calculating total harmonic distortion using a microcontroller

[Scott Ronald]

Hi

I was wondering if anyone knows of an efficient way to calculate the THD
of a 60Hz sine wave using a basic microcontroller. I was hoping there
is a way to do this without using a full FFT. Is this possible?

Scott

 

[[email protected]]

Hi

I was wondering if anyone knows of an efficient way to calculate the THD
of a 60Hz sine wave using a basic microcontroller. I was hoping there
is a way to do this without using a full FFT. Is this possible?

Scott

Think of how an analog THD meter does the "computation." Null the
fundamental and measure the noise. This is not really THD but SINAD.
However, if the THD is bad, the results will be close.

You can use a LMS scheme to create a signal that represents the
fundamental, then subtract it out to get the THD and noise.

 

[John Larkin]

Think of how an analog THD meter does the "computation." Null the
fundamental and measure the noise. This is not really THD but SINAD.
However, if the THD is bad, the results will be close.

You can use a LMS scheme to create a signal that represents the
fundamental, then subtract it out to get the THD and noise.

Or a DFT, which isn't too much crunching if you only want to dig out
the fundamantal and subtract it from everything else.

John

 

[Tim Wescott]

Hi

I was wondering if anyone knows of an efficient way to calculate the THD
of a 60Hz sine wave using a basic microcontroller. I was hoping there
is a way to do this without using a full FFT. Is this possible?

Scott

Yes, it is.

Calculate the total energy in the signal.

Then find the best-fit 60Hz sine wave in the signal (take John Larkin's
suggestion and do a DFT, or use the overly-hyped Goertzel algorithm).
Find its energy.

Subtract the two -- that's your harmonic energy + noise.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

 

[[email protected]]

Yes, it is.

Calculate the total energy in the signal.

Then find the best-fit 60Hz sine wave in the signal (take John Larkin's
suggestion and do a DFT, or use the overly-hyped Goertzel algorithm).
Find its energy.

Subtract the two -- that's your harmonic energy + noise.

--
Tim Wescott
Control systems and communications consultinghttp://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html

I see what you are doing, and it sounds simpler than my suggestion,
but if the THD isn't really crappy, this kind of subtraction could mix
rounding noise due to the finite bitsize, i.e. add quantization noise
that really is not part of the THD.

What I was thinking about was to unwrap the signal with an arcsin,
which produces a straight line. [Essentially phase accumulation.] Then
LMS that data. The intercept and slope should allow an optimal sine
wave to be created for the subtraction purpose.

However, the more I think about this, some sort of sampling scheme
phase locked to the 60Hz signal could be more productive. Once the
sampling is synchronous, you can notch the fundamental.

 

[Martin Griffith]

On Sun, 20 Jan 2008 00:59:04 -0800 (PST), in sci.electronics.design

Yes, it is.

Calculate the total energy in the signal.

Then find the best-fit 60Hz sine wave in the signal (take John Larkin's
suggestion and do a DFT, or use the overly-hyped Goertzel algorithm).
Find its energy.

Subtract the two -- that's your harmonic energy + noise.

--
Tim Wescott
Control systems and communications consultinghttp://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html

I see what you are doing, and it sounds simpler than my suggestion,
but if the THD isn't really crappy, this kind of subtraction could mix
rounding noise due to the finite bitsize, i.e. add quantization noise
that really is not part of the THD.

What I was thinking about was to unwrap the signal with an arcsin,
which produces a straight line. [Essentially phase accumulation.] Then
LMS that data. The intercept and slope should allow an optimal sine
wave to be created for the subtraction purpose.

However, the more I think about this, some sort of sampling scheme
phase locked to the 60Hz signal could be more productive. Once the
sampling is synchronous, you can notch the fundamental.

I did a 4046 PLL driving a MF10 (?)filter to notch out the fundamental
on mains about 20 years ago.ISTR that with a high Q filter any spikes
would detune the notch for quite some time, while it re settled. I
never got around to putting a BPF infront of the PLL, as something
else turned up to work on


martin

 

[MooseFET]

Hi

I was wondering if anyone knows of an efficient way to calculate the THD
of a 60Hz sine wave using a basic microcontroller. I was hoping there
is a way to do this without using a full FFT. Is this possible?

Scott

The first step is to remove the 60Hz part. This is harder than it
sounds. You need to match the signal frequency exactly. There are
two ways to go at this. One is to phase lock the sample rate of the
ADC to the input so that it does an integer number of samples per
cycle. The other is to work out exactly how many samples (with
fractional part) are in the cycle.

I will assume you do the former. If you do the latter, there is a bit
more work to this.

