### Summary

Beginning with version 6.9.0.3 of the SPARQ and Signal Integrity Studio software application, users can display impedance profile and rho traces with units of distance on the X-axis rather than with units of time. Additionally, when using time as the X-axis rather than distance, users can select whether the time coordinate corresponds to the time delay or round-trip time, as you would measure directly from a TDR waveform.

#### Figure 1:

SPARQ / SI STudio screenshot showing both time and frequency domain traces. The upper traces use distance on the X-axis instead of time.

### Displaying Impedance Profiles and other Time Domain Results

The SPARQ and SI Studio application can display Z, Rho, Step and Impulse Response waveforms derived from either S-parameters measured from a connected SPARQ Signal Integrity Network Analyzer or from imported S-parameters from a SPARQ or VNA. Users can select to display time domain results from the Result Display dialog and the SParam Import dialog for measured or imported S-parameters, respectively. Clicking the selector control as shown in the figure opens a chooser that includes all result types.

### Configuring the Time Domain Trace Properties

When selecting a time domain result type, the application displays a button labeled Config… Click this button to open the Time Domain Trace Properties window. This window configures the properties for the selected trace, or, optionally, for all time domain result traces. The window allows you to configure two groupings of settings: Trace Properties and X-axis Configuration. Also included is a checkbox to apply the settings to all time domain traces.

The settings in the window are:

### Trace Properties

Rise time: Sets the rise time of the step used to simulate the time domain result. The rise time setting can have a dramatic effect on the resulting Step, Z, Rho and Impulse responses, as is also the case when using TDR to make these measurements. Select a rise time that is appropriate for your application.
UpSample: Selects whether to use a factor 10 of sinx/x interpolation on the time domain waveforms. This results in a smoother display.

### X-axis Configuration

Time vs. Distance: Determines whether to use time or distance for Z and Rho traces. For Step and Impulse result types, the choice is locked to “Time”.
RoundTripTime: When selecting to use Time, you can select to have Z and Rho traces displayed with the X-axis scaled such that the time coordinate corresponds to round-trip or “Reflected” time. This is the time that would be measured when using a TDR to measure the impedance profile. When unchecked, the time coordinate corresponds to the time delay from the selected port.
Vprop/c: When selecting to use Distance, users can choose to enter a value for Vprop/c to determine the mapping of time to distance.
Er (εr ): When selecting to use Distance, users can choose to enter εr (the dielectric constant, or relative permittivity) to determine the mapping of time to distance.

Users can enter either Vprop/c or εr . Entering one will force the other to change, with the relationship between the two being:

$${{V_{prop}} \over c} = {1 \over {\sqrt{ε_r}}}$$

### Considerations When Configuring the X-axis as Distance

The SPARQ makes measurements in the time domain, and does not have any built-in concept of distance. To convert the X-axis from time to distance requires the user to have knowledge of the propagation speed of EM waves through the interconnect. The SPARQ converts from time to distance using a single conversion factor, which may or may not be a correct model of the user’s device under test. For example, if the device under test is a pair of PCBs acting as fixtures that provide access to a cable, then the system will include multiple dielectric constants, such that the speed of an EM wave will change as it propagates through the different connectors, cable and PCBs. In summary, users should make sure to understand the implications of using distance as the Xaxis rather than time in order to avoid misinterpretation of results.