Michael Roberg

Codesign of PA, Supply, and Signal Processing for Linear Supply-Modulated RF Transmitters

This paper presents a method for achieving high-efficiency linear transmitters by codesign of the RF power amplifier (PA), dynamic supply, and signal processing. For varying amplitude signals, the average efficiency of the PA is improved by adding a supply modulator with requirements derived from nonstandard PA modeling. The efficient PA and supply modulator both introduce signal distortion. A targeted linearization procedure is demonstrated with reduced complexity compared to standard digital predistortion. Experimental results on a 2.14-GHz 81% efficient 40-W peak power GaN PA illustrate the codesign method by achieving 52.5% composite power-added efficiency with high linearity for a W-CDMA signal with a 23-MHz supply modulator bandwidth.

Low-Power Wireless Power Delivery

This paper addresses design and implementation of integrated rectifier-antennas (rectennas) for wireless powering at low incident power densities, from 25 to 200 μW/cm2. Source-pull nonlinear measurement of the rectifying devices is compared to harmonic-balance simulations. Optimal diode RF and dc impedances for most efficient rectification, as a function of input power, are obtained. This allows optimized antenna design, which can eliminate or simplify matching networks and improve overall efficiency. As an example of the design methodology, Schottky diodes were characterized at 1.96 GHz and an antenna is matched to the optimal complex impedance for the most efficient rectifier. For incident power density range of interest, the optimal impedance is 137 + j149 Ω, with an RF to dc conversion efficiency of the rectifying circuit alone of 63% and total rectenna efficiency of 54%.

High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers

This paper presents a theoretical analysis of harmonically terminated high-efficiency power rectifiers and experimental validation on a class-C single Schottky-diode rectifier and a class- F-1 GaN transistor rectifier. The theory is based on a Fourier analysis of current and voltage waveforms, which arise across the rectifying element when different harmonic terminations are presented at its terminals. An analogy to harmonically terminated power amplifier (PA) theory is discussed. From the analysis, one can obtain an optimal value for the dc load given the RF circuit design. An upper limit on rectifier efficiency is derived for each case as a function of the device on-resistance. Measured results from fundamental frequency source-pull measurement of a Schottky diode rectifier with short-circuit terminations at the second and third harmonics are presented. A maximal device rectification efficiency of 72.8% at 2.45 GHz matches the theoretical prediction. A 2.14-GHz GaN HEMT rectifier is designed based on a class-F-1 PA. The gate of the transistor is terminated in an optimal impedance for self-synchronous rectification. Measurements of conversion efficiency and output dc voltage for varying gate RF impedance, dc load, and gate bias are shown with varying input RF power at the drain. The rectifier demonstrates an efficiency of 85% for a 10-W input RF power at the transistor drain with a dc voltage of 30 V across a 98-Ω resistor.

Analysis of High-Efficiency Power Amplifiers With Arbitrary Output Harmonic Terminations

This paper presents an analysis of ideal power amplifier (PA) efficiency maximization subject to a finite set of arbitrary complex harmonic terminations, extending previous results where only purely reactive harmonic terminations were treated. Maximum efficiency and corresponding fundamental output power and load impedance are analyzed as a function of harmonic termination(s). For a PA restricted to second harmonic drain waveform shaping, maximum efficiency as a function of second harmonic termination is treated for cases of both purely real and complex fundamental frequency impedances. For the case of a PA restricted to second and third harmonic drain waveform shaping, peak efficiency as a function of third harmonic impedance with an ideal second harmonic termination is analyzed. Additionally, the sensitivity of PA efficiency with respect to the magnitude and phase of the second and third harmonic load reflection coefficients is examined. The analysis is extended to include device and package parasitics. The paper concludes with a discussion of how the presented general analysis method provides useful insights to the PA designer.

