Linear Amplifier Research Articles

Precise Mathematical Model of PSCM Class-D Amplifiers

A mathematical analysis of four-level (three-phase) phase-shifted carrier modulation class-D amplifiers with analog feedback is proposed. The nonlinear difference equations are extracted and solved using the perturbation theorem. In this way, a closed-form function describes the low-frequency part of the output for an arbitrary input signal. The results are generalized for an arbitrary number of levels by analogy, well matched with the previous model of two-, three-, and the proposed four-level ones. The analytical results confirm that, apart from switching frequency, the multilevel class-D amplifiers converge to linear amplifiers as the number of output levels increases. An analytical equation expresses the harmonic distortion of practically interesting five-level amplifiers with bridge-tied load. The model is verified by system-level simulations and circuit-level implementation. In this way, a prototype fully differential five-level circuit is implemented on the printed circuit board to confirm the model.

Power Amplifier Linearization in the Presence of Crosstalk and Measurement Noise in MIMO System

The crosstalk and transceiver noise is an intrinsic part of the multiple-input and multiple-output (MIMO) System, becoming more prominent in low-cost systems. Moreover, the power amplifiers (PAs) cause nonlinearity, propagating to the complete chain. The conventional techniques do not provide the joint method for crosstalk, transceiver noise, and PA nonlinearity. This results in the performance limitation of the digital predistortion (DPD). Hence we propose a wavelet multiscale principal component analysis (PCA) based technique to deal with such problems (crosstalk, transceiver noise, and system nonlinearities). It is reported using measurement and simulation that numerical stability issue is no longer an issue when wavelet multiscale PCA-based DPD is applied. The effect of wavelet multiscale PCA on bit-resolution of DPD is shown to be better than established DPD Models. On a field-programmable gate array and direct conversion transceiver-based platform, the performance of the proposed model is analyzed using PA. Parameters like normalized mean square error have shown an improvement of around 23 dB and adjacent channel error power ratio has shown an improvement of around 22 dBc for a ZX60-V63+ power amplifier using LTE-OFDM signals.

A Comparison of Surrogate Behavioral Models for Power Amplifier Linearization under High Sparse Data.

A good approximation to power amplifier (PA) behavioral modeling requires precise baseband models to mitigate nonlinearities. Since digital predistortion (DPD) is used to provide the PA linearization, a framework is necessary to validate the modeling figures of merit support under signal conditioning and transmission restrictions. A field-programmable gate array (FPGA)-based testbed is developed to measure the wide-band PA behavior using a single-carrier 64-quadrature amplitude modulation (QAM) multiplexed by orthogonal frequency-division multiplexing (OFDM) based on long-term evolution (LTE) as a stimulus, with different bandwidths signals. In the search to provide a heuristic target approach modeling, this paper introduces a feature extraction concept to find an appropriate complexity solution considering the high sparse data issue in amplitude to amplitude (AM-AM) and amplitude to phase AM-PM models extraction, whose penalties are associated with overfitting and hardware complexity in resulting functions. Thus, experimental results highlight the model performance for a high sparse data regime and are compared with a regression tree (RT), random forest (RF), and cubic-spline (CS) model accuracy capabilities for the signal conditioning to show a reliable validation, low-complexity, according to the peak-to-average power ratio (PAPR), complementary cumulative distribution function (CCDF), coefficients extraction, normalized mean square error (NMSE), and execution time figures of merit. The presented models provide a comparison with original data that aid to compare the dimension and robustness for each surrogate model where (i) machine learning (ML)-based and (ii) CS interpolate-based where high sparse data are present, NMSE between the CS interpolated based are also compared to demonstrate the efficacy in the prediction methods with lower convergence times and complexities.

