Eduardo Carrasco
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Eduardo Carrasco has a total of 101 co-authors. Here are the top co-authors by number of shared publications:
- Jose Antonio Encinar
Information Processing and Telecommunications Center, Universidad Politcnica de Madrid (UPM), Madrid, Spain
26 shared publications Mariano Barba
Department of Electromagnetism and Circuit Theory Polytechnic University of Madrid Av. Complutense 30 28040 Madrid Spain
13 shared publications- Manuel Arrebola
Universidad de Oviedo, Gijón, Spain
9 shared publications - Gerardo Perez-Palomino
Department of Electromagnetism and Circuit Theory, Universidad Politécnica de Madrid, Madrid, Spain
7 shared publications Julien Perruisseau-Carrier
Ecole Polytechnique Federale de Lausanne, EPFL, Lausanne, Switzerland
6 shared publicationsRafael Florencio
University of Alcalá, Alcalá de Henares, 28870, Spain
5 shared publications
Latest Publications
- Open Access
- 18 August 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Wireless Communications Letters
- Vol. 14 (11) , 3630-3634
mmWave Dual-Coverage RIS-Aided 6G Wireless Communications: Experimental Demonstration
The integration of 5G wireless communication with millimeter wave reconfigurable intelligent surfaces (RIS) has received moderate attention in previous studies. In this paper, we designed, manufactured, and integrated a 27 GHz RIS prototype into a custom-built 5G NR platform that is compliant with the 3GPP standard. We propose a dual-coverage RIS designed with a single-layer reflecting panel to enhance mmWave 6G communication. Through a series of receiver points in an indoor environment, we demonstrated the effectiveness of dual-coverage RIS-aided 6G communication at 27 GHz in establishing a reliable end-to-end link. Experimental results reveal significant improvements in key performance indicators such as the received power of the reference signal (RSRP), the signal-to-interference and noise ratio (SINR), and the error vector magnitude (EVM). The RIS prototype was evaluated through field measurements and compared with two end-to-end mmWave communication scenarios.
- 18 August 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Wireless Communications Letters
- Vol. 14 (11) , 3630-3634
Open AccessmmWave Dual-Coverage RIS-Aided 6G Wireless Communications: Experimental Demonstration
The integration of 5G wireless communication with millimeter wave reconfigurable intelligent surfaces (RIS) has received moderate attention in previous studies. In this paper, we designed, manufactured, and integrated a 27 GHz RIS prototype into a custom-built 5G NR platform that is compliant with the 3GPP standard. We propose a dual-coverage RIS designed with a single-layer reflecting panel to enhance mmWave 6G communication. Through a series of receiver points in an indoor environment, we demonstrated the effectiveness of dual-coverage RIS-aided 6G communication at 27 GHz in establishing a reliable end-to-end link. Experimental results reveal significant improvements in key performance indicators such as the received power of the reference signal (RSRP), the signal-to-interference and noise ratio (SINR), and the error vector magnitude (EVM). The RIS prototype was evaluated through field measurements and compared with two end-to-end mmWave communication scenarios.
- Open Access
- 8 July 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Green Communications and Networking
- Vol. 10, 412-425
Prototype and Performance Assessment of mmWave Active RIS-Enhanced 6G Wireless Communications
This paper presents an innovative approach for the millimeter-wave (mmWave) band that utilizes an active reconfigurable intelligent surface (RIS) to implement a mmWave end-to-end wireless communication system. We propose a new type of RIS based on Liquid Crystals (LC), called LC-RIS, where each cell of the RIS array is electronically reconfigurable and can reflect the incident signal with an adjustable phase shift. For easy and low-cost manufacturing, we designed and fabricated a single polarization active LC-RIS that operates at 27 GHz and that can be used in 6G mobile communication networks. To the best of the authors knowledge, this is the first study to integrate an active LC-RIS prototype in a realistic environment into a fully open and flexible platform. A series of experiments were conducted with the fabricated active LC-RIS prototype to verify its effectiveness in both laboratory and corridor scenarios. The experiments and resulting studies revealed significant improvements in the signal strength and signal-to-noise ratio in the deployed RIS-aided mmWave wireless communication system.
