Third Order Intercept - Use Peaks or RMS?

[Natalie Johnson]

Hi, I have a tough or straight forward question... please can someone share knowledge

I have two sine waves at different frequencies, my fundamental frequencies, and they are summed together to produce a signal.

This signal is put through a non linear transfer curve of an amplifier, which is to say its signal power is incremented in steps, my power in and a power out is obtained (which is amplified). Towards the end of the transfer curve, it experiences non linearity and intermods are produced.

I perform an FFT and obtain the power contained at each frequency in the signal (at each incremented signal power along the transfer curve). This allows me to have the power of each sine wave and all the intermods for each increment of signal power along the transfer curve.This data then is plotted and I have 1:1 slope (power in vs power out) and 1:3 slope (power in vs intermod power). The slopes are correct.

Now to calculate the TOI, I can extrapolate a straight line along the transfer curve and see where it intercepts an extrapolated straight line of intermod gradient.

Do I use RMS or Peak on this plot?

Currently...
The 1:1 slope is the power of 1 fundamental frequency taken from the frequency domain of an FFT of the entire signal (hence its currently a peak and two fundamental frequencies are present in the FFT - I only use one)
The 1:3 slope is of the intermod power and its also from the frequency domain of FFT of the signal (hence its currently a peak)

Do I use RMS or Peak power of the fundamental frequency and intermod frequency on this TOI plot?

 

[tnich]

Hi, I have a tough or straight forward question... please can someone share knowledge

I have two sine waves at different frequencies, my fundamental frequencies, and they are summed together to produce a signal.

This signal is put through a non linear transfer curve of an amplifier, which is to say its signal power is incremented in steps, my power in and a power out is obtained (which is amplified). Towards the end of the transfer curve, it experiences non linearity and intermods are produced.

I perform an FFT and obtain the power contained at each frequency in the signal (at each incremented signal power along the transfer curve). This allows me to have the power of each sine wave and all the intermods for each increment of signal power along the transfer curve.This data then is plotted and I have 1:1 slope (power in vs power out) and 1:3 slope (power in vs intermod power). The slopes are correct.

Now to calculate the TOI, I can extrapolate a straight line along the transfer curve and see where it intercepts an extrapolated straight line of intermod gradient.

Do I use RMS or Peak on this plot?

Currently...
The 1:1 slope is the power of 1 fundamental frequency taken from the frequency domain of an FFT of the entire signal (hence its currently a peak and two fundamental frequencies are present in the FFT - I only use one)
The 1:3 slope is of the intermod power and its also from the frequency domain of FFT of the signal (hence its currently a peak)

Do I use RMS or Peak power of the fundamental frequency and intermod frequency on this TOI plot?

This is an area I don't know much about, but it seems to me that RMS power

Hi, I have a tough or straight forward question... please can someone share knowledge

I have two sine waves at different frequencies, my fundamental frequencies, and they are summed together to produce a signal.

This signal is put through a non linear transfer curve of an amplifier, which is to say its signal power is incremented in steps, my power in and a power out is obtained (which is amplified). Towards the end of the transfer curve, it experiences non linearity and intermods are produced.

I perform an FFT and obtain the power contained at each frequency in the signal (at each incremented signal power along the transfer curve). This allows me to have the power of each sine wave and all the intermods for each increment of signal power along the transfer curve.This data then is plotted and I have 1:1 slope (power in vs power out) and 1:3 slope (power in vs intermod power). The slopes are correct.

Now to calculate the TOI, I can extrapolate a straight line along the transfer curve and see where it intercepts an extrapolated straight line of intermod gradient.

Do I use RMS or Peak on this plot?

Currently...
The 1:1 slope is the power of 1 fundamental frequency taken from the frequency domain of an FFT of the entire signal (hence its currently a peak and two fundamental frequencies are present in the FFT - I only use one)
The 1:3 slope is of the intermod power and its also from the frequency domain of FFT of the signal (hence its currently a peak)

Do I use RMS or Peak power of the fundamental frequency and intermod frequency on this TOI plot?

This isn't really my field, but my guess is that the difference in the log-log plots of RMS vs. RMS and peak vs. peak power will be negligible. I suggest that you try them both and find out.

 

[Natalie Johnson]

It affects the location of intercept (co ords) and yes its log log plot

 

[tnich]

It affects the location of intercept (co ords) and yes its log log plot

You are going to have a scale factor between $P_{inRMS}$ and $P_{inPeak}$. Is there much difference in the intercept location $P_{in}$ coordinate between the two plots if you apply the scale factor?

