System Architecture

The system consists of:

model = 'simrfV2_sparam_t_vs_f';
open_system(model);

Run Simulation with the Default Settings

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:

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:

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:

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 ignored.

To continue the example:

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. The time-domain method better captures the time-domain effects of the fast-changing envelopes, but relies on a rationalfit approximation of the original data. The frequency-domain method is sensitive to the simulation time step; this option is recommended when the time-domain model does not provide a good fit.

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

See Also

S-Parameters | Configuration | Inport | Outport

Related Topics

Analysis of Frequency Response of RF System | Transmission Lines, Delay-based and Lumped Models