3. 1 of the Microstrip Calculator using H2 in place of h, εr,eff can be computed as specified in Eq. Design ChallengesIn this paper, single-ended microstrip lines and differential microstrip lines loaded with MLC resonators are studied, and potential applications are highlighted. The HIGH level is brought up to a logic level (5 V, 3. Going to a coplanar arrangement can provide more losses when the coplanar ground is close, which forces a thinner microstrip (more loss from skin effect). A split with size of g in the centre of each unit cell forms a gap capacitance. Reply. In differential pairs, each trace in the pair carries the same magnitude, but opposite polarity. It is mainly . 5. Keywords:In this paper, a new high-gain differential-fed dual-polarized microstrip filtering antenna with high common-mode rejection is presented. 2. Each of the following PCB transmission lines requires controlled impedance: Single-ended microstrip; Differential pairs of microstrip; Embedded microstrip; Single-ended stripline; Differential pairs of striplineAbstract. By changing the width of 22 selected short sides of microstrip cross mesh array. Also, the upper and lower microstrip lines are connected by copper pin with radius r which goes. For a differential microstrip circuit, for example, the E fields would be coupled between two signal conductors on the top layer and the ground plane below. Choose Type. On the calculation link you have indicated, can you please elaborate on the item you selected (is it "Differential Microstrip Impedance Calculator" ?), and then how you entered the values ? does H is the total thickness of the PCB or is it the distance between the top track and another layer. 15 mm spacing. The dipole antenna with semi-elliptic arms is introduced to transform the differential mode of DML to the TE10 mode of the rectangular waveguide directly. A robust and wideband differential microstrip line-to-WR6-waveguide transition for mixed multilayer PCBs at D-band is presented. Going to a coplanar arrangement can provide more losses when the coplanar ground is close, which forces a thinner microstrip (more loss from skin effect). The patch performs not only as the radiator, but also as the last resonator of the whole filter. This is based on antipodal finlines and Vivaldi-like antennas on an ultrathin liquid crystal polymer substrate inserted in a WR10. This page covers Differential Microstrip Impedance Calculator . The same ideas also apply to differential pair routing. A microstrip highly sensitive differential sensor for complex permittivity characterization of urine samples was designed, fabricated and tested. 38. The common mode signal in the coupled microstrip lines is highly rejected. – Microstrip lines are either on the top or bottom layer of a PCB. Remember : before you start. Routing Differential Microstrip Traces with Controlled Impedance Differential microstrip routing in high speed PCB design requires careful. These antennas have many advantages like low profile, low cost,. Figure 5. Wideband Dual-Polarized Differential-Fed Filtering Microstrip Patch Antenna with High Suppression and Wide Stopband Quanwei Wu, Yan Shi , and Long Li School of Electronic Engineering, Xidian University, Xi’an, 710071 Shaanxi, China. Microstrip is a modification to the stripline by getting rid of the top half of the dielectric and the top ground plane. 6. Differential Microstrip Patch Antenna as Feeder of a Hyper-Hemispherical Lens for F-Band MIMO Radars Dragos Dancila1, Václav Valenta2, Alina-Cristina Bunea3, Dan Neculoiu3, Hermann Schumacher4 and Anders Rydberg1 1 Uppsala University, Department of Engineering Sciences, Uppsala, Sweden, dragos. Surface microstrip lines are formed by etching one surface of a double-sided material. Based on a quarter-wavelength resonator, a new PCB filter is designed having an electrical size of only 0. 8 mm 1 mm diffPairpitch swept from 15 mil to 50 mil for 100 ohm microstrip. We present improved expressions for calculating the impedance match feed positions of a differential feed. 250 mil Length 35 –8. The designs are presented and the performance of the transitions is evaluated in simulation and measurements. Therefore, it is interesting to design the differential transition structure between differential SIW and microstrip lines. 10a), the second one with the inset feed point (Fig. Save. Page 3 of 11 Published in SAFETY & EMC magazine, English language ddition, March 2008, Figure 3 DM signals are partially converted into common-mode (CM) noise by differential skew Imbalances also cause degraded immunity, because they cause a proportion of the CMFor microstrip, you can (approximately) cut metal losses in half by doubling the dielectric thickness and keeping the same system impedance. The free version allows calculation of simple single-ended and differential microstrip and stripline structures. 