Cartesian Feedback Research Articles

Cartesian Feedback Loop 선형화 기법을 적용한 초단파 데이터 교환 시스템 (VDES) 송신기 설계 및 제작

본 논문에서는 국제항로표지협회(International Association Of Lighthouse Authorities, IALA)를 중심으로 논의되고 있는 e-Navigation 전략 이행계획의 일부인 초단파 데이터 교환 시스템(VHF Data Exchange System, VDES)의 송신기에 대해 기술하였다. VDES의 표준 권고안 중 송신출력 스펙트럼 마스크 규격은 인접한 채널 간의 간섭을 최소화하기 위해 엄격한 규격을 적용하고 있다. 본 논문에서는 이를 충족시키기 위한 송신기의 선형화 기법에 대해 기술하고 이러한 기법 중 초단파 대역(Very High Frequency, VHF)의 협대역 채널에 적합한 Cartesian Feedback Loop 선형화 방식의 송신기를 설계 및 제작하였다. 제작된 송신기를 통해 VDES 주파수 대역에서 응용지정메시지(Application Specific Message, ASM)채널과 초단파 데이터 교환(VHF Data Exchange, VDE) 채널의 Modulation Coding Scheme(MCS)별 송신출력 스펙트럼 마스크를 측정하였다. 측정결과 국제항로표지협회에서 권고하는 규격을 만족하였으며, 선형화 기법을 사용하지 않은 경우에 비해 상호변조왜곡(Inter Modulation Distortion, IMD) 성분이 약 30dBc이상 억제됨을 확인하였다.

Advantages of Second-Order Cartesian Feedback Linearizers for Radio Amplifiers

Cartesian feedback (CF) linearization for radio amplifiers is appealingly simple, but it imposes a trade-off between signal bandwidth and feedback delay. In almost all of the CF literature, it is a first-order circuit. In this paper, we examine two second-order CF linearizers and show that they can provide deeper suppression of intermodulation distortion or greater signal bandwidth at a given loop delay. Twin-loop CF with damping factor 0.707, for example, can provide 20 dB lower intermodulation distortion and half the error vector magnitude (EVM), relative to first-order CF. For twin-loop CF and proportional-integrator CF, we provide the first analyses of their behavior, stability limits, and linearization performance. Comparison with simulations using nonlinear amplifier models shows both the value and the shortcomings of linear analysis. Our new spectral separation approach leads to insights about linearization and EVM.

Digital Predistorters Go Multidimensional: DPD for Concurrent Multiband Envelope Tracking and Outphasing Power Amplifiers

Over at least the last two decades, digital predistortion (DPD) has become the most common and widespread solution to cope with the power amplifier's (PA's) inherent linearity-versus-efficiency tradeoff. When compared with other linearization techniques, such as Cartesian feedback or feedforward, DPD has proven able to adapt to the always-growing demands of technology: wider bandwidths, stringent spectrum masks, and reconfigurability. The principles of predistortion linearization (in its analog or digital forms) are straightforward, and the linearization subsystem precedes the PA (a nonlinear function in a digital signal processor in the case of DPD or nonlinear device in the case of analog predistortion and counteracts the nonlinear characteristic of the PA. Some excellent overviews on DPD can be found in [1]-[4]. Let us now look at the challenges that DPD linearization has faced and will continue to face in the near future with 5G new radio (5G-NR).

A 21-dm-OP1 dB 20.3%-Efficiency -131.8-dBm/Hz-Noise X-Band Cartesian Error Feedback Transmitter With Fully Integrated Power Amplifier in 65-nm CMOS

This article presents an $X$ -band Cartesian error feedback loop transmitter (CEFLT) with a fully integrated power amplifier (PA) in a 65-nm CMOS. The extra reference path cancels the feedback signal to mitigate the inherent linearity–noise tradeoff in the conventional Cartesian feedback loop transmitter (CFLT). In this way, the nonlinearities from the feedback path are suppressed without using large attenuation, and thus the noise contribution from the feedback path is reduced as well. Compared with the conventional CFLT, the proposed CEFLT can improve the linearity without degrading the noise performance. The PA-included transmitter delivers a maximum power ( $P_{\mathrm {SAT}}$ ) of 21.4 dBm and output-referred 1-dB compression point ( OP 1 dB) of 21 dBm, with 33.3% and 30.3% PA output stage efficiency, respectively, and 22.3% and 20.3% system efficiency, respectively. Compared with the open-loop condition, the closed-loop transmitter demonstrates up to 13.6-dB suppression of adjacent channel leakage ratio (ACLR) error vector magnitude (EVM) using 4 Msps 64 quadratic-amplitude modulation (QAM) signals. The out-of-band (OOB) noise at 100 MHz is −133/−131.8 dBm/Hz for the lower and upper sidebands, respectively.

