# Compare Time and Frequency Domain Simulation Options for S-parameters

This example shows how to use two different options for modeling S-parameters with the RF Blockset™ Circuit Envelope library. Time-domain (rationalfit) technique creates an analytical rational model that approximates the whole range of the data. This is a preferable technique when a good fit could be achieved with small number of poles. When the data has a lot of details or high level of noise, this model becomes large and slow to simulate.

The frequency-domain technique is based on convolution, where the baseband impulse response depends on the simulation time step and the carrier frequency.

## Contents

## System Architecture

The system consists of:

- An input envelope signal modeled with Simulink blocks. The input signal is a ramp that goes from 0 to 1 in
`TF_RAMP_TIME`; its initial value is`1e-6`s. The carrier frequency of the signal is`TF_FREQ`with initial value is`2.4e9`Hz. - Two SAW filters, modeled by two S-parameter blocks using the same data file,
`sawfilter.s2p`. The block labeled`SAW Filter (time domain)`has its**Modeling options**parameter in the Modeling tab set to`Time domain (rationalfit)`. The block labeled`SAW Filter (frequency domain)`has its**Modeling options**parameter in the Modeling tab set to`Frequency domain`and the**Automatically estimate impulse response duration**is checked. - A Scope block that displays the outputs of the two S-parameter blocks.

```
model = 'simrfV2_sparam_t_vs_f';
open_system(model);
```

## Run Simulation with the Default Settings

- Type
`open_system('simrfV2_sparam_t_vs_f')`at the Command Window prompt. - Select
**Simulation**>**Run**.

The outputs from both methods are very close to each other. The frequency-domain model (purple curve) captures the transfer function (steady-state value) a bit better.

scope = [model '/Scope']; open_system(scope); set_param(scope, 'YMax','0.45'); set_param(scope, 'YMin','0'); set_param(scope, 'TimeRange',num2str(1.01*TF_END_TIME)); sim(model);

## Run the Simulation with the Very Steep Ramp

In the previous simulation, the rise time of the envelope `TF_RAMP_TIME = 1e-6` was many orders of magnitude greater than the period of the carrier signal `T = 1/TF_FREQ = 4.1667e-10`. In other words, the envelope was much slower than the carrier. As the ramp time approaches the period of the carrier, the corresponding time effects are better captured by the time-domain model (yellow curve).

To continue the example:

- Type
`TF_RAMP_TIME = 1e-9; TF_END_TIME = 1e-7;`at the Command Window prompt. - Select
**Simulation**>**Run**.

```
TF_RAMP_TIME = 1e-9;
TF_END_TIME = 1e-7;
set_param(scope, 'TimeRange',num2str(1.01*TF_END_TIME));
sim(model);
open_system(scope);
```

The result of the frequency-domain simulation can be improved by decreasing the time step of the simulation and manually setting the impulse duration time.

To continue the example:

- Type
`TF_STEP = 5e-10;`at the Command Window prompt. - Uncheck
**Automatically estimate impulse response duration**in the modeling pane of`Saw filter (frequency domain)`block and specify the Impulse Response Duration as`1e-7`. - Select
**Simulation**>**Run**.

TF_STEP = 5e-10; sparam_freq = [model '/SAW Filter (frequency domain)']; set_param(sparam_freq, 'AutoImpulseLength', 'off'); set_param(sparam_freq, 'ImpulseLength', '1e-7'); sim(model); open_system(scope);

## Run Simulation with Different Frequency

Rational-function approximation is not exact. To see the approximation error, double-click the "SAW Filter (time domain)" block. Information about the approximation appears under "Rational fitting results" in the bottom of the dialog 'Modeling' pane.

```
open_system([model sprintf('/SAW Filter (time domain)')]);
```

For more details, select 'Visualization' panel, and click the 'Plot' button.

The rationalfit algorithm (dotted curve) does a very good job for the most of the frequencies. However, sometimes it does not capture the sharp changes of S-parameter data.

simrfV2_click_dialog_button('Block Parameters: SAW Filter (time domain)', 'PlotButton');

Conversely, the frequency-domain method exactly reproduces the steady-state behavior at all carrier frequencies (by definition). Running the simulation for `TF_FREQ = 2.54e9` produces drastically different results between the two S-parameter methods.

To continue the example:

- Type
`TF_FREQ = 2.54e9; TF_RAMP_TIME = 1e-6; TF_STEP = 3e-9; TF_END_TIME = 2.5e-6;`at the Command Window prompt. - Select
**Simulation**>**Run**.

In this case, the frequency-domain model provides a better approximation of the original data.

TF_STEP = 3e-9; TF_RAMP_TIME = 1e-6; TF_FREQ = 2.54e9; TF_END_TIME = 2.5e-6; set_param(scope, 'YMax','6e-3'); set_param(scope, 'TimeRange',num2str(1.01*TF_END_TIME)); sim(model); open_system(scope);

## Run Simulation with Impulse Duration Set to Zero.

There is a special case that could be very helpful in practice. When the "Impulse Response Duration" of the s-parameters block is set to zero, the history of the input is no longer taken into consideration. Still, the model captures the transfer function (steady-state value) correctly. This is a fast and reliable way to model the ideal devices when the transient effects could be ingnored.

To continue the example:

- Specify the
`Impulse Response Duration`of`Saw filter (frequency domain)`block as`0`. - Select
**Simulation**>**Run**.

set_param(sparam_freq, 'ImpulseLength', '0'); sim(model); open_system(scope);

## Conclusion

In most practical RF systems, time- and frequency-domain techniques give similar answers. Time-domain method better captures the time-domain effects of the fast-changing envelopes, but relies on rationalfit approximation of the original data. Frequency-domain method is sensitive to the simiulation time step; this option is recommended to use when the time-domain model does not provide a good fit.

close gcf; bdclose(model); clear model scope;