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Query: antenna gain
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Ten essential tips and truisms for understanding HF antenna: Non-resonant wire dipole antennas fed with open-wire line and an antenna tuner can function effectively as multiband antennas, as detailed in "The Classic Multiband Dipole Antenna" by WB8IMY in March 2004 QST. Coaxial cable, unlike balanced parallel-wire feed lines, can cause RF to travel on the outer shield braid, leading to RF feedback to the station; a 1:1 balun at the dipole center can mitigate this by isolating the unbalanced coaxial feed line. Antenna gain is achieved by shaping and directing RF energy, with beam antennas concentrating power in a specific direction, and wire antennas also exhibiting shaped radiation patterns. An antenna tuner's primary role is to match the transceiver's 50-ohm output to the antenna system's impedance, allowing modern transceivers to deliver full power. Wire antennas do not always require center feeding; end-fed long wires or off-center-fed dipoles (like the Windom) can be used, though they often necessitate an antenna tuner and a counterpoise or radial network. Dipole antennas do not need to be perfectly horizontal; their legs can be bent or inclined, which affects feed point impedance and may require SWR experimentation with coaxial feed. Vertical antennas shorter than a half wavelength require an efficient ground system, typically comprising elevated or buried radial wires, with more radials generally leading to better efficiency. A 1:1 SWR indicates an impedance match but does not guarantee antenna efficiency; an inefficient vertical antenna with a poor ground system can show a low SWR while wasting most RF as heat. Investing in high-quality, low-loss feed line, especially coaxial cable, is crucial for maximizing RF signal transfer and overall antenna system performance.
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A 17 3/4-inch radiating element and 18 3/4-inch ground plane radials form the basis of this quarter-wave ground plane antenna for 2 meters FM. The design, attributed to AA1PG, utilizes a panel-mount SO-239 UHF connector and three lengths of #12 copper wire, with a total material cost estimated at $3.00. Construction involves soldering the elements directly to the SO-239, emphasizing thorough solder flow for robust connections. Recommended feedline includes _RG-8X_ for longer runs, with _RG-58_ acceptable for shorter lengths, cautioning against _RG-174_ for VHF applications due to high loss. The antenna is designed for elevated deployment, such as in trees or on roof gables, to maximize line-of-sight propagation. It aims to improve repeater access compared to typical rubber duck antennas, even with low power output.
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Presents the construction of a 2-meter **Skeleton Slot Yagi** stack, detailing the design process and practical considerations for VHF operation. The author shares insights from building and testing this antenna, emphasizing its performance characteristics for local and extended range contacts. The project outlines the specific dimensions and materials used, providing a clear path for other radio amateurs to replicate or adapt the design for their own stations. The resource covers the unique aspects of the Skeleton Slot radiator, explaining how its geometry contributes to gain and pattern control. It includes discussions on impedance matching and feedline considerations crucial for optimizing power transfer and minimizing SWR. The article draws on real-world testing, offering practical results that validate the theoretical design. This project serves as a valuable reference for those interested in custom VHF antenna solutions.
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50 MHz extended 6-7 element ZX-Yagi antenna. Dimensions for the 7 elements and information on performance of a 2 stacked antennas featuring a total max gain of 20.8 dBi
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Six elements yagi antenna for 6 meters band. This antenna design is based on the QuickYagi 4 software by WA7RAI, uses a 6.5 m boom, feature 12.0 dBi gain and 35dB front/back
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A 200 kHz bandwidth digital transmission system for image transfer in the Amateur Service is under development, specifically targeting VHF allocations. John B. Stephensen, KD6OZH, leads this project under an FCC Special Temporary Authority (STA) valid until September 10, 2006, authorizing emissions up to 200 kHz bandwidth in the 50.3-50.8 MHz segment. Current regulations typically limit bandwidths to 20 kHz on VHF amateur bands, making this STA crucial for testing wideband digital modes. The modem, a modified **OFDM** (Orthogonal Frequency Division Multiplexed) unit, was initially tested on the 70-cm band. It splits a high-rate data stream into multiple low-rate subcarriers to mitigate multipath echoes. The system uses a DCP-1 card with a Xilinx XC3S400 FPGA and Oki Semiconductor ML67Q5003 microcontroller. The transmitter, located at 36d 46m 30s N, 119d 46m 22s W, generates 150 WPEP into an 8 dBi gain vertical antenna, while the mobile receiver uses a Ham-stick. Three data formats for 50, 100, and 200 kHz channels are being tested, with encoded data rates of 96, 192, and 384 kbps. Verilog code for the VHF OFDM modem is 95% simulated, with modifications from the UHF version including increased filter coefficient precision and a change from Ungerboeck **TCM** to BICM for improved performance over fading paths. Final tests will involve one-way over-the-air measurements of bit error rates and coverage area.