High-efficiency harmonically-terminated rectifier for wireless powering applications

In wireless powering, the rectifier efficiency has a large effect on overall system efficiency. This paper presents an approach to high-efficiency microwave rectifier design based on reduced conduction angle power amplifier theory. The analysis for an ideal rectifying device is derived to predict efficiency dependence on optimal dc load. A class-C 2.45 GHz Schottky-diode rectifier with short-circuit 2nd and 3rd harmonic terminations is designed using source-pull measurements, and demonstrates a maximum RF-DC conversion efficiency of 72.8% when matched to 50Ω. The approach is applied to integration of a rectifier with a dual-polarization patch antenna in a non 50Ω environment and free-space measurements demonstrate a lower bound on efficiency of 56% at 150 µW\cm2 power density which includes matching circuit and mismatch losses.

PA Efficiency and Linearity Enhancement Using External Harmonic Injection

This paper presents analysis and experimental demonstration of a high-efficiency linear power amplifier (PA) with second-harmonic injection at the output. In this circuit, the transistor is not driven hard into compression and does not produce significant harmonic content. External injection at the output enables voltage and current wave-shaping to achieve high efficiency. Theoretical analysis of the waveforms shows that the maximal drain efficiency is 89.9% with, at most, 0.13 dB of reduction in output power compared with the class-A case. The overall PA efficiency is derived in terms of the injector circuit efficiency. A harmonically injected prototype GaN HEMT 2.45-GHz PA demonstrates over 80% efficiency with linearity improved over the class-AB PA without harmonic injection. Two-tone measurements show a reduction of the third-order intermodulation by -30 dBc in the linear region and greater than -10 dBc in saturation.

Harmonic load pull of high-power microwave devices using fundamental-only load pull tuners

This paper presents a high-power high-efficiency PA design method using traditional fundamental-frequency load pull tuners. Harmonic impedance control at the virtual drain is accomplished through the use of tunable pre-matching circuits and full-wave FEM modeling of package parasitics. A 10-mm gate periphery GaN transistor from TriQuint is characterized using the method, and load-pull contours are presented illustrating the dramatic impact of varying 2nd harmonic termination. A 3rd harmonic termination is added to satisfy conditions for class-F-1 load pull, resulting in an 8% efficiency improvement over the best-case 2nd harmonic termination. The method is verified by design and measurement of a 36-W class-F-1 PA prototype at 2.14GHz with 81% drain efficiency and 14.5 dB gain (78% PAE) in pulsed operation.

Resonant Pulse-Shaping Power Supply for Radar Transmitters

The final radiofrequency power amplifier (PA) of a radar transmitter module is a large factor in system efficiency. Typical radar transmitter signals are frequency-modulated with constant-amplitude pulse envelopes in order to optimize efficiency, resulting in spectral broadening and power radiated outside of the radar frequency band. This paper demonstrates a PA with a dynamic power supply which enables high efficiency while reducing the spectral emissions. The resonant pulse-shaping power supply generates a raised-cosine pulse envelope waveform with efficiency greater than 90% and peak envelope power around 6 W. Measured results with a 2.14-GHz GaN power amplifier with an efficiency of 76% at peak power demonstrate over 67% transmitter efficiency.

Efficient and Linear Amplification of Spectrally Confined Pulsed AM Radar Signals

This letter presents a pulsed high-efficiency power amplifier with increased spectral purity obtained by supply modulation of the pulse envelope. The PA operates at 2.14 GHz with 78% efficiency at 6 W peak power, and with 66.4% average efficiency over a 14.7 μs pulse with a 4.1 dB PAR shaped by a 90% efficient resonant-pulse envelope supply modulator. For PARs greater than 4.1 dB, the signal envelope can be split between the supply modulator and the PA drive, with up to 25% improvement in composite efficiency.

Efficiency and linearity of power amplifiers with external harmonic injection

This paper discusses a method for improving the efficiency of linear power amplifiers by externally injecting power into the output at the second harmonic frequency. An experimental proof-of-concept PA based on class-A/AB mode with a 10-W GaN pHEMT at 2.45GHz is presented, and its efficiency improved from 58% to 75% with −6.5 dBc injected 2nd harmonic power. Two-tone measurements confirm improved linearity with simultaneous increase in efficiency, accompanied by gain compression at higher input power.