# Using Reciprocity Theorem to Troubleshoot Immunity Issues

When I first started working as an independent EMC consultant, I didn’t have nearly half of the equipment I do now. The first piece of equipment I owned was a Siglent swept-type spectrum analyzer, and I made my own near-field probes and RF current probes following Ken Wyatt’s book [1].

I remember a case in which I needed to troubleshoot an immunity issue, but I didn’t have any equipment to inject noise into the system. At the time, I called my mentor, Keith Armstrong, and asked him if there was any way to solve the problem, given the limited kit I had. He said to me, “Have you heard about the reciprocity theorem?”

Here, I quote Henry Ott’s explanation in his book [2]:

- Partner Content -

### A Dash of Maxwell’s: A Maxwell’s Equations Primer – Part One

Solving Maxwell’s Equations for real-life situations, like predicting the RF emissions from a cell tower, requires more mathematical horsepower than any individual mind can muster. These equations don’t give the scientist or engineer just insight, they are literally the answer to everything RF.

“Reciprocity means that if a structure (antenna) radiates well, then it will also pick up energy well, and vice versa. What prevents an antenna from radiating will also prevent an antenna from picking up energy. Therefore, the same techniques can be used to solve both emission and susceptibility problems.”

In this article, I will present a recent case study to demonstrate how useful this concept is in troubleshooting immunity issues.

## A Sensitive Smart Meter

A client of mine develops smart meters used in industrial kitchen environments. As one can imagine, variable speed drives and relays are widely seen in such environments. As a result, continuous RF interference and intermittent transient events are common. One of the most recent cases saw the emergency stop error showing on their product’s display, even though the button was never pressed. This nuisance obviously needed to be fixed.

I sat down and analyzed the noise sources in the environment. Having never been to the site where the issue was reported, my options were quite limited. I could only guess the spectrum the noise predominantly occupied, but the client also mentioned that the issue was only found recently.

For the past few years, the unit had been functioning well and without problems. They also mentioned that the most recent change in the environment was the addition of a LoRa communication link. A quick search on Google showed that LoRa operates at 863‑870/873 MHz in Europe.

## Testing the Smart Meter

So, my first attempt was to use my Tekbox TBDA3B, connect a near-field probe to the output of the amplifier, and inject 800-900 MHz RF power into the printed circuit board. I could also inject noise into the ribbon cable connection between the two boards. The TBDA3B has an output power of 40 dBmW (equivalent to 10 Watts). The field intensity of the near-field probe can be very high. To inject current into the ribbon cable, I used a BCI probe. The current injected into the ribbon cable via magnetic field coupling can reach tens of mA. However, I could not reproduce the same failure mode as the manufacturer saw in that particular location.

Here’s the question: How confident are we that it is 800-900 MHz causing the issue? Could it be some other frequency band?

To find out, I recalled the reciprocity theorem and wondered if performing an emission measurement by placing an RF current probe on the ribbon cable would provide some good indication. Figure 1 shows an RF current probe clamped on the ribbon cable and the measurement results.

It is not surprising to see a broad-band noise spectrum caused by the switched-mode power supply (between a few MHz and 200 MHz). However, I did notice something unusual, as shown in Figure 1. Notice that, between 400 and 500 MHz, the noise level on the ribbon cable is pretty high.

## A Walkie-Talkie Solution?

So, what noise source works in that frequency band and could potentially trigger the emergency stop? The first thing that came to mind was a two‑way walkie‑talkie (UK Business UHF Radios use frequencies from 400470 MHz). Could it be the walkie-talkie then?

A quick injection using my walkie-talkie triggered the emergency stop, and the coupling path was identified as either the ribbon cable or the wire link between the emergency stop button and the PCB. Once this was identified, a flat ferrite core on the ribbon cable solved the problem.

Most walkie-talkies have an RF power rating of 1W, although some can operate at up to 4W or higher. This makes a walkie-talkie an excellent tool for injecting noise. By simply pressing the send button and moving the antenna around a PCB, you can introduce exposed RF noise into the circuit under test[1]. If the antenna runs parallel to a cable in close proximity, strong near-field coupling can occur, inducing RF current in the cable and affecting the unit.

Another valuable application is placing the walkie‑talkie antenna in parallel with the seams or apertures of a metal enclosure. If the enclosure’s shielding is not properly done, the field generated from the walkie-talkie may upset the unit.

## The Limits of Walkie-Talkie Testing

The major disadvantages of walkie-talkie testing include:

1. The actual field strength that is being developed at the EUT is unknown; depending on the output power of the walkie-talkie, this could be very high,
2. Repeatable results are difficult to achieve, and
3. Spot frequency tests may well miss resonances in susceptibility that will appear in the compliance test.

This is not to say that a walkie-talkie test that does, in fact, create a susceptibility is useless, as it will prompt the designer to harden the design. But it can’t be relied on to predict compliance results. The same considerations apply to “testing” with a mobile phone.

## References

1. Ken Wyatt, Create Your Own EMC Troubleshooting Kit (Volume 1) 2nd Edition: Essential Tools for EMC Troubleshooting (EMC Troubleshooting Trilogy).
2. Henry W. Ott, Electromagnetic Compatibility Engineering.

### Setting Up a Benchtop Conducted Emission Test

Discover new products, review technical whitepapers, read the latest compliance news, and check out trending engineering news.