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Guides


 Evaluating EMF Compliance  Part 2: Using NearField Calculations to Determine Exclusion Zones
 Beyond Analytical Formulas: Accurate Coil Inductance Calculation with ANSOF
 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 FarField RF Exposure Assessments
 Design Guidelines for Skeleton Slot Antennas: A SimulationDriven Approach
 Simplified Modeling for Microstrip Antennas on Ungrounded Dielectric Substrates: Accuracy Meets Simplicity
 Fast Modeling of a Monopole Supported by a Broadcast Tower
 Linking LogPeriodic Antenna Elements Using Transmission Lines
 Wave Matching Coefficient: Defining the Practical NearFar Field Boundary
 ANSOF Mastery: Adding Elevated Radials Quickly
 Enhancing Antenna Design: Project Merging in ANSOF
 On the Modeling of Radio Masts
 RF Techniques: Implicit Modeling and Equivalent Circuits for Baluns
 ANSOF Antenna Simulation Best Practices: Checking and Correcting Model Errors


 ANSOF 9.50 Release: Streamlining Polarization, Geometry, and EMF Calculations
 ANSOF 9: Taking Antenna Design Further with New Feeder and Tuner Calculators
 ANSOF Antenna Simulation Software  Version 8.90 Release Notes
 ANSOF 8.70: Enhancing Your Antenna Design Journey
 Introducing ANSOF 8.50: Enhanced Antenna Design & Simulation Software
 Get Ready for the Next Level of Antenna Design: ANSOF 8.50 is Coming Soon!
 Explore the CuttingEdge World of ANSOF Antenna Simulation Software!
 Upgrade to ANSOF 8.20  Unleash Your Potential
 ANSOF 8: Elevating Antenna Simulation to the Next Level
 New Release: ANSOF 7.90
 ANSOF 7.80 is ready!
 New ANSOF User Guide
 New Release: ANSOF 7.50
 ANSOF 7.20 is ready!
 New Release :: ANSOF 7.10 ::
 ANSOF 7.0 is Here!
 New Release :: ANSOF 6.40 ::
 New Release :: ANSOF 6.20 ::
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Models

 Download Examples
 Modeling a CenterFed Cylindrical Antenna with ANSOF
 YagiUda Array
 Monopole Over Real Ground
 Helix Antenna in Axial Mode
 Modeling a Circular Loop Antenna in ANSOF: A StepbyStep Guide
 A Transmission Line
 An RLC Circuit
 Explore 5 Antenna Models with Less Than 50 Segments in ANSOF Trial Version

 Modeling a Super JPole: A Look Inside a 5Element 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 ANSOF for Magnetic Loop Antennas
 Advantages of ANSOF 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
 TopLoaded Short Monopole
 HalfWave Dipole
 Folded Dipole
 Dipole Antenna
 The 5in1 JPole Antenna Solution for Multiband Communications

 The LazyH Antenna: A 10Meter Band Design Guide
 Extended Double Zepp (EDZ): A Phased Array Solution for Directional Antenna Applications
 Transmission Line Feeding for Antennas: The FourSquare Array
 LogPeriodic Christmas Tree
 Enhancing VHF Performance: The Dual Reflector Moxon Antenna for 145 MHz
 Building a Compact HighPerformance UHF Array with ANSOF: A 4Element Biquad Design
 Building a Beam: Modeling a 5Element 2m Band Quad Array
 Broadside Dipole Array
 LogPeriodic Dipole Array
 Broadband Directional Antenna
 A Closer Look at the HF Skeleton Slot Antenna
 The 17m Band 2Element Delta Loop Beam: A Compact, HighGain Antenna for DX Enthusiasts
 Enhancing Satellite Links: The MoxonYagi Dual Band VHF/UHF Antenna


Validation


 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
 Validating Dipole Antenna Simulations: A Comparative Study with KingMiddleton

Radiation Resistance and Directivity of Small Loops
Among the advantages of the Conformal Method of Moments (CMoM) > implemented in ANSOF is the ability to model exactly the contour of curved antennas. Besides, calculations at extremely low frequencies are possible or, equivalently, when the antenna size is a tiny fraction of a wavelength. Both advantages will be demonstrated in this article for the small loop antenna.
One theoretical prediction for loop antennas whose size is much smaller than the wavelength is that the radiation resistance, R_{r}, is independent of the loop shape and it only depends on its area, A, measured in square wavelengths, λ^{2}, as follows:
This equation must be interpreted as the limit of the radiation resistance when the loop size tends to zero. To get this equation it is also assumed that the current distribution along the loop circumference is uniform.
The computed radiation resistances of small circular and square loops are plotted in Fig. 1 as a function of frequency, as well as the theoretical prediction. Both loops have an area of 0.01 m^{2} (square loop: 0.1 m x 0.1 m; circular loop: 0.05642 m in radius). For instance, the wavelength is λ = 3 m at 100 MHz, so the normalized loop area is A/λ^{2} = 0.0011. As the frequency increases, the theoretical prediction departs from the simulation results because it is no longer valid.
Another theoretical prediction for small loops is that the directivity becomes independent of the loop size and even of frequency. The peak directivity is a contact, 3/2, the radiation pattern is doughnutshaped and it has exactly the same expression as for a Hertzian dipole, namely,
This equation must also be considered as a limiting case when the loop size measured in wavelength tends to zero. This can be seen in Fig. 2, where the peak directivity is represented as a function of frequency for the small circular and square loops simulated with ANSOF, the horizontal asymptote being the theoretical result.
Fig. 3 shows the computed radiation patterns of the small circular and square loops at 30 MHz, and Fig. 4 shows a vertical slice of the patterns represented in a Cartesian chart. Only the radiation pattern for the circular loop is plotted in Fig 4 since the square loop results are so close to it that the difference cannot be seen with the naked eye.
These calculated results and the comparison with the asymptotic expressions predicted by theory demonstrate the ability of ANSOF to simulate small loop antennas.