Symbolic Analysis of Linear Amplifiers with Multi-Loop Feedbacks in Interacting Programs Maple and FASTMEAN

A technique of interaction of computer programs for symbolic analysis of complex electronic circuits with amplifying elements is proposed. FASTMEAN simulation program, used in the universities of telecommunications in Russia, has a symbolic analysis module and is capable of generating analytical expressions for Laplace images of a circuit determinant, currents and voltages in complex electronic circuits. However, the obtained expressions have a nested (folded) structure, which makes it difficult to analyze the influence of elements on the properties of a circuit with amplifiers and feedbacks, in particular on its stability. It is proposed to transfer the obtained expressions to Maplе program for their structural transformation and mathematical processing. . Amplifiers with local, common and crossed feedbacks are considered. The analysis of such circuits in Maple shows that an expression for the circuit determinant in the form of the products of the loop gain functions is a sign of the presence of several feedback loops in the circuit.

A Linear CMOS Power Amplifier With Efficiency-Optimized Transformer Matching

A 29.5-GHz power amplifier (PA) with a codesigned transformer-based matching network and a second harmonic control network is presented here. The efficiency of the transformer is well studied, and an accurate analytical solution to a high-efficiency transformer has been proposed. Guiding by it, a high-efficiency 1:2 transformer has been designed. A series <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> network has been added between the drain and the source as a second harmonic control network. Due to the codesign, the cost of the harmonic control network is negligible. The PA achieves a 3-dB gain bandwidth from 26.9 to 33.2 GHz (21%). The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\mathrm {1\, dB}}$ </tex-math></inline-formula> exceeds 16.5 dBm with power added efficiency (PAE) beyond 27% from 27.5 to 30 GHz. At 29.5 GHz, the proposed PA achieves a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\mathrm {1 \,dB}}$ </tex-math></inline-formula> of 17.4 dBm with 30% PAE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1dB</sub> and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\mathrm {sat}}$ </tex-math></inline-formula> of 17.8 dBm with the peak PAE of 30.7%.

A 24–29.5-GHz Highly Linear Phased-Array Transceiver Front-End in 65-nm CMOS Supporting 800-MHz 64-QAM and 400-MHz 256-QAM for 5G New Radio

This article presents a four-element phased-array transceiver (TRX) front-end for millimeter-wave (mm-Wave) 5G new radio (NR). The effects of amplitude-to-phase (AM–PM) and amplitude-to-amplitude (AM–AM) distortions on error vector magnitude (EVM) are detailed. A three-stage highly linear wideband class-AB power amplifier (PA) is described, mitigating AM–PM and AM–AM distortions without degrading other performances. A matching network embedded transmitting/receiving (T/R) switch is proposed to support time division duplex (TDD). With the proposed technique, RF switch insertion losses are reduced in both transmitter (TX) and receiving (RX) modes. In each TRX element, phase and gain controls are achieved by a 6-bit vector-modulated phase shifter (VMPS) with a phase tuning range of 360° and a 6-bit attenuator with a gain tuning range of 31.5 dB, respectively. Fabricated in 65-nm bulk CMOS, the proposed packaged TRX demonstrates the measured peak gains of 25.5/14.2 dB with the gain ripples of less than 2.5/1.9 dB across 24–29.5 GHz in the TX/RX mode. The measured peak <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\text {1 dB}}$ </tex-math></inline-formula> is 17.6 dBm with a power added efficiency (PAE) of 20.4%. The measured minimum noise figure (NF) is 4.3 dB. The TRX achieves an output power of 7.9–8.9 dBm and an EVM of −25 dB with 8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 100-MHz 5G NR frequency range 2 (FR2) orthogonal frequency division multiplexing (OFDM) 64-quadrature amplitude modulation (QAM) signals across 24–29.5 GHz, covering 3rd generation partnership project (3GPP) 5G NR FR2 operating bands (i.e., n257, n258, and n261) around 26 GHz.