15 λ × 0. An example of the parameterized differential stripline. Therefore, in order to meet the increasing demands for multifunctional systems in the recent wireless applications such as 4G and 5G systems, differential-fed. Its single row design offers a narrow beam in elevation and a wide beam in azimuth. A microstrip patch antenna with dual polariza-tion functionality can be realized while each polarization is excited with two 180 out phase ports which is called ideal differential feed patch antenna. Microstrip Differential Impedance is a key parameter in the design of high-speed digital and high-frequency analog circuits. A four port two stage branch-line differential-mode BPF is first designed. The S 11 parameter and the 3D gain pattern for the two configurations are given by Fig. Four design variants of MS-to-RWG have been proposed and prepared for the D-band (110–170 GHz) application. 2023. Example. 46 mm width traces to obtain 100 Ohms ZDiff while using 0. The common mode signal in the coupled microstrip lines is highly rejected. In addition to the characteristic impedance of a transmission line, the tool also calculates. Fourth, it classifies differential antennas into wire, slot, microstrip, printed, and dielectric resonator antennas to better present their suitability and functionality. Differential surface coplanar waveguide with ground calculations: *0. Differential signaling in flex circuits follows the design method of surface microstrip transmission lines. This letter presents a vertically integrated differential filtering antenna. 5 dBi and bandwidth of 135 MHz was designed and used for RF-EH applications. for differential operation than the microstrip patch antenna [4]–[8], due to its origin from the single-ended monopole. The differentially-driven microstrip antennas were fabricated. A microstrip line is a type of electrical transmission line used to convey. Much has been written about terminating PCB traces in their characteristic impedance, to avoid signal reflections. Based on the traditional one, the. Both LM and CM converge to zero as spacing goes to infinity. Their performances. The antenna has a gain of 8. A simple way to determine whether the mode is even or odd is to visualize the E dataset from the mode as a vector plot. The presented antenna mainly consists of. The antenna is designed and fabricated for GSM900 band (890-960 MHz). The microstrip differential phase-length method is based on two transmission-line circuits fabricated on the same material and ideally in close proximity of each other. Also, it has got similar arrangement as regular microstrip routing. I assigned PerfE boundaries to each microstrip and pad element in yellow. A differential rectifier (DR). Such signals typically contain high harmonic signal content, with harmonic signal characteristics distorted as a result of dispersion. The developed antenna can be used in either center grounded or differential configuration. (© CC BY SA 3. 5 dBi at the center frequency and. Note: valid for (w/h) from 0. Single-Ended Impedance. Modeling approximation can be used to design the microstrip trace. In this paper, a compact full Ka-band differential microstrip line (DML) to rectangular waveguide transition is proposed. 1. A microstrip patch antenna is differentially excited by a balun BPF through a pair of coupling slots on the ground plane. Differential Impedance Ω. A polydimethylsiloxane substrate is attached with the microfluidic channel aligned to the meander slot of the CSRR. 0 (modified)) A microstrip line is single-ended 1 in the sense that the conductor geometry is asymmetric and the one conductor – namely, the ground plane – also normally serves as ground for the source and load. The edge couple differential symmetric stripline transmission line is a common technique for routing differential traces. In microstrip, this technique is ideal for routing differential pairs. Ebrahimi, A, Scott, J and Ghorbani, K (2018) Differential sensors using microstrip lines loaded with two split ring resonators. If there is an insulator around the wire then this calculator will be an estimate. This is essential to achieve common-mode noise suppression and keep the differential signals unaltered. The figure-1 above. 75 psTr Forward crosstalk design limit for crosstalk depends on signal. Using this property, the TDT times of. Due to these advantages over. My fab's standard 1st-to-2nd layer dielectric thickness on FR-4 is 213µm (7628H). On the PCB side, each resulting differential pair object will be added to the default Differential Pair class: <All Differential Pairs>. It is good practice to match differential trace length and to keep the distances between the. 5 dB. The most important design goal is to keep the wave impedance as homogenous as possible. Match the etch lengths of the relevant differential pair traces. There are four different types of impedance used in. A microstrip highly sensitive differential sensor for complex permittivity characterization of urine samples was designed, fabricated and tested. Common-mode (CM) noise on differential microstrip lines can be suppressed by PCB-embedded filters. Abstract: Differential microstrip antennas have received considerable attention in the design of highly integrated radio transceivers for wireless communications. The solid circles denote the resonators. 