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.

A Wiener model for memory high power amplifiers using B-spline function approximation

In this paper we introduce a new Wiener system modeling approach for memory high power amplifiers in communication systems using observational input/output data. By assuming that the nonlinearity in the Wiener model is mainly dependent on the input signal amplitude, the complex valued nonlinear static function is represented by two real valued B-spline curves, one for the amplitude distortion and another for the phase shift, respectively. The Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first order derivatives recursion. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Joint Power Amplifiers and I/Q Modulator Impairments Modelling and Compensation for LTE Transmitters Using Artificial Neural Networks

This work introduces joint power amplifier (PA) and I/Q modulator modelling and compensation for LongTerm Evolution (LTE) transmitters using artificial neural networks (ANNs). The proposed solution util-izes a powerful nonlinear autoregressive with exogenous inputs (NARX) ANN architecture, which yieldsnoticeable results for high peak to average power ratio (PAPR) LTE signals. Given the ANNs learning capa-bilities, this one-step solution, which includes the mitigation of both PA nonlinearity and I/Q modulatorimpairments, is both accurate and adaptable

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.

Analysis and compensation of power amplifier nonlinearity in MIMO transmit diversity systems

The nonlinearity of high-power amplifiers (HPAs) has a crucial effect on the performance of multiple-input-multiple-output (MIMO) systems. In this paper, we investigate the performance of MIMO orthogonal space-time block coding (OSTBC) systems in the presence of nonlinear HPAs. Specifically, we propose a constellation-based compensation method for HPA nonlinearity in the case with knowledge of the HPA parameters at the transmitter and receiver, where the constellation and decision regions of the distorted transmitted signal are derived in advance. Furthermore, in the scenario without knowledge of the HPA parameters, a sequential Monte Carlo (SMC)-based compensation method for the HPA nonlinearity is proposed, which first estimates the channel-gain matrix by means of the SMC method and then uses the SMC-based algorithm to detect the desired signal. The performance of the MIMO-OSTBC system under study is evaluated in terms of average symbol error probability (SEP), total degradation (TD) and system capacity, in uncorrelated Nakagami-m fading channels. Numerical and simulation results are provided and show the effects on performance of several system parameters, such as the parameters of the HPA model, output back-off (OBO) of nonlinear HPA, numbers of transmit and receive antennas, modulation order of quadrature amplitude modulation (QAM), and number of SMC samples. In particular, it is shown that the constellation-based compensation method can efficiently mitigate the effect of HPA nonlinearity with low complexity and that the SMC-based detection scheme is efficient to compensate for HPA nonlinearity in the case without knowledge of the HPA parameters.

Pressure field in the cathode-anode region of a high-power klystron amplifier

The pressure field of a high-power klystron amplifier in the cathode and anode region was investigated. The investigation was performed using a 1.3 GHz, 100 A and 240 kV high-power klystron with five reentrant coaxial cavities, assembled in cylindrical drift tube 1.2 m long. The diffusion equation in mathematical model was also solved by using a 3-D finite element method code, in order to obtain pressure profile in region of interest. The results show that density profile of molecules between cathode-anode region was determined, where cathode pressure is approximately 10% higher than anode pressure.

Design methodology in multiphase buck converter based on minimum time control for high efficiency RF amplifiers

This paper proposes an interleaved multiphase buck converter with minimum time control strategy for envelope amplifiers in high efficiency RF power amplifiers. The solution of the envelope amplifier is to combine the proposed converter with a linear regulator in series. High system efficiency can be obtained through modulating the supply voltage of the envelope amplifier with the fast output voltage variation of the converter working with several particular duty cycles that achieve total ripple cancellation. The transient model for minimum time control is explained, and the calculation of transient times that are pre-calculated and inserted into a look-up table is presented. The filter design trade-off that limits capability of envelope modulation is also discussed. The experimental results verify the fast voltage transient obtained with a 4-phase buck prototype.

