An RLC Circuit

The ability of AN-SOF to simulate at extremely low frequencies can be demonstrated with a model of an RLC circuit that will resonate at only 800 Hz, so the wavelength is 375 km!

Step 1 | Setup

Go to Tools > Preferences > in the main menu and select Hz, mm, mH and uF as the units for frequency, length, inductance, and capacitance, respectively. Then, 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 600 Hz and end at 1,000 Hz, incrementing by 10 Hz for each calculation, Fig. 1. In the Environment panel >, set a perfect ground plane at Z = 0.

Step 2 | Draw

Go to the Workspace tab, right click on the screen, and select Line from the pop-up menu >. Draw the three wires with the coordinates indicated in Fig. 2 using the Line dialog box. The left vertical wire has 1 segment, the horizontal wire has 1 segment, and the right vertical wire has 2 segments. The wire radius is 0.5 mm.

Right click on the left vertical wire, select the Source/Load command from the pop-up menu and put a 1 Volt voltage source. Then, right click on the horizontal wire, select Source/Load from the pop-up menu and connect a load impedance with R = 10 Ohm. Finally, right click on the right vertical wire, select Source/Load from then pop-up menu and put an inductance L = 20 mH on the first segment and a capacitance C = 2 uF on the second segment. Refer to Adding Sources > and Adding Loads > for adding sources and load impedances.

Step 3 | Run

Go to the Run menu and click on the Run Currents command. Since we are only interested in the input impedance, it is not necessary to calculate the radiated field (you can do it to check that it is practically negligible).

Right click on any of the three wires composing the circuit, select the List Currents command and click on the Current on Segment button of the displayed toolbar >. A table will be shown, where the current is tabulated vs. frequency. Next, press the Plot button to the right of the table to plot the current versus frequency, Fig. 3.

Since this is a series RLC circuit, the current flowing must be the same in all three wires (check this). As can be seen, resonance occurs at a frequency near to 800 Hz. Repeat the calculation for frequencies around 800 Hz, with a step of 1 Hz, and verify that the resonant frequency is 796 Hz. On the other hand, according to circuit theory, the resonance frequency is given by

The agreement between AN-SOF and theory is remarkable!