From: louis@tronix.SignalPath.on.ca (Louis Bertrand)
Subject: Re: Distortion in amps.
Newsgroups: rec.audio.car
Date: 5 Apr 92 19:18:36 GMT
Distribution: world
Organization: Signal Path Designs

yystg@lims02.lerc.nasa.gov (Steve Graham) writes:

> What is the method for calculating THD, I asume now that what 
> I said on what THD is was was right, but I was asking how you calculate it.

There seems to be a lot of questions about THD and other 
(occasionally meaningless) numbers.  Bear with me as
I attempt to explain the basics.  Those who have facts
to add or corrections to bring, e-mail me and I will
attempt to roll it into a FAQ document.  Any suggestions
for the organisation of this document or topics to be 
covered are also welcome.

Now that I've firmly put my head in the noose, 
watch me dance on the audio specmanship balance beam!

Amplifiers:
Amplifiers amplify the input signal voltage and provide the current
to deliver the power into the load (speakers in our case).
Car stereo amplifiers are voltage amplifiers.  They take a
voltage signal (aprox 1Vrms) at their high impedance input
(10Kohms typically).  They provide a given voltage output
at whatever current is required to maintain the voltage
into the load.  In other words, V(out) = Gain x V(in).
The output also amplifies the noise inherent in both the
input signal and the amplifier's circuitry.

Real-world amplifiers have a Gain value that is not a constant
for all input voltages, and at all frequencies.  Thus, amplifiers
distort (don'tcha know?).

If the load impedance is too low for the amp, the voltage
waveform collapses.  If the input voltage is beyond what the
amplifier can handle, the output waveform clips.
Cross-over distortion results from the push-pull output
stage of the amplifier.  Picture a waveform that is going
down through the zero-voltage point.  The positive side of
the amplifier circuit is turning off, but the negative side
hasn't begun turning on.  The turn-on delay causes the output
waveform to momentarily flatten out, leading to distortion.

Feedback in amplifiers compensates for distortion by comparing
the output with what it ought to be.  This works to a certain
extent but massive amounts of feedback cannot make a crappy
output section design sound good.

Power Specifications:
Amplifiers quote their power into a given load (4 ohms
is standard in car audio), assuming (ha ha ha) that the
load is simply a resistor.  The power spec must include
the THD level measured at that power level (can be
as high as 10% -- read carefully!).  The measurement is
typically made with a 1KHz sine wave.

Power is the RMS voltage squared over the load impedance.
Theoretically, an amplifier's power doubles if the load
impedance is halved (two equal loads in parallel)


THD+N: Total Harmonic Distortion plus noise
Harmonics of a sine wave are sine waves at integer multiples of
the original sine wave.  They are due to distortion of the shape
of the sine wave by the amplifier's non-linear response.

The usual measurement method is to use a sine wave as an input,
and null the sine wave in the output with a good notch filter.
Whatever is left over is assumed to be harmonics of the
original sine wave plus the thermal noise of the amplifier.

Measurements are the ratio of the original sine wave over what's
left over (power measurement into a reference load), quoted 
either as a percentage (e.g. 0.01%)  or in decibels (dB).
A-weighting is a filter applied to the distortion products
(after nulling, before measuring) to simulate the response
of the ear.  It always gives you a better number, so is 
almost always used in car audio to knock out noise to the
switchmode DC-DC converters.  For reference, 1% THD is when
the waveform just starts clipping, and 10% is when you start
complaining.

THD+N is the easiest measurement to make, and is best at high 
levels (but before clipping!) because the signal swamps the 
crossover distortion and the thermal noise.
But who listens to sine waves anyway?


IMD: Inter-modulation distortion:
The technique is similar to THD+N, except the input signal is
two sine waves (1KHz and 7KHz) at a 4:1 amplitude ratio.  Knock
out the two sine waves with notch filters and whatever is left 
over is due to THD and the inter-modulation (a.k.a mixing, 
heterodyning, multiplication) of one signal by the other.
IMD is rarely quoted in car audio but is useful in the engineering
lab to ferret out any bizarre circuit effects.  It is more useful
in broadcasting applications.


TIM: Transient Inter-Modulation Distortion.
The theory behind this is that THD and IMD are continuous signals
and don't tell you anything about high an amplifier will
respond to a suddenly applied signal, how how the amplifier
will distort the shape of a transient waveform.
[your humble author will leave the exact definition of the
subject for later -- there are many Audio Engineering Society
Journal articles about this, and they all disagree with each other]

Newer test instruments use complex test signals to simultaneously 
measure time and frequency response.  The high end audiophile
journals (The Absolute! Sound and Audiophile) use the MLSSA 
waterfall display to analyse amplifiers and speakers.  Audio 
Precision uses DSP techniques to provide separate distortion 
and noise measurements.  If car audio manufacturers (and 
reviewers) started quoting more sophisticated test measurements, 
we might have a better chance of evaluating an amplifier on specs 
alone.  Unfortunately, marketroids would blow their head gaskets.

Until then, listen and trust your ears.  
If you don't like it, it's not for you

Thank you for your time.
 -- Louis
--
Louis Bertrand   *   Lynden, Ontario, Canada   *   (416) 648-8066
Signal Path Designs (Analog - Digital - Audio - Embedded uCs)
louis@SignalPath.on.ca (new -- may not work yet)
louis%tronix@maccs.dcss.mcmaster.ca (old -- still works fine)