A 2.4-GHz 10-W class bridge rectifier and its efficiency analysis with the behavioral model

IEEE Transactions on Microwave Theory and Techniques

Published On 2021/12/10

This article presents a 2.4-GHz band 10-W class bridge rectifier that achieves a high-measured efficiency of 90.2%. To clarify the mechanism for obtaining high efficiency, a theoretical analysis with the novel behavioral model of bridge rectifiers is demonstrated. The behavior model includes three functional blocks, namely; 1) impedance transform, which defines the RF impedance for the bridge diode; 2) RF impedance matching; and 3) rectification with the ideal current waveform of the bridge diode. Closed-form formulas for the rectification efficiency and the maximum input power are derived using the behavioral model. The RF impedance can be optimized to obtain high efficiency with the derived formulas, similar to source-pull operations in harmonic balance simulations or experiments. The fundamental limitation on the rectification efficiency is obtained for a bridge rectifier with the optimum RF impedance. In the …

Journal

IEEE Transactions on Microwave Theory and Techniques

Published On

2021/12/10

Volume

70

Issue

3

Page

1994-2001

Authors

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

Position

H-Index(all)

8

H-Index(since 2020)

6

I-10 Index(all)

0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

Microwave circuit

Wireless power transfer

Rectifier

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Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

An Integrated Planar Guanella Balun with the Quasi-Coaxial Structure on GaAs Substrate

This paper proposes a planar Guanella balun with the quasi-coaxial structure. This is the first report of the Guanella balun fabricated on a GaAs substrate. The quasi-coaxial structure is configured with metal layers on three thin dielectric layers of a few micrometers thickness. These layers are laminated on the GaAs substrate. The metal on the second layer (the second metal) is an inner conductor, which is surrounded by the first and third metals correspond to an outer conductor. The first and third metals are split lines to widen the inner conductor. The fabricated Guanella balun has a spiral shape, and its size is by . The fabricated Guanella balun shows less than of amplitude imbalance and 7.3 degrees of phase imbalance from 5 GHz to 15GHz. The fabricated Guanella balun is realized with half elements of a Marchand balun and achieves good performance with small size.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

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Graded Index Fiber-Inspired 3-D Printed Surface Focusing Porous Dielectric Structure With GaAs MMIC Rectenna Towards Millimeter Wave Wireless Power Transfer Application

Borrowing the idea of the graded-index (GRIN) fiber, we propose an all-dielectric porous structure with a unique surface focusing feature to improve the performance of the rectenna for millimeter-wave (mm-Wave) wireless power transfer (WPT) applications in this letter. The on- and off-axis focusing properties of the proposed structure are analyzed by the full-wave electromagnetic simulation. Moreover, benefitting from the low-cost 3-D printing technique, the designed GRIN structure prototype with different pore densities of the polylactic acid material is fabricated. The near-field phase transform experiment at 28 GHz was carried out to verify the excellent focusing performance of the fabricated structure prototype. Besides, the characteristics of multifocal spots on the surface of the proposed structure are further confirmed by the mm-Wave WPT experiments with a GaAs monolithic microwave integrated circuit rectenna …

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

高効率・大電力レクテナ

本報告では,金沢工業大学における高効率・大電力レクテナの研究状況について述べる.ドローンなどのUAVへの無線給電を行う場合,限られた受電面積から所望の直流電力を取り出すために,レクテナの大電力化,高効率化が必要となる.本稿ではその手法を述べる.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

GaAs E-pHEMT gated anode diode を用いた 5.75 GHz 帯 1W レクテナ

空間伝送型ワイヤレス電力伝送の法制度化が進み,実用化に向けた開発が行われている.その中で,金沢工大ではダイポールアンテナとE-pHEMT gate anode diode(GAD)による整流素子を直接整合し,整合回路の損失を抑制した高効率レクテナを報告している[1].本報告は,レクテナを低姿勢化させる上で有利なパッチアンテナ用い,[1]と同様の直接整合構成の1Wレクテナを開発したので,その結果を報告する.[1] N. Sakai, K. Itoh et.al, "5.8GHz Band 10W Rectenna with GaAs E-pHEMT Gated Anode Diode on the Aluminum Nitride Antenna for Thermal Dispersion," IEEE MTT-S IMS2023, pp.1003 – 1005, 2023-8.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