A Cartesian Error Feedback Architecture

A Cartesian error feedback architecture is proposed to address the linearity-noise tradeoff in the conventional Cartesian feedback architecture. First, the tradeoff in the conventional Cartesian feedback architecture is identified, which is caused by the contradictory requirements imposed by linearity and noise on the attenuation ratio in the feedback path. Then, this paper investigates how the signal cancellation provided by the new architecture mitigates the tradeoff. The effects of nonlinearities and noise from the feedforward path are also presented in detail. Furthermore, the matching requirements of the feedforward path for effective signal cancellation are discussed and proven not stringent due to the loop effect. To verify the concept, a WCDMA signal is taken as the application example, in which our proposed error feedback architecture presents more than 8 dB noise improvement while maintaining comparable linearity performance compared with the conventional architecture. This validates the deployment of the proposed Cartesian error feedback architecture in today’s application scenarios with congested frequency spectrum.

Even-odd mode excitation for stability investigation of Cartesian feedback amplifier used in parallel transmit array.

A 7 Tesla Magnetic Resonance Imaging (MRI) system with parallel transmission (pTx) for 32 near-magnet Cartesian feedback loop power amplifiers (PA) with output power of 1kW is under construction at Erwin L. Hahn Institute for Magnetic Resonance Imaging. Variation of load impedance due to mutual coupling of neighborhood coils in the array may lead to instability of the Cartesian feedback loop amplifier. MRI safety requires unconditional stability of the PAs at any load. In order to avoid instability in the pTx system, conditions and limits of stability have to be investigated for every possible excitation mode for the coil array. In this work, an efficient method of stability check for an array of two transmit channels (Tx) with Cartesian feedback loop amplifier and a selective excitation mode for the coil array is proposed which allows extension of stability investigations to a large pTx array with any arbitrary excitation mode for the coil array.

Feedback Linearization of RF Power Amplifier for TETRA Standard

In wireless transmission systems, non-ideal response of different functional components along with power amplifier’s nonlinearity plays a major role in degrading the transmitter performance. Several parameters defines the performance of a wireless transmitter, such as adjacent channel power ratio (ACPR), error vector magnitude (EVM), spectral mask, etc., and the effect of non-ideal behaviour of the transmitter affects these parameters. For many standards these parameter specifications are defined such that the concern for transmitter linearization is very much relaxed. Standards like Terrestrial Trunked Radio (TETRA) specify strict regulation on these parameters. Therefore, the requirement of linearity is a great challenge for the design of the transmitter. Many linearization schemes is available for linearizing the nonlinear effect of a transmitter, and among those the Cartesian feedback technique is a well known concept for linearization of transmitter operating according to TETRA standard, as well as employing a narrowband operation. In our research, distortion effect of the transmitter has been analysed, and a practical demonstration of the linearization effect over distortion has been implemented using the Cartesian feedback concept.

Mixed Cartesian feedback for Zero-IF WCDMA transmitter

In this paper, a new adaptive power amplifier (PA) linearization technique is presented. The idea is to consider a classic WCDMA zero-intermediate frequency (Zero-IF) transmitter with a modified Cartesian feedback (CFB) loop. The new transmitter architecture consists of an analog stage including forward I/Q modulator and feedback I/Q demodulator, and a digital stage adjusting the phase rotation around the loop. The whole system consumes 500 and 2.94 mW, respectively, for the analog and the digital part. System level simulation gave a maximum improvement of 35 dBc at 5 MHz from the carrier for the W-CDMA signal.

Digitally Assisted Feedforward Compensation of Cartesian-Feedback Power-Amplifier Systems

This brief describes digitally assisted feedforward compensation to extend the bandwidth and to enhance the in-band linearity of Cartesian-feedback (CFB) power-amplifier (PA) systems. The proposed technique combines the strength of the CFB, which is chiefly relaxed PA modeling requirements, with the increased speed of digital predistortion (DPD). CFB is used initially to train efficiently a lookup table for a predistorted feedforward path. Then, both the CFB and the predistorted feedforward path run simultaneously during transmission. Viewed as a bandwidth-enhancement technique for analog CFB, the feedforward-compensated system shows a linearization bandwidth improvement of almost six times over the unaided feedback system. Viewed as a means of improving the in-band linearity of CFB, the proposed system realizes up to 10 dB of reduction in distortion products over CFB or DPD alone and does so without compromising the stability of the feedback system.

Frequency-offset Cartesian feedback for MRI power amplifier linearization.