15 mm spacing. Dispersion can be a bad thing for high speed digital signals. Using the minimum trace spacing of 76. An embedded microstrip is a microstrip transmission line or flat conductor separated from the ground place via a dielectric material. 8x16 Patch Array Antenna: An 8x16 Patch Array Antenna was designed and simulated using the FDTD Simulator in EMPro. 1109/JSEN. The board house achieves these tolerances by observing how their process affects impedance historically,. A new microstrip tri-mode balun bandpass filter (BPF) with good filter-type and balun-type functions is presented. This article presents a magnetless differential microstrip circulator for high frequency operation. is desired. This provides common-mode noise cancellation in addition to isolation from other circuit blocks in an RF system. coupledmicrostrip = coupledMicrostripLine (Name=Value) sets Properties using one or more name-value arguments. Two symmetrical trapezoid-shaped slots and four triangle-cut corners on the ground are used to improve the impedance matching over the UWB. Together with the differential. 1. Abstract: A differential microstrip lines-based microwave microstrip sensor loaded with multiple magnetic-LC (MLC) resonators is proposed in this. It is shown that the potential method is equivalent to classical coupled. Differential Microstrip Impedance Calculator. This calculator is designed to calculate the characteristic impedance of a microstrip - a flat conductor suspended over a ground plane with a dielectric between them (see diagram below). However, few papers reported on the asymmetrical confinement. Fig. 2. 15 mm spacing. Types of Planar Transmission Lines. 5. It can smear out the edges, contributing to collapse of the eye. Dimensional units: mm mils Zo (single ended impedance, Ohms) = d (trace separation) = h (dielectric thickness) = Zd (Impedance, Ohms) = Differential Stripline Impedance. Next, a novel differential microstrip geometry specifically designed [12], [13] to suppress commonmode (CM) noise in specific frequency intervals is analyzed. The differential micro strip calculator requires some parameters. To use this calculator, simply input your microstrip geometry and Dk value, and the tool will return the differential impedance value for a pair of microstrip traces. A new kind of differential microstrip lines by introducing periodic subwavelength corrugation in the edge, which is able to support low-frequency spoof surface plasmon polaritions, is proposed. A novel differential microstrip patch antenna (DMPA) is designed for autonomous cruise control radar systems at 79 GHz. Microstrip differential pair routing: This technique is used for routing differential pairs and has the same arrangement as regular microstrip routing, but its model is more complex due to the additional. 2 of the Microstrip Calculator, h=H1 and b=H2-H1. To use this calculator, simply input your microstrip geometry and Dk value, and the tool will return the differential impedance value for a pair of microstrip traces. It also causes the characteristic impedance to be frequency dependent. 1 Even and Odd Mode Differential microstrip lines support two quasi-TEM modes, that is, the even and odd modes. The compact rat-race coupler and an 180 0 hybrid junction, provide the differential signal to the inverted microstrip patch. DOI: 10. Third, the effects of imperfect differential signal conditions on the performance of differentially-driven microstrip antennas are investigated for the first time. The sensing area contains two pairs of open-stub. 8 mm 1 mm diffPairpitch swept from 15 mil to 50 mil for 100 ohm microstrip. Antenna design and analysis. 8 dB. It is shown that the DSPA has a smaller. Formulas for the characteristic impedance and effective permittivity of symmetric coupled microstrip lines, with the cross section shown in Figure 5. A novel transition from rectangular waveguide to differential microstrip lines is illustrated in this paper. My design requires that the pairs travel over very thin flexible PCB, about 50mm total transmission length. 1. Typical PCIe boards with lower lane count can use a 4 layer stackup with two interior power planes and two signal layers on each outer surface (microstrip routing, Tx and Rx routed on different sides of the board). The proposed microstrip sensor is evolved from a traditional microstrip sensor, which has a single resonator unit excited by a single microstrip line. A balanced pair of microstrip lines is a convenient solution because it does not need an additional PCB layer, as a stripline does. Visit to learn more about the EEWeb communit. 02400 . IEEE Sensors Journal. as it can not only convert an input unbalanced. 