Dr. Steve Cripps presented a talk on the IEEE Industry Webinar series entitled, “**Facts and Fallacies in RFPA Waveform Engineering**.” This blog shares highlights from the informative question and answer session following his talk, the full video of which is available for on-demand viewing at the IEEE MTT-S webinar page.

**Webinar Abstract**

Waveform engineering has been an important concept in RF power amplifier (RFPA) design, resulting in the definition of important new PA modes. The concept can, however, be taken too far. A set of voltage and current waveforms can be used to define an impedance environment, but that environment will not guarantee that the same waveforms can be reproduced in a practical implementation. The impedance environment is a necessary, but not a sufficient, condition for a specific waveform realization. Widely-touted switch modes are one example of this frequently misunderstood principle. This webinar will illustrate some common misconceptions using various design examples, including both switched and analog cases.

**About Dr. Cripps**

After starting his career working with the pioneering gallium arsenide (GaAs) group at Plessey Research, Dr, Cripps emigrated to the U.S., where he spent 15 years working in various engineering and management positions at Watkins Johnson, Loral, and Celeritek. After returning to the UK he took on an academic post at Cardiff University, where he is currently a distinguished research professor. Dr. Cripps obtained his master’s and Ph.D. degrees from Cambridge University.

**Q&A**

**You mention adding even harmonics to the current waveform, resulting in a "sawtooth" waveform. How about only adding odd harmonics? **

**Dr. Cripps** - The sawtooth current was intended as something of a "reduction ad absurdum" example of how the current waveform cannot be engineered independently, but only as a derivative of the input waveform and the clipping effects of the output voltage. As such, it is not really viable to add harmonics to the current waveform; odd harmonics would, in a mathematical sense, lead to a square waveform, which is the basis for the "inverted Class F" mode. But my view of this is still the same—the odd harmonics arise through the clipping of the base sinusoidal waveform.

**Can the third harmonic analysis be extended to the fifth as well? Can it provide an additional advantage to boost the power added efficiency (PAE)?**

**Dr. Cripps** - Yes, in theory it can, but in practice it becomes increasingly difficult to maintain prescribed impedances at multiple harmonics. This is another limitation of waveform engineering, and one reason why it becomes important to analyze non-optimum terminations, which can be provided by realizable networks. This is a surprisingly lightly explored area by the power amplifier (PA) theorists, despite being essentially what any PA design results in.

**For class F PAs, does GaAs (high N) give similar results for the V3/V1 analysis?**

**Dr. Cripps** - Although I implied that the math becomes too cumbersome with much higher N values, there are several ways around this. In particular, given the likely low value of V3/V1, the higher polynomial terms that result in the expressions for current components can be ignored, resulting in very similar, albeit slightly modified, values for power and efficiency when the expressions are truncated down to terms up to third power. The power ends up a bit higher due to the sharper clipping function, but the general form of the graphs is the same.

**Are there certain high efficiency classes that allow more operating bandwidth?**

**Dr. Cripps** - In general, the continuous mode Class BJ allows the second harmonic design space, and, as such, offers the potential for wideband performance, as has been demonstrated by many papers in the literature. Push-pull operation further increases bandwidth but is potentially limited by balun performance.

**Is it possible to build real PA with 2-5W output power, 20dB gain, and PAE more than 50-60% for frequencies up to 20GHz with band around 10-15 %?**

**Dr. Cripps** - It is quite possible these days with gallium nitride (GaN) technology, although the only processes accessible commercially would be monolithic microwave integrated circuit (MMIC) foundries (such as WIN .15 micron). Efficiencies do start to drop above 10GHz, as the higher harmonics exceed cutoff frequencies. Although 40% has been reported up to 20GHz at these power levels, 60% would still be a stretch.

**You mentioned engineering the input current waveform as a possibility, any specific ideas for this?**

**Dr. Cripps** - Analog shaping has been somewhat investigated, and there are a few papers (mainly conferences) that play around a bit with this, but in general to do anything significant several harmonics need to be generated. I think it remains an interesting and potentially fruitful area for future research using the fast DSP now available, albeit at very low power levels.

**Can you comment on the knee clipping effect on inverse Class F PAs?**

**Dr. Cripps** - With a sinusoidal voltage (as prescribed for inverse Class F), the current will naturally assume a more square-like appearance, and indeed in practice this is the actual mechanism for realizing the current waveform, as opposed to the rather nebulous explanations surrounding the effect of open circuiting the second harmonic. I would say, however, that it is worthy of further investigation.

**Many PA designers in my field are dealing with poorly performing metal oxide semiconductor (MOS) transistors supporting waveforms with high peak-to-average power ratios (PAPRs). Do you have any insight into the effectiveness of waveform engineering to achieve high efficiencies in such cases?**

**Dr. Cripps** - I assume you are working at lower frequencies, below 2GHz, maybe more VHF than microwave, using MOS devices? I have always observed what I characterize as a “cultural divide" between VHF PA design and microwave PA design. It's a pity; the latter is much more well documented in the technical literature (IEEE/MTT journals and conferences) whereas VHF tends to be regarded as more in the realm of the amateur Ham radio enthusiast. In fact, both camps could learn a lot from each other.