塗布型カーボンナノチューブ薄膜トランジスタによる Gated anode diode を用いる 920MHz 帯レクテナ

本報告では薄形で安価な塗布プロセスが適用可能なカーボンナノチューブ薄膜トランジスタ (carbon nanotube thin –film transistor: CNT-TFT) による920MHz帯レクテナについて述べる.ここでは高い移動度が得られるCNT-TFTによりgated anode diode (GAD)を構成し,整流素子としている.このCNT-TFT GADは強い周波数分散特性を有するため,直流特性と高周波特性を用いモデル化している.このCNT-TFT GADにより倍電圧整流器を構成し,さらに高利得特性を有するデュアルループアンテナと接続し,レクテナを構成している.試作した920MHz帯レクテナの大きさは46mm x 92mmであり,基準アンテナへの受電電力0dBmの条件で0.41Vの出力電圧を確認した.これはEIRP 2Wの送信機から1.48m離れた場所での受電に相当する測定条件である.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

倍電圧整流器 IC の高調波輻射量の評価結果

本報告では,倍電圧整流器ICの高調波輻射量の評価結果を報告する.一般的な倍電圧整流器の等価回路をもとにしたレイアウト(Layout A)と平滑用MIMキャパシタの配置を変え,対称構造にしたレイアウト(Layout B)を比較する.その結果として,Layout Aは入力電力25.6dBmのとき,整流効率67.2%,出力電圧8.6Vを得ている.Layout Bも同等である.また,2倍波電力への変換損の測定値は,Layout Aでは-38.5dBc@Pin = 25.6dBm,Layout Bでは-41.3dBc@Pin = 25.6dBmである.レイアウトを対称とすることにより2倍波の高調波輻射レベルが2.8dB抑制することができる.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

量子ビット駆動用 X 帯偶高調波リングミクサ MMIC の特性

量子ビット駆動用マイクロ波信号源では,演算の判定誤りを抑制するため低スプリアス特性が要求される.これに適用するため,アンチパラレルダイオードペア(APDP)を用いる偶高調波ミクサを検討している.ここでは X帯偶高調波リングミクサMMICの評価結果を示す.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

インピーダンス変成微小ループアンテナを用いる 28GHz 帯 GaAs 高感度レクテナ MMIC

Beyond 5Gに向け,ミリ波における通信と無線電力伝送(WPT)の融合システムを検討している. WPTのサービスエリア拡大のためには高感度レクテナが必要となる.本報告では,小形に高インピーダンス特性を実現できる微小ループアンテナ(SLA)を適用した28GHz帯GaAs高感度レクテナMMICの試作結果を示す.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

整合回路付き高周波倍電圧整流回路の整流効率の理論式

本報告は整合回路を含む高効率倍電圧整流回路の設計に向けて,整合回路を装荷した倍電流整流回路の整流効率の理論式を導出する.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

準同軸構造グァネラバラン GaAs IC の試作結果

平衡-不平衡変換を行う高周波回路としてマーチャントバランが良く用いられている.ただし,2つのλ/4結合線路で構成されるため小型化の課題がある.ここではバランの小型化に向けて,1つのλ/4同軸伝送線路で構成可能なグァネラバランを準同軸構造によりGaAs IC上に形成した.試作の結果,4~15GHzで,3dBの分配損とI/O パッドの損失を含む挿入損失は6.3±1.4 dB,振幅インバランスは0.7dB以下,位相インバランスは10.9度以下が得られた.I/O パッドを除くグァネラバランのコアサイズは425μm×345μmである.併せて作製したマーチャントバランと比較して同等の性能で22.2%の小型化が図れた.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

