Reflectarray antennas for dual polarization and broadband telecom satellite applications

A reflectarray antenna with improved performance is proposed to operate in dual-polarization and transmit-receive frequencies in Ku-band for broadcast satellite applications. The reflectarray element contains two orthogonal sets of four coplanar parallel dipoles printed on two surfaces, each set combining lateral and broadside coupling. A 40-cm prototype has been designed, manufactured, and tested. The lengths of the coupled dipoles in the reflectarray cells have been optimized to produce a collimated beam in dual polarization in the transmit and receive bands. The measured radiation patterns confirm the high performance of the antenna in terms of bandwidth (27%), low losses, and low levels of cross polarization. Some preliminary simulations at 11.95 GHz for a 1.2-m antenna with South American coverage are presented to show the potential of the proposed antenna for spaceborne antennas in Ku-band.

Development of Efficient Techniques for the Analysis and Design of Antennas in Dual-Reflectarray Configuration

This thesis contributes to the analysis and design of printed reflectarray antennas. The main part of the work is focused on the analysis of dual offset antennas comprising two reflectarray surfaces, one of them acts as sub-reflector and the second one acts as mainreflector. These configurations introduce additional complexity in several aspects respect to conventional dual offset reflectors, however they present a lot of degrees of freedom that can be used to improve the electrical performance of the antenna. The thesis is organized in four parts: the development of an analysis technique for dualreflectarray antennas, a preliminary validation of such methodology using equivalent reflector systems as reference antennas, a more rigorous validation of the software tool by manufacturing and testing a dual-reflectarray antenna demonstrator and the practical design of dual-reflectarray systems for some applications that show the potential of these kind of configurations to scan the beam and to generate contoured beams. In the first part, a general tool has been implemented to analyze high gain antennas which are constructed of two flat reflectarray structures. The classic reflectarray analysis based on MoM under local periodicity assumption is used for both sub and main reflectarrays, taking into account the incident angle on each reflectarray element. The incident field on the main reflectarray is computed taking into account the field radiated by all the elements on the sub-reflectarray.. Two approaches have been developed, one which employs a simple approximation to reduce the computer run time, and the other which does not, but offers in many cases, improved accuracy. The approximation is based on computing the reflected field on each element on the main reflectarray only once for all the fields radiated by the sub-reflectarray elements, assuming that the response will be the same because the only difference is a small variation on the angle of incidence. This approximation is very accurate when the reflectarray elements on the main reflectarray show a relatively small sensitivity to the angle of incidence. An extension of the analysis technique has been implemented to study dual-reflectarray antennas comprising a main reflectarray printed on a parabolic surface, or in general in a curved surface. In many applications of dual-reflectarray configurations, the reflectarray elements are in the near field of the feed-horn. To consider the near field radiated by the horn, the incident field on each reflectarray element is computed using a spherical mode expansion. In this region, the angles of incidence are moderately wide, and they are considered in the analysis of the reflectarray to better calculate the actual incident field on the sub-reflectarray elements. This technique increases the accuracy for the prediction of co- and cross-polar patterns and antenna gain respect to the case of using ideal feed models. In the second part, as a preliminary validation, the proposed analysis method has been used to design a dual-reflectarray antenna that emulates previous dual-reflector antennas in Ku and W-bands including a reflectarray as subreflector. The results for the dualreflectarray antenna compare very well with those of the parabolic reflector and reflectarray subreflector; radiation patterns, antenna gain and efficiency are practically the same when the main parabolic reflector is substituted by a flat reflectarray. The results show that the gain is only reduced by a few tenths of a dB as a result of the ohmic losses in the reflectarray. The phase adjustment on two surfaces provided by the dual-reflectarray configuration can be used to improve the antenna performance in some applications requiring multiple beams, beam scanning or shaped beams. Third, a very challenging dual-reflectarray antenna demonstrator has been designed, manufactured and tested for a more rigorous validation of the analysis technique presented. The proposed antenna configuration has the feed, the sub-reflectarray and the main-reflectarray in the near field one to each other, so that the conventional far field approximations are not suitable for the analysis of such antenna. This geometry is used as benchmarking for the proposed analysis tool in very stringent conditions. Some aspects of the proposed analysis technique that allow improving the accuracy of the analysis are also discussed. These improvements include a novel method to reduce the inherent cross polarization which is introduced mainly from grounded patch arrays. It has been checked that cross polarization in offset reflectarrays can be significantly reduced by properly adjusting the patch dimensions in the reflectarray in order to produce an overall cancellation of the cross-polarization. The dimensions of the patches are adjusted in order not only to provide the required phase-distribution to shape the beam, but also to exploit the crosses by zero of the cross-polarization components. The last part of the thesis deals with direct applications of the technique described. The technique presented is directly applicable to the design of contoured beam antennas for DBS applications, where the requirements of cross-polarisation are very stringent. The beam shaping is achieved by synthesithing the phase distribution on the main reflectarray while the sub-reflectarray emulates an equivalent hyperbolic subreflector. Dual-reflectarray antennas present also the ability to scan the beam over small angles about boresight. Two possible architectures for a Ku-band antenna are also described based on a dual planar reflectarray configuration that provides electronic beam scanning in a limited angular range. In the first architecture, the beam scanning is achieved by introducing a phase-control in the elements of the sub-reflectarray and the mainreflectarray is passive. A second alternative is also studied, in which the beam scanning is produced using 1-bit control on the main reflectarray, while a passive subreflectarray is designed to provide a large focal distance within a compact configuration. The system aims to develop a solution for bi-directional satellite links for emergency communications. In both proposed architectures, the objective is to provide a compact optics and simplicity to be folded and deployed.