 

[Tom.G]

Take a look at this whitepaper explaining how to measure TOI of an RF amplifier.
http://www.ni.com/white-paper/4384/en/

Above found with:
https://www.google.com/search?&q=third+order+intercept+measurement

 

[Natalie Johnson]

Take a look at this whitepaper explaining how to measure TOI of an RF amplifier.
http://www.ni.com/white-paper/4384/en/

Above found with:
https://www.google.com/search?&q=third+order+intercept+measurement

It does not mention which to use

 

[tnich]

It does not mention which to use

Here is what I am driving at. I expect the only difference in the plots will be due to a small difference in the ratio of peak to RMS power for the signal vs. the signal cubed. It also occurs to me that you may be calculating the peak power by multiplying RMS power by $\sqrt 2$. In either case it will not matter whether you plot peak or RMS power as long as you label your axes appropriately.

 

[donpacino]

in real world terms RMS power has no significance vs average power.

Please see the following paper for an explanation:http://eznec.com/Amateur/RMS_Power.pdf

you should use average power and peak power in comparisons. In general terms both can be important.

for your application, I would use average power for a particular pulse, not peak. try calculating it using both and seeing the difference. It depends on how high the peak is, and what the signal width is.

 

[tech99]

Do I use RMS or Peak on this plot?

Currently...
The 1:1 slope is the power of 1 fundamental frequency taken from the frequency domain of an FFT of the entire signal (hence its currently a peak and two fundamental frequencies are present in the FFT - I only use one)
The 1:3 slope is of the intermod power and its also from the frequency domain of FFT of the signal (hence its currently a peak)

Do I use RMS or Peak power of the fundamental frequency and intermod frequency on this TOI plot?

It sounds as if you have a spectrum analyser type of display generated using FFT. This is displaying log freq versus dB I think.
In the intermod test, we see single frequencies, therefore sine waves. Two of these are the fundamental frequencies and several others are intermodulation products, also sine waves.
We wish to compare one fundamental with one IMP product. The dB reading indicates the power in the sine wave, as when using a power meter. You do not need to consider the shape of the wave or its peak to average ratio etc. Just read the max value at each frequency and take the difference in dB.
(As a matter of interest, if a spectrum analyser has sufficient bandwidth to allow two sine waves to reach the detector, then it will give wrong readings unless the detector is a square law type. But if the bandwidth is narrow enough so that only one sine wave reaches the detector then it reads correctly).

 

[sophiecentaur]

In the intermod test, we see single frequencies, therefore sine waves.

Yes, this the main point. A spectrum analyser should give the amplitude of the sinusoidal components and the ratio of peak to RMS is the same for all. (Of course, the bandwidth has to be small enough to resolve the individual components so that there is a definite 'dip' between any two.)

 

[Natalie Johnson]

It sounds as if you have a spectrum analyser type of display generated using FFT. This is displaying log freq versus dB I think.
In the intermod test, we see single frequencies, therefore sine waves. Two of these are the fundamental frequencies and several others are intermodulation products, also sine waves.
We wish to compare one fundamental with one IMP product. The dB reading indicates the power in the sine wave, as when using a power meter. You do not need to consider the shape of the wave or its peak to average ratio etc. Just read the max value at each frequency and take the difference in dB.
(As a matter of interest, if a spectrum analyser has sufficient bandwidth to allow two sine waves to reach the detector, then it will give wrong readings unless the detector is a square law type. But if the bandwidth is narrow enough so that only one sine wave reaches the detector then it reads correctly).

Yes, this the main point. A spectrum analyser should give the amplitude of the sinusoidal components and the ratio of peak to RMS is the same for all. (Of course, the bandwidth has to be small enough to resolve the individual components so that there is a definite 'dip' between any two.)

Hm okay I will do some more investigation.
By the way, this is not using a Spectrum Analyser, its using MATLAB script and their FFT function and the transfer curve is a polynomial. The sine waves are fed into the polynomial and FFT used on output

 

[sophiecentaur]

Hm okay I will do some more investigation.
By the way, this is not using a Spectrum Analyser, its using MATLAB script and their FFT function and the transfer curve is a polynomial. The sine waves are fed into the polynomial and FFT used on output

That's fine. The bandwidth will be of the order of the inverse of the overall time for all the samples. It's only an alternative method for spectrum analysis and in no way inferior.