# Understanding "dBc" in the context of IM3

Let's say I'm doing a two-tone test to measure intermodulation distortion in an RF power amplifier. I look at my spectrum analyzer1, and I see this:

The tops of those main lobes are at -105dB, and the IM3 products next to them are -128dB. How do I specify IM3 in this example? I understand the IM3 value is normally specified in dBc, or decibels relative to carrier power. But when there are two tones, what's the carrier? One? Both? Does it matter?

1I don't actually have a spectrum analyzer, which is why the Y axis is in dB and not dBm. This screenshot is GNURadio doing an FFT on the audio output of a 2nd receiver which I'm using as a poor man's spectrum analyzer.

• Are you trying to measure the 3rd order intercept point, IP3? Feb 11, 2017 at 2:37
• @Dave I'm hoping to get there, eventually. But first I need to measure IM3 at several powers, right? Feb 11, 2017 at 2:43

When measuring the IM3 suppression, you take the difference between big tone and small tone, that's how it's specified, don't wory about 'total' carrier power. In this case it's 23dB (or -23dB).

To get from IM3 suppression to IP3 (making the usual assumptions***) you take the big tone + half the suppression, to get -105 + 23/2 => -93.5dB. Now as dB is a ratio, what absolute power is this? Well, it's -93.5(dB_whatever_that_scale_reference_is).

***What usual assumptions? Glad you asked. If a non-linearity is sending power to 2f-f frequencies, then for small amounts of distortion, the cubic term will be the strongest, it's a 3rd order IP. This means as we drop the power, the main tone will drop dB for dB, the 3rds will drop 3dB per dB. That's why the sum above gives you the power (the theoretical power) at which they become equal.

However, that only works if we assume that the 3rd order terms are dominant. As the intermodulation power rises, higher order terms can cause significant distortion, changing the way the distortion power rises, and changing the validity of the main_tone+0.5suppression equation. With only 23dB suppression, I think it's possible we are in, or at least near, that region.

This means that instead of taking a single measurement, you should take a measurement at a range of power levels, and plot the IPs against the main tone power. If the plot is a straight line with gradient 3, then you can estimate IP3 from it. If it is not, then it is not possible to estimate an IP3 from it. You can quote suppression, but an extrapolation to IP3 will be meaningless. Note that some manufacturers do present a graph of IP3 versus power level, which is better than quoting a single IP3 level, but it is an admission that they are outside of the single IP3 figure range.

Your SA Y scale should be dBm. If in dB, it must be reference to something. Anyway this does not matter in IM3 calculation. The IM3 is always versus the main carrier power, that is how you get dBc.

You are using identical tone and having identical 3rd order product. Hence, IM3 will be

-128 - (-105) = -23 dBc

If you are using unequal tone power and having unequal 3rd order product power your IM3 will be

total power of 3rd order product / total tone power

• Regarding the actual question asked, the picture shows you measure the power in one IM3 tone vs the power in one of the carrier tones. Feb 11, 2017 at 13:37
• If you pump in 2 tone of equal power level, getting 2 almost equal power 3 order product. [low 3rd order power / low carrier] ≈ [total power of 3rd order product/total power of carrier]. Feb 11, 2017 at 14:27

Lets have the 2-tone input power reduce 1dB. For IM3, the shoulders (F1+-2*F2, 2*F1+-F2) will drop 3dB. The difference drops 2dB. Lets call this difference "2X"

You've got the heads at -105, the shoulders at -128; difference is 23dB, which is our "2X". Thus "X" is 11.5dB.

To compute IP3, add X to the input power(the heads), thus IP3 is -105 + 11.5 = -93.5dB.

To make this work, the 2-tone inputs are set to the SAME power levels, and combined in stripline combiners or resistive summers. Since Frequency Generators will have some intolerance for unexpected frequencies imposed on their outputs, use some small attenuators between the 2 FreqGens and the combiners. Unless you are testing at -105dBm, as you are here.

The purpose of using TWO STRONG TONES is to examine how the energy in the shoulders might become strong enough to cause bit errors in the channels allocated to the shoulders [F1+-2*F2, or 2*F1+-F2]. Thus 1,000MHz and 999MHz, given some IM3, produces 998MHz (2*999 - 1,000) and 1,001MHz (2*1,000 - 999).

If the 2 tones have equal power, the intermods will strongest.

Only one set of measurements (powers of the 4 peaks) is needed, as shown in the example above with -105 and -128. Additional measurements [again, the 4 peaks], with "2X" computed, cut in half, and added to the input 2-tone powers, will give more confidence.

To catch localized VSWR peaks/dips, try several combinations of head-frequencies across the band.