Electronic Steering antenna onboard for satellite communications in X band.

The antenna presented in this article will be developed for satellite communications onboard systems based on the recommendations ITU-R S.580-6 and ITU-R S.465-5. The antenna consists of printed elements grouped in an array, this terminal works in a frequency band from 7.25 up to 8.4 GHz (14.7% of bandwidth), where both bands, reception (7.25 - 7.75 GHz) and transmission (7.9 - 8.4 GHz), are included simultaneously. The antenna reaches a gain about 31 dBi, and it has a radiation pattern with a beamwidth smaller than 10° and a dual circular polarization. The antenna has the capability to steer in elevation from 90° to 40° electronically and 360° in azimuth with a motorized junction.

Mutual Coupling Reduction Techniques in Electronic Steering Antennas in X Band

This work provides the development of an antenna for satellite communications onboard systems based on the recommendations ITU-R S.580-6 [1] and ITU-R S.465-5 [2]. The antenna consists of printed elements grouped in an array, working in a frequency band from 7.25 up to 8.4 GHz (15% of bandwidth). In this working band, transmission and reception are included simultaneously. The antenna reaches a gain about 31 dBi, has a radiation pattern with a beam width smaller than 10oand dual circular polarization. It has the capability to steer in elevation through a Butler matrix to 45

Low-Profile Dual Circularly Polarized Antenna Array for Satellite Communications in the X Band

A planar antenna is introduced that works as a portable system for X-band satellite communications. This antenna is low-profile and modular with dimensions of 40 × 40 × 2.5 × cm. It is composed of a square array of 144 printed circuit elements that cover a wide bandwidth (14.7%) for transmission and reception along with dual and interchangeable circular polarization. A radiation efficiency above 50% is achieved by a low-loss stripline feeding network. This printed antenna has a 3 dB beamwidth of 5°, a maximum gain of 26 dBi and an axial ratio under 1.9 dB over the entire frequency band. The complete design of the antenna is shown, and the measurements are compared with simulations to reveal very good agreement.

Modular Planar Antenna at X-band for satellite communications

An antenna which has been conceived as a portable system for satellite communications based on the recommendations ITU-R S.580-6 [1] and ITU-R S.465-5 [2] for small antennas, i.e., with a diameter lower than 50 wavelengths, is introduced. It is a planar and a compact structure with a size of 40×40×2 cm. The antenna is formed by an array of 256 printed elements covering a large bandwidth (14.7%) at X-Band. The specification includes transmission (Tx) and reception (Rx) bands simultaneously. The printed antenna has a radiation pattern with a 3dB beamwidth of 5°, over a 31dBi gain, and a dual and an interchangeable circular polarization

Mutual coupling reduction using EBG in steering antennas

In this letter, a dual circular polarized steering antenna for satellite communications in X-band is presented. This antenna consists of printed elements grouped in an array, able to work from 7.25 up to 8.4 GHz in both polarizations: left-handed circular polarization (LHCP) and right-handed circular polarization (RHCP). The module antenna is compact, with narrow beamwidth, and reaches a gain of 16 dBi. It has the capability to steer in elevation to and electronically with a Butler matrix. In order to reduce the mutual coupling between adjacent patches, electromagnetic band-gap (EBG) structures are introduced. These EBGs combine double-layer and edge location via in order to reduce the size, without changing the low-permittivity substrate, and therefore maintaining the high radiation efficiency of the antenna.