I think one of the main differences is that the microwave designer (at multiple GHz) needs to deal with device parasitics in order to de-embed the intrinsic device and its waveforms. But the intrinsic GaN or GaAs device, once de-embedded, is much more well behaved than is a MOS device at 100MHz. And furthermore, I should not imply that parasitic effects are absent in MOS VHF transistors; feedback effects are, I believe, much more present and slew the whole concept of separating input and output as independent entities. I have always thought that the microwave power transistor community could do a useful service, both for themselves as well as the VHF PA community, to try applying their methodologies and characterization techniques on higher power MOS devices. I imagine this has been done, to some extent here and there over the years, but a solid peer-reviewed publication channel for this kind of work to be reported is lacking.

**Shouldn't the dimple occur naturally as the device goes into knee region? If so, then how do we engineer it further to get different kinds of waveforms on the current?**

**Dr. Cripps** - This is essentially the subject of my talk. Basically, the dimple is the result of the voltage dependency of the current on the voltage (Vds) while in the knee region. If the voltage is sinusoidal, and in antiphase with the current, the current will display a symmetrical dimple feature. If the voltage waveform is modified, the current can in effect be re-engineered using this functionality. Examples of this are presented in the webinar.

**What is your opinion on viewing the intrinsic device as a resistor with on-resistance R_on, when the V_DS falls below the knee voltage (triode region)?**

**Dr. Cripps** - This to me would appear to be a case of physical versus behavioral modeling. The advantage of the behavioral approach that was presented in the webinar is that it is a continuous function, which is much more useful for further mathematical analysis. The knee-resistor model only applies in the knee region, so there is a break point where the device gets out of the knee and a different behavior ensues. This is fine for computational analysis, but not as good for analytical treatment.

**In base station (BTS) design for wireless infrastructures, the performance of the PA sizes the dimension and weight of the full BTS. While output power and efficiency are key, the ability to linearize the PA is crucial through digital predistortion (DPD). How do you integrate this third parameter in your PA designs to make sure the BTS can actually meet the 3GPP standard with reasonably sized DPD?**

**Dr. Cripps** - I am fully aware of the need for meeting regulatory emission specs! Prior to my current academic position, I was myself heavily hands-on in the wireless communications industry, designing both mobile and base station PAs. My experience, over 20 years or more, has been a gradual improvement (primarily digital speed) in DSP techniques such as predistortion. The point has been reached, I surmise, where the DSP can correct a very wide range of nonlinearities in the basic PA, provided some guidelines are followed. This topic is a webinar in itself, possibly a 3-day course, and academics (as I now am) should steer away from proposing techniques that would pose problems for linearizers in meeting regulatory specs. But as academics, part of our mission is to investigate novel techniques. Class BJ continuous modes, in my experience, have been successfully implemented in many commercial BTS products and, as such, do not pose any greater challenges for linearization than do older techniques.

**If we neglect harmonics > 2, can you comment on the difference between a saturated Class J and a Class E PA?**

**Dr. Cripps** - I am assuming higher harmonics are either specifically shorted, or negligible in amplitude. Of course, this is an approximation, but it is one frequently made in PA mode analysis. My view has always been, a Class AB waveform is dominated by fundamental and second harmonic; the most questionable assumption would be to ignore/assume shorted second harmonic, which is almost axiomatic in most textbooks analyzing Class ABC modes. At least I am giving full treatment of the 2H behavior. There is the additional issue of higher frequencies. Once 10GHz is reached, the chances of seeing much harmonic content above 20GHz is minimal; indeed it is hard enough to generate enough second harmonic to see the expected efficiency enhancement of Class AB modes.

Regarding a Class E/Class J comparison, this was covered later in the webinar, and I have published extensively on the subject (see my book, 2nd edition). The short answer is that Class J has a current waveform that is symmetrical about the vertical axis. As this becomes more asymmetrical it approaches (but in practice never reaches) true Class E operation.

**Slide 17 addresses the idea of predicting contours by introducing the knee model in analysis as a close analysis to real world. How is it different from Pedro's model?**

**Dr. Cripps** - I’m sorry, I’m not not sure what you mean by Pedro's model? One can, of course, always run a design on a simulator that uses a more comprehensive model, which will usually contain both physical and behavioral elements. There has, however, always been a more theoretical approach, which will simplify the behavior using mathematical functions. Historically, before computers, this approach was the only one available. But I, for one, along with the editorial management of MTT journals such as the Transactions, firmly believe that the theoretical approach can still give deeper insight into the behavior of a device, and acts as a useful starting point for more detailed simulation using modern CAD tools.

For more on Dr. Cripps and power amplifier theory, check his keynote "**Active and Passive Matching in RF Power Amplifiers**" from RF/MW PA Forum 2019 as on-demand video. Info and registration can be found on this page: https://www.awr.com/adf