The first test of this benchmark uses two nearly identical capacitors which should give
nearly identical results. The capacitors are formed with identical top plates a very small
distance above a ground plane. Thus, the ground plane forms the bottom plate of the
capacitors. In both cases, loss is present only in the ground plane. The two capacitors
are different in that the ground plane of one is formed from regular subsectioned metal
while the other is formed from the bottom cover of the box.
The second test (which uses Test Structure C), uses loss only in the capacitor
dielectric. The loss used creates a 50 Ohm resistor. Difference in the resistance from 50
Ohms is error in the evaluation of dielectric loss.
Failure of an analysis to pass either test at the desired level of error is sufficient
to conclude that the analysis is inappropriate for use at that error level for the
analysis of ground plane loss (first test) or dielectric loss (second test).
Ground plane loss is important when magnetic current subsections are used to simulate
gaps in a ground plane. Gaps in a ground plane might be used to simulate coplanar
waveguide or slot line. If the ground plane loss is incorrect, then the coplanar waveguide
loss calculation is also incorrect.
As for microstrip, most of the microstrip loss is in the microstrip conductor. But
there is also some loss in the microstrip ground. Thus if ground plane loss is
underestimated, then microstrip loss is underestimated.
This is also a problem for high speed digital. If the ground is a perfect conductor,
"ground bounce" and "ground loops" can not happen. If loss is not
calculated correctly, then ground bounce and ground loops are not calculated correctly.
Ground Plane Loss Test
Ground plane loss and dielectric loss, unlike normal conductor loss, require the
calculation of a complex (i.e., real and imaginary) Green's function. In contrast, loss in
subsectioned circuit metal does not require a complex Green's function.
Since ground plane loss requires a modified Green's function, there is a chance that
bugs or numerical errors might cause incorrect results. This test is based on two
different models of the same capacitor. In both cases, the capacitor is formed with normal
subsectioned metal forming a lossless top plate. The bottom plate of the capacitor is a
ground plane. In Test Structure A, the ground plane is formed from normal subsectioned
metal, a so-called "artificial" ground plane. The metal of the artificial ground
plane is lossy. In this case, the usual analysis ground plane (bottom cover of the box) is
moved far from the capacitor so that it has no influence. Even though the analysis ground
plane has no influence on Test Structure A, it should be lossless so that a complex
Green's function is not calculated.
Figure 14. Top and side views of both test structures. In
structure A, the lossy ground plane is composed of regular subsectioned metal. In
structure B, the box bottom cover forms the lossy ground plane. Results from each should
be nearly identical.
The bottom plate of the capacitor in Test Structure B uses the ground plane usually
used in the analysis (i.e., the box ground plane or bottom cover). Subsectioned metal is
not used for the ground plane. This means that 1) No subsections are used for the ground
plane, and 2) A complex Green's function must now be calculated.
Both structures should give close to the same result, the only difference being due to
the difference between a subsectioned ground (in Test Structure A) and the usual analysis
ground plane (used in Test Structure B).
Important parameters for the test structures are summarized below.
Parameter |
Value |
| Type of Structure |
Thin dielectric capacitor connected in shunt to ground. |
| Ports |
One port, along one side of the square capacitor. |
| Connecting transmission line length |
0 (not critical). |
| Capacitor Placement |
Along one edge of the substrate, for port attachment. |
| Capacitor Top Plate |
Normal subsectioned metal. |
| Capacitor Bottom Plate |
Normal subsectioned metal covering entire substrate surface. |
| Dielectric Thickness |
0.1 micron (not critical). |
| Dielectric Constant |
10.0 (not critical). |
| Capacitor Area |
0.5 x 0.5 mm (not critical). |
| Substrate Size |
1.0 x 1.0 mm (not critical). |
| Frequency of Analysis |
10 GHz (not critical). |
| Cell Size |
So substrate is 8 x 8 cells (not critical). |
| Top Plate Resistance |
Lossless (critical). |
| Bottom Plate Resistance |
10.0 Ohms/square, frequency independent (large value means
more sensitive to loss error, must be same as Box Ground Plane Loss in Test Structure B.) |
| Ground Plane Resistance |
Lossless (ground plane positioned far from the capacitor). |
Table 4: Test Structure
B -- Important Parameters |
Parameter |
Value |
| Capacitor Bottom Plate |
Box ground plane. |
| Box Ground Plane Loss |
10.0 Ohms/square, frequency independent (must be same as
Bottom Plate Resistance in Test Structure A.) |
| All Other Parameters |
Identical to test structure A. |
Results For Ground Plane Loss
Analysis of both structures with Sonnet Version 4.0 yields the following results:
>
Table 5: Results With
Lossy Subsectioned Metal (A) and With Lossy Ground Plane (B) |
| |
S11 (mag) |
S11 (ang) |
Structure A |
0.9700 |
-179.4 |
Structure B |
0.9704 |
-179.4 |
For unknown reasons, when a smaller subsection size is used, the difference between the
two structures increases slightly as we see in the following data for which the cell size
has been cut in half (the substrate is now 16 x 16 cells):
Table 6: Results With
Cell Size Cut In Half |
| |
S11 (mag) |
S11 (ang) |
Structure A |
0.9743 |
-179.0 |
Structure B |
0.9748 |
-178.9 |
Dielectric Bulk Conductivity Test
This test is based on a slightly modified version of the above capacitor structure.
