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Loop Antenna

A good example where we need curved segments to model an antenna is the circular loop case. When the loop is small compared to the wavelength, the radiation resistance is proportional to the square of the loop area.

Step 1 | Setup

Go to the Setup tab and select Sweep in the Frequency panel >. Choose Lin for a linear sweep and set the Start, Step, and Stop frequencies. The frequency sweep will start at 3 MHz and end at 30 MHz, incrementing by 1 MHz for each calculation, Fig. 1. Make sure None is selected in Environment panel > Ground Plane box and Discrete Sources is selected in the Excitation panel.

Fig. 1: Setting a linear frequency sweep.
Step 2 | Draw

Go to the Workspace tab, right click on the screen, and select Circle from the displayed pop-up menu >. The Draw dialog box for the Circle will be shown, Fig. 2. Set a radius of 0.5 m, 8 segments, and a cross-section radius of 5 mm for the loop.

At 30 MHz, which is the highest frequency, the wavelength is λ = 10 m. A loop of radius 0.5 m will then have a circumference of 3.14 m, or 0.314λ. Measuring almost 1/3 of a wavelength in perimeter, this loop cannot be considered small. However, at the lower frequency of 3 MHz it will be.

Right-click on the loop, choose the Source/Load command from the displayed pop-up menu, and put a voltage source in the first segment. Refer to Adding Sources > to add the source.

Fig. 2(a): Setting the loop dimensions.
Fig. 2(b): Setting the number of segments and wire cross-section radius for the loop.
Step 3 | Run

Click on the Run Currents and Far-Field (F11) button on the toolbar. After the calculations are complete, click on the Far-Field 3D Plot button on the toolbar to display the radiation pattern, Fig. 3. At the right of the AN-3D Pattern toolbar there is a dropdown menu to select the frequency. There are also buttons with arrows that allow us to raise or lower the frequency. Press the buttons to see how the radiation pattern changes with frequency. At low frequencies, the pattern is doughnut-shaped as expected.

Go to the Results tab > in AN-SOF to see that the input resistance is very small, only 0.000195 Ohm at 3 MHz. The radiation resistance is given by R = 31,200 (A/λ2)2 for a small loop of area A. If we use this formula obtained from textbooks, the result is R = 0.000192 Ohm at 3 MHz. Therefore, the loop behaves according to the theory at low frequencies.

Fig. 3(a): Radiation pattern of the loop at 3 MHz.
Fig. 3(b): Radiation pattern of the loop at 15 MHz.
Fig. 3(c): Radiation pattern of the loop at 30 MHz.
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