port 4) (Port 15)```
```n2m = [3 16 4 15]; crosstalk4portdata = snp2smp(backplane.Parameters,z0,n2m,z0); crosstalk4portsparams = sparameters(crosstalk4portdata,freq,z0) ```
```crosstalk4portsparams = sparameters: S-parameters object NumPorts: 4 Frequencies: [1496x1 double] Parameters: [4x4x1496 double] Impedance: 50 rfparam(obj,i,j) returns S-parameter Sij ```

Plot `S21`, `S43`, `S12` and `S34` to show the crosstalk between these two channels.

```figure rfplot(crosstalk4portsparams,2,1) hold on rfplot(crosstalk4portsparams,4,3,'-r') rfplot(crosstalk4portsparams,1,2,'-k') rfplot(crosstalk4portsparams,3,4,'-g') % % If you want to write the 4-port S-parameters of the crosstalk into an % % .s4p file, then uncomment the line below. % % rfwrite(crosstalk4portsparams,'crosstalk.s4p') ```

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