- 8 July 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Green Communications and Networking
- Vol. 10, 412-425
Open AccessPrototype and Performance Assessment of mmWave Active RIS-Enhanced 6G Wireless Communications
This paper presents an innovative approach for the millimeter-wave (mmWave) band that utilizes an active reconfigurable intelligent surface (RIS) to implement a mmWave end-to-end wireless communication system. We propose a new type of RIS based on Liquid Crystals (LC), called LC-RIS, where each cell of the RIS array is electronically reconfigurable and can reflect the incident signal with an adjustable phase shift. For easy and low-cost manufacturing, we designed and fabricated a single polarization active LC-RIS that operates at 27 GHz and that can be used in 6G mobile communication networks. To the best of the authors knowledge, this is the first study to integrate an active LC-RIS prototype in a realistic environment into a fully open and flexible platform. A series of experiments were conducted with the fabricated active LC-RIS prototype to verify its effectiveness in both laboratory and corridor scenarios. The experiments and resulting studies revealed significant improvements in the signal strength and signal-to-noise ratio in the deployed RIS-aided mmWave wireless communication system.
- 4 June 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 72 (7) , 5626-5636
Electronically Reconfigurable Reflectarray Antenna Based on Single-Layer Liquid Crystal With Independent Dual-Polarization Control
This paper introduces a low-cost, easy-to-manufacture, dual polarization reconfigurable reflectarray antenna based on Liquid Crystal (LC) that operates at W-band. The antenna is electrically large and is capable of independently steering the beam of two orthogonal polarizations. Two different implementations of single-layer unit cells (single resonant and multi-resonant) capable of providing suitable phase range to independently control the two RF polarizations with enough isolation have been investigated. The single resonant cell was finally used to design, manufacture and test a complete reflectarray antenna made of 55×55 elements, for which an accurate and efficient modeling of the cells was implemented. The effect of the LC bias lines is minimized by following a thorough impact study. At a cell level, the measurements validate both the modeling and the capability of the LC to be locally biased at the same cell provided that the biasing network and the resonators of each polarization are properly distributed. At an antenna level, the measurements are predicted by simulations with excellent accuracy, which validates the design and modeling process. The measured antenna shows 35° of 1D scanning range with 25dBi gain and a maximum SLL of -9dB in the entire range for both polarizations at 98 GHz.
- 4 June 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 72 (7) , 5626-5636
Electronically Reconfigurable Reflectarray Antenna Based on Single-Layer Liquid Crystal With Independent Dual-Polarization Control
This paper introduces a low-cost, easy-to-manufacture, dual polarization reconfigurable reflectarray antenna based on Liquid Crystal (LC) that operates at W-band. The antenna is electrically large and is capable of independently steering the beam of two orthogonal polarizations. Two different implementations of single-layer unit cells (single resonant and multi-resonant) capable of providing suitable phase range to independently control the two RF polarizations with enough isolation have been investigated. The single resonant cell was finally used to design, manufacture and test a complete reflectarray antenna made of 55×55 elements, for which an accurate and efficient modeling of the cells was implemented. The effect of the LC bias lines is minimized by following a thorough impact study. At a cell level, the measurements validate both the modeling and the capability of the LC to be locally biased at the same cell provided that the biasing network and the resonators of each polarization are properly distributed. At an antenna level, the measurements are predicted by simulations with excellent accuracy, which validates the design and modeling process. The measured antenna shows 35° of 1D scanning range with 25dBi gain and a maximum SLL of -9dB in the entire range for both polarizations at 98 GHz.