High-quality magnetic resonance imaging (MRI) requires precise control of the transmit radio-frequency (RF) field. In parallel excitation applications such as transmit SENSE, high RF power linearity is essential to cancel aliased excitations. In widely-employed class AB power amplifiers, gain compression, cross-over distortion, memory effects, and thermal drift all distort the RF field modulation and can degrade image quality. Cartesian feedback (CF) linearization can mitigate these effects in MRI, if the quadrature mismatch and dc offset imperfections inherent in the architecture can be minimized. In this paper, we present a modified Cartesian feedback technique called "frequency-offset Cartesian feedback" (FOCF) that significantly reduces these problems. In the FOCF architecture, the feedback control is performed at a low intermediate frequency rather than dc, so that quadrature ghosts and dc errors are shifted outside the control bandwidth. FOCF linearization is demonstrated with a variety of typical MRI pulses. Simulation of the magnetization obtained with the Bloch equation demonstrates that high-fidelity RF reproduction can be obtained even with inexpensive class AB amplifiers. Finally, the enhanced RF fidelity of FOCF over CF is demonstrated with actual images obtained in a 1.5 T MRI system.

Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers

A modified Cartesian feedback method called "frequency-offset Cartesian feedback" and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems.In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200-1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90° phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback.In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems.

An adaptive phase alignment algorithm for cartesian feedback loops [Applications corner

An adaptive algorithm to correct phase misalignments in Cartesian feedback linearization loops for power amplifiers has been presented. It yields an error smaller than 0.035 rad between forward and feedback loop signals once convergence is reached. Because this algorithm enables a feedback system to process forward and feedback samples belonging to almost the same algorithm iteration, it is suitable to improve the performance not only of power amplifiers but also any other digital feedback system for communications systems and circuits such as all digital phase locked loops. Synchronizing forward and feedback paths of Cartesian feedback loops takes a small period of time after the system starts up. The phase alignment algorithm needs to converge before the feedback Cartesian loop can start its ideal behavior. However, once the steady state is reached, both paths can be considered synchronized, and the Cartesian feedback loop will only depend on the loop parameters (open-loop gain, loop bandwidth, etc.). It means that the linearization process will also depend only on these parameters since the misalignment effect disappears. Therefore, this algorithm relieves the power amplifier linearizer circuit design of any task required for solving phase misalignment effects inherent to Cartesian feedback systems. Furthermore, when a feedback Cartesian loop has to be designed, the designer can consider that forward and feedback paths are synchronized, since the phase alignment algorithm will do this task. This will reduce the simulation complexity. Then, all efforts are applied to determining the suitable loop parameters that will make the linearization process more efficient.

TEDS Base-Station Power Amplifier Using Low-Noise Envelope Tracking Power Supply

This paper demonstrates a highly linear and efficient TETRA enhanced data service (TEDS) base-station RF power amplifier (RFPA). Based on the well-known combination of an envelope tracking (ET) power supply and a linear class-A/B RFPA, adequate adjacent channel power ratio (ACPR) and wideband noise performance is shown to be enabled only by further incorporating high-bandwidth Cartesian feedback (CFB) and using a low-noise ET power supply. It is demonstrated that CFB loop bandwidth is limited by modulator/demodulator/RF path group delay to around 2 MHz in the considered setup, and that there exists a significant tradeoff between the depth of the ET and open-loop RFPA linearity, as well as overall efficiency. An empirical method for determining the permissible amount of switching ripple on the ET supply is presented, showing very good accuracy. Performance of the prototype RFPA system is verified experimentally with a 9.6-dB peak-to-average 50-kHz 16 quadrature amplitude modulation TEDS carrier, the setup providing 44-dBm (25 W) average RF output power at 400 MHz with 44% dc-to-RF efficiency state-of-the-art ACPR of less than -67 dBc, switching noise artifacts around - 85 dBc, and an overall rms error vector magnitude below 4.5%.

1-W high linear broadband RF power amplifier with Certesian feedback for TETRA modulation [Application Notes

Designing a high-linearity, high-efficiency RF power amplifier with wide bandwidth design is a real challenge. This article explores a technique to achieve 30 dBm output power with an adjacent channel power ratio (ACPR) of more than -65 dBc for frequency range of 800-900 MHz. A three-stage gallium arsenide heterojunction bipolar transistor (GaAs HBT) RF power amplifier with Cartesian feedback in closed-loop form is the main architecture of the design. An adaptive bias technique was used in the RF power amplifier design to achieve high linearity while preserving good efficiency.

