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Hello. And welcome to Part 2 of this four-part video demo on generating X-parameters from
circuit-level designs. My name is Jack Sifri, and I will show you how you can easily generate
a load-dependent X-parameter model for our power amplifier circuit that would hold accurate
not only with a 50-ohm load, but for any load on the Smith chart.
In Part 1, I explained to you what X-parameters are. And I demonstrated, using ADS, how easy
and fast it is to generate a 1-tone 50-ohm load X-parameter model from an LTE circuit-level
PA. I showed how the X-parameter model is as accurate as the circuit-level design in
all dimensions – linear and nonlinear – and ideal to use in a system that contains
cascaded 50-ohm matched modules.
But now, what if my system contains cascaded modules that are not well-matched to 50-ohms?
We need to have a more versatile model that can be accurately used with any load impedance.
For example, in this picture, you see the power amplifier interfacing with a duplexer
and an antenna. Sometimes, we do not really know what the impedance load on that power
amplifier is.
As a result, we get impedance mismatch in magnitude and phase with the PA at both the
fundamental frequency and the harmonics. Only a load-dependent X-parameter model, which
contains accurate information on the magnitude and phase of the fundamental frequency and
all the harmonics, would allow us to accurately predict the behavior of the PA in the system
under any load impedance.
Now here’s another situation. Let’s say the gamma load of the second harmonic on the
PA is generating some distortion that interferes and degrades the efficiency of the PA and
battery life. To fix this problem, designers need to know the exact magnitude and phase
content of this second harmonic tone, so they can filter it out.
Unlike all the available models in industry that capture the nonlinear behavior only on
the fundamental frequency, the X-parameter model accurately captures the behavior on
all the harmonics. Therefore, it would allow you to solve this problem and design your
cell phone for better efficiency and improved battery life.
Let me now demonstrate this for you. Generating the load-dependent model in ADS is very easy.
All I have to do is insert my power amplifier into this template, just as we did in Demo
1. The only difference here is I add a load sweep, instead of keeping my load at a constant
value of 50-ohms. So when I double-click on this X-parameter load, a window opens up that
allows me to sweep the load.
In this demo, I will generate a load-dependent model with gamma = 0.5 and phase between -180
degree to +180 degrees. So the model I will generate will accurately work with any load
impedance that lies within 50% or half of the Smith chart. So by clicking on the Simulate
button now, a new load-dependent X-parameter model is generated within a few minutes, and
automatically stored in the data set folder of the project.
Next, let me test my model, to see how accurate it is, as compared with the circuit-level
PA. Here, I have inserted the X-parameter model into this ADS template that automatically
generates load-pull contours for delivered power and power-added efficiency. I set up
my simulation to sweep the load impedance over 50% of the Smith chart, identical to
the setup I used when I generated my load-dependent model.
Next, I simulate, and the data display page with the contours plot appears. Notice the
simulation with the X-parameter model took only one second to run. Next, I do the same
exact thing. But now I insert the circuit-level PA, instead of the X-parameter model, and
I simulate. Notice in this simulation, it takes about nine seconds, as compared to the
one-second simulation time it took using the X-parameter model.
This means in this specific example, the X-parameter model simulated nine times faster than the
circuit-level PA. Please note we had also experienced more than 25 times of simulation
speedup factor in other examples. Now this data display contains both results from the
X-parameter model and from the circuit-level PA overlaid on top of each other.
Notice how accurate the X-parameter model is, as compared with the circuit-level PA
in both power-delivered contours and power-added efficiency contours. The results are right
on, and the X-parameter model can be used now in place of the PA circuit with exactly
the same accuracy and with much faster simulation speed.
As I stated earlier, you can generate a load-pull model that covers a wider area on the Smith
chart, or even the whole Smith chart. Also, you can add another dimension and sweep the
power, as you generate these load-pull contours. Here’s an example. What you see is a data
display that shows another generated model that covers 70% of the load impedance on the
Smith chart. I have also included another dimension and swept the input power.
So here, on this data display, I can use the slider to vary the input power to the PA and
the X-parameter model. And notice how the delivered power and the power-added efficiency
contours update immediately, and are still very accurate at all power levels. Next, I
will insert two cascaded PAs with mismatch between them, and compare their simulated
results with the results from two cascaded X-parameter models.
But before I do this, I want to bring to your attention that the output return loss of the
PA, S22, is excellent when driven hard, just the way it was designed as a power amplifier.
On the other hand, if we drive the PA with a small signal, the S22 naturally degrades
and moves away from 50-ohms, as shown here. Because the output FET capacitance and resistance
change as a function of drive level. Therefore, cascading two of these PAs will result in
a mismatch between them.
The source impedance of the second PA is no longer 50-ohms. It is now the degraded S22
of the first PA, since it is driven with a small signal. And our generated model covers
that load impedance, as shown by the blue shaded area. So this would be a good case
to test our model with mismatched, cascaded modules. So here’s the setup of two cascaded
PAs with mismatch, and here are the simulation results for them. And here’s the setup for
two cascaded X-parameter models with mismatch, and here are the results.
Notice that the simulation took less than one second to finish. This data display shows
the results of the cascaded PAs and the cascaded X-parameter models overlaid on top of each
other. Notice how accurate the results are. They are right on, on top of each other. What’s
shown here is the magnitude and phase of the fundamental, second harmonic, and third harmonic.
So this clearly demonstrates the high accuracy of the model under any load impedance and
with a cascaded, mismatched condition.
So let me recap and summarize a few key points on this video. We saw how X-parameters unify
the linear and nonlinear scattering parameters and load-pull data all over the Smith chart.
And this data allows you to efficiently design your power amplifiers and other nonlinear
circuits. And this X-parameter data can be generated as a nonlinear function of frequency,
RF power, DC bias, load impedance, temperature, or any variable that you wish to sweep. And
once you have generated this nonlinear model, you can immediately start simulating all over
the entire Smith chart.
In the next video, Part 3, I will show you how to generate a two-tone model that can
be used to determine the intermodulation distortion products and third order intercept. And in
Part 4, I will show how the X-parameter model is used in wireless verification, with much
faster simulation and verification speed.
Thank you for watching this video. For more information on X-parameters, please visit
us at the following two Web pages. Please proceed next to Video Demo 3 on generating
an X-parameter models with two tones.