An enhanced ultra-wideband single phase hybrid supply envelope tracking modulator for modern wireless communications

This paper presents a Single Phase Hybrid Supply Envelope tracking Modulator (HSEM) for RF-Power Amplifiers (RF-PAs) used in modern wireless communication systems such as 5G and 6G applications. The proposed HSEM consists of an ultra-wideband linear amplifier to track the input signals with several Mega Hertz of bandwidth, a switching amplifier to provide a high-efficiency supply voltage for the main power amplifier, and a new sensing circuit to generate the required voltage for the switching amplifier. The designed HSEM uses a two-stage rail-to-rail linear class-AB amplifier with constant Gm, high gain bandwidth (GBW), high slew rate (SR), and good phase margin (PM). Most conventional modulators use a sensing resistor or a resistor structure that increases the output ripple and the power loss. The proposed structure uses a linear amplifier output stage sensing circuit and a hysteresis low power current comparator without any resistors, external capacitors, filters, or multi-phase modulator structures. Additionally, using a current comparator eliminates the need for an external reference voltage or a current-to-voltage converter. The proposed structure does not need to remove the switching ripple through the linear amplifier, leading to a more relaxed linear amplifier design. A comprehensive analysis and guide on how to optimally select the inductor values, and the mathematical equation for the switching frequency of the hybrid modulator is given. The efficiency of the proposed structure is 84.3 %, and the maximum output power is 27.3dBm. The average output ripple is 4.16 mV in the wide range of the input voltages, and its minimum is 0.4 mV. In addition, the new structure can track a signal with 400 MHz bandwidth with FOM of the HSEM about 18. The proposed modulator is suitable for broadband and emerging telecommunications applications such as 5G and 6G, and as a power supply for RF power amplifiers. The proposed HSEM is evaluated with TSMC 180 nm CMOS technology parameters.

Efficiency characteristics for changes in amplitude and power factor of diode‐clamped linear amplifier unequally divided voltage power supply

AbstractA diode‐clamped linear amplifier (DCLA) is proposed to realize low electromagnetic interference (EMI) caused by switching operations. A new concept of the DCLA, namely the higher efficiency unequally divided voltage power supply DCLA (DCLA‐UeDV), is proposed. In previous studies, the optimal voltage ratio was derived, and a 1.7% points improvement in efficiency was realized for a rated unity power factor load. However, it has not been examined whether the conversion efficiency can be improved, except during the rated operation. In this study, operation of the DCLA is analyzed for changes in the amplitude of the output voltage and load power factor. Then, the advantageous operating region of the DCLA‐UeDV against DCLA‐eDV is clarified.

Research on the Brushless Excitation System with Linear Current Amplifier Characteristics

In terms of improving the dynamic response characteristics of brushless AC synchronous generators, the concept of integrated design of AC exciter and rotating rectifier and their electromagnetic characteristics are studied, and the conditions and judgment methods for determining their operating modes are obtained in theoretical design and simulation design, pointing out that when the brushless excitation system operates in or is close to mode III, i.e., the rectifier always has three or four diodes in each operating cycle. The linear current amplifier characteristics can be basically achieved when the brushless excitation system is operated in mode III or is close to mode III, i.e., the rectifier always has three or four diodes alternating in each operating cycle. The impact of the key parameters of the AC exciter at different rotational speeds and temperatures on the characteristics of the linear current amplifier was explored, and an engineering prototype was manufactured. The related test verified the correctness of the concept of integrated electromagnetic design and simulation calculation. This study provides an engineered design method for enhancing the dynamic response properties of the brushless AC synchronous generators.