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In this article the author provides some guidelines on how to solve a common problem when stacking different types of yagi antennas on the same mast, limiting the effects on gain and radiation pattern of both antennas
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An comprehensive article on 40 meters antenna comparing vertical height to the resulting gain
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The advantage of 5/8 wave antenna is that it has the lowest angle of radiation and has about 1dB more gain when compared to 1/4 and 1/2 verticals. So the 5/8 should be the favourite choice for DX.
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The configuration of this antenna is a triangle with apex in the top of a very tall tree. The antenna is fed at a bottom corner using 450 ohm ladder line.
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A .64 wave antenna is the highest gain single element design available anywhere with at least a 0.8 dB/d of gain towards the horizon, than any 5/8 wave element.
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Experimenting vertical wire antennas for 40 and 20 meters supported by balloons resulting in excellent gain in RX and good overall performance against horizontal dipole
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Constructing a 2-meter Moxon antenna for MURS channels, this resource details the antenna's geometry and expected radiation pattern. The design, optimized for low SWR, high gain, and front-to-back ratio on the first three MURS channels, uses 1/8-inch bronze brazing rod for elements. Author John E. Davis provides specific geometric parameters (A, B, C, D dimensions) rounded to the nearest 16th of an inch, along with a link to the final _.nec_ file for further analysis. Performance results show the attic-mounted Moxon performs well on the 2-meter band, despite its MURS optimization, with measured SWR plots provided. NEC-2 modeling predicts over 6 dBi gain and 40 dBi front-to-back ratio in free space. The author compares its directional performance to a _J-pole_ antenna, demonstrating substantially better signal strength for a nearby repeater when the Moxon is pointed in its general direction, confirming its superior gain and directivity.
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The W6NL Moxon Yagi is a high-efficiency two-element 40m Yagi that uses cross elements to provide both loading and Moxon coupling, addressing the challenge of deploying a directional antenna on the 40-meter band. This resource details the transformation of a _Cushcraft XM240_ Yagi into this Moxon configuration, replacing the original loading coil LCA sections with four new assemblies. The guide provides comprehensive instructions for building the boom and elements, including specific dimensions for new sections and tee loading elements, along with detailed drawings and a full parts list for the conversion. Performance data indicates the converted antenna achieves **10.73 dBi** gain at 7.050 MHz with 99.5% efficiency and a high front-to-back ratio. The VSWR bandwidth is over **300 kHz**, ensuring good performance across a significant portion of the 40m band. Construction involves reinforcing element sections, attaching tee loading elements with U-bolts, and implementing element guying using materials like _Phillystran_ to manage sag and maintain structural integrity.
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The collinear antenna, or Marconi-Franklin antenna, is an omnidirectional, high-gain antenna composed of in-phase half-wave dipoles aligned vertically. By using quarter-wave transmission line segments, it maximizes gain at a low horizon angle, outperforming a half-wave dipole. Adding segments increases gain but narrows bandwidth. A popular DIY version, the CoCo antenna, uses half-wave coaxial cable segments connected by non-radiating transmission lines. Built with stable velocity factor cables, a matching quarter-wave sleeve balun, and ferrite rings for attenuation, the antenna achieves performance comparable to commercial models.
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A presentation of the Yagi Antennas, and other interesting tid-bits by Brian Mileshosky. The document provides an in-depth exploration of the Yagi-Uda antenna, detailing its historical development, design principles, and performance characteristics. Originally described in the 1920s, the Yagi antenna features a driven element and parasitic elements, including reflectors and directors, which collectively determine its behavior. The document highlights how element lengths, diameters, and spacing influence gain, impedance, and directivity. It also discusses the antenna's reciprocal nature and presents data on typical gain values for various element configurations. Additionally, the text covers practical considerations, such as the construction of a "Tape Measure Yagi" for amateur use, and touches on related antenna types like dipoles and their application in Near Vertical Incident Skywave (NVIS) communication.