Contribución a los arrays de antenas activos en microondas = Contribution to active array antennas at microwave bands

Esta tesis que tiene por título "Contribución a los arrays de antenas activos en banda X", ha sido desarrollada por el estudiante de doctorado Gonzalo Expósito Domínguez, ingeniero de telecomunicación en el Grupo de Radiación del Departamento de Señales, Sistemas y Radiocomunicaciones de la ETSI de Telecomunicación de la Universidad Politécnica de Madrid bajo la dirección de los doctores Manuel Sierra Castañer y José Manuel Fernández González. Esta tesis contiene un profundo estudio del arte en materia de antenas activas en el campo de apuntamiento electrónico. Este estudio comprende desde los fundamentos de este tipo de antenas, problemas de operación y limitaciones hasta los sistemas actuales más avanzados. En ella se identifican las partes críticas en el diseño y posteriormente se llevan a la práctica con el diseño, simulación y construcción de un subarray de una antena integrada en el fuselaje de un avión para comunicaciones multimedia por satélite que funciona en banda X. El prototipo consta de una red de distribución multihaz de banda ancha y una antena planar. El objetivo de esta tesis es el de aplicar nuevas técnicas al diseño de antenas de apuntamiento electrónico. Es por eso que las contribuciones originales son la aplicación de barreras electromagnéticas entre elementos radiantes para reducir los acoplamientos mutuos en arrays de exploración electrónica y el diseño de redes desfasadoras sencillas en las que no son necesarios complejos desfasadores para antenas multihaz. Hasta la fecha, las barreras electromagnéticas, Electronic Band Gap (EBG), se construyen en sustratos de permitividad alta con el fin de aumentar el espacio disponible entre elementos radiantes y reducir el tamaño de estas estructuras. Sin embargo, la utilización de sustratos de alta permitividad aumenta la propagación por ondas de superficie y con ellas el acoplo mutuo. Utilizando sustratos multicapa y colocando la vía de las estructuras en su borde, en vez de en su centro, se consigue reducir el tamaño sin necesidad de usar sustratos de alta permitividad, reducir la eficiencia de radiación de la antena o aumentar la propagación por ondas de superficie. La última parte de la tesis se dedica a las redes conmutadoras y desfasadoras para antenas multihaz. El diseño de las redes de distribución para antenas son una parte crítica ya que se comportan como un atenuador a la entrada de la cadena receptora, modificando en gran medida la figura de ruido del sistema. Las pérdidas de un desfasador digital varían con el desfase introducido, por ese motivo es necesario caracterizar y calibrar los dispositivos correctamente. Los trabajos presentados en este manuscrito constan de un desfasador reflectivo con un conmutador doble serie paralelo para igualar las pérdidas de inserción en los dos estados y también un conmutador de una entrada y dos salidas cuyos puertos están adaptados en todo momento independientemente del camino del conmutador para evitar las reflexiones y fugas entre redes o elementos radiantes. El tomo finaliza con un resumen de las publicaciones en revistas científicas y ponencias en congresos, nacionales e internacionales, el marco de trabajo en el que se ha desarrollado, las colaboraciones que se han realizado y las líneas de investigación futuras. ABSTRACT This thesis was carried out in the Radiation Group of the Signals, Systems and Radiocomunications department of ETSI de Telecomunicación from Technical University of Madrid. Its title is "Contribution to active array antennas at X band" and it is developed by Gonzalo Expósito Domínguez, Electrical Engineer MsC. under the supervision of Prof. Dr. Manuel Sierra Castañer and Dr. José Manuel Fernández González. This thesis is focused on active antennas, specifically multibeam and electronic steering antenas. In the first part of the thesis a thorough description of the state of the art is presented. This study compiles the fundamentals of this antennas, operation problems and limits, up to the breakthrough applications. The critical design problems are described to use them eventually in the design, simulation and prototyping of an airborne steering array antenna for satellite communication at X band. The main objective of this thesis is to apply new techniques to the design of electronically steering antennas. Therefore the new original contributions are the application of Electromagnetic Band Gap materials (EBG) between radiating elements to reduce the mutual coupling when phase shift between elements exist and phase shifting networks where special characteristics are required. So far, the EBG structures have been constructed with high permitivity substrates in order to increase the available space between radiating elements and reduce the size of the structures. However, the surface wave propagation modes are enhanced and therefore the mutual coupling increases when high permitivity substrates are used. By using multilayered substrates and edge location via, the size is reduced meanwhile low permitivity substrates are used without reducing the radiation efficiency or enhancing the surface propagation modes. The last part of the thesis is focused on the phase shifting distribution networks for multibeam antennas. This is a critical part in the antenna design because the insertion loss in the distribution network behaves as an attenuator located in the first place in a receiver chain. The insertion loss will affect directly to the receiver noise figure and the insertion loss in a phase shifter vary with the phase shift. Therefore the devices must be well characterized and calibrated in order to obtain a properly operation. The work developed in this thesis are a reflective phase shifter with a series-shunt switch in order to make symmetrical the insertion loss for the two states and a complex Single Pole Double Through (SPDT) with matched ports in order to reduce the reflections and leakage between feeding networks and radiating elements. The end of this Ph D. dissertation concludes with a summary of the publications in national and international conferences and scientific journals, the collaborations carried out along the thesis and the future research lines.