Novel Energy Harvesting and SWIPT System at 28 GHz with a Simple Phased Array

The realization of future radiative wireless power transfer products necessitates a simple and low-cost phased array with higher frequency to increase the beam efficiency. Further, simultaneous wireless power and information transfer (SWIPT) are also expected. This study developed a simple phased array at 28 GHz while considering energy harvesting from 5G radio waves. The number of antenna elements in the phased array with parasitic elements were reduced and novel, simple, and low-cost phase shifters were employed. Consequently, beam steering and SWIPT experiments were conducted using the developed phased array. This study expanded upon the developed phased array and the experimental results in Japan.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

920 MHz band rectenna with the CNT-TFT GAD

This paper presents the first demonstration of rectification with the carbon nanotube thin film transistor (CNT-TFT) for wireless power transfer (WPT) in the 920 MHz band. The CNT-TFT that is a coated TFT using semiconducting single-walled carbon nanotubes has advantage of low-cost fabrication and planner integration with an antenna on a thin film. On the other, reported frequency ranges were within HF bands due to their wider channel size. For applying the CNT-TFT to GHz-order rectification, the gated anode diode (GAD) is employed and is characterized for its modeling. As the results, practical operations of 920 MHz band rectenna with the CNT-TFT GAD and the dual loop antenna can be confirmed in experimental investigations.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

電子情報通信学会論文誌 C

AMC 動作基板上の誘導性高インピーダンスモノポールアンテナを用いる 5.8 GHz 帯大電力レクテナ

本論文では薄形レクテナを地導体上に配置するために,AMC(Artificial Magnetic Conductor)動作基板上に配置した誘導性高インピーダンスモノポールアンテナを用いる5.8 GHz帯大電力レクテナの設計,試作結果を示す.ここではAMCから想起され,同様の動作をするグリッド導体を有する薄形基板であるAMC動作基板を用いることにより,地導体から2 mmの高さでモノポールアンテナを実現する.これを誘導性かつ高インピーダンス動作するよう設計し,整流用ダイオードとして用いる0.5 μm GaAs E-pHEMTによるGated Anode Diode(GAD)と共役整合する.整合回路を不要とすることで,高効率化を図っている.試作したレクテナの大きさは15 mm × 17.2 mm × 2.1 mmであり,地導体・金属上に実装可能である.測定の結果,整流器への入力電力31.8 dBm(1.51 W)に対し整流効率84.4%,出力電圧37.7 Vの良好な結果が得られている.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

5.8 GHz band 10 W rectenna with GaAs E-pHEMT gated anode diode on the aluminum nitride antenna for thermal dispersion

In this paper, the 5.8 GHz band 10 W rectenna is demonstrated. The GaAs bridge rectifier IC with GaAs E-pHEMT gated anode diodes (GADs) is employed to obtain input power of 10 W. The IC is directly connected with the inductive high-impedance antenna to reduce circuits’ loss. Furthermore, the antenna is implemented on the aluminum nitride (AlN) substrate for thermal dispersion. With migrated circuit functionalities, simulated radiation efficiency of the antenna is 99.2 %. Measured rectification efficiency of the rectifier is 83.7 % at input power of 10 W. This is the top performance among 10 W class rectifies

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Technical Report; IEICE Tech. Rep.

5.8 GHz band 10 W rectenna on the aluminum nitride antenna for thermal dispersion

(in English) This paper presents the 5.8 GHz band 10W rectenna with GaAs E-pHEMT gated anode diode (GAD) on the aluminum nitride (AlN) antenna. The rectifier IC on the prototyped AlN antenna achieved a rectification efficiency of 83.7% at an input power of 10.5 W while maintaining a GAD junction temperature of 48 degrees. These results demonstrate that the rectenna can continuously receive RF power of 10 W with high rectification efficiency. Furthermore, we demonstrate a 3x3 rectenna array with the prototyped rectenna in a microwave power transfer (MPT) system. The MPT system with the rectenna array could transmit a DC power of 43.4 W, allowing a drone to fly continuously for ten minutes.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

