Calculation of resistance of an arbitrary-shape metal sheet by EM simulator Issued on August 26, 2009

### Abstract

It is difficult to calculate resistance of an arbitrary-shape metal sheet. But with an EM simulator we can easily know it. Here I show an example to calculate resistance of a metal sheet with an EM simulator.

I used Sonnet Lite of Sonnet Software Inc.

## 1. Basic analysis of sheet resistance

First I made sure that we could know sheet resistance with Sonnet Lite.
By definition of the sheet resistance, if a sheet conductor is square, the resistance is identical to its sheet resistance.
That is, sheet resistance can be observed by measuring the resistance between a pair of facing sides of a square conductor film. (Fig. 1.1) Fig. 1.1

I started to enter the analysis object to Sonnet.
I drew a 5.0mm*5.0mm sheet metal of which sheet resistance was 500 ohms, and placed 2 trace lines contacting to a pair of facing sides.  The port used here is an ungrounded internal port of Sonnet. Fig. 1.2

Sonnet has a measure to enter a sheet  resistance of metal. In this window I entered the sheet resistance, 500 homs. Fig. 1.3

Then I ran analysis at 1MHz. After analysis I ran emgraph and set the curve setting like below.
Data Type: Z Params
Data Format: Real Fig. 1.4 Fig. 1.5

Then I got the resistance, 500 ohms. This is entirely identical to the sheet resistance.

## 2. Analysis of a diamond-shape metal

Second I analyzed a diamond-shape metal. This shape is often seen in a touchpad electrode.
The length of the horizontal and vertical diagonal line is 5.2mm. But the editor resolution of Sonnet was set to 0.2mm. So the entered shape was rounded to the staircase shape in Fig. 2.1. Fig. 2.1

I got 2935 ohms in this unit shape. Required memory by this analysis was 2MB.
Then I made an analysis of 3 successive units of the diagonal electrode. The required memory by this analysis was 13MB and nearly the limitation of Sonnet Lite. I can not analyze longer electrode with Sonnet Lite. Fig. 2.2

I got 8805 ohms. This is just 3 times as big as the basic unit resistance, 2935 ohms.
Then we understand that we just add the resistance of a basic unit repeatedly so as to calculate the resistance of a longer electrode. That is, you have 10 units of the diagonal then the resistance would be 29.35k ohms.

## 3. Conclusion

I showed that we could easily calculate resistance of a metal sheet with an EM simulator. Without an EM simulator we have to use Van der Pauw method or something complicated.
Use of an EM simulator is actually wider. Its application is not limited to RF application.

End of document.
(C)KANAYA Hidenori