here to go to our main page on S-parameters
here to go to the page that describes our S-parameter Utilities
spreadsheet which is available in our download
New for December 2005!
S-parameters for a device (in
particular their angles), refer to fixed reference planes at each
port, whether you are dealing with measured or simulated data. Quite
often, the desired reverence plane is NOT where you are able to
measure the device, because the device must be mounted in a test
fixture in order to measure it. If you know the approximate length
of the test fixture you can perform a "poor-man's de-embedding"
procedure to move the reference plane of the measurement toward
the device. You can also move reference planes just to flatten out
phase characteristics, which is particularly useful when looking
at phase tracking between two or more widgets.
Below we'll discuss an example
where we move the reference planes using Agilent's Eagleware Genesys
software, then we'll repeat the same data manipulation using our
S-parameter Utilities file which runs in Excel. It will perform
the same operation on any device that you have S-parameters for.
We started by downloading the
S-parameters of a Hittite amplifier, the HMC397. Hittite is perhaps
the only MMIC vendor that makes it easy
to download S-parameters on their web site, so that's why we pick
on them. They should take it as a compliment!
In Genesys we pull up the S-parameters
in an "S2P" block. On the input and output we have added
adjustable delays for moving the reference planes. In the initial
analysis we have zeroed out the delays so you can look at the raw
Below is the gain magnitude and
phase. Not that the phase has a negative slope, which is true of
most real devices. This amplifier is DC coupled, so it has gain
down to zero Hertz. The slight phase slope is indicative of a part
that was RF probed, with the reference plane right at the probe
Here's the reflection coefficients
(S11 and S22) plotted on a Smith chart. You can see that they too
have a negative phase slope, as they wind clockwise around the chart,
starting at 0 degrees.
Now let's see what happens when
we add 0.2 nanoseconds of delay on the input and output. This is
the equivalent of moving the reference planes by 6 centimeters away
from the device (recall that electromagnetic energy moves almost
exactly 30 centimeters in one nanosecond, it's a Microwaves101
rule of thumb). Here is the revised schematic:
Now lets look the gain phase
angle. The angle wraps around zero four times. This is more like
what you'd see if you measured the device embedded in a small test
fixture (perhaps one inch alumina fixture).
Let's also look at the reflection
coefficients. They too are now wrapped around the chart multiple
Now you can visualize what moving
the reference planes does to phase angles of the S-parameters. This
example is actually the reverse of how you would move reference
plans in real life; you'd take fixtured data that wraps multiple
times, subtract delay from it to get "de-embedded" data.
The problem with de-embedding this way is that you'll need at least
one standalone measurement of the fixture with nothing in it to
compute how long it is.
Next we loaded the same HMC397
S-parameters into our S-Parameter Utilities spreadsheet, and made
the same gain magnitude/phase plot. It agrees with the first Genesys
plot as it should. Unfortunately we don't have Smith chart capability
in the spreadsheet, but rest assured that the polar coordinates
of the reflection coefficients are correct.
Finally, we added -6 centimeters
to the input and output reference planes and replotted that gain
magnitude and phase. Why -6 and not +6? Call it a Microwaves101
convention, but we believe that "positive" reference plane
extensions move into the device, not away from it. The result is
the same, our free download performs the same function as a $5000
piece of linear analysis software, and
we won't come after you every year for "maintenance fees!"!
What happens to group delay when
you move the reference planes? It changes by the amount of delay
that you added. Below is the raw data group delay plot. Without
moving the reference planes, we see that the device "measures"
about 0.04 nanoseconds in length.
Adding 0.2 nanoseconds delay
to both the input and the output increases the group delay by 0.4
nanoseconds total, as it should.
What's with the "raw"
and "smoothed" data? Learn more about smoothing
group delay here!
Now let's go back to the original
reference planes and plot the "unwrapped" phase of S21
(another option in the S-Parameter
Utilities spreadsheet). By unwrapped, we mean that whenever
it crosses -180/180 on the Smith chart, we'll fix it so it just
keeps going in a straight line. Here it is (although in this case
the part has so little phase variation that unwrapping was not needed!):
You can see some noise in the
data, but it is hard to quantify at this scale. Now let's use the
reference plane extension until we flatten out the phase, and then
zoom in on it. After a few tries we find that 0.5 centimeters on
input and output makes S21 phase nearly horizontal. In the time
domain this is equivalent to 0.017 nanoseconds. Now we can see the
noise on the measurement much better. The total reference plane
adjustment (0.034 nanoseconds) is roughly equal to the average group
delay of the part. Moving reference planes until phase flattens
is another way of measuring or calculating group delay.
Now when we look
at group delay, we see that it is essentially zero, which verifies
that we have moved the reference planes so that the DUT has zero
The data that Hittite supplied
was measure just about every 50 MHz. At this interval the phase
only moves about 1.5 degrees between each point. It the data is
only accurate to 0.1 degrees, this is the source of error that makes
the group delay jumpy.
It's time for another Microwaves101
rule of thumb!
When measuring S-parameters to get group delay, you should pick
the frequency interval to achieve about 10 degrees S21 phase difference
between frequency points. Less than this will make the measurement
jumpy, greater than 10 degrees might mask some real problems in
group delay flatness. How do you know in advance what frequency
interval to pick? Excuse us while we go think up a formula for this...
That's a subject for another