GaAs E-pHEMT GAD を用いる準ミリ波帯 1W 整流器 MMIC

GaAs E-pHEMT Gated anode diode を用いて26GHz帯1W倍電圧整流器MMICを設計した.測定結果は,26GHzにおいて入力電力29.5dBmのとき整流効率62.2%,出力電圧31.1Vである.GADにより準ミリ波帯において大電力・高効率整流が可能であることを示した.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

5.8 GHz 帯 10W 級倍電圧整流器 MMIC

マイクロ波での無線電力伝送(MPT)が法制化され,その実用化が進められている.筆者らは,MPT用レクテナの大電力化のため,GaAs E-pHEMTによるGated anode diode (GAD)を用いる大電力レクテナの検討を行っている.本報告では5.8GHz帯10W級倍電圧整流器MMICの評価結果を示す.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

ダイオードの閾値と降伏電圧を考慮した倍電流整流回路の解析

無線電力伝送システムにおいて,整流回路は受電した高周波電力を直流に変換し負荷へ給電するために欠かせない回路である.倍電流整流回路はモーターや電池などの低電圧・大電流で動作する負荷へ直流電力を供給するのに向いている.過去の発表ではダイオードを理想的なスイッチと仮定し,倍電流整流回路の動作および理論効率をまとめている.本稿では閾値電圧ならびにブレイクダウン(降伏)電圧を含んだダイオードモデルを用い,倍電流整流回路の動作について報告する.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Conferences Archives

GaAs E-pHEMT gated anode diode を用いる 5.8 GHz 帯 5W レクテナ

大電力化に適するGaAs E-pHEMTによるgated anode diode(GAD)を用いる5.8GHz帯5Wレクテナの試作結果を示す.入力電力Pin=37dBm(5W)のときに整流効率=85.2%,出力電圧Vout=35.8Vである.

Naoki Sakai

Naoki Sakai

Kanazawa Institute of Technology

IEICE Technical Report; IEICE Tech. Rep.

Quasi millimeter wave high-power rectifier with GaAs E-pHEMT GADs

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IEEE Transactions on Microwave Theory and Techniques

A -Band Low-Noise and High-Gain Receiver Front-End Adopting -Driven Active Mixer

Phased-array systems are extensively utilized in wireless transmission and reception links operating at frequencies above 100 GHz to compensate for significant path loss. Regardless of beamforming architectures, the low-power implementation of a high-gain and low-noise receiver (RX) front-end (FE) plays a crucial role in large-scale RX arrays to maintain link margin. This article presents a 154 GHz low-power, high-gain, and low-noise CMOS RX FE adopting a proposed active mixer driven by a -stage based on a -core. To ensure high-gain and low-noise characteristics, a two-stage low-noise amplifier (LNA) is implemented using the gain boosting technique, while its first stage features a simultaneous noise-and input-matched -core. The proposed active mixer consists of the -based -stage and switching stages. The -stage driving the switching stage is realized using the -core …

Yingsong Li

Yingsong Li

Harbin Engineering University

IEEE Transactions on Microwave Theory and Techniques

Transient Electromagnetic–Thermal Co-Simulation of Microwave/RF Integrated Circuits by the HIE-FDTD Method

In this article, we present an efficient transient electromagnetic–thermal co-simulation solver based on the hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method. This solver is designed to model the multiscale structure and multiphysics field effects of 3-D microwave integrated circuits (ICs). For the first time, we introduce the HIE-FDTD method to solve the heat conduction equation and establish a unified 3-D electromagnetic–thermal co-simulation framework based on the HIE-FDTD algorithm. In addition, this article provides a detailed explanation of the thermal continuity condition, which is rooted in the principle of energy conservation. It addresses the significant variation in thermal conductivity among the different layers of advanced package structures and highlights the potential for substantial errors if the thermal continuity condition is not considered. The stability condition of the proposed method …