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Operating a ham station often involves encountering radio frequency interference (RFI), RF feedback, or RF burns, which are frequently misattributed to poor equipment grounding. This resource meticulously dissects these assumptions, asserting that RF grounds on the operating desk often merely mask more significant system flaws. It identifies five primary causes for RF problems, including antenna system design flaws, proximity of the antenna to the operating position, DC power supply ground loops, equipment design defects, and poorly installed connectors or defective cables. The content emphasizes that issues like "hot cabinets" or changes in SWR when connecting a ground indicate substantial RF flowing over wiring or cabinets, a phenomenon known as common-mode current. The article provides detailed explanations of common-mode current generation, particularly from single-wire fed antennas like longwires, random wires, and OCF dipoles, which inherently present high levels of RF in the shack. It also illustrates how vertical antennas, lacking a perfect ground system, can excite feed lines with significant common-mode current. Through simulations, the author demonstrates how a dipole without a proper _balun_ can cause RF problems at the operating desk, showing current patterns and voltage distributions on feed line shields. The discussion extends to the proper application of _RF isolators_ and _ferrite beads_, clarifying their role in modifying common-mode impedance on cable shields and cautioning against their use as a band-aid for fundamental system defects. The resource advocates for correcting the actual source of RF problems, such as antenna system issues or poor connector mounting, rather than relying on internal shack grounding or isolators. It highlights that properly functioning two-conductor feed lines, like coaxial or open-wire lines, should result in minimal RF levels at the operating position, even without a desk RF ground. The author shares personal experience, noting that his stations since the late 1970s have operated without RF grounds at the desks, relying instead on proper antenna system design and feed line integrity.
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Dedicated to serving for all rotator parts needs. Stock and provide rotor parts for antenna rotators from companies such as Alliance, C.A.T.S., CDE, Channel Master, and Hy-Gain, both young and old.
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Constructing a compact directional antenna for the 17-meter band, this resource details the build process for a Moxon rectangle, a two-element Yagi variant with folded-back elements. It covers the antenna's evolution from the _VK2ABQ beam_ and provides specific dimensions for a version built using fishing pole whips. The content includes a discussion of the antenna's radiation pattern, feedpoint impedance, and its inherent front-to-back ratio, which is often superior to a standard two-element Yagi. Practical considerations for element spacing and material choices are also addressed, alongside a visual representation of the antenna's physical layout. Performance data presented includes a comparison showing the Moxon rectangle's **2.5 dB gain** over a half-wave dipole and a front-to-back ratio of **20 dB**. The resource also touches upon the antenna's relatively wide bandwidth for a two-element beam and its suitability for portable operations due to its compact footprint. It offers insights into optimizing the design for specific operating conditions and discusses the advantages of its lower take-off angle compared to omnidirectional wire antennas, making it effective for DX contacts on the 17-meter band.
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PSK Reporter provides a real-time visualization of amateur radio digital mode reception reports, aggregating data from a global network of monitoring stations. This platform is particularly useful for operators utilizing modes such as FT8, FT4, and PSK, allowing them to observe signal propagation paths and assess their station's reach. The interactive maps display reception reports, enabling hams to analyze band conditions and optimize antenna performance for various frequencies and times of day, aiding in understanding ionospheric conditions. Operators can filter reports by callsign, band, mode, and time, gaining insights into specific propagation events or evaluating the effectiveness of their transmit setup. The data collected helps in predicting optimal operating windows for DX contacts across various digital modes. Philip Gladstone is the contact person for comments and discussions regarding the system.
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Constructing a directional antenna for the 6-meter band (50 MHz) can significantly improve signal strength and reduce QRM during local ragchews or **Field Day** operations. This project details the assembly of a Moxon rectangle antenna, known for its compact size and respectable gain, making it a practical choice for portable or fixed station use on the magic band. The design utilizes readily available materials such as 14 AWG copper wire for the radiating elements and PVC pipe for the frame, ensuring an inexpensive build. The article provides specific dimensions and construction steps, allowing radio amateurs to replicate the antenna with confidence. It emphasizes achieving a low **SWR** across a bandwidth exceeding 1 MHz, crucial for efficient power transfer from the transceiver. Performance characteristics include a reported 5.5 dBi gain and a front-to-back ratio of 20 dB, offering effective directivity. The project also highlights the antenna's suitability for Field Day, where quick deployment and reliable performance are paramount for maximizing contacts.
