1. Generic S-parameters
Considerations for Extending the Touchstone File Format EEsof EDA John Moore R&D Tech Lead January 10, 2007
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007

2. Generic S-parameter Component
Generic representation of a 5-port device
different reference for every port
thus, 10 terminal representation of a 5-port
Generic representation of a 5-port device with a common reference terminal
one ground pin and 5 port pins
thus, 6 terminal representation of a 5-port
ADS represents an S5P component with a common reference terminal
Data from a 5-port Touchstone file
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007

3. Generic S-parameter Simulation
A different reference impedance can be defined for each port
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007

4. S-parameter Basics (1)
S-parameters relate incident and reflected wave variables [a] and [b] at the device ports in the frequency domain by
[S] [a] = [b]
For “power wave variables” (a la Kurokawa) these are related to the port voltages and currents as
ai = (Vi + Zci * Ii) / (2 * sqrt(Real(Zci)))
bi = (Vi – Zci* * Ii) / (2 * sqrt(Real(Zci)))
where Zci is the complex characteristic impedance at port ‘i’.
[K. Kurokawa, “Power waves and the scattering matrix,” IEEE Trans. Microwave Theory and Tech., pp , March 1965.]
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007

5. S-parameter Basics (2)
S-parameters characterize both the characterized device, and the measurement (simulation) system. The measurement reference impedances must also be specified.
The matrix elements Sij will be different for the same device measured by a different system (i.e. having a different reference impedance)
Improperly interpreting the reference impedances results in an incorrect representation of the device
S-parameters can be ‘re-normalized’ to another reference impedance, not necessarily the same impedance as the measurement system.
It can be convenient to reference S-parameters to the ‘natural’ impedance of the ports, but this is not necessary to completely characterize the device.
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007

6. S-parameter Basics (3)
Given the Kurokawa convention, the Z-parameters can be computed from the S-parameters as:
[Z] = [y]-1 ([I] – [S])-1 ([S] + [Zc]* [Zc]-1) [Zc] [y]
Where
[y] is a diagonal matrix with elements yii = 1/sqrt(Real(Zci))
[Zc] is a diagonal matrix with elements Zci
[I] is the identity matrix
For real valued Zci, this becomes
[Z] = sqrt([Zc]) ([I] – [S])-1 ([S] + [I]) sqrt([Zc])
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007

7. Problems with Complex Reference Impedances
The Kurokawa definition for the wave variables is commonly (but not universally?) used.
For evanescent modes in loss-less waveguides, Real(Zi) = 0. The Kurokawa power wave variables can not be used to characterize evanescent mode S-parameters.
Most (if not all?) simulators use a consistent definition under the assumption of real valued reference impedances.
This will lead to different results in different simulators unless
A common standard can be established in the circuit simulation community
The reference impedance is restricted to being real valued
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007

8. Recommendations for Extending the Touchstone File Format
1. Add an explicit new keyword/block to define a unique reference impedance for each port.
Force a failure if the new file format is used in an ‘old’ simulator.
2a. Support complex reference impedances consistent with the Kurokawa definitions. OR
2b. Support only real valued reference impedances.
Generic S-parameters
Considerations for Extending the Touchstone File Format
January 10, 2007