If you write a bit of code that does this sort of thing:

FOR J = 1 to SAMPLES_PER_CYCLE
Y(J)=0
NEXT J

FOR I = 1 TO CYCLES_PER_SAMPLE
FOR J = 1 TO SAMPLES_PER_CYCLE
Y(J) = Y(J) + ADC
DELAY AS NEEDED
NEXT J
NEXT I

When you get done you have an array that holds the shape of the
waveform with the signal to noise improved by
sqrt(CYCLES_PER_SAMPLE). If you now remove the 60Hz, you have the
distortion with the noise reduced.

I real life, it is likely that you will want to remove the 60Hz as you
total up the distortion. This takes less memory than leaving the 60Hz
in place until you are ready to find the distortion because you can
use shorter numbers.

 

[Vladimir Vassilevsky]

Hi

I was wondering if anyone knows of an efficient way to calculate the THD
of a 60Hz sine wave using a basic microcontroller. I was hoping there
is a way to do this without using a full FFT. Is this possible?

Of course. Pretty much any microcontroller would do. There are two very
simple ways:

1. Measure the energy of a fundamental and all required harmonics
sequentually doing one or two frequencies at a time. Just multiply by
sin/cos LUT and accumulate.

2. Find the distortion curve by the synchronous accumulation over a period
of the fundamental. Then convert the distortion curve to THD by method of N
ordinates.

Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com

 

[John Larkin]

Hi

I was wondering if anyone knows of an efficient way to calculate the THD
of a 60Hz sine wave using a basic microcontroller. I was hoping there
is a way to do this without using a full FFT. Is this possible?

Scott

If you're not trying to measure very low distortion levels, it might
be feasible to pull out the 60 Hz fundamental with a digital filter
algorithm, either a highpass or a notch, possibly a combination, ie a
highpass elliptical filter. The good thing about AC line frequency is
that it doesn't usually change much.

So compute the trms value of the unfiltered and the filtered samples
and do the math... fairly simple.

Or use an *analog* filter and a 2-channel adc to sample the raw and
filtered signals. Some of the switched-capacitor filter chips are
spiffy, with a bit of anti-aliasing help.

I did an ac power meter that computed harmonics. It had a sine lookup
table and did DFTs on a line-by-line basis, on successive harmonics of
60 Hz, up to the 16th or something like that, brute force. It ran on
an MC6803 (min instruction time 2 usec) and wasn't terribly slow. The
assumption was that both the 60 Hz line and the sample rate were
precisely known, which is fine for things connected to the grid. I
might be able to find the code.

John

 

[Don Lancaster]

Hi

I was wondering if anyone knows of an efficient way to calculate the THD
of a 60Hz sine wave using a basic microcontroller. I was hoping there
is a way to do this without using a full FFT. Is this possible?

Scott

http://www.tinaja.com/magsn01.asp


--
Many thanks,

Don Lancaster voice phone: (928)428-4073
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552
rss: http://www.tinaja.com/whtnu.xml email: [email protected]

Please visit my GURU's LAIR web site at http://www.tinaja.com

 

[Tim Wescott]

Yes, it is.

Calculate the total energy in the signal.

Then find the best-fit 60Hz sine wave in the signal (take John Larkin's
suggestion and do a DFT, or use the overly-hyped Goertzel algorithm).
Find its energy.

Subtract the two -- that's your harmonic energy + noise.

--
Tim Wescott
Control systems and communications
consultinghttp://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html

I see what you are doing, and it sounds simpler than my suggestion, but
if the THD isn't really crappy, this kind of subtraction could mix
rounding noise due to the finite bitsize, i.e. add quantization noise
that really is not part of the THD.

What I was thinking about was to unwrap the signal with an arcsin, which
produces a straight line. [Essentially phase accumulation.] Then LMS
that data. The intercept and slope should allow an optimal sine wave to
be created for the subtraction purpose.

However, the more I think about this, some sort of sampling scheme phase
locked to the 60Hz signal could be more productive. Once the sampling is
synchronous, you can notch the fundamental.

_I_ suspect that anything either of us could cook up would be subject to
quantization noise, so a designer would want to carefully check for that,
and cope with it.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

 

[[email protected]]

I see what you are doing, and it sounds simpler than my suggestion, but
if the THD isn't really crappy, this kind of subtraction could mix
rounding noise due to the finite bitsize, i.e. add quantization noise
that really is not part of the THD.

What I was thinking about was to unwrap the signal with an arcsin, which
produces a straight line. [Essentially phase accumulation.] Then LMS
that data. The intercept and slope should allow an optimal sine wave to
be created for the subtraction purpose.

