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Guides
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- Beyond Analytical Formulas: Accurate Coil Inductance Calculation with AN-SOF
- Complete Workflow: Modeling, Feeding, and Tuning a 20m Band Dipole Antenna
- DIY Helix High Gain Directional Antenna: From Simulation to 3D Printing
- Evaluating EMF Compliance - Part 1: A Guide to Far-Field RF Exposure Assessments
- Design Guidelines for Skeleton Slot Antennas: A Simulation-Driven Approach
- Simplified Modeling for Microstrip Antennas on Ungrounded Dielectric Substrates: Accuracy Meets Simplicity
- Fast Modeling of a Monopole Supported by a Broadcast Tower
- Linking Log-Periodic Antenna Elements Using Transmission Lines
- Wave Matching Coefficient: Defining the Practical Near-Far Field Boundary
- AN-SOF Mastery: Adding Elevated Radials Quickly
- Enhancing Antenna Design: Project Merging in AN-SOF
- On the Modeling of Radio Masts
- The Equivalent Circuit of a Balun
- AN-SOF Antenna Simulation Best Practices: Checking and Correcting Model Errors
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- AN-SOF 9: Taking Antenna Design Further with New Feeder and Tuner Calculators
- AN-SOF Antenna Simulation Software - Version 8.90 Release Notes
- AN-SOF 8.70: Enhancing Your Antenna Design Journey
- Introducing AN-SOF 8.50: Enhanced Antenna Design & Simulation Software
- Get Ready for the Next Level of Antenna Design: AN-SOF 8.50 is Coming Soon!
- Explore the Cutting-Edge World of AN-SOF Antenna Simulation Software!
- Upgrade to AN-SOF 8.20 - Unleash Your Potential
- AN-SOF 8: Elevating Antenna Simulation to the Next Level
- New Release: AN-SOF 7.90
- AN-SOF 7.80 is ready!
- New AN-SOF User Guide
- New Release: AN-SOF 7.50
- AN-SOF 7.20 is ready!
- New Release :: AN-SOF 7.10 ::
- AN-SOF 7.0 is Here!
- New Release :: AN-SOF 6.40 ::
- New Release :: AN-SOF 6.20 ::
- Show All Articles (2) Collapse Articles
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Models
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- Download Examples
- Modeling a Center-Fed Cylindrical Antenna with AN-SOF
- Yagi-Uda Array
- Monopole Over Real Ground
- Helix Antenna in Axial Mode
- Modeling a Circular Loop Antenna in AN-SOF: A Step-by-Step Guide
- A Transmission Line
- An RLC Circuit
- Explore 5 Antenna Models with Less Than 50 Segments in AN-SOF Trial Version
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- Modeling a Super J-Pole: A Look Inside a 5-Element Collinear Antenna
- Simulating the Ingenious Multiband Omnidirectional Dipole Antenna Design
- The Loop on Ground (LoG): A Compact Receiving Antenna with Directional Capabilities
- Precision Simulations with AN-SOF for Magnetic Loop Antennas
- Advantages of AN-SOF for Simulating 433 MHz Spring Helical Antennas for ISM & LoRa Applications
- Radio Mast Above Wire Screen
- Square Loop Antenna
- Receiving Loop Antenna
- Monopole Above Earth Ground
- Top-Loaded Short Monopole
- Half-Wave Dipole
- Folded Dipole
- Dipole Antenna
- The 5-in-1 J-Pole Antenna Solution for Multiband Communications
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- The Lazy-H Antenna: A 10-Meter Band Design Guide
- Extended Double Zepp (EDZ): A Phased Array Solution for Directional Antenna Applications
- Transmission Line Feeding for Antennas: The Four-Square Array
- Log-Periodic Christmas Tree
- Enhancing VHF Performance: The Dual Reflector Moxon Antenna for 145 MHz
- Building a Compact High-Performance UHF Array with AN-SOF: A 4-Element Biquad Design
- Building a Beam: Modeling a 5-Element 2m Band Quad Array
- Broadside Dipole Array
- Log-Periodic Dipole Array
- Broadband Directional Antenna
- A Closer Look at the HF Skeleton Slot Antenna
- The 17m Band 2-Element Delta Loop Beam: A Compact, High-Gain Antenna for DX Enthusiasts
- Enhancing Satellite Links: The Moxon-Yagi Dual Band VHF/UHF Antenna
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Validation
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- Simple Dual Band Vertical Dipole for the 2m and 70cm Bands
- Linear Antenna Theory: Historical Approximations and Numerical Validation
- Validating Panel RBS Antenna with Dipole Radiators against IEC 62232
- Directivity of V Antennas
- Enhanced Methodology for Monopoles Above Radial Wire Ground Screens
- Dipole Gain and Radiation Resistance
- Convergence of the Dipole Input Impedance
- Impedance of Cylindrical Antennas
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Impedance of Cylindrical Antennas
Since there is a lot of theoretical data available for the input impedance of a linear antenna, we will compare the simulation results with those obtained theoretically.
Among the theoretical results, we have chosen the King-Middleton’s because from our point of view it is the most elaborate analytical solution. It is based on an expansion of the current distribution along a linear antenna in terms of sinusoidal functions and integrals of those functions, which is used in an iterative method to approach the solution of an integral equation. However, King-Middleton’s solution should not be taken as completely “correct” as it neglects edge effects at the antenna feed point, so the gap where the source is connected is considered to be infinitesimal. Besides, the King-Middleton’s solution is just a second order approximation. Even today it is in doubt if this solution really converges when more iterations are performed. Needless to say, it is impressive that an analytical second-order iteration of the solution of an integral equation could be obtained in King’s days.
Beyond these observations, the King-Middleton second-order solution can be taken as a good reference to validate a numerical method.
Fig. 1 shows the input impedance of a center-fed cylindrical antenna as a function of its normalized half-length, ßh (in radians), ß being the wavenumber. For a wavelength λ = 1 m, the antenna diameter is (a) 3/32″ (radius/λ = 0.001191), (b) 1/4″ (radius/λ = 0.003175), (c) 3/4″ (radius/λ = 0.009525). The solid lines are AN-SOF simulation results while the dashed lines are King’s results. Refer to Table 30.12 of “The Theory of Linear Antennas” by Ronold W. P. King, Harvard Univ. Press, 1956.
Since King’s results neglect the finite gap effect at the source position, the following gap sizes have been used in AN-SOF in order to better approximate the King’s curves: (a) 0.02λ, (b) 0.04λ, (c) 0.1λ. In the AN-SOF model the antenna does not have any gap, in fact, since the continuity of the electric current must be guaranteed along the antenna. To fill in the gap, a short wire having the same length as the gap is used. The source feeding the antenna is at the center of this short wire.
Fig. 2 shows the AN-SOF model. The number of segments was increased as ßh increases in order to maintain a practically constant segment length of 0.02λ. This segment length is more than enough to obtain a convergent value of the input impedance, as the convergence analysis will show. Fig. 2 also shows the number of segments N used in each arm of the antenna as a function of ßh, which is practically a linear function of course.
As can be seen, an excellent agreement is achieved between the King-Middleton second-order approximation and the results obtained from AN-SOF.