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A 2m band Moxon antenna design is presented, centered at 145.2 MHz, with dimensions derived from Moxgen software. The design features a calculated 6 dBi gain, an 80-degree beamwidth, and an impressive 43 dB front-to-back ratio with minimal back lobes, concentrating RF energy in the forward direction. The antenna is balanced to 50 Ohms, facilitating direct feed. SWR sweep data from 144 MHz to 146 MHz demonstrates a near 1:1 SWR at the center frequency, maintaining healthy SWR values across the entire 2m amateur band. This performance is comparable to a 3-element Yagi, yet the Moxon offers advantages in compact size and ease of mast mounting, making it suitable for various operating environments.
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A 7 dB directional gain is reported for this portable VHF Yagi antenna design, which utilizes cut metal tape measure sections for its elements. The resource details the construction process for a 2-meter band antenna, emphasizing its ease of build and portability. It specifically mentions the design's suitability for radio direction finding (RDF), fox hunting, and communication with satellites and the International Space Station (ISS), highlighting its practical applications for amateur radio operators. The construction cost is estimated at under $20, with potential for even lower expense if salvaged materials like old tape measures and PVC pipes are used. The article references _Joe Leggio's_ (WB2HOL) original design, noting specific alterations made by the author. It also compares this design to other DIY Yagi antennas, including _FN64's_ 2-meter band and _manuka's_ 70-cm band tape measure Yagis, underscoring its unique combination of simplicity, portability, and effective performance with a 1:1 SWR achievable on the 2-meter band.
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This home made antenna provides around 10.5dBd gain on 70cm, and 6.5dBd gain on 2m, which is more than adequate to work the FM satellites with a handheld dual band radio
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The Hexbeam is a great little antenna! It should be high on your list of options if you want a design that can be multi-banded, exhibits useful gain and directivity, is very lightweight, has a small turning radius, and which lends itself readily to Do It Yourself construction.
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Antenna gain and directivity explained in this article at radio electronics antenna pages
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The resource examines the operational characteristics and potential of Moxon Yagi antennas, drawing insights from Les Moxon's work and subsequent NEC modeling. It presents simulated current distributions and radiation patterns for a 40-meter Moxon, comparing its performance against a standard 2-element Yagi on the same band. Specific data points include forward gain, front-to-back (F/B) ratio, and feedpoint impedance, which are critical parameters for antenna design and optimization. Further analysis extends to a 20-meter Moxon, detailing its gain, F/B ratio, and SWR bandwidth across the band. The discussion highlights the Moxon's compact footprint and its ability to achieve respectable performance metrics, making it a viable option for hams with limited space. The content provides a technical assessment of the Moxon's advantages in terms of pattern purity and impedance stability compared to other compact directional arrays. The article also touches upon the practical considerations for constructing and deploying Moxon antennas, emphasizing the trade-offs between physical size and electrical performance. It includes graphical representations of antenna currents and radiation patterns, offering visual aids to understand the theoretical concepts discussed.
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A monoband delta loop antenna for the 7 MHz. This vertically polarized DX Antenna is a full wavelength sngle side antenna and has a total length of 42.3 meters (137,1 inch) Can be easily setup with a flag pole or fishing pole as center top mast. For optimal performance lower side should be at 2 meter above the ground. This antenna offers a low radiation angle and 1 DB Gain.
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1500 watts PEP SSB is the power handling capability of the MFJ-989C HF Antenna Tuner, a popular choice among amateur radio operators. Users have shared a wide range of experiences, with some praising its durability and performance over decades of use, while others criticize its build quality and accuracy. The tuner features a built-in dummy load, SWR-wattmeter, and a balun for balanced line feeders, making it versatile for various antenna setups. However, discrepancies in RF power readings and SWR measurements have been noted, with some users finding the dual scale meter to be off by about 20% compared to a Bird wattmeter. Long-term users report that the MFJ-989C performs well with proper antenna setups, but caution against tuning at high power without initial adjustments at lower power levels. Some have experienced issues such as arcing when exceeding 400 watts, while others have had no problems even at higher power levels. The roller inductor and capacitors are functional, though some users have had to perform maintenance like tightening screws or cleaning components to ensure reliable operation. Despite mixed reviews, the MFJ-989C remains in production, suggesting continued demand. It's a tuner that requires careful handling and possibly some DIY fixes to achieve optimal performance.
