Using the Si9000 multiple frequency loss tangent goal seek
Applicatiopn Note AP8207


Goal seeking is a powerful method for seeking an unknown quantity, however it should be used and approached with care. Should the input data be uncertain, goal seeking can easily lead to erroneous results. You should always bear in mind the result you expect to get before seeking and consider the results output against "sanity" tests – such as, "Do the results obtained obey the laws of physics?" 

The loss tangent you obtain with goal seeking, for example, should be similar to that of the material vendors data sheet. There should not be any sudden discontinuities in the loss tangent at a specific frequency. Should you see anomalies, that is a pointer to go back and look at the measurement technique – both the system, the de embedding math and the design of the test vehicle.


Using the Si9000 multiple frequency loss tangent goal seek

Measuring insertion loss yields the total losses of a transmission line, but sometimes it is useful to further process that information and deduce the contribution of copper losses and dielectric losses to the overall loss figure. Si9000e provides loss tangent goal seeking for both single frequency and multiple frequencies. This note describes goal seeking for loss tangent for multiple frequencies. For single frequency goal seek see Application Note AP8193

The Si9000e simplifies the complexity of the process of estimating dielectric loss by allowing you to:

  • enter the total measured attenuation
  • calculate an estimate of copper losses from cross section data
  • remove the copper loss from the total attenuation to leave the losses from the substrate alone.

This figure can then be processed to provide a useful estimate of the dielectric loss tangent for the substrate material.

Single and multiple-frequency loss tangent goal seeking

Si9000e provides loss tangent goal seeking for both single frequency and multiple frequencies.  For multiple-frequency loss tangent goal seeking, up to five Loss Tangent values can be calculated in a single process; the calculated results can be exported to the Extended Substrate Data Library

This application note describes the sequence of steps for a multiple frequency goal seek for loss tangent

Edge-Coupled Offset Stripline example

Select Edge-Coupled Offset Stripline 1B1A structure:

On the Lossless Calculation tab supply the structure parameters and calculate the impedance.

Switch to the Frequency Dependent tab:

Note: When using the Set from FOI option the Total Attenuation data will depend on the Frequency of Interest Result Selection setting on the main interface.

The readings in the example below have been derived from measured data, so for this example it will be necessary to choose Measured Attenuation from the Result Selection pane.

Result Selection

  • From the Frequency of Interest dropdown choose Measured Attenuation

Surface Roughness Compensation

From the Surface Roughness Compensation option group:

  • Ensure the Smooth Surface Roughness Compensation option is not selected
  • Select the Surface Roughness Compensation option (Huray in the example below)

Extended Substrate Data

From the Extended Substrate Data option group:

  • Select the Multiple Er / TanD Extended Substrate Data option
  • Click the Multiple Er / TanD Goal Seek button

The Loss Tangent Multiple Frequency Goal Seek dialog is displayed. The dialog allows for up to five Loss Tangent values to be calculated in a single process.

Input data and results are displayed simultaneously, with a separate column for each frequency. If frequencies of interest have been specified via the Frequency of Interest dialog, the first five frequencies of interest with their associated attenuation values can be added to the table via the Set from FOI button

Step 1 – Enter the Total Attenuation

Under Step 1, for each frequency, enter the Total Attenuation for the point of interest: the Frequency and the loss per length of line –dB / LL and the Dielectric Constant. The length of line will be the value entered into the Length of Line (LL) parameter on the main frequency dependent tab,

Using the frequencies of interest



Set from Frequency of Interest

If frequencies of interest have been specified click the Set from FOI (Frequency of Interest) button to add up to the first five frequencies of interest with their associated attenuation values to the table. Frequencies of interest may be set directly or obtained from measured data.*


Import Measurement Data from Atlas

* Note for Polar Atlas Users: Atlas users have the option of importing Polar Atlas measurement data into the Si9000e using the Import Measurement Data from Atlas toolbar option. Once imported, it is useful to use the Set from FOI’ button to automatically set the Total Attenuation values from the imported Measured Attenuation.  Similarly, the ‘Set from EEr’ button will populate the Dielectric Constant values from the Measured Effective Er

In the case of the Edge-coupled Offset Stripline 1B1A structure, the default value for LL is 10 mm – so Total Attenuation is displayed in dB/cm. The Total Attenuation is shown at each frequency.

Using the Measured Effective Er


The Dielectric Constant values may be entered directly – or you can use the Set from EEr button to populate the Dielectric Constant values from the Measured Effective Er

Step 2 – Calculate the Conductor and Dielectric Loss

Under Step 2, Calculate the Conductor and Dielectric Loss. Si9000e will take the parameters for the current selected structure (in this case Edge-Coupled Stripline 1B1A) and calculate the conductor loss at each of the chosen frequencies. It will then take the calculated conductor loss from the total attenuation entered in Step 1 to calculate the remaining dielectric loss at each frequency. Typical results are shown below.

In this case the conductor loss and remaining dielectric loss for each frequency are displayed in tabular form.

Step 3 Calculate Loss Tangent

The Step 3 Calculate Loss Tangent option will allow the Si9000e to calculate the Loss Tangent (TanD) required to achieve the dielectric loss at each frequency as shown above. Using the Goal Seek Parameters to limit the min / max range of TanD the Si9000e will now sweep the range of TanD values until a suitable TanD is calculated to achieve the displayed dielectric loss (i.e. Attenuation – Conductor loss) at each frequency. The progress of the calculation is updated on the dialog.

The result table above shows the Loss Tangent (TanD) required to achieve the dielectric loss at each frequency – the convergence value is used to give the target dielectric loss a tolerance.

Step 4 Export results as an Extended Substrate Data table

The results can be exported in tabular form as an Extended Substrate Data table. Supply a descriptive name for the table and click Export

The exported table can be specified in Extended Substrate Data calculations – select the exported table using the Multiple Er / Tan D Edit option.

Comparing Single to Multiple Frequency Goal Seek

Using the results from the single and multiple frequency goal seek as an exported extended substrate data table illustrates the improvement in the correlation between the modelled Attenuation with Roughness (cyan) and Measured Attenuation (brown).

Single Frequency Goal Seek

In the graph below, Attenuation with Roughness (cyan) and Measured Attenuation (brown) do not exhibit a high degree of correlation when using Constant Er / TanD mode

Constant Er /TanD goal seeking

Multiple Frequency Goal Seek

Once the Multiple Er / TanD Loss Tangent Goal Seek is complete, the exported results show the improvement in the correlation between the calculated Attenuation with Roughness (cyan) and Measured Attenuation (brown).

Multiple Er /TanD goal seeking