A high‐power Cartesian feedback transmitter including a compact inverted Doherty amplifier

AbstractA high‐power Cartesian feedback transmitter including a compact inverted Doherty amplifier is presented. The system efficiency was further improved using a bias line adjustment method for the compact inverted Doherty amplifier. After the bias line adjustment from a λ/4 line for the Doherty amplifier, a power‐added efficiency (PAE) of 6.9% points was improved from 41.3 to 48.2% at an output power level of 45 dBm. The whole Cartesian feedback transmitter system exhibited an efficiency of 40% and an adjacent channel leakage ratio of‐51 dBc at an output power of 45 dBm for 859 MHz band π/4‐DQPSK applications. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 944–946, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23265

DESIGN OF CARTESIAN FEEDBACK RF POWER AMPLIFIER FOR L-BAND FREQUENCY RANGE

A phase-alignment system is used fully integrate a power amplifier, Cartesian feedback linearization circuitry, and a phasealignment system. The phase-alignment system employs a new technique for offset-free analog multiplication that enables it to function without manual trimming. This paper demonstrates how the phase-alignment system improves the stability margins of the fully integrated Cartesian feedback system. The power amplifier itself, integrated on the same die, operates at 1 GHz and delivers a maximum of 30 dBm of output power into a 50-load. The class AB design for open loop and close loop power amplifier with Cartesian feedback, demonstrated a good linearity of 50 dBc and 80 dBc, respectively. The operating power is 2 W at 1000 MHz frequency.

Overcoming high-field RF problems with non-magnetic Cartesian feedback transceivers

In extending human MR to field strengths approaching 10 T, the wavelength of electromagnetic radiation at the proton Larmor frequency becomes less than human body size and conventional radio-frequency coil circumference. Consequently, radio-frequency magnetic fields are better generated by an array of small coils than by one large coil. In this article, the primary problem of array coil interactions during transmission is examined, and a standard proposed whereby secondary induced currents should be less than 1% of the primary coil current. The use of cancellation methods and of power amplifiers with high output impedance to reduce interactions is examined in the light of this standard and found wanting. Non-magnetic Cartesian feedback transceivers functioning at the magnet entrance are then proposed as a solution that both reduces instrumentation cost and increases the bandwidth over which the standard may be met. The compromises inherent in instrument design are detailed and examples given of the innovative circuitry used. It is shown experimentally that when connected to interacting coils, two Cartesian feedback instruments function stably in accord with theory and such that the proposed standard is typically attained over a bandwidth of 22 kHz during transmission (much greater during signal reception)-enough for all current MR protocols.

860 MHz 대역 고출력 Cartesian 피드백 송신기 설계

본 논문은 Cartesian 피드백 방법을 이용하여 전력 증폭기의 선형성을 개선한 860 MHz 대역의 송신기의 설계에 관한 것이다. 피드백 루프를 통하여 발생하는 이득 및 위상의 불일치와 DC offset에 의한 영향을 제거하기 위하여 ADS simulation을 이용하여 특성 변화를 예측하였다. 제작된 Cartesian 피드백 송신기는 출력 전력 43 dBm에서 -54 dBc의 IMD3 특성을 나타내었으며, 이는 선형화 전과 비교하여 22.4 dB의 선형성 개선 효과가 있음을 의미한다. 따라서 본 논문에서 제작한 Cartesian 피드백 송신기를 이용하여 협-대역 전송시스템에 적용할 수 있음을 확인하였다. This paper presents the design of 860 MHz band transmitter for improving power amplifier's linearity using Cartesian feedback method. For eliminating the effects of gain, phase mis-match, and DC offset, we estimate the property variations using ADS software. The implemented Cartesian feedback transmitter exhibits IMD3 of -54 dBc at an output power of 43 dBm and this result shows that the linearity is improved for 22.4 dB, compared with the test of the power amplifier without Cartesian feedback system. Thus, we verify that the proposed Cartesian feedback transmitter can be applied to narrow-band transmitter systems.

CONTROL OF A CLIMBING ROBOT USING REAL-TIME CONVEX OPTIMIZATION

This paper presents a controller for a free-climbing robot. Given a pre-planned path, a loop is closed around desired robot chassis position to generate cartesian feedback forces. A convex optimization problem is then solved in real-time to find a torque input to the robot that will achieve these feedback forces while not exceeding torque limits or violating friction constraints. The effectiveness of this controller is demonstrated both in simulation and with experimental hardware.

A transmitter IC for TETRA systems based on a Cartesian feedback loop linearization technique

A fully integrated linearized transmitter for the next generation TETRA systems for PMR and public safety applications in a CMOS-based SiGe technology is described. The presented single-chip transmitter employs a Cartesian feedback loop technique in order to improve the linearity of the externally connected power amplifier. The transmitter is usable in a frequency range from 300 MHz up to 800 MHz, providing a linearity improvement of more than 40 dB.