- 5 June 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 71 (8) , 6535-6545
Characterization and Application of Dual-Frequency Liquid-Crystal Mixtures in mm-Wave Reflectarray Cells to Improve Their Temporal Response
Liquid Crystal-based mm-wave spatially fed antennas with electronic reconfiguration are a promising solution at the higher frequencies required in next generation networks. However, one of the main drawbacks of the technology in these bands stems from the high reconfigurability times they present. Through this work, a relevant step towards overcoming the temporal problem by using Dual Frequency Liquid Crystals (DFLC) is presented. This paper details, for the first time, both the electromagnetic and temporal characterization of four commercially available DFLC mixtures in W-band, enabling their use in designing faster devices. To evaluate the experimental characterization, a reflectarray surface (made of 50x50 cells) specifically designed to achieve fast switching times with a sufficient phase range has been manufactured and measured. For this cell, a preliminary addressing technique based on overdriving has been used, exhibiting reconfigurability (rise and decay) times of 20 ms, one order of magnitude faster than the current state of the art of LC-based mm-wave planar devices. The measured results match the simulations, and reveal that a precisely designed biasing technique using overdrive must be used for DFLC-cells to achieve time reduction. Additionally, the benefits of this technology compared with other LC acceleration strategies in mm-wave are discussed.
- 5 June 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 71 (8) , 6535-6545
Characterization and Application of Dual-Frequency Liquid-Crystal Mixtures in mm-Wave Reflectarray Cells to Improve Their Temporal Response
Liquid Crystal-based mm-wave spatially fed antennas with electronic reconfiguration are a promising solution at the higher frequencies required in next generation networks. However, one of the main drawbacks of the technology in these bands stems from the high reconfigurability times they present. Through this work, a relevant step towards overcoming the temporal problem by using Dual Frequency Liquid Crystals (DFLC) is presented. This paper details, for the first time, both the electromagnetic and temporal characterization of four commercially available DFLC mixtures in W-band, enabling their use in designing faster devices. To evaluate the experimental characterization, a reflectarray surface (made of 50x50 cells) specifically designed to achieve fast switching times with a sufficient phase range has been manufactured and measured. For this cell, a preliminary addressing technique based on overdriving has been used, exhibiting reconfigurability (rise and decay) times of 20 ms, one order of magnitude faster than the current state of the art of LC-based mm-wave planar devices. The measured results match the simulations, and reveal that a precisely designed biasing technique using overdrive must be used for DFLC-cells to achieve time reduction. Additionally, the benefits of this technology compared with other LC acceleration strategies in mm-wave are discussed.
- Open Access
- 2 December 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Access
- Vol. 10, 127928-127938
mm-Wave Metasurface Unit Cells Achieving Millisecond Response Through Polymer Network Liquid Crystals
The slow response time of planar Liquid Crystal (LC)-based phase-shift metasurface and Reconfigurable Intelligent Surfaces (RIS) cells is addressed in this paper by introducing a polymer network LC (PNLC) mixture suitable at mm-wave bands. Since the conventional effective isotropic model used in optical cells for describing the PNLC is not suitable in RF, an effective anisotropic and uniaxial model for such mixture is provided and experimentally validated at 100 GHz for the first time. In order to compare the temporal performance and tunability of the PNLC, transmissive and reflective cells, containing conventional LC and PNLC, have been manufactured and measured at optical and mm-wave frequencies. The temporal responses of PNLC are also compared for both RF and optical cells, obtaining relevant differences between their improvement factors, which are also discussed. Specifically, a 50 fold response time improvement is attained in cells designed to work at 100 GHz, although at the expense of a 3X tunability reduction. The model, which is robust to varying angle of incidence and cell dimensions, has been experimentally validated by designing and manufacturing a PNLC reflectarray cell of a different geometry. The cell shows reconfigurability times of 210ms, representing a significant improvement with respect to state-of-the-art response time in mm-wave cells, which are in the order of several seconds.