Envelope amplifier based on switching capacitors for high efficiency RF amplifiers

Modern transmitters usually have to amplify and transmit signals with simultaneous envelope and phase modulation. Due to this property of the transmitted signal, linear power amplifiers (class A, B, or AB) are usually used as a solution for the power amplifier stage. These amplifiers have high linearity, but suffer from low efficiency when the transmitted signal has high peak-to-average power ratio. The Kahn envelope elimination and restoration technique is used to enhance the efficiency of RF transmitters, by combining highly efficient, nonlinear RF amplifier (class E) with a highly efficient envelope amplifier in order to obtain a linear and highly efficient RF amplifier. This paper presents a solution for the envelope amplifier based on a multilevel converter in series with a linear regulator. The multilevel converter is implemented by employing voltage dividers based on switching capacitors. The implemented envelope amplifier can reproduce any signal with a maximum spectral component of 2 MHz and give instantaneous maximum power of 50 W. The efficiency measurements show that when the signals with low average value are transmitted, the implemented prototypes have up to 20% higher efficiency than linear regulators used as a conventional solution.

Wide bandwidth envelope trackers with reduced switching frequency for RF power amplifier

El requerimiento de proveer alta frecuencia de datos en los modernos sistema de comunicación inalámbricos resulta en complejas señales moduladas de radio-frequencia (RF) con un gran ancho de banda y alto ratio pico-promedio (PAPR). Para garantizar la linealidad del comportamiento, los amplificadores lineales de potencia comunes funcionan típicamente entre 4 y 10 dB de back-o_ desde la máxima potencia de salida, ocasionando una baja eficiencia del sistema. La eliminación y restauración de la evolvente (EER) y el seguimiento de la evolvente (ET) son dos prometedoras técnicas para resolver el problema de la eficiencia. Tanto en EER como en ET, es complicado diseñar un amplificador de potencia que sea eficiente para señales de RF de alto ancho de banda y alto PAPR. Una propuesta común para los amplificadores de potencia es incluir un convertidor de potencia de muy alta eficiencia operando a frecuencias más altas que el ancho de banda de la señal RF. En este caso, la potencia perdida del convertidor ocasionado por la alta frecuencia desaconseja su práctica cuando el ancho de banda es muy alto. La solución a este problema es el enfoque de esta disertación que presenta dos arquitecturas de amplificador evolvente: convertidor híbrido-serie con una técnica de evolvente lenta y un convertidor multinivel basado en un convertidor reductor multifase con control de tiempo mínimo. En la primera arquitectura, una topología híbrida está compuesta de una convertidor reductor conmutado y un regulador lineal en serie que trabajan juntos para ajustar la tensión de salida para seguir a la evolvente con precisión. Un algoritmo de generación de una evolvente lenta crea una forma de onda con una pendiente limitada que es menor que la pendiente máxima de la evolvente original. La salida del convertidor reductor sigue esa forma de onda en vez de la evolvente original usando una menor frecuencia de conmutación, porque la forma de onda no sólo tiene una pendiente reducida sino también un menor ancho de banda. De esta forma, el regulador lineal se usa para filtrar la forma de onda tiene una pérdida de potencia adicional. Dependiendo de cuánto se puede reducir la pendiente de la evolvente para producir la forma de onda, existe un trade-off entre la pérdida de potencia del convertidor reductor relacionada con la frecuencia de conmutación y el regulador lineal. El punto óptimo referido a la menor pérdida de potencia total del amplificador de evolvente es capaz de identificarse con la ayuda de modelo preciso de pérdidas que es una combinación de modelos comportamentales y analíticos de pérdidas. Además, se analiza el efecto en la respuesta del filtro de salida del convertidor reductor. Un filtro de dampeo paralelo extra es necesario para eliminar la oscilación resonante del filtro de salida porque el convertidor reductor opera en lazo abierto. La segunda arquitectura es un amplificador de evolvente de seguimiento de tensión multinivel. Al contrario que los convertidores que usan multi-fuentes, un convertidor reductor multifase se emplea para generar la tensión multinivel. En régimen permanente, el convertidor reductor opera en puntos del ciclo de trabajo con cancelación completa del rizado. El número de niveles de tensión es igual al número de fases de acuerdo a las características del entrelazamiento del convertidor reductor. En la transición, un control de tiempo mínimo (MTC) para convertidores multifase es novedosamente propuesto y desarrollado para cambiar la tensión de salida del convertidor reductor entre diferentes niveles. A diferencia de