Linearization of Upcoming High-Efficient RF Power Amplifiers, Part 4: PA Behavioral Modeling Challenges for Broadband Applications

Thank you very much. I would like to first thank my copresenter for the invitation for this workshop, especially . And I'm glad to share my experience on the modeling of power amplifier. So I'm Wissam Saabe. I'm an application engineer. I'm working from AMCAD engineering. We are based in in France, and it stands for Advanced Modeling for Computer-Aided Design. And I will show you how we use the approach we have to the modeling of the power amplifier.

So already presented the-- and Marcus-- the context of the use of the amplifier. So here, just to highlight that we the aim is to predict the performances of such a system of antenna, for example. And it's a complex system because it's mixed-- different domain. So we try to predict the performances of the antenna as well as, especially, the radiation pattern, taking into account all the impairments from this different circuit.

So there is a large number of circuits, and all these controlled by the digital baseband. And in the middle, there is a key element, which is the power amplifier in which we have this compromise between the efficiency and the linearity. And the blackbox models-- the models is a good candidate to introduce all the phenomenon we can see in the power amplifier and to have a precise simulation results in this context.

So this is the modeling flow we follow. We start from a characterization of the DUT based on a vector signal generator and analyzer. So we take this measurement data to be able to extract a model, that try to do the relationship between the output and the input. So there is a method to identify the coefficient of this model. And then we use this model into a system simulation to include the behavior of the power amplifier in a large system design.

So about the system simulation-- so, in this context, we consider-- that is a bandpass system. That is to say, we don't consider all the harmonics. We only focus on the fundamental. So we deal only with the envelope of the signal. And so we take the data from the measurement. And we try to find functions that try to describe the relation between the input and the output.

So, first, we need to know the nature of the system we try to model. And the PA is a nonlinear system with memory-- that is to say, a nonlinear system. A nonlinear system is a system with output at a given time-- depends on the input at the same time and at the previous time. And our problem is to find the mathematical formalism that allows to describe this phenomenon, both nonlinearity and the memory.

And before to go to the model, in this slide, we try to put some definition-- what is the cause of this memory? So here, we have a layout of a mimic, a multistage mimic. And we separate the two memory effects-- first, the high-frequency memory effect or the short-term memory response that is linked to the different matching networks, input/output, and the interstage, in this case, that will, in fact, change the performances over the frequency.

So we have a variation of the gain according to the frequency. So we know the classic s-parameter that describe this phenomenon. And at the other hand, we have the low frequency memory effect. This is due to the long time constant of phenomenon such as the self-heating in the transistor and the trapping effects. So depending of the transistor technology, we have a larger impact of this low frequency memory effect.

And the difficulties that is mutual coupling between the low frequency and high frequency memory that severely affects especially the wideband modulated signals. On top of that, there is also the bilateral effect. So it is, in fact, the variation of the source and load impedance that will also affect the performances of the power amplifier. And so all this phenomenon are excited by the interaction between the circuit connected to the power amplifier and also the signal use in the application.

So here, just to show two characterization techniques that highlights this phenomenon-- so first, for the high frequency memory effect, we can use a single tone that is swept in frequency and power. So on the bottom left, we have the gain according to the function of the input power for different carrier frequency. And we can see that there is a different performances depending of this carrier frequency.

And we can also on such topology have different gain compression, nonlinear characteristics. So for one frequency, we can have an expression gain and compression and for the other just a compression. So these different characteristics will affect system level metrics such as EVM and ECTR, depending of the operating points.

On the other hand, we can characterize the low frequency memory effect using a 2-tone test-- 2-tone signals-- in which we can sweep the frequency spacing to scan this memory effect. So here, we plot the ratio EMD3 lower and upper for 3 input power. And it allows to analyze the asymmetry between the lower and upper EMD3 and also to identify some resonance that shows, for example, the interaction with the bias circuit for example, or the phenomenon linked to the low frequency memory effects.

So as you can see, depending of the carrier frequency input power bandwidth-- so we highlight this with the spacing of the two tones-- we can have different behavior. And currently, if using the classic models such as the memory polynomials, you need to extract a model for each signal characteristics in order to predict accurately the output.

And in with the approach we try to follow at AMCAD is to try to have a more robust model, that is to say, try to extract a model that will be once that will be valid for different signals, different operating points, so to avoid to extract each time for each different, depending of the scenario, behavior models. So this is a table that try to categorize these two approach.

So the first one, the common models that are full black box, such as the memory polynomials where the coefficient mix the low frequency and high frequency memory effects, and the identification mode is linked to the signal. So it's a discrete time kernel identification. So it's really linked to the characteristic of the signal, the sampling, and so on.

And the model we try to push here, it's more gray box. So we try to analyze the phenomenon by following the path of the signal and try to identify separately the low frequency and high frequency memory. And we do that for a power range and bandwidth in which we have this kind of continuous time identification. That is to say, whatever the signal you use and whatever the input power range, we have a model that is valid for different conditions.

So here, before to move on the model-- so just to show that we deals with the input and output power raise. So the goal is to find the equation that will be able to predict the b1 and b2, depending of the excitation a1 and a2 in the complex domain. So this is the formulism we use for the model.

So in the matrix form-- so we find the-- so we use again the-- we try to predict the B1 and B2 in the envelope of B1 and B2, depending of A1 and A2. And the model follow the polynomial form in which we find the different coefficients. And we find again the classic S-parameters, such as the S1,1 and S2,1 that can be obtained from the ET ohm measurement. And for the other coefficient, we need to apply a load-pull measurement, load-pull characterization. That is to say to show different output excitation.