- 2 December 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Access
- Vol. 10, 127928-127938
Open Accessmm-Wave Metasurface Unit Cells Achieving Millisecond Response Through Polymer Network Liquid Crystals
The slow response time of planar Liquid Crystal (LC)-based phase-shift metasurface and Reconfigurable Intelligent Surfaces (RIS) cells is addressed in this paper by introducing a polymer network LC (PNLC) mixture suitable at mm-wave bands. Since the conventional effective isotropic model used in optical cells for describing the PNLC is not suitable in RF, an effective anisotropic and uniaxial model for such mixture is provided and experimentally validated at 100 GHz for the first time. In order to compare the temporal performance and tunability of the PNLC, transmissive and reflective cells, containing conventional LC and PNLC, have been manufactured and measured at optical and mm-wave frequencies. The temporal responses of PNLC are also compared for both RF and optical cells, obtaining relevant differences between their improvement factors, which are also discussed. Specifically, a 50 fold response time improvement is attained in cells designed to work at 100 GHz, although at the expense of a 3X tunability reduction. The model, which is robust to varying angle of incidence and cell dimensions, has been experimentally validated by designing and manufacturing a PNLC reflectarray cell of a different geometry. The cell shows reconfigurability times of 210ms, representing a significant improvement with respect to state-of-the-art response time in mm-wave cells, which are in the order of several seconds.
- Open Access
- 26 October 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Open Journal of Antennas and Propagation
- Vol. 3, 1234-1241
Influence of the Mesh Size on the Computation of the Close Near Fields of Dipole Antennas
While evaluating the near field of dipole antennas, it is noted that different software suites yield values of the electric and the magnetic fields, at the surface of antennas, that can be substantially different, especially at the tips and at the feed gap. The close near field of dipoles has not been yet analysed in detail. An asymptotic expansion method for the near fields at the surface of these antennas has been developed and compared to the computed fields. The results show that the software of the computed field should not use a uniform mesh. The mesh should be much tighter at the metal extremities than in the dipole body. The proposed technique can be used to check complex field computations, producing diverging values, with simple analytical equations.
- 26 October 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Open Journal of Antennas and Propagation
- Vol. 3, 1234-1241
Open AccessInfluence of the Mesh Size on the Computation of the Close Near Fields of Dipole Antennas
While evaluating the near field of dipole antennas, it is noted that different software suites yield values of the electric and the magnetic fields, at the surface of antennas, that can be substantially different, especially at the tips and at the feed gap. The close near field of dipoles has not been yet analysed in detail. An asymptotic expansion method for the near fields at the surface of these antennas has been developed and compared to the computed fields. The results show that the software of the computed field should not use a uniform mesh. The mesh should be much tighter at the metal extremities than in the dipole body. The proposed technique can be used to check complex field computations, producing diverging values, with simple analytical equations.
- 3 October 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 70 (12) , 11847-11857
Dynamic Modeling of Liquid Crystal-Based Metasurfaces and Its Application to Reducing Reconfigurability Times
This paper describes and validates for the first time the dynamic modelling of Liquid Crystal (LC)-based planar multi-resonant cells, as well as its use as bias signals synthesis tool to improve their reconfigurability time. The dynamic LC director equation is solved in the longitudinal direction through the finite elements method, which provides the z - and time-dependent inhomogeneous permittivity tensor used in an electromagnetic simulator to evaluate the cells behaviour. The proposed model has been experimentally validated using reflective cells for phase control (reflectarray) and measuring the transient phase, both in excitation and relaxation regimes. It is shown how a very reduced number of stratified layers are needed to model the material inhomogeneity, and that even an homogeneous effective tensor can be used in most of the cases, which allows a model simplification suitable for design procedures without losing accuracy. Consequently, a novel bias signal design tool is proposed to significantly reduce the transition times of LC cells, and hence, of electrically large antennas composed of them. These tools, similar to those used in optical displays, are experimentally validated for the first time at mm- and sub-mm wave frequencies in this work, obtaining an improvement of orders of magnitude.
