Cross-Section Equivalent Radius

While AN-SOF is based on wire modeling, it allows you to simulate structures with various physical cross-sections. This is achieved by calculating an equivalent radius: the radius of a circular wire that would produce the same average electromagnetic fields as the actual shape.

You can select the cross-section type from the Attributes page of the Draw dialog box (Fig. 1).

Cross-Section Types and Formulas

AN-SOF provides six geometry options, automatically converting them to an equivalent radius $a_{eq}$ for the simulation engine:

Cross-Section	Shape	Parameters	Equivalent Radius
Circular		Radius $a$	$a$
Square		Width $w$	$0.59017w$
Flat		Width $w$	$w / 4$
Elliptical		Semi-axes $a, b$	$(a + b) / 2$
Rectangular		Width $w$, Thickness $t$	Numerical solution to an integral equation
Triangular		Width $w$ (equilateral)	$0.42w$

Key Technical Insights

• The Flat Strip Approximation: The equivalent radius for a flat strip ($w/4$) is a classic result in antenna theory, often used to model PCB traces or metal ribbons.
• Rectangular Precision: For rectangular cross-sections, AN-SOF doesn’t use a simple linear factor. Instead, it employs a sophisticated polynomial and logarithmic approximation to solve an integral equation, ensuring high accuracy even for high aspect ratios.
• Physical Meaning: The equivalent radius ensures that the capacitance per unit length and the inductance per unit length of the modeled wire accurately represent the chosen physical shape.

Selecting the Attribute

To change the wire cross-section type for an existing wire, follow these steps:

1. Select the Wire: Right-click on the wire in the workspace and choose Modify from the pop-up menu (Fig. 2).
2. Navigate to Attributes: In the Draw dialog box that appears, click on the Attributes tab.
3. Choose Cross-Section: Locate the Cross-Section dropdown menu and select the desired shape.
4. Enter Dimensions: Provide the required dimensions for that specific shape to allow AN-SOF to calculate the equivalent radius.

To modify the cross-section of wires in bulk, follow the instructions in this guide to select and modify the wires:

• Selecting and Modifying Multiple Wires