29 mm width traces to obtain 100 Ohms ZDiff while using 0. These lines are placed on a dielectric material of height h and there is also some coupling between the lines. dBm to Watt converter Stripline Impedance calculator Microstrip line impedance Antenna G/T Noise temp. They cover the single-ended and equivalent differential microstrip line case and result from a common design procedure. Choose a routing style (microstrip, stripline, coplanar waveguide, single-ended vs differential) Calculate the trace width needed to give the required impedance; After everything is routed, it’s now a question of whether it’s appropriate to fill in the unused regions of the surface and internal layers with the grounded copper pour. (b) Equivalent circuit model of the sensor. P. First, the design formulas to determine the patch dimensions and the location of the feed point for single-ended microstrip antennas are examined to design differentially-driven microstrip antennas. differential stripline. Using Saturn's PCB Toolkit, it seems to be extremely difficult to achieve 100R. Two identical sensing elements. Intra-pair skew is the term used to define the difference between the etch length of the + and - lane of a differential pair. Where: Dkeff MS = effective dielectric constant surrounding the trace in microstripDifferential Microstrip Impedance. A differential microstrip antenna with improved gain for RF energy harvesting is presented in this paper. It is the same configuration as. These filters use resonating or broadband structures such that only the field from the CM signal couples to them. The edge coupled differential microstrip transmission line is a common technique for routing differential traces. – Microstrip lines are either on the top or bottom layer of a PCB. Because the differential impedance for symmetrical lines is equal to twice the odd-mode impedance, this measurement translates to an equivalent differential impedance of 85 Ω . 75 psTr Forward crosstalk design limit for crosstalk depends on signal risetime. Use an online differential microstrip impedance calculator; Use an online differential stripline impedance calculator; Calculating Differential vs. The proposed filter is composed of four quarter-wavelength coupled lines and four quarter-wavelength microstrip lines. What is more, the STM biases of the two SE. D = Distance between two differential pair signals; W = Width of a trace in a. Routing Differential Microstrip Traces with Controlled Impedance Differential microstrip routing in high speed PCB design requires careful impedance calculations. – Striplines are embedded between two reference layers, which results in a higher capacitance versus microstrip lines. – Microstrip lines are either on the top or bottom layer of a PCB. The feeding structure consisting of one line resonator and one H-shaped resonator as well as the microstrip antenna elements together provide the three stages in the bandpass filter design. 1. The designs are presented and the performance of the transitions is evaluated in. se 2 European. Their flexible layout is excellent, giving microstrip lines optimal versatility. Firstly, two symmetrical rectangular slots are cut on the radiating patch where the zero-current position of the TM 30 mode excites another resonant slot mode. 4 µm. You will want to control impedance with smaller variations in gap. Under differential-mode. However, I am having trouble achieving that in my design. Expand. For example, going from 10 mil to 20 mil alumina, or two-mil to four-mil GaAs. A Microwave Sensor Based on Frequency-Locked-Loop and Multiple Complementary Split-Ring Resonators for Retrieving Complex Permittivity of Liquid Samples. 4 GHz to 2. 6 Ω and ε e = 6. Explore Solutions The main difference between these types of traces is their location in the PCB: microstrips are on the surface layer, while striplines are on an inner. This calculator finds both odd and even transmission line impedance. It's time for a Microwaves101 Rule of Thumb! For pure alumina (ε R =9. To use this tool, enter the values for trace thickness, substrate height, trace width, trace spacing and subtrate dielectric in the calculator above. $$Z_{0_{diff}} = 2Z_{0_{odd}}$$ Common Impedance ($$Z_{0_{common}}$$): The impedance between. It is shown that the impedance of a differential feed antenna exhibits cosine squared behavior over the feed distance. A 50 Ω resistor is considered in series with the resonator. However, I am having trouble achieving that in my design. 12. It is identical to microstrip, but with ground planes both above and below the trace. IEEE Sensors Journal 2022-10-15 | Journal article. Using Saturn's PCB Toolkit, it seems to be extremely difficult to achieve 100R. Based on the traditional one, the differential microstrip lines are added, which can improve the. The two arms of the dipole antenna are connected together by a shorting strip to reduce the size of the dipole. 