- 3 October 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 70 (12) , 11847-11857
Dynamic Modeling of Liquid Crystal-Based Metasurfaces and Its Application to Reducing Reconfigurability Times
This paper describes and validates for the first time the dynamic modelling of Liquid Crystal (LC)-based planar multi-resonant cells, as well as its use as bias signals synthesis tool to improve their reconfigurability time. The dynamic LC director equation is solved in the longitudinal direction through the finite elements method, which provides the z - and time-dependent inhomogeneous permittivity tensor used in an electromagnetic simulator to evaluate the cells behaviour. The proposed model has been experimentally validated using reflective cells for phase control (reflectarray) and measuring the transient phase, both in excitation and relaxation regimes. It is shown how a very reduced number of stratified layers are needed to model the material inhomogeneity, and that even an homogeneous effective tensor can be used in most of the cases, which allows a model simplification suitable for design procedures without losing accuracy. Consequently, a novel bias signal design tool is proposed to significantly reduce the transition times of LC cells, and hence, of electrically large antennas composed of them. These tools, similar to those used in optical displays, are experimentally validated for the first time at mm- and sub-mm wave frequencies in this work, obtaining an improvement of orders of magnitude.
- Open Access
- 11 April 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Open Journal of Antennas and Propagation
- Vol. 3, 425-434
Design of Microfluidic Reflectarray Elements for Multi-Reconfiguration Using Liquid Metal
Using an alloy of non-toxic liquid metal (Galinstan) is proposed to implement multi-reconfiguration in reflectarray elements. Reflectarray antennas are an interesting technology for dynamically controlling, simultaneously or individually, different properties of the antenna (beam shape and pointing direction, field polarization, and frequency of operation) according to the system’s demand. The use of liquid metal, which can potentially be used to re-shape the topology of the unit cell, along with advances in the micro-and nanofluidics field, provides more flexibility for efficiently implementing such multi-reconfiguration. A frequency-reconfigurable reflectarray element is based on the well-known aperture-coupled cell, and a phase-reconfigurable cell based on single-and multi-resonance dipoles is proposed at 28 GHz. One advantage of microfluidics is that the concept can easily be extended to much higher frequencies, where other devices start to be expensive, inefficient, or limited in terms of multi-reconfiguration. The microfluidic technology required to implement the dipole-based element is demonstrated using a microfluidic burst-valve chip. Additionally, a simplified RF proof-of-concept is presented using the well-known waveguide simulator technique from 15 GHz to 22 GHz (WR51). The results obtained constitute an important first step toward the implementation of multi-reconfigurable reflectarray antennas.
- 11 April 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Open Journal of Antennas and Propagation
- Vol. 3, 425-434
Open AccessDesign of Microfluidic Reflectarray Elements for Multi-Reconfiguration Using Liquid Metal
Using an alloy of non-toxic liquid metal (Galinstan) is proposed to implement multi-reconfiguration in reflectarray elements. Reflectarray antennas are an interesting technology for dynamically controlling, simultaneously or individually, different properties of the antenna (beam shape and pointing direction, field polarization, and frequency of operation) according to the system’s demand. The use of liquid metal, which can potentially be used to re-shape the topology of the unit cell, along with advances in the micro-and nanofluidics field, provides more flexibility for efficiently implementing such multi-reconfiguration. A frequency-reconfigurable reflectarray element is based on the well-known aperture-coupled cell, and a phase-reconfigurable cell based on single-and multi-resonance dipoles is proposed at 28 GHz. One advantage of microfluidics is that the concept can easily be extended to much higher frequencies, where other devices start to be expensive, inefficient, or limited in terms of multi-reconfiguration. The microfluidic technology required to implement the dipole-based element is demonstrated using a microfluidic burst-valve chip. Additionally, a simplified RF proof-of-concept is presented using the well-known waveguide simulator technique from 15 GHz to 22 GHz (WR51). The results obtained constitute an important first step toward the implementation of multi-reconfigurable reflectarray antennas.