A 44–64-GHz mmWave Broadband Linear Doherty PA in Silicon With Quadrature Hybrid Combiner and Non-Foster Impedance Tuner

The proliferation of millimeter-wave (mmWave) bands across 24–90 GHz and the strict spectral efficiency requirements demand future transmitter front ends to operate across multiple bands with simultaneously back-off efficiency and high linearity—characteristics that typically trade off strongly with each other. In this article, we propose a simultaneously broadband, back-off efficient and linear mmWave Doherty power amplifier (PA) architecture with a quadrature hybrid, and a non-Foster inspired impedance tuner on-chip. The combination of transformer-based hybrid and the quasi-non-Foster tuner allows the architecture to synthesize optimal impedances to the PA across the 2-D variations of power back-off and frequency, enabling high back-off efficiency across a broad frequency range. In addition, the unique location of the tuner at the isolation port of the hybrid allows us to exploit its benefits while shielding the architecture from effects of tuner non-linearity, power losses, and typical stability concerns of traditional non-Foster circuits. For high linearity, we implement an emitter follower-based class-C bias network with boosting effect. The PA is implemented in a 130-nm SiGe BiCMOS process. Across 44–64 GHz, the PA achieves 18.5–21.5-dBm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\text {sat}}$ </tex-math></inline-formula> , the peak collector efficiency of 26%–34.7% and 14%–23.2% at 6-dB back-off, maintaining back-off enhancement ratio of 2.77/2.53/2.37 (1.39/1.27/1.19) at 46/52/62 GHz compared to the class-A (class-B) operation. It supports 6-gigabit-per-second (Gb/s) 64-QAM signal with −26.5-dB/−28.3-dBc error vector magnitude (EVM)/adjacent channel leakage ratio (ACLR) at average <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\text {out}}$ </tex-math></inline-formula> /power added efficiency (PAE) of 14.6 dBm/15% at 54 GHz. This work achieves the state-of-the-art bandwidth among silicon-based mmWave PAs where higher than class-B back-off efficiency is achieved.

Achievable rate analysis of a generalized uplink asynchronous non-orthogonal multiple access with MSK-type signals

Non-orthogonal multiple access (NOMA) is a key technology for future wireless access. Recently, asynchronous NOMA (ANOMA) has attracted attention due to its large achievable rate. However, almost all work to date on NOMA employs linear modulation formats dedicated to linear amplifiers with low power efficiency. In this paper, we propose an uplink ANOMA scheme based on continuous phase modulation (CPM). In particular, a generalized system model with any number of users, response lengths, and frequency pulses is established, and the traditional ANOMA with linear waveforms (considering the nonlinearity of the power amplifier) is provided as a comparison. Furthermore, the achievable rate of each user and its asymptotic value under successive interference cancellation (SIC) and joint maximum likelihood (JML) detectors are derived respectively, and the achievable sum rates are also given. Numerical results show that the achievable rate converges to its asymptotic value. The nonlinear system can provide a larger achievable rate compared with the linear system. The relationship between the achievable sum rate of nonlinear systems and response length, transmit power, channel gain, frequency pulse, time offset and received signal-to-noise ratio (SNR) between users is also investigated via numerical simulations.

Design and Analysis of the Self-Biased PLL with Adaptive Calibration for Minimum of the Charge Pump Current Mismatch

A digital adaptive mismatch calibration (DAMC) circuit is proposed to decrease the output jitter of phase-locked loop (PLL). After amplifying the phase error with a linear time amplifier (TA), the DAMC adopts a successive approximation pulse width calibration method to reduce the mismatch current of the charge pump. The PLL prototype is fabricated in a 40nm process, the static phase error of the proposed PLL can be reduced from 358 ps to 10 ps at a 50 MHz reference clock approximately, and the RMS jitter of the PLL output is reduced from 4.91 ps to 3.59 ps, and the extended DAMC area only occupies 1.3% of the whole PLL area.

