Exploring figures of merit associated with the suboptimum operation of class-E power amplifiers

Closed-form design equations for the operation of a class-E amplifier for zero switch voltage slope and arbitrary duty cycle are derived. This approach allows an additional degree of freedom in the design of class-E amplifiers which are normally designed for 50 duty ratio. The analysis developed permits the selection of non-unique solutions where amplifier efficiency is theoretically 100 but power output capability is less than that the 50 duty ratio case would permit. To facilitate comparison between 50 (optimal) and non-50 (suboptimal) duty ratio cases, each important amplifier parameter is normalised to its corresponding optimum operation value. It is shown that by choosing a non-50 suboptimal solution, the operating frequency of a class-E amplifier can be extended. In addition, it is shown that by operating the amplifier in the suboptimal regime, other amplifier parameters, for example, transistor output capacitance or peak switch voltage, can be included along with the standard specification criteria of output power, DC supply voltage and operating frequency as additional input design specifications. Suboptimum class-E operation may have potential advantages for monolithic microwave integrated circuit realisation as lower inductance values (lower series resistance, higher self-resonance frequency, less area) may be required when compared with the results obtained for optimal class-E amplifier synthesis. The theoretical analysis conducted here was verified by harmonic balance simulation, with excellent agreement between both methods. © The Institution of Engineering and Technology 2007.

Analysis and Design of Class-E3F and Transmission-Line Class-E3F2 Power Amplifiers

In this paper, analysis and synthesis approach for two new variants within the Class-EF power amplifier (PA) family is elaborated. These amplifiers are classified here as Class-E3 F2 and transmission-line (TL) Class-E3 F 2. The proposed circuits offer means to alleviate some of the major issues faced by existing topologies such as substantial power losses due to the parasitic resistance of the large inductor in the Class-EF load network and deviation from ideal Class-EF operation due to the effect of device output inductance at high frequencies. Both lumped-element and transmission-line load networks for the Class-E 3 F PA are described. The load networks of the Class-E3 F and TL Class-E 3 F2amplifier topologies developed in this paper simultaneously satisfy the Class-EF optimum impedance requirements at fundamental frequency, second, and third harmonics as well as simultaneously providing matching to the circuit optimum load resistance for any prescribed system load resistance. Optimum circuit component values are analytically derived and validated by harmonic balance simulations. Trade-offs between circuit figures of merit and component values with some practical limitations being considered are discussed. © 2010 IEEE.

Holistic design of 8-way combining transformers in SiGe technology for use in millimetre-wave power amplifiers

This paper presents the design of a novel 8-way power-combining transformer for use in mm-wave power amplifier (PA). The combiner exhibits a record low insertion loss of 1.25 dB at 83.5 GHz. A complete circuit comprised of a power splitter, two-stage cascode PA array, a power combiner and input/output matching elements was designed and realized in SiGe technology. Measured gain of at least 16.8 dB was obtained from 76.4 GHz to 85.3 GHz with a peak 19.5 dB at 83 GHz. The prototype delivered 12.5 dBm OP and 14 dBm saturated output power when operated from a 3.2 V DC supply voltage at 78 GHz. © 2013 IEEE.

High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers with Enhanced Maximum Operating Frequency

The recently introduced Class-EF power amplifier (PA) has a peak switch voltage lower than that of the Class-E PA. However, the value of the transistor output capacitance at high frequencies is typically larger than the required Class-EF optimum shunt capacitance. Consequently, soft-switching operation that minimizes power dissipation during off-to-on transition cannot be achieved at high frequencies. Two new Class-EF PA variants with transmission-line load networks, namely, third-harmonic-peaking (THP) and fifth-harmonic-peaking (FHP) Class-EF PAs are proposed in this paper. These permit operation at higher frequencies at no expense to other PA figures of merit. Analytical expressions are derived in order to obtain circuit component values, which satisfy the required Class-EF impedances at fundamental frequency, all even harmonics, and the first few odd harmonics as well as simultaneously providing impedance matching to a 50- Ω load. Furthermore, a novel open-circuit and shorted stub arrangement, which has substantial practical benefits, is proposed to replace the normal quarter-wave line connected at the transistor's drain. Using GaN HEMTs, two PA prototypes were built. Measured peak drain efficiency of 91% and output power of 39.5 dBm were obtained at 2.22 GHz for the THP Class-EF PA. The FHP Class-EF PA delivered output power of 41.9 dBm with 85% drain efficiency at 1.52 GHz.