GEODA-SARAS: Multi-Phased array planar antenna for satellite communications

Nowadays, earth stations have as a common feature the use of large reflector antenna for downloading data from satellites. Large reflectors have impairments such as mechanical complexity, low flexibility and high cost. Thus, the feasibility of other antenna technologies must be evaluated, such as conformal adaptive antennas based on multiple planar active arrays. In the scenery under study, the capability to track several satellites simultaneously, higher flexibility, lower production and maintenance cost, modularity and a more efficient use of the spectrum; are the most important advantage to boost up active antenna arrays over large dishes.

Large aperture antenna arrays with subband delay compensation for reception of wideband satellite signals

Con esta disertación se pretenden resolver algunos de los problemas encontrados actualmente en la recepción de señales de satélites bajo dos escenarios particularmente exigentes: comunicaciones de Espacio Profundo y en banda Ka. Las comunicaciones con sondas de Espacio Profundo necesitan grandes aperturas en tierra para poder incrementar la velocidad de datos. La opción de usar antennas con diámetro mayor de 35 metros tiene serios problemas, pues antenas tan grandes son caras de mantener, difíciles de apuntar, pueden tener largos tiempo de reparación y además tienen una efeciencia decreciente a medida que se utilizan bandas más altas. Soluciones basadas en agrupaciones de antenas de menor tamaño (12 ó 35 metros) son mas ecónomicas y factibles técnicamente. Las comunicaciones en banda Ka tambien pueden beneficiarse de la combinación de múltiples antennas. Las antenas de menor tamaño son más fáciles de apuntar y además tienen un campo de visión mayor. Además, las técnicas de diversidad espacial pueden ser reemplazadas por una combinación de antenas para así incrementar el margen del enlace. La combinación de antenas muy alejadas sobre grandes anchos de banda, bien por recibir una señal de banda ancha o múltiples de banda estrecha, es complicada técnicamente. En esta disertación se demostrará que el uso de conformador de haz en el dominio de la frecuencia puede ayudar a relajar los requisitos de calibración y, al mismo tiempo, proporcionar un mayor campo de visión y mayores capacidades de ecualización. Para llevar esto a cabo, el trabajo ha girado en torno a tres aspectos fundamentales. El primero es la investigación bibliográfica del trabajo existente en este campo. El segundo es el modelado matemático del proceso de combinación y el desarrollo de nuevos algoritmos de estimación de fase y retardo. Y el tercero es la propuesta de nuevas aplicaciones en las que usar estas técnicas. La investigación bibliográfica se centra principalmente en los capítulos 1, 2, 4 y 5. El capítulo 1 da una breve introducción a la teoría de combinación de antenas de gran apertura. En este capítulo, los principales campos de aplicación son descritos y además se establece la necesidad de compensar retardos en subbandas. La teoría de bancos de filtros se expone en el capítulo 2; se selecciona y simula un banco de filtros modulado uniformemente con fase lineal. Las propiedades de convergencia de varios filtros adaptativos se muestran en el capítulo 4. Y finalmente, las técnicas de estimación de retardo son estudiadas y resumidas en el capítulo 5. Desde el punto de vista matemático, las principales contribución de esta disertación han sido: • Sección 3.1.4. Cálculo de la desviación de haz de un conformador de haz con compensación de retardo en pasos discretos en frecuencia intermedia. • Sección 3.2. Modelo matemático de un conformador de haz en subbandas. • Sección 3.2.2. Cálculo de la desviación de haz de un conformador de haz en subbandas con un buffer de retardo grueso. • Sección 3.2.4. Análisis de la influencia de los alias internos en la compensación en subbandas de retardo y fase. • Sección 3.2.4.2. Cálculo de la desviación de haz de un conformador de haz con compensación de retardo en subbandas. • Sección 3.2.6. Cálculo de la ganancia de relación señal a ruido de la agrupación de antenas en cada una de las subbandas. • Sección 3.3.2. Modelado de la función de transferencia de la agrupación de antenas bajo errores de estimación de retardo. • Sección 3.3.3. Modelado de los efectos de derivas de fase y retardo entre actualizaciones de las estimaciones. • Sección 3.4. Cálculo de la directividad de la agrupación de antenas con y sin compensación de retardos en subbandas. • Sección 5.2.6. Desarrollo de un algorimo para estimar la fase y el retardo entre dos señales a partir de su descomposición de subbandas bajo entornos estacionarios. • Sección 5.5.1. Desarrollo de un algorimo para estimar la fase, el retardo y la deriva de retardo entre dos señales a partir de su descomposición de subbandas bajo entornos no estacionarios. Las aplicaciones que se pueden beneficiar de estas técnicas son descritas en el capítulo 7: • Sección 6.2. Agrupaciones de antenas para comunicaciones de Espacio Profundo con capacidad multihaz y sin requisitos de calibración geométrica o de retardo de grupo. • Sección 6.2.6. Combinación en banda ancha de antenas con separaciones de miles de kilómetros, para recepción de sondas de espacio profundo. • Secciones 6.4 and 6.3. Combinación de estaciones remotas en banda Ka en escenarios de diversidad espacial, para recepción de satélites LEO o GEO. • Sección 6.3. Recepción de satélites GEO colocados con arrays de antenas