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Distributed Antenna Systems technology used for gaining better coverage and using a lower power.
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Rotatable Antenna with Phased Elements based on the orignal design concept of HB9CV antennas, is considered to have an higher gain than standard quad antennas. The Swiss Quad Antenna does not need any spreader or boom.
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The calculator designs the Yagi-Uda antenna based on the DL6WU model with boom correction, following the G3SEK-DL6WU method. It optimizes the antenna for maximum gain and allows adjustment of passive elements without affecting SWR. DL6WU antennas are known for their high gain, minimal sensitivity to nearby objects, and stable performance in various weather conditions.
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Elk Antennas to give the Ham log periodic antennas with the best gain, directivity, and front to back ratio possible for the size and price.
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Installing a mobile rig in a vehicle requires careful planning and execution to ensure optimal performance and safety. The process begins with selecting the right equipment, such as the ICOM IC706MKII for low bands and the ALINCO DR-610 for VHF/UHF operations. Proper mounting is crucial; both radios are strategically placed under the back seat of the Silverado, allowing for a clean installation while maintaining passenger comfort. The Hustler antenna, equipped with various resonators, ensures coverage across multiple bands, while the LDG automatic antenna tuner fine-tunes the match for efficient operation. A remote head for the tuner enhances accessibility, making adjustments easier while driving. Each step of the installation is documented to provide insights and tips for fellow operators looking to enhance their mobile setup. The experience shared here reflects practical knowledge gained through hands-on work, aiming to inspire others in the ham community to undertake similar projects.
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An interesting guide to aerials comparing height, gain and angles
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A two element beam antenna for ten meters band. This home-brew two-element beam is the perfect introduction to rolling your own gain antenna
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The standard J-Pole antenna is a end fed 1/2 wavelength antenna, in this article is explained also how to build an expanded Super J Pole that provides about 4.5 dbd gain. These antennas can be built from EMT electric conduit pipe
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The Homebase-10 is a wire halo antenna for 10m built with DIY store parts, effective despite its small size. Includes a dual-band version for 10m and 6m with gain around 0 to -2dBd, near omnidirectional pattern, and horizontal polarization. Overview based on a 2008 Practical Wireless article.
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Constructing a multi-band fan dipole for HF operation presents unique challenges, as VE2XIP demonstrates through his 2012 project to replace an existing commercial antenna. He details the process of calculating wire lengths using the 468/frequency formula, emphasizing the critical importance of equal leg lengths for each dipole element. The author shares practical insights gained from building at ground level, noting how elevation impacts resonant frequency and SWR, particularly for lower and higher bands. VE2XIP's experience highlights the iterative nature of antenna tuning, starting with the lowest frequency band (80m) and working upwards. He provides a specific example of trimming calculations and offers a clever tip for accurate wire removal. The article also touches on the mechanical aspects, such as dowel spacing for wire support and the benefits of a pulley system for repeated raising and lowering during the tuning process. Field results showed significant performance gains over the previous Alpha-Delta DX LB Plus, with **20 dB over 9** signal reports on 80m compared to 57. The project cost around **$100** for hardware, proving a cost-effective alternative. The author also discovered a bonus 6m capability and achieved an inverted-V _obtuse angle_ of approximately 115 degrees, contributing to a surprisingly stealthy installation.
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Italian ham radio dealer for major brands like Icom Kenwood Yaesu HY-GAIN Heil Sound Rigexpert Palstar GAP antennas Diamond SteppIR and others
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Presents an alternative construction method for isolated element Yagi antennas, specifically for VHF/UHF operation. The technique utilizes commercially available vibration damping clamps (resin support blocks) to isolate 1/4-inch aluminum rod elements from a 1-inch square aluminum boom, simplifying the build process by eliminating the need for custom-machined insulators. This approach is demonstrated through the construction of 6-element Optimized Wide-Band (OWA) Yagis for the 2-meter, 1.25-meter, and 70-centimeter bands, which are well-suited for portable contesting arrays due to their light weight and decent gain. The document provides detailed specifications for element and boom materials, along with step-by-step procedures for cutting, drilling, and tapping. It also covers the fabrication of a feedpoint bracket for a direct 50-ohm SO-239 coax connection and discusses considerations for horizontal versus vertical polarization, including mast placement. The resulting 6-element models achieve an average free-space gain of 10.2 dBi and a 25 dB front-to-back ratio, with the construction technique being scalable for higher gain designs. Included are parts lists with sources, detailed mechanical drawings for each band, and EZNEC data for the 2-meter and 70-centimeter designs, showing both free-space and 30-foot elevation performance. The designs are optimized from W4RNL's original concepts using HAMCALC, ensuring good gain, passband characteristics, and front-to-back ratios for wideband Yagi operation.
