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This document describes the process of extracting S-parameters from a simple structure: a microstrip line discontinuity, changing from a high impedance line to a low impedance line, and vice-versa.
The transition between lines of differing impedances will naturally
produce a reflected (S11) and transmitted (S12) wave. This example is simple
enough for us to find the reflected and transmitted signals using a
transmission line model:
where the impedance Z of a microstrip line is estimated to be 
LC specific references are explained here.
main command||subcommand, where
main commandis the menu button on the main menu, and
subcommandis selected from the drop down menu that appears as a result of selecting
The design starts with a microstrip over a ground plane (figure 1) and substrate extending to infinity, simulated by the boundary conditions. The substrate used is a material with a permittivity , approximating that of duroid, a material commonly used in CU-Boulder microstrip fabrication.
The microstrip is built so that the signal propagates from the source region to the incident measurement and hits the discontinuity. Then the signal splits into reflected and transmitted waves, to be measured by the two probe regions. Initial simulations were done with a 4mm wide microstrip at the far end (figure 2).
For microstrip analysis the quantities of interest are voltage, current, charge, and magnetic flux (figure 3). The source block produces a voltage pulse, and two dimensional visualizations of the propagating signal usually measure the voltage at various points on the microstrip.
The source block is placed near one end of the grid, positioned to inject a signal into the microstrip. The injected signal has a frequency content in the desired range, from 0Hz up to at least 10Ghz, and injects the signal as a voltage source.
The probes are placed in sets of four - the traditional quartet used for the LC pulse measurements - as shown in figure 3. The S-parameter analysis only uses the voltage and current measurements, but we might want to use the other probes (charge and magnetic flux) when examining line impedance or other parameters. Note that the probes are not specified as ideal; for instance, although we only need a to specify single infinitely thin line of integration to find the voltage, in this analysis a thick pillar is used. The probe is set to find the average voltage in the entire pillar. This is done partly because it gives a a smoother measurement value, and partly because it is convenient to design and place all the probes if they have the same width and depth.
Now that all the probes are defined, they are grouped together into
pulse sets. Three pulses are defined using
define||pulses, as shown in
table 1. The terms ``narrow'' and ``wide'' refer to
the pulses placed on the narrow or wide part of the microstrip (see
figure 1. An anomaly seen by looking at this
table is that the same set of probes is used to look at both the
incident and reflected waves! This is because the ``narrow'' probe
sees both the incident and the reflected wave, at different
times. So to get the two signals we have to extract them by cutting
out certain time ranges from the probe readings. This cutting occurs
later, after the simulation is run and the probe readings are made.
Dialog box snapshots are shown in section 5.1.
|Magnetic Flux Probe||magflux.narrow||magflux.narrow||magflux.wide|
Finally the simulation is started. The LC probes produce some time domain data, which can then be processed to make S-parameter graphs.
analysis||plot pulses window in LC,
we can take a look at all the data collected by the probes. A glance
at the raw voltages (figure 4) clearly shows the
overlap of the incident and reflected pulse: both the ``narrow'' and
``narrow.reflected'' probes see both the incident and reflected
signals. By going back to
define||pulses, we can place certain time ranges into each
pulse, so that each pulse set contains only the data for a
The timesteps containing each pulse are specified in
pulse start and
pulse end fields, which
can be set manually or by
experimenting with the
Guess From Data and
From Graph commands. The time ranges should be chosen so that each
pulse definition has a clearly specified signal.
After this, using
analysis||plot pulses again and looking at
``time'' plots instead of ``raw'' plots (figure 5) we can easily see which signal
corresponds to what pulse.
Now that the pulses are well defined, all that remains unfinished is
analysis||S parameters. Specifying the
proper pulses as
transmitted, we can produce either S11 or S21, or
both-see figure 6.
The analytical results are found using equations 1,
2, and 3. For a microstrip
2mm away from the groundplane, on a substrate with ,with a width varying from 2mm to 4mm, we get:
Which produces results within 16% of the numerical simulation. For a more accurate result we might want to clean up the signals in figure 3 as well as the parts selected in
Because this is numerical analysis and not analytical analysis, the model is not ideal; certain simulation artifacts must be recogized and somehow dealt with.
The width of the groundplane, substrate, and surrounding air must be
chosen to keep most of the signal energy away from the boundaries;
there is some distortion caused by waves propagating along the
boundaries which we want to avoid. A reasonable amount of spacing
around a microstrip line is to make the ``padding'' as thick as the
microstrip width or the substrate height, whichever is larger.
Figure 7 shows that the effect of the boundary
conditions does not produce a noticable effect until the total grid
has shrunk down to 10mm in size, corresponding to a padding of about
the width of the wider part of the microstrip line. If the 4mm
microstrip was the only line we wanted to look at, we could use a
smaller simulation grid than is shown in
figure 1 and reduce the simulation run time;
however, later on we will look at other, much wider, lines and will
need this extra padding. Therefore all simulations will use the 20mm
The source and probe blocks are placed on the microstrip line; there are restrictions on the locations we can use, because we need to produce a clean signal for analysis.
The ``raw'' output from a source will not produce a perfect waveguide mode, unless someone labors to derive the exact field values for a given waveguide (figure 8 and configures the sources appropriately.
An alternative is to inject a signal using a simple block source. The fields produced by this source (figure 9) contain a bunch of modes: one mode is the propagating mode that we want (figure 8) and the other modes will either propagate at a different velocity or not propagate at all. So, if we let this block shaped signal travel down the microstrip, many of the unwanted modes will simply decay and die out. Other modes will propagate at different velocity; typically the strongest mode is the one we wanted in the first place.
Using this process to generate the desired modes requires that the signal propagate a distance away from the source. This requirement means that the source cannot be placed directly next to the incident wave probe or the structure we are studying (in this case, the discontinuity). So there must be a short propagation distance between the source and the probes/structure.
The effect of placing a source too close to the probe is shown in figure 10. The distance from source to probe has a drastic effect on the high frequency, less so at low frequency. This indicates that the source block is injecting a wide frequency range into the microstrip, but much of the higher frequency content quickly decays. Since S-parameters are only relevant for propagating signals and not decaying modes, we must place the source at least 14mm away from the first probe - and possibly further if the high frequency S21 parameter is wanted to any accuracy.
The probes are placed reasonably close to the discontinuity; what does ``reasonable'' mean in this context? The microstrip discontinuity causes field distortion with the same net effect as with the block source: parts of the field constitute a guided wave mode, and propagate away, while other parts of the field quickly decay. Because of this effect, we will get better results if the probe is placed further away from the discontinuity - if placed too near the discontinuity, then the transient fields will effect the measurement. However, by placing the probe a long distance away you will naturally require more simulation grid space and time. The goal in this case is to place the probe as close to the point of interest (in this case, a microstrip discontinuity) while minimizing distortion from transient fields.
We can find a good spot to measure by taking multiple measurements at progressive points along the waveguide. Looking at figure 11, we see that the transmitted wave produces a large number of high frequency modes that quickly decay out, leaving only the smooth gaussian profile of the original signal, 15mm out from the discontinuity. The forward traveling wave evidently carried all the transients with it, since the reflected wave (figure 12) shows no real distortion with distance.
Once the ideal probe locations are found, the other testing probes can be eliminated and the grid shrunk down to enclose only these probes. Make sure at this point that boundary reflections will not effect the results too dramatically.
This section contains a graphical view of various parts of LC showing, visually, how to perform some of the feats described in previous sections.
These pictures show the dialog boxes as they appear once all the probes have been properly assigned to the three pulse definitions, as specified in table 1.