So here, this is A2. And this A2 excitation will be monitoring by the load impedance we will present in the characterization. So in the measurement, what is the measurement we use? So it based on the Vectorial Network Analyzer that allows to collect the input and output power waves. We have a load tuner that will allow us to define the different output load impedance. And we apply this kind of characterization on the covert device. And we will highlight the capability of this model later.

So to do that, we use the IQSTAR Measurement Automation tools that allow us to connect the software to the measurement bench and to then perform the different power sweep and frequency sweep. So the tool allows us to connect the software to the different instruments and also to proceed to the calibration to be able to really measure at the duty plane. Also, we can perform CW or pulse characterization, depending of the power amplifier.

And also that allows us to be in a isothermal condition to define really the temperature of the device. So this is a screenshot of the configuration we can have. So you can define the power range frequency, the different carrier frequency, the pattern you want to apply in term of impedance. And during the measurement you can really see directly the performances.

So you have an example of the gain in function of the output power for the different carrier frequencies and the impedance. And in the same time, we start to trace the contour on the Smith chart. So here, this is the results of the measurement catheterization of the covert device we use in this work. So we start with the AM-AM characteristics. So on the left, you have the gain in function of the input power for the different load impedance and carrier frequency.

So as you can see, there is a larger number of data. And we can have an idea of the variation of the performances. So there is at the small signal 3dBA variation, depending of this operating point. And in the second graph, you can see still the AM-AM but again, depending of the frequency. So this is just to have an idea of the gain dispersion over the bandwidth. So in this case, we characterize between 3.4 and 3.8 to be in the application of the 5G Fr1.

Also we can get the AM-PM. So here are just limits for a few set of carrier frequency. And for each carrier frequency, we can see the variation depending of the load impedance. So the model is able to take into account this nonlinear behavior in term of phase. So also we measure the ratio B1, A1, so S1, 1 for the linear case. And we can see there is also a nonlinear behavior. So depending of the operating point, the signal will follow this nonlinear characteristics.

So you can see the characteristics according to the input power. And in the other graph, you see this one according to the frequencies. And so depending of the carrier frequency, you don't have the same performances, the same impairments in the output signal and the same for the phase. The model is also able to model the power consumption. So we can reach the goals to find the best compromise between efficiency and linearity. So I will not show the results on this one, but I'll let you that we have this capability also.

So from this measurement data, we can use the VISON tools that allow us to extract the model. So you can use exactly this measurement data into the tool, and you have some parameters to adjust to choose the right compromise between the accuracy of the model and the complexity. So we start with the low order, and we increase a little bit until we reach the good accuracy and directly after the extraction. So it takes a few seconds so you can directly check the accuracy by comparing the measurement data and the model that try to feed the characteristics in term of power and frequency.

So here, I would like to show you some comparison between the measurement and the model. So here, we see again the gain according to the input power. And so you can appreciate the accuracy of the model according to the input power. And in this case, I did a cut of this characteristics for the input power of 0 dBm, and I plot the contour on the Smith chart. So we can see in the middle the Smith chart, the contour of the gain.

So in solid line you have the measurement. And in the dotted line you have the model. And in the right Smith chart, I compute the absolute error between the measurement and the data. And in this case, the maximum error is less than 0.04. And it depends of this maximum error. It's not on all the area on the Smith chart. It's really located. So globally, we have a good fit between the model and the data. And we can do this evaluation for different input power.

So here, we can see in the compression that we really follow the different contour. And again, the error is very low until the maximum output power in which we can see the different contours, the circle that defines the maximum gain on the Smith chart. And in this case, the error is less than 0.0.1 gB. So we extract the model on a specific area on the Smith chart because in the measurement, we don't want to damage the PA by showing a large reflection coefficient.

But the model is able to have a nice extrapolation capability how we can show here. So on the right, you have the simulation of the model with this large pattern of impedance. And as you can see, there is a good capability to give a result. That is to say there is no issue of in term of convergence during the simulation.

Then a last assessment is to use modulated signals. So I let Georgia show you some examples in MathWorks in Simulink. Here, I just use the 2-tone test I've shown previously just to show that-- and to feel the capability of the model. So here, we have a 2-tone test, and we plot this figure of merit, the gain on each carrier and also the DMB3, the lower and upper. And here is just to show that first, depending of the load impedance, we don't have the same characteristics.

So the model is able to react depending of the load impedance. And also we can see it's not symmetric. So we have a different behavior on the left and the right side in term of the carrier but also on the intermodulation products. So the model is start to take into account this memory effect. And here, especially it is a high frequency memory effect. So this is the case for a spacing of 40 megahertz. But also if we increase at with 100 megahertz frequency spacing, we don't have the same behavior as before.

And also, again, we can see the asymmetry between the left side and the right side. And by the way, the simulation takes a few minutes to get this full evaluation. So just to conclude with this modeling approach, we try to bridge the gap between the circuit level to the system. So here, we highlight this with a measurement data. But if we have access to the PA design in your favorite circuit simulator, you can also do the same calculation-- the load pull simulation-- and use these characteristics to do system level evaluation.

Because we know at the circuit level is quite time consuming to do some simulation with a complex modulated signals. And that's all. Later, Georgia show you how we can use this modeling capability for the assessment of the system level simulation, especially for the phased array antenna system simulation. Thank you very much.

[APPLAUSE]