S-Parameter Calculations in Q3D Extractor

The fundamental solution quantities in Q3D are the lumped RLGC parameters for a 3D structure. It is important to understand that in the low frequency limit where lumped parameters are defined, many different circuit arrangements lead to the same RLGC values. For example, a single-section T network or a single-section Pi network are both valid representations of the same RLGC values. Even a multi-section ladder model could reduce to the same lumped RLGC values. Each of these networks would have different S-parameters, but the same RLGC values.

Therefore, if Q3D is asked to compute S-parameters from its RLGC solution, there is no unique way to accomplish that. Q3D must pick one circuit topology from the infinite universe of possible circuits, and then compute the S-parameters from it.

When computing S-parameters in Q3D, you can choose from two options: the Equivalent transmission line model and the Lumped RLGC model. The differences in the two approaches are described below.

Equivalent Transmission Line Model Approach

In this approach, Q3D assumes that the structure being analyzed is a collection of parallel interconnects of similar length. It then takes the lumped RLGC parameters for this structure and distributes them uniformly across a system of coupled transmission lines. Distributed transmission line theory (similar to what 2D Extractor uses) is then used to calculate the S-parameters.

This approach works well when the 3D structure being analyzed matches the above assumptions: a collection of parallel wires of similar length. However, it can lead to non-physical results when the structure deviates substantially from this situation. Examples of structures that might cause problems are ones that involve wires with very different lengths, such as a 50 cm long wire next to a 5 mm long wire. For such structures, the new Lumped RLGC model approach is more appropriate.

Lumped RLGC Model Approach

In the lumped circuit approach, Q3D simply lumps all the capacitance and conductance (C and G) at the sink end of the model, and places the inductance and resistance (L and R) between the sources and sinks. See the following figure:

The S-parameters are then calculated from this network. This approach is recommended when dealing with arbitrary 3D structures.