8), the ratio of W/H for fifty-ohm microstrip is about 95%. Matching the differential trace length and keeping the distances between the traces consistent is a common practice. This paper presents a planar grid array antenna with a 100 Ω differential microstrip line feed on a single layer of standard soft substrate. By understanding the microstrip transmission line, designers can. 46 mm width traces to obtain 100 Ohms ZDiff while using 0. For differential pairs of microstrips, the formulas involved are much more complicated because coupling between the traces in the differential pair must be included in the impedance calculation. However, I was wondering if it was possible to also have a controlled impedance. First: there is not such thing "differential microstrip". The closer you place the pairs together, the differential impedance gets smaller because LM and CM get larger. (In other words, 5 times Wn. This paper presents a microwave sensor using a pair of split-ring resonators (SRRs). Several people have developed procedures that can be used to synthesize microstrip lines. INTRODUCTION . It is shown that using current methods of length matching could make worse mode conversion and EM loss than with no length matching at all. A microstrip line is a transmission line that is a basic building block for most RF planar microwave devices. There are generally longer. The theory of microstrip antennas based on the improved cavity model is expanded to analyze the input impedance and radiation characteristics of the differentially-driven microstrip antennas. Microstrip Impedance -Differential Figure 8. Anyway, for nearby traces, we can have a differential microstrip arrangement, and consider the coupling factor between them. Two differential pairs of probe feeding ports are utilized. This configuration is known to be useful to enhance signal-to-noise ratio. Differential Trace Routing. The trace widths are 7 mils wide with 8 mil separation. There will be some slight coupling of the signal onto the adjacent grounds, so they should be adequately grounded by vias to the microstrip ground, at least every λ/10, to prevent coupling into structures that. You can rename differential pair objects on the PCB. In microstrip form, differential transmission lines are still somewhat dispersive, and this can be a concern for circuits handling wideband analog or high-speed digital signals. A split-ring resonator (SRR) with. 3 shall be used. A cross section of microstrip is shown in Figure 1. In the proposed antenna, the driven patch operates in a TM10 mode with an inherent radiation null caused by a higher mode TM12. This paper presents a wideband dual-polarized filtering antenna with high suppression level and wide stopband. The calculator below uses Wadell’s. , often all on the same PCB. Differential microstrip impedance calculator is an online electronic tool to measure the opposition to alternating current. 1 of the Microstrip Calculator using H2 in place of h, εr,eff can be computed as specified in Eq. 01450Microstrip Differential Impedance is a key parameter in the design of high-speed digital and high-frequency analog circuits. Afterward, the port's dimensions is altered to span both microstrip lines. If vias are unavoidable, an absolute minimum number of vias need to be used. In the proposed antenna, the driven patch operates in a TM10 mode with an inherent radiation null caused by a higher mode TM12. Place directives on the schematic to define differential pairs. Differential. It renders fairly accurate results suitable for use in circuit board manufacturing and engineering analysis. This technique can result in a compact structure with a sharp roll-. Edge. Press Analyze to see the results. The simulated results based on full-wave simulator will provide a good reference for the design of differential coupled microstrip lines over LPC-EBG power/ground planes. All these combinations should give you a 100-ohm differential microstrip impedance under the following conditions: Dielectric thickness = 5 mil ; Relative permittivity at 1 GHz = 4. differential stripline. A transmission line always features a differential microstrip impedance. Figure 1: Differential Microstrip Transmission Line. In one such group, only the central patch with truncated opposite corners is probe-fed whereas the surrounding patches act as parasitic patches for bandwidth and. 3 V, etc. To realise the tri-mode BPF performance, the multimode stepped-impedance resonator is introduced and parallel coupled to both the balanced and the unbalanced ports. High-frequency circuit designers must often consider the performance limits, physical dimensions, and even the power levels of a particular design when deciding upon an optimum printed-circuit-board (PCB) material for that design. This paper presents a wideband dual-polarized filtering antenna with high suppression level and wide stopband. The differential line model consists of two single microstrip lines printed on a substrate with a permittivity value of 3. The antenna is composed of the main patch, the short-end parasitic patch, and the matching network. 5 dBi at the center frequency and. With Z 0: the characteristic impedance of the microstrip line. Differential Impedance Ω. A microstrip is a type of transmission line that consists of a conductor fabricated on dielectric substrate with a grounded plane. 2. Another consequence is the following: If you densely route several single-ended lines, I suggest you throw the values into a differential line calculator. That said, microstrip is marginally easier to deal with to meet the correct impedance since the trace will be fatter. 15 mm spacing. A compact structure with slot splitting meandered lines defected ground is proposed to reduce the mutual coupling between two microstrip antennas with a center-to-center distance of 0. Use an online differential microstrip impedance calculator; Use an online differential stripline impedance calculator; Calculating Differential vs. The differential line is excited and terminated by port features. The plots show the magnitude and phase of the input impedance. The traditional synthesis procedure of bandpass. . 