Possibilities of Conventional PD Measurements with Non-Sinusoidal Waveforms for Electric Vehicles

Electrical traction machines in electric vehicles are normally fed by converters with DC link voltages up to 800 V. The resulting voltage pulses place particular stress on the insulating system of the drivetrain. In order to be able to investigate insulating material samples, e.g. twisted pair enameled wire, with voltages of different shapes and high frequency, a shielded experimentalsetup for the investigation of partial discharges (PD) at low voltages and high frequencies is presented. A medium frequency transformer with a frequency range up to 2500 Hz is used for this purpose, fed by a linear power amplifier on the primary side. The amplifier has a slew rate of 52 V/μs and is capable of sourcing various voltage waveforms such as sinusiodal, triangularor rectangular, with a maximum frequency of 30 kHz. Electrical PD measuring methods according to IEC 60270 as well as acoustic and optical measurement methods are applied for PD diagnosis. The experimental setup is intended to demonstrate the possibilities and limitations of conventional PD diagnostics for nonsinusoidal voltages. Focus is placed on the application of filters, the damping behavior of the step-up transformer and the rise times of the voltages.

Digital Predistortion of RF Power Amplifiers Robust to a Wide Temperature Range and Varying Peak-to-Average Ratio Signals

In this work, a digital predistortion (DPD) model for the linearization of RF power amplifiers (PAs) is presented. The model provides a linearized gain (DPD &#x002B; PA) independent of the instantaneous transistor channel temperature within a predefined temperature window. Channel temperature variations due to varying ambient temperatures or changes in the signal probability density function (PDF) cause long-term memory effects, which results in dispersed (dynamic) AM/AM and AM/PM characteristics. The presented model is used to compensate for the memory effects due to self-heating and external temperature changes by estimating the transistor channel temperature through a linear single-pole Foster thermal network. The DPD model uses a first-order Taylor approximation to cancel out temperature-based nonlinearities. Gaussian pulses are used to extract the PA intrapulse gain at different temperatures without being affected by the signal PDF, thus allowing temperature- and signal-independent PA characterization. The model is validated from <inline-formula> <tex-math notation="LaTeX">$20~^\circ \text{C}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$80~^\circ \text{C}$ </tex-math></inline-formula> and by considering a class-B 3.75-GHz 10-W gallium nitride (GaN)-on-SiC PA. The DPD performance is evaluated by considering the normalized root-mean-squared error (NRMSE), the output spectra, and adjacent channel power ratio (ACPR) with and without DPD for multiple signals bandwidths and peak-to-average power ratio (PAPR) and finally compared with other approaches.

Segmented Statistical Error-Based Adaptive Method for Linearization of Power Amplifiers

In this letter, we present an adaptive method for linearizing radio frequency (RF) power amplifier (PA). The input and output error is segmented in light of the signal magnitude to improve the convergence speed of the linearizer’s parameter optimization. The feedback bandwidth and the sampling rate of the feedback loop are only 1/8 of the input signal with the proposed method. Experimental results show that the convergence speed of the proposed method is eight times faster than that of the conventional method, and the adjacent channel power ratio (ACPR) is improved from −35.18 to −46.91 dB.

Noiseless linear amplification in quantum target detection using Gaussian states

Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal–idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplifier at the detection stage of a quantum illumination-based quantum target detection protocol. Such a non-Gaussian amplifier offers a means of probabilistically amplifying an incoming signal without the addition of noise. Considering symmetric hypothesis testing, the quantum Chernoff bound is derived and limits on detection error probability is analysed for both the two-mode squeezed vacuum state and the coherent state classical benchmark. Our findings show that in such a scheme the potential quantum advantage is amplified even in regimes where quantum illumination alone offers no advantage, thereby extending its potential use. The same cannot be said for coherent states, whose performances are generally bounded by that without amplification.

On the Use of Class D Switching-Mode Power Amplifiers in Visible Light Communication Transmitters.