Stephen McLaughlin

Stephen McLaughlin

Heriot-Watt University

IEEE Transactions on Microwave Theory and Techniques

FM Rider: Two-FSK Modulation-Based Ambient FM Backscatter Over 100 m Distance

Backscatter communication (BackCom) technology represents a low-cost and battery-free technology for Internet-of-Things (IoT) applications. One variant of BackCom, termed as ambient BackCom, which uses ambient signals to eliminate the need for a dedicated carrier source is more advantageous due to reduced system complexity and cost. Previous studies on ambient BackCom have primarily relied on amplitude modulation-based systems like on–off-keying (OOK) modulation, which achieved a maximum tag-to-receiver (Rx) distance of less than five meters. Alternatively, frequency-shift-keying (FSK)-based ambient BackCom systems have demonstrated improved distance, but with limitations. This work introduces an ambient broadcast frequency-modulation (FM) BackCom system utilizing in-band 2FSK-based modulation, designed to be compatible with both mono and stereo radio systems and extend communication …

Luca Steinweg

Luca Steinweg

Technische Universität Dresden

IEEE Transactions on Microwave Theory and Techniques

Performance Evaluation of Ultra-Wideband 246-GHz BPSK Transmitters on an Organic Substrate With External Chip and Substrate Antenna

This work presents the design and evaluation of two binary phase-shift keying (BPSK) transmitter modules operating around 246 with tested real-world data transmission rates of up to 32 Gbit s and demonstrated transmission of 10 Gbit s . The systems use external antennas bonded to the massive monolithic integrated circuit (MMIC) to allow maximum assembly and antenna design flexibility. This work presents the first transmitter system fully integrated into a printed circuit board (PCB) and paves the way for future commercial exploitation of the frequency band. The chosen antenna concepts are novel and offer great flexibility for future system. No previous demonstrated system utilized and exploited the benefits of a differential radio frequency (RF) interconnect and antennas solution. The overall system performance and the antenna patterns are measured. Bit error rate measurements are used to evaluate …

Mostafa Essawy

Mostafa Essawy

Oregon State University

IEEE Transactions on Microwave Theory and Techniques

A Frequency Doubler With Second Harmonic Feedback for Wideband, Efficient Frequency Multiplication at Millimeter-Wave

Frequency multipliers are widely used in scalable millimeter-wave (mm-wave) arrays in communication and radar. This article presents an mm-wave frequency doubler (FDB) topology that exploits odd-mode/even-mode operation to create different feedback networks at the fundamental frequency and second harmonic. Theoretical analysis of the FDB network is detailed. The FDB topology is well-suited for CMOS integration, and a stand-alone FDB in 65-nm CMOS achieves a saturated output power ( ) of 10.1 dBm with a maximum drain efficiency (DE) of 32.7% at 60 GHz. The wideband FDB is also cascaded with a power amplifier (PA) to achieve a total of 15 dBm with a maximum dc-to-RF efficiency ( ) of 24.5%. Measurements demonstrate wideband FDB chirp bandwidths and suitability for frequency-modulated continuous wave (FMCW) radar applications.

Stefania Marconi

Stefania Marconi

Università degli Studi di Pavia

IEEE Transactions on Microwave Theory and Techniques

Low-Cost Method for Internal Surface Roughness Reduction of Additively Manufactured All-Metal Waveguide Components

In this study, a novel low-cost polishing method for internal surface roughness reduction of additively manufactured components, developed for waveguide (WG) circuits operating in the millimeter frequency range is proposed. WG components fabricated using powder bed fusion (PBF) generally feature roughness of ten to fifty microns, which influences the increase of roughness-related conductor power losses having a major effect on the electrical performance of additively manufactured all-metal WGs. To improve and decrease the surface roughness of circuits fabricated using PBF, glass microbeads as an abrasive medium are proposed to be used in combination with a rotary tumbler. This technique allows the abrasive medium to efficiently penetrate internal long channels and cavities, having cross section dimensions in the range of sub-to a few millimeters. An experimental study was carried out on an example of WG …