Performance Limits of MIMO Systems with Nonlinear Power Amplifiers

The development of 5G enabling technologies brings new challenges to the design of power amplifiers (PAs). In particular, there is a strong demand for low-cost, nonlinear PAs which, however, introduce nonlinear distortions. On the other hand, contemporary expensive PAs show great power efficiency in their nonlinear region. Inspired by this trade-off between nonlinearity distortions and efficiency, finding an optimal operating point is highly desirable. Hence, it is first necessary to fully understand how and how much the performance of multiple-input multiple-output (MIMO) systems deteriorates with PA nonlinearities. In this paper, we first reduce the ergodic achievable rate (EAR) optimization from a power allocation to a power control problem with only one optimization variable, i.e. total input power. Then, we develop a closed-form expression for the EAR, where this variable is fixed. Since this expression is intractable for further analysis, two simple lower bounds and one upper bound are proposed. These bounds enable us to find the best input power and approach the channel capacity. Finally, our simulation results evaluate the EAR of MIMO channels in the presence of nonlinearities. An important observation is that the MIMO performance can be significantly degraded if we utilize the whole power budget.

2.4 GHz high-efficiency power-combining Class-E amplifier with transmission-line harmonic traps

Experimental assessments of the modified power-combining Class-E amplifier are described. The technique used to combine the output of individual power amplifiers (PAs) into an unbalanced load without the need for bulky transformers permits the use of small RF chokes useful for the deployment in the EER transmitter. The modified output load network of the PA results in excellent 50 dBc and 46 dBc second and third-harmonic suppressions, dispensing the need for additional lossy filtering block. Operating from a 3.2 V dc supply voltage, the PA exhibits 64% drain efficiency at 24 dBm output power. Over a wide bandwidth of 350 MHz, drain efficiency of better than 60% at output power higher than 22 dBm were achieved. © 2010 IEICE Institute of Electronics Informati.

Characterisation of nonlinear distortion and intermodulation in passive devices and antennas

The paper presents a conceptual discussion of the characterisation and phenomenology of passive intermodulation (PIM) by the localised and distributed nonlinearities in passive devices and antennas. The PIM distinctive nature and its impact on signal distortions are examined in comparison with similar effects in power amplifiers. The main features of PIM generation are discussed and illustrated by the example of PIM due to electro-thermal nonlinearity. The issues of measurement, discrimination and modelling of PIM generated by nonlinearities in passive RF components and antennas are addressed.

Power combining techniques into unbalanced loads for Class-E and inverse Class-E amplifiers

A power combining strategy for Class-E and inverse Class-E amplifiers operating at high frequencies such that they can operate into unbalanced loads is proposed. This power combining method is particularly important for the inverse Class-E amplifier configuration whose single-stage topology is naturally limited for small-to-medium power applications. Design examples for the power combining synthesis of classical Class-E and then inverse Class-E amplifiers with specification 3 V-1.5 W-2.5 GHz are given. For this specification, it is shown that a three-branch combiner has a natural 50 V output impedance. The resulting circuits are simulated within Agilent Advanced Design Systems environment with good agreement to theoretical prediction. Further the performance of the proposed circuits when operated in a Linear amplification using Nonlinear Components transmitter configuration whereby two-branch amplifiers are driven with constant amplitude conjugate input phase signals is investigated.

Analysis and Synthesis of pHEMT Class-E Amplifiers with Shunt Inductor including ON-State Active-Device Resistance Effects

In this theoretical paper, the analysis of the effect that ON-state active-device resistance has on the performance of a Class-E tuned power amplifier using a shunt inductor topology is presented. The work is focused on the relatively unexplored area of design facilitation of Class-E tuned amplifiers where intrinsically low-output-capacitance monolithic microwave integrated circuit switching devices such as pseudomorphic high electron mobility transistors are used. In the paper, the switching voltage and current waveforms in the presence of ON-resistance are analyzed in order to provide insight into circuit properties such as RF output power, drain efficiency, and power-output capability. For a given amplifier specification, a design procedure is illustrated whereby it is possible to compute optimal circuit component values which account for prescribed switch resistance loss. Furthermore, insight into how ON-resistance affects transistor selection in terms of peak switch voltage and current requirements is described. Finally, a design example is given in order to validate the theoretical analysis against numerical simulation.

