*Read other posts in the “Elephant in the Test Room” series here.*

__Linearization of EMC Amplifiers__

This section of the posting got a little long-winded but it at least serves two purposes. It is a step closer to closing Elephant in the Test Room #2 ‘Disharmony in Harmonic Limits,’ and it also helps determine the linearization target on the TWT amplifier we are working with.

The $64,000 question – What is a practical level of harmonics in a RF immunity system?

In order to be in a position to give an answer, we need a better feel for how sensitive the relative level of harmonics is to the variations / variables in the components that create the RF test field. So for instance we know that the antenna will likely favour the higher frequency harmonic when it is creating the field. OK, but by a great amount for a small change in antenna gain, or by a small amount for a big change in antenna gain? And is the change linear? In the case of an amplifier approaching saturation, we know the change in harmonics is not linear with power.

The commercial standard focuses on the harmonic content in the test field itself, which makes eminent sense, so we shall do the same thing. Note, I am well aware that readers are at different places, some very familiar with dB notation, some fairly new to it. If familiar, I recommend you skip to the bottom. The rest of you – hang on in there, the math is not too heavy, and by the end of it you will be in the same position as those more familiar.

Let’s try to pull together what we need. We want to follow the commercial sector approach so we start with the equation for calculating the field strength.

Where E (v/m) is the field strength, G is the linear gain of the antenna at the frequency in question, P (watts) is the RF input power at the antenna connector, and d (meters) is distance from the antenna.

If you want to know how the equation is derived we already did so in a previous posting under the title ‘The Magic Number 30’ here.

The diagram shows the antenna treating the fundamental (wanted) signal and the harmonic (unwanted) signal differently; where the gain the harmonic sees (G2) is generally higher than the gain the fundamental sees (G1). However the fundamental power is normally far greater than the harmonic power and so the wanted test field is usually greater than the harmonic field. Both signals actually follow the same physical path of course, the separation is purely for ease of explanation.

Applying the equation to the shown field strengths E1 and E2,

We want the ratio of one to the other so,

And cancelling

We would like the level of E2 relative to E1 in dBc, so we take 20 log10 of E2/E1. (We multiply by 20 because the field is in volts per meter, not watts per square meter. Also, the c in dBc stands for carrier, another name for our fundamental signal F1).

And of course to keep the equation valid we have to do the same to the right hand side.

[An important thing to remember here is that E1 is bigger than E2, so the ratio of E2 to E1 will be less than 1, so 20 log10 (E2/E1) will have a negative value.]

In dBc,

So,

Now we are in a position to establish how sensitive the left hand side is to changes to the variables on the right hand side. Technically we should couch the sensitivity in terms of ratios, but for ease of understanding we will determine the sensitivity by numerical example.

Let us assume that the gains and powers are such that E2 is -10dBc.That is the harmonic field level is 10dB down from the fundamental field level.

What would happen if we increased one of the variables by the linear equivalent of 1dB?

Aside: I know in my head that adding 1dB is approximately the same as adding 27% in the linear world (or equivalently multiplying by 1.27). For no other reason than it comes first, we will pick G2. So we will add the equivalent of 1dB to G2, that is multiply by it 1.27.

Here we go:

Let the original E2 be E2a and let the new E2 be E2b. All in dBc of course.

The harmonic got bigger and the fundamental stayed the same, so things got worse.

Therefore, an increase in G2 by the equivalent of 1dB worsens the relative harmonic level by 1dB. That all makes sense because if the antenna favored the harmonic even more, then the harmonic level would worsen. It is easy to see that if we added the equivalent of 1dB to P2 the same thing would happen.

However if we increased either G1 or P1 by the equivalent of 1dB, the situation would get better by 1dB as shown:

There is now a wider gap between the fundamental (the carrier c) and the unwanted harmonic. A good thing.

OK, we are a step closer to figuring out the thinking behind the automotive amplifier harmonic limit, and simultaneously deciding on the level of harmonic improvement we want from the TWT amplifier we are linearizing.

*To be continued…… *

**Elephant #3 – Fixing the Broken Automotive Emissions Test Fixture**

The Room: Automotive RF Emissions Testing

The Elephant: Hard to justify systemic uncertainties

The Culprit: An over-reliance on weakly related historical methods compounded by the turning of a blind eye to known serious flaws

In this post I would like to plant the seed of an idea, that although unable to be used quite as elegantly as will be described, might direct our thinking to a way of nullifying some of the variables in the current emissions test system.

Walk into any RF design house and you will find various stations used in the development of new designs. Let’s home in on one where the development engineer is just setting up to measure the RF performance of a newly designed RF power module. There will be an analyzer of sorts that provides the swept input signal to the module (EUT) and monitors its output signal. To conduct the test the engineer will need cables and a high power attenuator. Both the attenuator and the cables will have different loss at different frequencies, but the engineer only wants to see what the EUT is doing, and so he first measures the performance of the cables / attenuator combo.

This is shown in the first picture. He tells the analyzer to remember the power / frequency trace, and then tells it to subtract this trace, leaving a flat line as shown in the second picture. This is known as ‘normalizing’ the test set up. The EUT is then introduced and any trace on the screen is due to the EUT alone (third picture).

How could we use this general idea to nullify the imperfections of the E-Field transducer measurement?

I believe any test house already has everything at hand to do so. Modern spectrum analyzers and receivers have tracking generators, and if we want to do the calibration at a sensible test field level, we have the RF amplification train used in RF immunity testing. Perhaps we can put our minds to capturing a trace showing imperfections for fixed input power, or better still, for input power for fixed RF field strength at 1m (make this the independent variable). Won’t be as elegant, but….

*To be continued …*

**Other Live Topics**

Sorry, but as previously mentioned, the linearization section got long winded and so I will pick up and concentrate on the other topics next time.

-Tom Mullineaux