Strictly speaking, it tests only for bulk conductivity error. However, since loss tangent
is exactly equivalent to a frequency dependent bulk conductivity, this test
is likely to
be sensitive to loss tangent modeling error as well. This test is most easily performed
with Sonnet 4.0 or higher where bulk conductivity can be directly specified for each
dielectric layer.
Table 7: Test Structure
C -- Important Parameters |
Parameter |
Value |
| Capacitor Dimensions |
0.5 x 0.5 mm (same as before, but now critical). |
| Dielectric Bulk Conductivity |
0.008 S/M (critical). |
| Dielectric Constant |
1.0 (not critical). |
| Cell Size |
So substrate is 64 x 64 cells (not critical). |
| Ground Plane Resistance |
Lossless (Critical). |
| All Other Parameters |
Identical to test structure B. |
The given bulk conductivity makes the structure behave as a 50 Ohm resistor to within
the degree allowed by the cell size. The magnitude of S11 should approach zero as the
analysis frequency approaches zero. Any difference is error. Sonnet provides the following
results:
Table 8: Sonnet results
for the dielectric loss test. |
Frequency |
S11 (mag)
(no de-embedding) |
S11 (mag)
(with de-embedding) |
1 GHz |
0.96133 |
0.96122 |
1 MHz |
0.00405 |
0.00369 |
1 kHz |
0.00206 |
0.00122 |
1 Hz |
0.00206 |
0.00122 |
At 1 GHz, the capacitor dominates, creating a short circuit. Without de-embedding, S11
magnitude converges to 0.002 which means the calculated resistance is in error by 0.4%. A
portion of that error is due to the lack of de-embedding. With de-embedding, the error
decreases to 0.24%.
The equivalent circuit of the structure is a capacitor and resistor in parallel. The
resistor should be 50 Ohms. Any difference is error. De-embedding removes only second
order error because the port discontinuity is almost purely capacitive and simply
increases the value of the total capacitance, it has little effect on the resistance of
the equivalent circuit. Sonnet's SPICE lumped model synthesis option was used to generate
the equivalent circuit (analysis at two frequencies required). Alternatively, one could
also simply invert the real part of the calculated Y-Parameter. Sonnet provides the
following results:
Table 9: Sonnet SPICE
model synthesis results for the dielectric loss test (no de-embedding). |
Frequencies for SPICE model synthesis |
Resistance (Ohms) |
| 1 and 1.1 GHz |
49.786 |
| 1 and 1.1 MHz |
49.795 |
| 1 and 1.1 kHz |
49.795 |
| 1 and 2 Hz |
49.795 |
The convergence seen here is due to the increasing validity of a lumped model at lower
frequency. A frequency of 2 Hz was used for the last analysis because Sonnet does not
allow a difference of 0.1 Hz between two frequencies.
Note that this approach has also converged to the same 0.4% error.
We repeated the analyses with de-embedding. Sonnet now provides the following results:
Table 10: Sonnet SPICE
model synthesis results for the dielectric loss test (with de-embedding). |
Frequencies for SPICE model synthesis |
Resistance (Ohms) |
| 1 and 1.1 GHz |
49.870 |
| 1 and 1.1 MHz |
49.878 |
| 1 and 1.1 kHz |
49.879 |
| 1 and 2 Hz |
49.878 |
The error is now 0.24%, consistent with the previous de-embedded results.
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