Guy A E Vandenbosch

Guy A E Vandenbosch

Katholieke Universiteit Leuven

IEEE Transactions on Microwave Theory and Techniques

A Dedicated Modeling Scheme for Nonclassical Optical Response From the Nanosphere-on-Mirror Structure

Within the framework of the T-matrix method, we present a modeling tool that predicts the optical response from the Nanosphere-on-Mirror (NSoM) construct. The nonclassical effects in metals are accounted for by the nonlocal hydrodynamic Drude model (NLHDM) or the surface response model (SRM). Two essential elements in the T-matrix method, i.e., the T-matrix of the sphere and the R matrix accounting for the effects of the mirror, have been fully upgraded to include longitudinal waves for the NLHDM and the augmented interface conditions for the SRM. The proposed tool is quantitatively validated both in the near and the far-field by an in-house developed BEM solver for the NLHDM where the gap between the sphere and the mirror is as small as 1 nm. Two physical checks are performed, where the results from the classical local response model (LRM) are compared with the ones from the NLHDM and the …

Haiyan Ou

Haiyan Ou

Danmarks Tekniske Universitet

IEEE Transactions on Microwave Theory and Techniques

A New Unconditionally Stable FDTD Method Based on Artificial Neural Network

This article presents a new unconditionally stable finite-difference time-domain (FDTD) method combined with the artificial neural network (ANN) for multiscale problems. The input of ANN-FDTD is the point location of spatial grid division in FDTD, and the output is the field data at these points. At each time step, the hypothetical solution of Maxwell’s equations is constructed using a known forced excitation source and the output of ANN. The error of ANN is determined by the gradient of its output with respect to the input vector. This error value is used to update ANN parameters with the backpropagation (BP) algorithm, so the training does not have to involve labeled samples. Here, ANN is trained to ensure that the hypothetical solution satisfies the boundary conditions. ANN is trained individually at each time-marching step, and thus, the results of the previous step do not affect those of the next step. The time step of …

Yuan Ding

Yuan Ding

Heriot-Watt University

IEEE Transactions on Microwave Theory and Techniques

FM Rider: Two-FSK Modulation-Based Ambient FM Backscatter Over 100 m Distance

Backscatter communication (BackCom) technology represents a low-cost and battery-free technology for Internet-of-Things (IoT) applications. One variant of BackCom, termed as ambient BackCom, which uses ambient signals to eliminate the need for a dedicated carrier source is more advantageous due to reduced system complexity and cost. Previous studies on ambient BackCom have primarily relied on amplitude modulation-based systems like on–off-keying (OOK) modulation, which achieved a maximum tag-to-receiver (Rx) distance of less than five meters. Alternatively, frequency-shift-keying (FSK)-based ambient BackCom systems have demonstrated improved distance, but with limitations. This work introduces an ambient broadcast frequency-modulation (FM) BackCom system utilizing in-band 2FSK-based modulation, designed to be compatible with both mono and stereo radio systems and extend communication …

Bai-Ou Guan

Bai-Ou Guan

Jinan University

IEEE Transactions on Microwave Theory and Techniques

Photonic-Assisted Frequency Diverse Array

A new microwave photonic signal processor for use in a frequency diverse array (FDA) to generate a dot-shaped beampattern is presented. The microwave photonic signal processor is implemented based on a dual-polarization quadrature phase shift keying (DP-QPSK) modulator and a phase modulator (PM), with the amplitude and phase of an input radio frequency (RF) signal controlled by the bias voltages to the DP-QPSK modulator, and the frequency offset to the RF signal is realized by Serrodyne modulation at the PM. The operation of the signal processor is analyzed theoretically and demonstrated experimentally. The results show that the proposed signal processor can generate an RF signal with arbitrary controlled amplitude and phase and a frequency offset ranging from 240.2 to 8.4 kHz. A dot-shaped beampattern generated by a 32-element nonuniform FDA is calculated using the experimentally …