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Guides
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- Modeling Common-Mode Currents in Coaxial Cables: A Hybrid Approach
- Evaluating EMF Compliance - Part 2: Using Near-Field Calculations to Determine Exclusion Zones
- 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
- RF Techniques: Implicit Modeling and Equivalent Circuits for Baluns
- AN-SOF Antenna Simulation Best Practices: Checking and Correcting Model Errors
- Show All Articles (1) Collapse Articles
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- AN-SOF 9.50 Release: Streamlining Polarization, Geometry, and EMF Calculations
- 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 (3) 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) Antenna: A Compact Solution for Directional Reception
- 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
- Validating V Antennas: Directivity Analysis with AN-SOF
- Enhanced Methodology for Monopoles Above Radial Wire Ground Screens
- Dipole Gain and Radiation Resistance
- Convergence of the Dipole Input Impedance
- Validating Dipole Antenna Simulations: A Comparative Study with King-Middleton
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Input Impedance and Directivity of Large Circular Loops
Assuming a uniform current distribution along a small circular loop > has allowed us to obtain closed-form expressions for the radiation resistance and directivity. When the loop circumference is comparable to the wavelength, the current distribution cannot longer be assumed uniform but a Fourier series is applied to approximate it. Also, a delta gap voltage source is used as the excitation in the theory of large loops, so the drawbacks regarding lack of convergence of the input impedance will appear here as in the case of the cylindrical antenna with delta-gap source. Nevertheless, the theoretical results are still useful as a reference frame.
In the theory of loops, the circumference C is measured in wavelengths, C/λ, and the wire thickness is taken into account via the Ω parameter,
where r is the loop radius, so C = 2πr, and a is the wire radius. Fig. 1 shows the computed radiation pattern in decibels for a loop with C/λ = 1 and Ω = 10. This pattern is quite similar to that shown in Fig. 5.12 of “Antenna Theory Analysis and Design” by Constantine A. Balanis, 4th Edition, Wiley 2016, for the same loop dimensions.
To establish a numerical comparison between AN-SOF and theory, and to demonstrate that the radiation pattern in Fig. 1 is actually that predicted by theory, the following table shows the directivity in dBi of the circular loop antenna for various electrical sizes (C/λ) and thicknesses (Ω):
Ω | C/λ | D [dBi] Theory | D [dBi] AN-SOF | Error % |
8 | 1 | 3.344 | 3.36 | 0.478 |
10 | 1 | 3.412 | 3.411 | -0.0293 |
12 | 1 | 3.442 | 3.439 | -0.0872 |
20 | 1 | 3.476 | 3.473 | -0.0863 |
Ω | C/λ | D [dBi] Theory | D [dBi] AN-SOF | Error % |
8 | 1.48 | 4.626 | 4.684 | 1.25 |
10 | 1.45 | 4.592 | 4.615 | 0.501 |
12 | 1.43 | 4.523 | 4.54 | 0.376 |
20 | 1.39 | 4.354 | 4.368 | 0.322 |
We can see that the percentage error between the AN-SOF and theoretical results is negligible from a practical point of view. The largest discrepancies, around 1%, appear when the loop is made of a thicker wire (Ω = 8) as we could have expected since AN-SOF uses the exact kernel and the theoretical loop a thin-wire approximation.
Regarding the loop input impedance, Fig. 2 shows the comparison between theory and AN-SOF of the input resistance and reactance as a function of the loop circumference normalized to the wavelength and for a wire thickness of Ω = 10. A constant segmentation of 35 segments has been used in the AN-SOF model, so each segment is about 7% of a wavelength long for the largest loop, C/λ = 2.5 (2.5/35 ~ 0.07).
It is remarkable that the agreement between theory and the computed results is quite satisfactory over such a large range of variation.