- 22 March 2021
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-5
W-Band Confocal Antenna System Based on Liquid Crystal Reflectarray for Beam Scanning Applications
A confocal antenna system is designed and simulated to demonstrate beam scanning capabilities at W-band. The steering component is a reconfigurable reflectarray based on liquid crystal (LC) technology. Full-wave analysis is performed to obtain the frequency response of the reflectarray cells while Physical Theory of Diffraction (PTD) and Physical Optics (PO) are used to calculate reflected fields and radiation patterns. The simulated results give a maximum gain of 30 dB and a scanning range of 20° in both planes φ = 0° and φ=90°.
- 22 March 2021
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-5
W-Band Confocal Antenna System Based on Liquid Crystal Reflectarray for Beam Scanning Applications
A confocal antenna system is designed and simulated to demonstrate beam scanning capabilities at W-band. The steering component is a reconfigurable reflectarray based on liquid crystal (LC) technology. Full-wave analysis is performed to obtain the frequency response of the reflectarray cells while Physical Theory of Diffraction (PTD) and Physical Optics (PO) are used to calculate reflected fields and radiation patterns. The simulated results give a maximum gain of 30 dB and a scanning range of 20° in both planes φ = 0° and φ=90°.
- Open Access
- 27 February 2020
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Access
- Vol. 8, 44947-44956
Analysis and Design of Reflectarray Antennas Based on Delay Lines: A Filter Perspective
The analysis and design of reflectarray (RA) antennas based in delay lines is introduced for the first time from a filter perspective. To this purpose, each unit-cell of the RA is considered as a network composed of two ports, one being the delay line and the other one the free-space. This approach allows to borrow the coupling matrix formalism from filter theory and apply it to design unit-cells exhibiting broadband operation together with very sharp frequency responses. The concept is demonstrated with the aid of planar printed unit-cells coupled to substrate integrated waveguides (SIWs) through slots, a configuration that offers significant advantages to shape its frequency response while providing relatively low loss. With the aim of validation, a third order filter structure integrated in SIW-based unit-cells has been experimentally tested using the waveguide simulator technique, at a center frequency of 9 GHz. Measurements demonstrate a high-quality linear phase variation and range, and large frequency selectivity together with broadband response for the element of about 18%. The experimental results show the feasibility of this approach for the design of broadband reflectarray antennas exhibiting sharp gain responses. To illustrate the concept, a medium size reflectarray has been theoretically designed using the proposed unit cell at 9 GHz, showing a directive beam with 35.8 dB gain, sharp gain selectivity over 18 dB, and confirms the wide band operation with 20.3% bandwidth for a 3 dB gain variation.
- 27 February 2020
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Access
- Vol. 8, 44947-44956
Open AccessAnalysis and Design of Reflectarray Antennas Based on Delay Lines: A Filter Perspective
The analysis and design of reflectarray (RA) antennas based in delay lines is introduced for the first time from a filter perspective. To this purpose, each unit-cell of the RA is considered as a network composed of two ports, one being the delay line and the other one the free-space. This approach allows to borrow the coupling matrix formalism from filter theory and apply it to design unit-cells exhibiting broadband operation together with very sharp frequency responses. The concept is demonstrated with the aid of planar printed unit-cells coupled to substrate integrated waveguides (SIWs) through slots, a configuration that offers significant advantages to shape its frequency response while providing relatively low loss. With the aim of validation, a third order filter structure integrated in SIW-based unit-cells has been experimentally tested using the waveguide simulator technique, at a center frequency of 9 GHz. Measurements demonstrate a high-quality linear phase variation and range, and large frequency selectivity together with broadband response for the element of about 18%. The experimental results show the feasibility of this approach for the design of broadband reflectarray antennas exhibiting sharp gain responses. To illustrate the concept, a medium size reflectarray has been theoretically designed using the proposed unit cell at 9 GHz, showing a directive beam with 35.8 dB gain, sharp gain selectivity over 18 dB, and confirms the wide band operation with 20.3% bandwidth for a 3 dB gain variation.