However, the more I think about this, some sort of sampling scheme phase
locked to the 60Hz signal could be more productive. Once the sampling is
synchronous, you can notch the fundamental.

_I_ suspect that anything either of us could cook up would be subject to
quantization noise, so a designer would want to carefully check for that,
and cope with it.

--
Tim Wescott
Control systems and communications consultinghttp://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html

I've used FFT based distortion analyzers, though not any late model
gear. They tend not to be as good as the traditional notch filter
scheme UNLESS the THD is really bad.

 

[MooseFET]

On Sun, 20 Jan 2008 04:00:38 +0000, Scott Ronald wrote:
Hi
I was wondering if anyone knows of an efficient way to calculate the
THD of a 60Hz sine wave using a basic microcontroller. I was hoping
there is a way to do this without using a full FFT. Is this
possible?
Scott
Yes, it is.
Calculate the total energy in the signal.
Then find the best-fit 60Hz sine wave in the signal (take John Larkin's
suggestion and do a DFT, or use the overly-hyped Goertzel algorithm).
Find its energy.
Subtract the two -- that's your harmonic energy + noise.
--
Tim Wescott
Control systems and communications
consultinghttp://www.wescottdesign.com
Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html
I see what you are doing, and it sounds simpler than my suggestion, but
if the THD isn't really crappy, this kind of subtraction could mix
rounding noise due to the finite bitsize, i.e. add quantization noise
that really is not part of the THD.
What I was thinking about was to unwrap the signal with an arcsin, which
produces a straight line. [Essentially phase accumulation.] Then LMS
that data. The intercept and slope should allow an optimal sine wave to
be created for the subtraction purpose.
However, the more I think about this, some sort of sampling scheme phase
locked to the 60Hz signal could be more productive. Once the sampling is
synchronous, you can notch the fundamental.

_I_ suspect that anything either of us could cook up would be subject to
quantization noise, so a designer would want to carefully check for that,
and cope with it.

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html

I've used FFT based distortion analyzers, though not any late model
gear. They tend not to be as good as the traditional notch filter
scheme UNLESS the THD is really bad.

The FFT method can perform as well as the notch type but to do so,
they end up costing more than the notch type. They have to maintain a
very low distortion all the way to the digitization. This needs about
as much design work as making the notch type.

 

[[email protected]]

00:38 +0000, Scott Ronald wrote:
Hi
I was wondering if anyone knows of an efficient way to calculate the
THD of a 60Hz sine wave using a basic microcontroller. I was hoping
there is a way to do this without using a full FFT. Is this
possible?
Scott
Yes, it is.
Calculate the total energy in the signal.
Then find the best-fit 60Hz sine wave in the signal (take John Larkin's
suggestion and do a DFT, or use the overly-hyped Goertzel algorithm).
Find its energy.
Subtract the two -- that's your harmonic energy + noise.
--
Tim Wescott
Control systems and communications
consultinghttp://www.wescottdesign.com
Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html
I see what you are doing, and it sounds simpler than my suggestion, but
if the THD isn't really crappy, this kind of subtraction could mix
rounding noise due to the finite bitsize, i.e. add quantization noise
that really is not part of the THD.
What I was thinking about was to unwrap the signal with an arcsin, which
produces a straight line. [Essentially phase accumulation.] Then LMS
that data. The intercept and slope should allow an optimal sine wave to
be created for the subtraction purpose.
However, the more I think about this, some sort of sampling scheme phase
locked to the 60Hz signal could be more productive. Once the sampling is
synchronous, you can notch the fundamental.
_I_ suspect that anything either of us could cook up would be subject to
quantization noise, so a designer would want to carefully check for that,
and cope with it.
--
Tim Wescott
Control systems and communications consultinghttp://www.wescottdesign.com
Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html

I've used FFT based distortion analyzers, though not any late model
gear. They tend not to be as good as the traditional notch filter
scheme UNLESS the THD is really bad.

The FFT method can perform as well as the notch type but to do so,
they end up costing more than the notch type. They have to maintain a
very low distortion all the way to the digitization. This needs about
as much design work as making the notch type.

My mind was back in the day when all you had were 16 bit converters.
However, Crystal makes 24 bit converters that look super on paper.
Most sound card implementation of these mash chips don't live up to
the datasheets.

 

[Vladimir Vassilevsky]

My mind was back in the day when all you had were 16 bit converters.
However, Crystal makes 24 bit converters that look super on paper.
Most sound card implementation of these mash chips don't live up to
the datasheets.

Very mediocre audio cards have the input with the THD at the order of
0.01%. This is more then enough for the measurement of the harmonics of
the power frequency.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com