Known Issues in Version 1.1
Origin of the Limitations in Handling Stripline Structures
Trace Analyzer employs the method of moment (MOM) technique to compute the capacitance parameters for a cross section of defined metallic objects. The inductance parameters are derived from the capacitance parameters. The most critical elements in MOM is to compute the Green's function G(|r,r'|).
- Green’s function for layered dielectric medium is computed in the spectral domain, which is related to G(|r,r'|) by a 2D Fourier transform
- The desired approach would be to compute Green’s function in the stripline scenario, assuming two infinite ground planes, as shown is Figure 1(a).
- An efficient technique is the so-called discrete complex image method (DCIM) which sums up the total field interaction in terms of direct term plus multiple image terms. The image terms are attributed to the reflections off the infinite ground plane(s).
- The DCIM method is very robust for handling microstrip type of scenarios where only one infinite plane is present
- The DCIM method becomes unstable for the stripline cases, where too many reflections need to be included, which defeats the purpose of DCIM approximation
- TA 1.1 makes use of DCIM while circumventing the trouble with too many reflections between two infinite planes. This is achieved by admitting only the LOWER plane infinite and treating the UPPER plane as finite size (effectively another signal conductor) at the beginning. This intermediate problem is illustrated by Figure 1(b). Effort is made to have the finite-sized plane wide enough to have all traces ’covered’.
- After the intermediate (N+1) transmission-line system is solved, a grounding algorithm is applied, so the effect of the finite ground plane is removed mathematically. The whole scheme is built into a flow that is not noticeable to the user, because only the final N-transmission-line results are displayed.
- In some cases tested, it is evident that the intermediate plane width is not wide enough ("leaky" to allow more magnetic flux to wrap around than desired).
Known Pathological Cases
- Single stripline structure with h1>h2. Since TA uses the LOWER plane as the infinite plane. In this case, the LOWER plane is the secondary reference plane. Treating the primary reference (UPPER) plane finite, therefore somewhat "leaky", is the root-cause of inaccuracy.
- Weakly edge-coupled striplines. Since the edge-edge spacing between the two stripline traces is relatively large. TA's internal algorithm tends to use a intermediate finite plane that's not wide enough.
- Symmetric broad-side coupled dual striplines. When the distances from the upper and lower traces are identical to their respective near reference planes, the RLGC matrices should be symmetric. However, due to the use of the intermediate finite plane, the RLGC parameters exhibit minor asymmetry.
Work-around and Remedies
- Single stripline structure with h1>h2. Edit the layer stack-up to swap values of h1 and h2.
- Weakly edge-coupled striplines. Some of the parameters might be non-physical, e.g. L12<0. User can manually set those non-physical terms to ZERO in the W-element model file.
- Symmetric broad-side coupled dual striplines. If this is intended to be a differential pair, the differential- and common-mode impedances can be evaluated by
Detailed derivations leading to the above formulas can be found in the application note.