controles convencionales de tiempo mínimo para convertidores multifase con inductancia equivalente, el propuesto MTC considera el rizado de corriente por cada fase basado en un desfase fijo que resulta en diferentes esquemas de control entre las fases. La ventaja de este control es que todas las corrientes vuelven a su fase en régimen permanente después de la transición para que la siguiente transición pueda empezar muy pronto, lo que es muy favorable para la aplicación de seguimiento de tensión multinivel. Además, el control es independiente de la carga y no es afectado por corrientes de fase desbalanceadas. Al igual que en la primera arquitectura, hay una etapa lineal con la misma función, conectada en serie con el convertidor reductor multifase. Dado que tanto el régimen permanente como el estado de transición del convertidor no están fuertemente relacionados con la frecuencia de conmutación, la frecuencia de conmutación puede ser reducida para el alto ancho de banda de la evolvente, la cual es la principal consideración de esta arquitectura. La optimización de la segunda arquitectura para más alto anchos de banda de la evolvente es presentada incluyendo el diseño del filtro de salida, la frecuencia de conmutación y el número de fases. El área de diseño del filtro está restringido por la transición rápida y el mínimo pulso del hardware. La rápida transición necesita un filtro pequeño pero la limitación del pulso mínimo del hardware lleva el diseño en el sentido contrario. La frecuencia de conmutación del convertidor afecta principalmente a la limitación del mínimo pulso y a las pérdidas de potencia. Con una menor frecuencia de conmutación, el ancho de pulso en la transición es más pequeño. El número de fases relativo a la aplicación específica puede ser optimizado en términos de la eficiencia global. Otro aspecto de la optimización es mejorar la estrategia de control. La transición permite seguir algunas partes de la evolvente que son más rápidas de lo que el hardware puede soportar al precio de complejidad. El nuevo método de sincronización de la transición incrementa la frecuencia de la transición, permitiendo que la tensión multinivel esté más cerca de la evolvente. Ambas estrategias permiten que el convertidor pueda seguir una evolvente con un ancho de banda más alto que la limitación de la etapa de potencia. El modelo de pérdidas del amplificador de evolvente se ha detallado y validado mediante medidas. El mecanismo de pérdidas de potencia del convertidor reductor tiene que incluir las transiciones en tiempo real, lo cual es diferente del clásico modelos de pérdidas de un convertidor reductor síncrono. Este modelo estima la eficiencia del sistema y juega un papel muy importante en el proceso de optimización. Finalmente, la segunda arquitectura del amplificador de evolvente se integra con el amplificador de clase F. La medida del sistema EER prueba el ahorro de energía con el amplificador de evolvente propuesto sin perjudicar la linealidad del sistema. ABSTRACT The requirement of delivering high data rates in modern wireless communication systems results in complex modulated RF signals with wide bandwidth and high peak-to-average ratio (PAPR). In order to guarantee the linearity performance, the conventional linear power amplifiers typically work at 4 to 10 dB back-off from the maximum output power, leading to low system efficiency. The envelope elimination and restoration (EER) and envelope tracking (ET) are two promising techniques to overcome the efficiency problem. In both EER and ET, it is challenging to design efficient envelope amplifier for wide bandwidth and high PAPR RF signals. An usual approach for envelope amplifier includes a high-efficiency switching power converter operating at a frequency higher than the RF signal's bandwidth. In this case, the power loss of converter caused by high switching operation becomes unbearable for system efficiency when signal bandwidth is very wide. The solution of this problem is the focus of this dissertation that presents two architectures of envelope amplifier: a hybrid series converter with slow-envelope technique and a multilevel converter based on a multiphase buck converter with the minimum time control. In the first architecture, a hybrid topology is composed of a switched buck converter and a linear regulator in series that work together to adjust the output voltage to track the envelope with accuracy. A slow envelope generation algorithm yields a waveform with limited slew rate that is lower than the maximum slew rate of the original envelope. The buck converter's output follows this waveform instead of the original envelope using lower switching frequency, because the waveform has not only reduced slew rate but also reduced bandwidth. In this way, the linear regulator used to filter the waveform has additional power loss. Depending on how much reduction of the slew rate of envelope in order to obtain that waveform, there is a trade-off between the power loss of buck