multihaz. Las publicaciones a las que ha dado lugar esta tesis son las siguientes • A. Torre. Wideband antenna arraying over long distances. Interplanetary Progress Report, 42-194:1–18, 2013. En esta pulicación se resumen los resultados de las secciones 3.2, 3.2.2, 3.3.2, los algoritmos en las secciones 5.2.6, 5.5.1 y la aplicación destacada en 6.2.6. • A. Torre. Reception of wideband signals from geostationary collocated satellites with antenna arrays. IET Communications, Vol. 8, Issue 13:2229–2237, September, 2014. En esta segunda se muestran los resultados de la sección 3.2.4, el algoritmo en la sección 5.2.6.1 , y la aplicación mostrada en 6.3. ABSTRACT This dissertation is an attempt to solve some of the problems found nowadays in the reception of satellite signals under two particular challenging scenarios: Deep Space and Ka-band communications. Deep Space communications require from larger apertures on ground in order to increase the data rate. The option of using single dishes with diameters larger than 35 meters has severe drawbacks. Such antennas are expensive to maintain, prone to long downtimes, difficult to point and have a degraded performance in high frequency bands. The array solution, either with 12 meter or 35 meter antennas is deemed to be the most economically and technically feasible solution. Ka-band communications can also benefit from antenna arraying technology. The smaller aperture antennas that make up the array are easier to point and have a wider field of view allowing multiple simultaneous beams. Besides, site diversity techniques can be replaced by pure combination in order to increase link margin. Combination of far away antennas over a large bandwidth, either because a wideband signal or multiple narrowband signals are received, is a demanding task. This dissertation will show that the use of frequency domain beamformers with subband delay compensation can help to ease calibration requirements and, at the same time, provide with a wider field of view and enhanced equalization capabilities. In order to do so, the work has been focused on three main aspects. The first one is the bibliographic research of previous work on this subject. The second one is the mathematical modeling of the array combination process and the development of new phase/delay estimation algorithms. And the third one is the proposal of new applications in which these techniques can be used. Bibliographic research is mainly done in chapters 1, 2, 4 and 5. Chapter 1 gives a brief introduction to previous work in the field of large aperture antenna arraying. In this chapter, the main fields of application are described and the need for subband delay compensation is established. Filter bank theory is shown in chapter 2; a linear phase uniform modulated filter bank is selected and simulated under diverse conditions. The convergence properties of several adaptive filters are shown in chapter 4. Finally, delay estimation techniques are studied and summarized in chapter 5. From a mathematical point of view, the main contributions of this dissertation have been: • Section 3.1.4. Calculation of beam squint of an IF beamformer with delay compensation at discrete time steps. • Section 3.2. Establishment of a mathematical model of a subband beamformer. • Section 3.2.2. Calculation of beam squint in a subband beamformer with a coarse delay buffer. • Section 3.2.4. Analysis of the influence of internal aliasing on phase and delay subband compensation. • Section 3.2.4.2. Calculation of beam squint of a beamformer with subband delay compensation. • Section 3.2.6. Calculation of the array SNR gain at each of the subbands. • Section 3.3.2. Modeling of the transfer function of an array subject to delay estimation errors. • Section 3.3.3. Modeling of the effects of phase and delay drifts between estimation updates. • Section 3.4. Calculation of array directivity with and without subband delay compensation. • Section 5.2.6. Development of an algorithm to estimate relative delay and phase between two signals from their subband decomposition in stationary environments. • Section 5.5.1. Development of an algorithm to estimate relative delay rate, delay and phase between two signals from their subband decomposition in non stationary environments. The applications that can benefit from these techniques are described in chapter 7: • Section 6.2. Arrays of antennas for Deep Space communications with multibeam capacity and without geometric or group delay calibration requirement. • Section 6.2.6. Wideband antenna arraying over long distances, in the range of thousands of kilometers, for reception of Deep Space probes. • Sections 6.4 y 6.3. Combination of remote stations in Ka-band site diversity scenarios for reception of LEO or GEO satellites. • Section 6.3. Reception of GEO collocated satellites with multibeam antenna arrays. The publications that have been made from the work in this dissertation are • A. Torre. Wideband antenna arraying over long distances. Interplanetary Progress Report, 42-194:1–18, 2013. This article shows the results in sections 3.2, 3.2.2, 3.3.2, the algorithms in sections 5.2.6, 5.5.1 and the application in section 6.2.6. • A. Torre. Reception of wideband signals from geostationary collocated satellites with antenna arrays. IET Communications, Vol. 8, Issue 13:2229–2237, September, 2014. This second article shows among others the results in section 3.2.4, the algorithm in section 5.2.6.1 , and the application in section 6.3.

