In effect, the post-processing solution mentioned above represents a software equivalent to a PLL locked to the fundamental.
For illustration, enclosed is a plot showing a variable-frequency argument used to generate a sine signal (upper curve) that consists of a unity amplitude 8Hz sine signal, frequency modulated by a 0.01 amplitude 1Hz sine signal.
The lower plot shows the instantaneous frequency recovered from the frequency-modulated signal generated as described. The original and the recovered signals agree in magnitude and phase; the latter can subsequently be used to perform the resampling of the acquired oscillator output.
Regards,
Braca
P.S. Never mind the terminology used in the plot - I presented this to an audience of engine specialists, hence the terms "RPM" and "Pressure".
For illustration, enclosed is a plot showing a variable-frequency argument used to generate a sine signal (upper curve) that consists of a unity amplitude 8Hz sine signal, frequency modulated by a 0.01 amplitude 1Hz sine signal.
The lower plot shows the instantaneous frequency recovered from the frequency-modulated signal generated as described. The original and the recovered signals agree in magnitude and phase; the latter can subsequently be used to perform the resampling of the acquired oscillator output.
Regards,
Braca
P.S. Never mind the terminology used in the plot - I presented this to an audience of engine specialists, hence the terms "RPM" and "Pressure".
Attachments
Hi Simon,
I've got a few resistors that I'd like to test along with some of the Xicon
types, Dale, Browns, Blues, along with RPR. I can duplicate test on
a Rohde & Schwarz UPD distortion analyzer, verify with ShibaSoku 725D
post the results. The HP 339A isn't applicable in this case...
...as you were.
Yes it is, I can verify R&S Generator with either HP339A generator and
check the results with them also. I needed something to do with the
QA FFT also.
The good news is in keeping with the
Low-Distortion Audio-Range Analyzer
theme...in this case measuring the resistor
distortion products.
I"ve got a couple of others I can measure as well, might include the
dreaded Xicon "Carbon film" along with some vintage Texas Instrument
Unknown film, and some Corning Glass Resistors....somewhere I have a
LT resistor network resistor.
Davada, did I send you one of them in the
batch of Chips?
If we use the same process and parameters, we should see some
similar results right?
Just has to be on one of those days where there isn't a big power demand
and everyone in Texas has their Air Conditioners maxed out.
Cheers,
Sync
PBj - are you on board with this?
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@ DNi can you send me or post here the MatLAB file? We've got that at the
College Laboratory. I can bring in other equipment as needed.
@Richard, DNi - When we discuss the "Harmonic Number" are we talking about
the specific frequency relative to the fundamental?
Or
A quantity of harmonic frequencies identified in an FFT plot?
or
Looking at 2f, 3f, vice ...7f, 8f, 9f...?
In my little test realm here I can measure harmonic content, so far
up to almost 1MHz. with my audio distortion instruments....
If I just had a few RF measurement instruments
and an RF spectrum analyzer....
Maybe if I'm good Santa might be good for me.
I'll have to be nice to my little girl too.
Cheers,
Sync
College Laboratory. I can bring in other equipment as needed.
@Richard, DNi - When we discuss the "Harmonic Number" are we talking about
the specific frequency relative to the fundamental?
Or
A quantity of harmonic frequencies identified in an FFT plot?
or
Looking at 2f, 3f, vice ...7f, 8f, 9f...?
In my little test realm here I can measure harmonic content, so far
up to almost 1MHz. with my audio distortion instruments....
If I just had a few RF measurement instruments
and an RF spectrum analyzer....
Maybe if I'm good Santa might be good for me.
I'll have to be nice to my little girl too.
Cheers,
Sync
Scott Wurcer may be too shy to mention it
but wouldn't the AD797 be ideal for this?V noise is much better, 1.2 nV rt Hz compared to 4.7 max at 1kHz.
Current noise only a little worse 2.0 pA rt Hz versus 1.6.
So should be a clear win at any impedance that's reasonable for this circuit.
Distortion should also be better.
Not a double of course.
Best wishes
David
Looking at the Fourier series, the frequency of each harmonic term is a product of the respective harmonic number and the fundamental frequency. Now if the fundamental changes by a small amount DeltaF, the frequency of the k-th harmonic will change by k*DeltaF.
Since the DFT (Discrete Fourier Transform) has a constant absolute resolution, the energy of the k-th harmonic will be distributed (smeared) over more "bins" than the energy of the fundamental, hence the increase of the amplitude error with the harmonic number.
This is also of interest at the low harmonic numbers, for at the low levels even small frequency deviations can cause smearing that could lead to a particular harmonic being visible or buried in the noise.
Regards,
Braca
I'll be glad to send you the Matlab script, but the original one is the company property and was written for a different purpose anyway. So I'll have to write a new one, and it'll take a few days time.
If you're interested I can send you the paper to your email address - the Conference Proceedings are unfortunately not downloadable.
Re. the terminology used to describe the results, since in the case of a varying fundamental there is no single frequency, we can only talk in terms a fundamental and the 2nd, 3rd, etc. harmonic. For lack of a better term I labeled the plot abscissas as "Harmonic order No." in the paper.
Regards,
Braca
Scott Wurcer may be too shy to mention it
V noise is much better, 1.2 nV rt Hz compared to 4.7 max at 1kHz.
Current noise only a little worse 2.0 pA rt Hz versus 1.6.
So should be a clear win at any impedance that's reasonable for this circuit.
Distortion should also be better.
Not a double of course.
Best wishes
David
The AD797 might be a good choice. But it depends on the resistance in the circuit. With typical noise values the noise from the AD797 and the LME49710 will be the same at around 2k2. Above 2k2 the AD797 will probably be noisier.
The AD797 does have a very low distortion, but in the inverting configuration the LME49710 is also very good.
Does this effect become more pronounced as the harmonic amplitude approaches the noise floor. I guess if the a lot of averaging must be used then the harmonics are already in the noise.
I noticed years ago what looks like compression when the harmonics are close to the bottom of the resolution of an ADC causing an inaccuracy. Perhaps the effect is as you describe a product of DFT.
Richard Moore also sighted this and Richard Marsh claims nothing is accurate below -100dBV measuring a sound card. A notch filter and gain help with this.
No one will argue the excellent performance of the AD797 but even AD has a note in the data sheet for any Z much above 1k. There are better choices in this case.
Scott Wurcer may be too shy to mention it
V noise is much better, 1.2 nV rt Hz compared to 4.7 max at 1kHz.
Current noise only a little worse 2.0 pA rt Hz versus 1.6.
So should be a clear win at any impedance that's reasonable for this circuit.
Distortion should also be better.
Not a double of course.
Best wishes
David
How is your oscillator coming along?
"LT resistor network resistor."
No you don't. I have it.
Just kidding. I'll take look and see if you sent me one.
Jeff Smith and I did ours, long time ago now, and got -130dB thirds. The noise at that time was not an issue, but it's easily computed. I don't think the composite amps in the LT oscillator are extremely low noise.
I can load my SVO up with 797 and see how it goes. I have done this with other op amp of similar noise specs and found no difference in harmonics but a small elevated noise at higher frequency no worse than 3dB.
I just can't justify the cost unless there is a significant performance increase.
The LT1468 and AD797 are similar in some respects and have remarkable distortion performance as Samuel found.
This is what Shibasoku did with the 725 and a 12 bit convertor but with synchronous sampling at a multiple of the fundamental. Typically 32 or 64 sample per cycle.
I ran into Bob Adams at lunch, he said with Sigma-Delta it doesn't matter anyway.