2.4 GHz Class-E power amplifier with transmissionline harmonic terminations

The design procedure, fabrication and measurement of a Class-E power amplifier with excellent second- and third-harmonic suppression levels are presented. A simplified design technique offering compact physical layout is proposed. With a 1.2 mm gate-width GaAs MESFET as a switching device, the amplifier is capable of delivering 19.2 dBm output power at 2.41 GHz, achieves peak PAE of 60% and drain efficiency of 69%, and exhibits 9 dB power gain when operated from a 3 V DC supply voltage. When compared to the classical Class-E two-harmonic termination amplifier, the Class-E amplifier employing three-harmonic terminations has more than 10% higher drain efficiency and 23 dB better third-harmonic suppression level. Experimental results are presented and good agreement with simulation is obtained. Further, to verify the practical implementation in communication systems, the Bluetooth-standard GFSK modulated signal is applied to both two- and three-harmonic amplifiers. The measured RMS FSK deviation error and RMS magnitude error were, for the three-harmonic case, 1.01 kHz and 0.122%, respectively, and, for the two-harmonic case, 1.09 kHz and 0.133%. © 2007 The Institution of Engineering and Technology.

Analysis of the effect of finite d.c. blocking capacitance and finite d.c. feed inductance on the performance of inverse class-E amplifiers

The first analysis and synthesis equations for the newly introduced inverse Class-E amplifier when operated with a finite d.c. blocking capacitance and a finite d.c.-feed inductance are presented in the paper. Closed-form design equations are derived in order to establish the circuit component values required for optimum synthesis. Excellent agreement between numerical simulation results and theoretical prediction is obtained. It is shown that drain efficiency approaching 100 at a pre-specified output power level can be achieved as zero-current switching and zero-current derivative conditions are simultaneously satisfied. The proposed analysis offers the prospect for realistic MMIC implementation.

Series-L/parallel-tuned comparison with shunt-C/series-tuned class-E power amplifier

An analysis of the operation of a series-L/parallel-tuned class-E amplifier and its equivalence to the classic shunt-C/series-tuned class-E amplifier are presented. The first reported closed form design equations for the series-L/parallel-tuned topology operating under ideal switching conditions are given. Furthermore, a design procedure is introduced that allows the effect that nonzero switch resistance has on amplifier performance efficiency to be accounted for. The technique developed allows optimal circuit components to be found for a given device series resistance. For a relatively high value of switching device ON series resistance of 4O, drain efficiency of around 66% for the series-L/parallel-tuned topology, and 73% for the shunt-C/series-tuned topology appear to be the theoretical limits. At lower switching device series resistance levels, the efficiency performance of each type are similar, but the series-L/parallel-tuned topology offers some advantages in terms of its potential for MMIC realisation. Theoretical analysis is confirmed by numerical simulation for a 500mW (27dBm), 10% bandwidth, 5 V series-L/parallel-tuned, then, shunt-C/series-tuned class E power amplifier, operating at 2.5 GHz, and excellent agreement between theory and simulation results is achieved. The theoretical work presented in the paper should facilitate the design of high-efficiency switched amplifiers at frequencies commensurate with the needs of modern mobile wireless applications in the microwave frequency range, where intrinsically low-output-capacitance MMIC switching devices such as pHEMTs are to be used.

Analysis of the Second Harmonic Effect on Power Amplifier Intermodulation Products

A theoretical analysis is reported in this paper to investigate the effect that a second harmonic signal which might be present at an amplifier’s input has on generating additional intermodulation products, particularly the third-order intermodulation (IM3) products. The analysis shows that the amplitude of an extra generated IM3 component is equal to the product of the fundamental amplitude, the second harmonic amplitude, and the second order Taylor series coefficient. The effect of the second order harmonic on the IM3 is examined through a simulated example of a 2.22-GHz 10-W Class-EF amplifier whereby the IM3 levels have been reduced by 2-3 dB after employing a second harmonic termination stub at the input.