converter related to the switching frequency and the power loss of linear regulator. The optimal point referring to the lowest total power loss of this envelope amplifier is identified with the help of a precise power loss model that is a combination of behavioral and analytic loss model. In addition, the output filter's effect on the response is analyzed. An extra parallel damping filter is needed to eliminate the resonant oscillation of output filter L and C, because the buck converter operates in open loop. The second architecture is a multilevel voltage tracking envelope amplifier. Unlike the converters using multi-sources, a multiphase buck converter is employed to generate the multilevel voltage. In the steady state, the buck converter operates at complete ripple cancellation points of duty cycle. The number of the voltage levels is equal to the number of phases according the characteristics of interleaved buck converter. In the transition, a minimum time control (MTC) for multiphase converter is originally proposed and developed for changing the output voltage of buck converter between different levels. As opposed to conventional minimum time control for multiphase converter with equivalent inductance, the proposed MTC considers the current ripple of each phase based on the fixed phase shift resulting in different control schemes among the phases. The advantage of this control is that all the phase current return to the steady state after the transition so that the next transition can be triggered very soon, which is very favorable for the application of multilevel voltage tracking. Besides, the control is independent on the load condition and not affected by the unbalance of phase current. Like the first architecture, there is also a linear stage with the same function, connected in series with the multiphase buck converter. Since both steady state and transition state of the converter are not strongly related to the switching frequency, it can be reduced for wide bandwidth envelope which is the main consideration of this architecture. The optimization of the second architecture for wider bandwidth envelope is presented including the output filter design, switching frequency and the number of phases. The filter design area is restrained by fast transition and the minimum pulse of hardware. The fast transition needs small filter but the minimum pulse of hardware limitation pushes the filter in opposite way. The converter switching frequency mainly affects the minimum pulse limitation and the power loss. With lower switching frequency, the pulse width in the transition is smaller. The number of phases related to specific application can be optimized in terms of overall efficiency. Another aspect of optimization is improving control strategy. Transition shift allows tracking some parts of envelope that are faster than the hardware can support at the price of complexity. The new transition synchronization method increases the frequency of transition, allowing the multilevel voltage to be closer to the envelope. Both control strategies push the converter to track wider bandwidth envelope than the limitation of power stage. The power loss model of envelope amplifier is detailed and validated by measurements. The power loss mechanism of buck converter has to include the transitions in real time operation, which is different from classical power loss model of synchronous buck converter. This model estimates the system efficiency and play a very important role in optimization process. Finally, the second envelope amplifier architecture is integrated with a Class F amplifier. EER system measurement proves the power saving with the proposed envelope amplifier without disrupting the linearity performance.

Design of a Two-Phase buck converter with fourth-order output filter for envelope amplifiers of limited bandwidth

The use of techniques such as envelope tracking (ET) and envelope elimination and restoration (EER) can improve the efficiency of radio frequency power amplifiers (RFPA). In both cases, high-bandwidth DC/DC converters called envelope amplifiers (EA) are used to modulate the supply voltage of the RFPA. This paper addresses the analysis and design of a modified two-phase Buck converter optimized to operate as EA. The effects of multiphase operation on the tracking capabilities are analyzed. The use of a fourth-order output filter is proposed to increase the attenuation of the harmonics generated by the PWM operation, thus allowing a reduction of the ratio between the switching frequency and the converter bandwidth. The design of the output filter is addressed considering envelope tracking accuracy and distortion caused by the side bands arising from the nonlinear modulation process. Finally, the proposed analysis and design methods are supported by simulation results, as well as demonstrated by experiments obtained using two 100-W, 10-MHz, two-phase Buck EAs capable of accurately tracking a 1.5-MHz bandwidth OFDM signal.