38. A kind of differential to single. Stripline is another type of transmission line that can be easily built on a circuit board. 3 gives differential multilayer microstrip transition structure which has three dielectric layers and four metal layers. However, it may not be clear when transmission line techniques are appropriate. These modes maybepresent inthedifferential line simultaneously, whichmeans that these lines propagate hybrid even- and odd-mode waves. The edge couple differential microstrip transmission line is a common technique for routing differential traces. At the receiver, the signal is recovered by taking the difference between the signal levels on. 2. Download scientific diagram | Section of differential microstrip line. Here's two references: R. Overview. Examining ɛ e, the phase velocity of a transmission line with a narrower width is faster than that of a transmission line with a broader width. Differential microstrip lines with reduced crosstalk and common mode effect based. There are four different types of impedance used in characterizing differential trace impedances. The properties of a microstrip line, and uniform transmission lines in general, can be described very well by considering the geometric filling factor, (q), and. Try This New Tool. The measurements, however, can be carried out easily by utilizing a standard two-port vector network analyzer and using three different waveguide standards from a commercial. 4. For instance, the waveguide-to-microstrip transition is an essential component in millimeter wave detector. 0-mm. The top surface and the sides of the traces are exposed to air and are referenced to a power or ground plane. The slower rise-time caused by dispersion results in less reflection after 2. The differential line was chosen in the proposed antenna due to. Due to the strong field confinement of spoof SPP TL, as well as the mode mismatching between the spoof SPP TL and conventional MS lines, the transmitting electromagnetic. Microstrip is the conducting medium used to transmit the electric signals at microwave frequency and. Microstrip and CPW Power Divider Design. The characteristic impedance is given by: Eq. S. Any of the common transmission line geometries (microstrip, stripline, or waveguides) can be placed in rigid-flex or flex PCBs with a meshed ground plane. The PCB stack is composed of three standard RF core materials with standard thicknesses. J. (a) Layout of the device with yellow areas indicating the metallization and grey showing the dielectric substrate. Differential signalling is a method for electrically transmitting information using two complementary signals. Microstrip is a type of transmission line to carry microwave-frequency signals, and it can be made up of a flat copper conductor suspended over a ground plane with a dielectric between them. where Z 0,surf can be computed as specified in Eq. With t = 35 um (typical for copper with plating on a pcb), Z odd drops to 44 ohms, according to LineCalc. pled from the conductors to the ground planes. A new model of the differential structure, employing an LC equivalent circuit is discussed. A differential third-order Chebyshev filtering microstrip antenna array with high common-mode (CM) rejection is presented. This calculator determines the impedance of a symmetric differential stripline pair. An example of a wire microstrip might most often be found in prototypes or reworked boards where a wire is used over the top of pcb or copper clad material. 1. Figure 1. 6mm board, 100R microstrip differential impedance, they suggest 4/5 mil trace/space, which is a bit different than 9/4. The passband ranging from 0. S1: The separation between the two traces of the differential pair By loading two identical SRRs into a microstrip splitter/combiner configuration, a differential-mode sensor was designed in . To verify the active differential reflection coefficient definition, the differential three-element microstrip patch antenna array is designed, fabricated and measured. It’s meant to provide a consistent reference so that a trace can be designed to have the desired impedance. PCB Impedance Calculator. The input impedance, Zin, of the shorted microstrip line is shown in Figure 3. This is a frequency dependent speed of the signal. 1,373. Several designs have been proposed in an effort to introduce an efficient transition from waveguide to microstrip such as transitions based on antipodal finline, 1–3 based on ridged waveguide, 4–6 based on iris coupling, 7 or based. In this paper, a new type of transition is described. Figure 5 Differential impedance of topology with 50 mil gap when driven from each end. The tapered transition is only 8. A stripline resembles a microstrip line and comprises a center conductor pattern symmetrically embedded completely within a dielectric, the top and bottom layers of which are conducting ground planes.