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The Cambridge University Wireless Society (CUWS) serves as the amateur radio society for students and staff at Cambridge and Anglia Ruskin Universities, fostering interest and activity in two-way radio communication. It provides a platform for members to engage with various aspects of amateur radio, including operating, technical experimentation, and community building within the university environment. The society's activities typically encompass station operation, antenna construction, and participation in contests and DXing. As a university-affiliated club, CUWS offers practical experience in radio theory and application, often utilizing the club callsign _G6UW_. Members learn about different modes of operation, such as CW, SSB, and digital modes, and gain hands-on experience with transceivers and associated equipment. The society's focus includes preparing members for amateur radio licensing exams and promoting ethical operating practices. Participation in CUWS provides a foundation for future involvement in the broader amateur radio community.
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Showcasing innovative RF solutions, Hofi Hochfrequenztechnik manufactures high-quality _antennas_ and RF switches. Their products, including the **versatower** and **fritzel** brands, cater to both casual operators and serious DXers. With a commitment to performance, Hofi's offerings enable operators to achieve optimal signal gain and reliability in various conditions. The company's expertise in antenna design ensures that users can effectively communicate across _HF_ bands, enhancing their overall operating experience. Whether setting up a new station or upgrading existing equipment, Hofi provides essential tools for successful ham radio operations.
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A 70 cm yagi antenna design by YU7EF includes tables with antenna elements dimension and spacing. This UHF Yagi antenna plan provides a maximum gain of 17.93 db
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The Tri-pole antenna, a clever modification of a standard dipole, allows for dual-band operation by integrating a third element. This design effectively shortens the overall dipole length by 10 to 20 percent, simplifying antenna rotation and offering a compact footprint. KK4OBI's article delves into the operational principles, using a 6 and 10-meter Tri-pole as a primary example, and provides comprehensive instructions for constructing any Tri-pole antenna within the 6 to 15-meter range. Key to the Tri-pole's performance is its off-center feed, necessitating a common mode choke at the feed point for optimal tuning and reduced noise. The author outlines a methodical approach to determining element dimensions, starting with a vertical element frequency calculated as 0.47 times the sum of the desired upper and lower band frequencies. This calculation, along with K-values derived from trend lines, guides the initial lengths for the horizontal arms, demonstrating how a 10m-6m Tri-pole can achieve a total horizontal length 78% shorter than a conventional 10-meter dipole. Tuning and balancing are critical, with the article detailing adjustments to arm lengths and the vertical element to achieve balanced SWR values, as validated through 4NEC2 simulations. Radiation patterns are analyzed at various elevations, showing gains around 5.7 dBi and favorable take-off angles for DX contacts. Construction details specify aluminum tubing dimensions, U-bolts, and an SO-239 connector, emphasizing the importance of a ferrite-based choke for wideband operation.
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AN-SOF is a professional comprehensive software tool for the modeling and simulation of antenna systems. AS-SOF allows to describe antenna geometry, Choose construction materials, Describe the environment and ground conditions, Describe the antenna height above ground, Analize radiation pattern and front-to-back ratio, Plot directivity and gain, Analize input impedance and VSWR,Predict antenna bandwidth
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Gain we can expect of a parabolic antenna by F4DAY
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Antuino is an accurate instrument that can be used in the field to measure SWR, field strength, modulation, etc. In the lab, it can be used to sweep filters, measure gain, distortion, frequency response, etc. It works upto 150 Mhz. On the third harmonic, it is usable on 435 Mhz band as well (with reduced sensitivity).
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This page describes a comparison study on seven different beam antennas for 40 meters band. Yagi antennas, moxon antennas, mini horse all antennas are described with schema diagram , azimuth plot and SWR F/B Gain diagram