Visible Light Communication (VLC) is a wireless communication technology that uses visible light to transmit information. The most extended implementation of a VLC transmitter employs a DC-DC power converter that biases the High-Brightness LEDs (HB-LEDs), and a Linear Power Amplifier (LPA) that reproduces the communication signal. Unfortunately, the power efficiency of LPAs is very low, thus reducing the overall system efficiency and requiring huge cooling systems to extract the heat. In this work, the use of Class D Switching-Mode Power Amplifiers (SMPAs) is explored in order to overcome that limitation. It is important to note that this SMPA is widely used for different applications, such as audio and RF power amplifiers. Therefore, there are a lot of versions of a Class D SMPA depending on the topology used for the implementation and the modulation strategy used to control the switches. Hence, this work aims to identify, adapt and explain in detail the best approach for implementing a Class D SMPA for VLC. In order to validate the proposed idea, a power-efficient VLC transmitter intended for short-range and low-speed applications was built and evaluated.

Automatic golden device selection and measurement smoothing algorithms for microwave transistor small-signal noise modeling

AbstractWe propose the techniques for automatic processing of measurement results in the context of golden (typical) device selection and noise figure measurement. These techniques are for golden (typical) device selection and noise figure measurement processing. Automation of measurement result processing and microwave element modeling speeds up a modeling routine and decreases the risk of possible errors. The techniques are validated through modeling of 0.15 μm GaAs pHEMTs with 4 × 40 μm and 4 × 75 μm total gate widths. Two test amplifiers were designed using the developed models. The amplifier modeling results agree well with measurements which confirms the validity of the proposed techniques. The proposed algorithm is potentially applicable to other circuit types (switches, digital, power amplifiers, mixers, oscillators, etc.) but may require different settings in those cases. However, in the presented work, we validated the algorithm for the linear and low-noise amplifiers only.

Compensation of nonlinear distortion in hybrid beamforming MIMO transmitters

Compensation of nonlinear distortion in hybrid beamforming MIMO transmitters is an open and challenging field of research. The goal of the study is to find an efficient method for linearization of power amplifiers in fully connected hybrid beamforming MIMO transmitters, which would not additionally increase the complexity of the system too much. In this paper, the polynomial-based compensation method of nonlinear distortion in hybrid beamforming MIMO transmitters is presented. The method is verified through comprehensive Matlab simulations. A 64x64 fully connected hybrid beamforming MIMO system with 2 RF branches on the transmitting side and 2 RF branches on the receiving side was considered. The proposed memory polynomial digital predistortion model is based on direct transmit-end feedback. Simulations were performed for different parameters of the memory polynomial model and analyzed. The obtained results are presented in graphical form, using Power Spectrum Density, and in numerical form, using metrics in time and frequency domain, such as Normalized Mean-Squared Error and Error Vector Magnitude. It is shown that the proposed memory polynomial digital predistortion model can very well compensate nonlinear distortion in fully connected hybrid beamforming MIMO transmitter. It has been also demonstrated that with increasing model complexity, ie with increasing memory depth and nonlinearity order of memory polynomial model, better compensation of nonlinear distortion in hybrid beamforming MIMO transmitters can be achieved.

Cav1.3 calcium channels are full-range linear amplifiers of firing frequencies in lateral DA SN neurons.

The low-threshold L-type calcium channel Cav1.3 accelerates the pacemaker rate in the heart, but its functional role for the extended dynamic range of neuronal firing is still unresolved. Here, we show that Cav1.3 calcium channels act as unexpectedly simple, full-range linear amplifiers of firing rates for lateral dopamine substantia nigra (DA SN) neurons in mice. This means that they boost in vitro or in vivo firing frequencies between 2 and 50 hertz by about 30%. Furthermore, we demonstrate that clinically relevant, low nanomolar concentrations of the L-type channel inhibitor isradipine selectively reduce the in vivo firing activity of these nigrostriatal DA SN neurons at therapeutic plasma concentrations. Thus, our study identifies the pacemaker function of neuronal Cav1.3 channels and provides direct evidence that repurposing dihydropyridines such as isradipine is feasible to selectively modulate the in vivo activity of highly vulnerable DA SN subpopulations in Parkinson’s disease.