Novel dual-band single circular polarization antenna feeding network for satellite communications

In this paper a novel dual-band single circular polarization antenna feeding network for satellite communications is presented. The novel antenna feed chain1 is composed of two elements or subsystems, namely a diplexer and a bi-phase polarizer. In comparison with the classic topology based on an orthomode transducer and a dual-band polarizer, the proposed feed chain presents several advantages, such as compactness, modular design of the different components, broadband operation and versatility in the subsystems interconnection. The design procedure of this new antenna feed configuration is explained. Different examples of antenna feeding networks at 20/30 GHz are presented. It is pointed out the excellent results obtained in terms of isolation and axial ratio.

A Transportable Reflectarray Antenna for Satellite Ku-band Emergency Communications

The design of a Ku-band reconfigurable reflectarray antenna for emergency satellite communications is presented. Bidirectional high data rate satellite links are needed in emergency conditions where other telecommunication infrastructures are not available. In order to operate in this type of scenario, an antenna should be deployable, transportable, and easily repointable. The need of an automatic and fast satellite location and pointing system leads to a completely electronic reconfigurable antenna. The operative bandwidth is from 10.7 to 12.5 GHz for reception and from 14 up to 14.5 GHz for transmission (30% of relative bandwidth). The selected antenna architecture is based on a dual reflectarray system comprising a passive subreflectarray and an active main reflectarray made of reconfigurable 1-bit elementary cells based on PIN diodes.