# Conservation of Energy

I’m a firm believer in the conservation of energy, especially my own, so the topic of this post is how we can use some of the features in LTspice to make our simulations quicker and easier.  If you missed my previous post you can find it here.

## Outline

I came across an interesting article written by Richard Anslow and Sylvain Le Bras, How to Get the Best Results Using LTspice for EMC Simulation—Part 1.  EMC testing lab time can be expensive, so in the article, they use LTspice to simulate the EMC behavior of a switching regulator to gain insight into whether the system is likely to pass EMC testing or whether to add some mitigation techniques ahead of booking EMC lab time.

The article has a nice LTspice model of the LISN (Line Impedance Stabilization Network) used to test for Electromagnetic Compatibility and walks through using LTspice to generate FFT plots of the common-mode (CM) and differential mode (DM) noise spectra.  It even uses a custom plot settings file to add an EN 55022 conducted emissions limit line – a nice touch!

## 500000 is a Magic Number?

The LISN enables us to measure both common mode and differential mode noise because the voltages at V1 and V2 include both CM and DM noise.  Because the directions are the same at V1 and in opposite directions at V2, looking at the sum and difference enables us to view them separately.  This is shown in Figure 1 below which is taken from the following Analog Dialogue article by Ling Jiang, Frank Wang, Keith Szolusha, and Kurk Mathews: A Practical Method for Separating Common-Mode and Differential-Mode Emissions in Conducted Emissions Testing.

Figure 1. The CM noise path and DM noise path in a buck converter

Typically conducted emissions in a lab are measured in dBµV, while the default LTspice unit is 1 dbV, so we need to do some scaling of the plot where 1 dbV = 120 dBµV as 1 V = 1,000,000 µV.  The final LTspice expression for CM noise is therefore (V(v2)+V(v1)) / 2 x 1000000 which represents the average of the sum of voltages v1 and v2, scaled to dBµV.  In a similar way, the DM noise is V(v1,v2) / 2 x 1000000 which represents half of the difference in voltage between v1 and v2, again scaled to dBµV.

The simulation is really nice but I found it a bit of a pain to keep typing in 500000*V(v1,v2) and 500000*(V(v2)+V(v1)) into the expression editor.  This was partly due to the easy opportunity to introduce errors: 500000 has too many ‘0’s in it to visually check you have typed the correct amount of them and there are far too many brackets as well.  I also feel that you lose the sense of what the expressions mean as the ÷ 2 x 1000000 is simplified to x 500000.

## Oh, Behave!

Every once in a while, as an engineer, you find something so useful that you wonder how you ever managed before without it.  In the case of LTspice, this tool is the Behavioral Source.  There are different types of behavioral sources but we’re going to use the simplest one, a behavioral voltage source.  Here, the output voltage depends on a mathematical function we define.

I thought rather than typing in 500000*… every time on the FFT plot, why not set up a couple of behavioral sources to calculate the DM and CM noise.  In Figure 2 below you can see how these have been set up in the schematic, along with a comment, of course, to explain what we are doing.

Figure 2. Behavioral sources used to generate differential and common mode noise, scaled to dBµV

## The Plot Thickens…

Now, all we need to do is select the voltages ‘DM’ and ‘CM’ for our FFT plot, open the plot settings file with the limit line and everything is Hunky-Dory.  Well, I say, Hunky-Dory but the plot in Figure 3 shows that I should probably look into a little more common-mode filtering at around 800 kHz before I spend money hiring out the EMC testing facility…

Figure 3. The final FFT plot with limit line and annotation

LISN_dBuV.zip