How to measure speaker impedance?

This question is asked SO often, and I try to answer it SO often, that I
thought I would sit down and take the time to write a real FAQ about it.
Below is the opus I created today. I am also sending it off to the FAQ
masters in hopes that it will be included somewhere.

++
THE IMPEDANCE MEASURING FAQ
Dick Pierce

Copyright 1998 Dick Pierce. Public, non-
commercial distrubution allowed with this
copyright noticed attached. All other uses
prohibited, including use in for-fee media
or distribution of any kind.

INTRODUCTION

An oft-asked question is "What's a simple way I can measure the
impedance of my loudspeaker or driver?" The answer to that
depends upon a lot of things, like what equipment you might have
at your disposal, how much work you want to put into the
enterprise, and so on. I'll present one method here that can
give reasonably accurate results with the bare minimum of test
equipment needed.

WHAT IS IMPEDANCE?

Simply stated, it's the obstacle to current flow provided by an
electrical circuit to the imposition of an AC electrical signal.
It is like resistance in that sense, but different in that it is
almost always (in these applications) frequency-dependent (it's
value is different at different frequencies) and it is "complex"
(meaning that, mathematically, it is a vector quantity,
consisting of a resistive and a reactive part)

The law governing the relationship between DC resistance,
voltage and current, known as Ohm's law, is:

E = I * R

where E is the impressed voltage in volts across the resistance
R in ohms, resulting in a current I in amperes flowing through
that resistance. Simple high school algebra allows us to
rearrance this basic equation:

E E
R = --- and I = ---
I R

AC impedance, voltage and current follow the same basic rules:

E = I * Z

where, now, E is the impressed voltage magnitude in volts
impressed across the impedance magnitude Z in ohms, resulting in
a current magnitude of I in amperes flowing through that
impedance. And, as above, we can rearrange out equations:

E E
Z = --- and I = ---
I Z

Now, I use the terms like "impedance magnitude" here. The AC
impedance, as mentioned above, is a complex value: it is vector
sum of the resistive (or "real") and reactive (or "imaginary')
components of the impedance. That vector sum is computed as (for
example):

2 2
Zm = sqrt ( R + X )

where R is the resistive portion and X is the reactive portion.
(In this context, real and imaginary have very specific
mathematical meanings: an imaginary number is not one that
exists only in one's imagination, rather it is a number that has
the square root of negative one as one of its factors.)

Because of the enrgy storage properties of the reactive portion,
the instantaneous current flowing through the impedance is not
in step or in phase with the instantaneous voltage across it.
Rather is precedes or follows the voltage by some amount
dependent upon the ratio of reactance to the resistance,
specifically:

-1 X
P = tan ( --- )
R

where P (more properly, the Greek letter Phi) is the phase
angle, usually expressed in degrees. It should be noted that in
the grand scheme of things, both the resistance R and the
reactance X can take on any value, positive, negative or zero.
However, in the case of loudspeaker impedance, R will never be
negative, and almost certainly never 0, while X can either be
positive (inductive) or nagative (capacitive) or 0. Looking at
the equation for the impedance phase angle, this means that the
phase angle of the impedance will always be outside the range of
-90 to +90 degrees. (Indeed, it is quite unusual to find the
impedance phase to be outside the range of +- 70 degrees). The
fact that the real or resistive portion of the impedance is
always positive ensures that the impedance phase angle never
exceeds these 90 degree limits. (for thosewith a mor etechnical
inclination, that means that the entire impedance is confined to
the right of the imaginary axis in the complex s-plane).

Basically, all we need to do is then to put a voltage across the
unknown impedance, measure the current going through it, plug
the numbers into the following equation (from above):

E
Z = ---
I

And out pops the impedance, Z.

In principle, this is abosolutely correct, but in practice, it
is more difficult. The main reason for this is the range of
typical values for the impedance of most loudspeakers and
drivers (from a few ohms to a few dozen ohms) combined with the
sensitivity of most common measurement instruments.

Imagine putting a voltage of 10 volts across an 8 ohm
loudspeaker. Ohms law says that the current going through that
speaker will be:

E 10
I = --- = = 1.25 amps
R 8

While 1.25 amps is a convenient current to measure (it's large
enough to ensure reasonable accuracy with many comment meters)
it is a LOT of current to put through the voice coil, and that
poor speaker and the people near it will be subjected to a
rather deafening level of sound. Additionally it does pose some
risk of damage to some drivers.

MEASUREMENT SCHEMES

A common assumption is that one needs two meters: one to measure
voltage placed across the impedance and one to measure current
placed in series with the impedance. Then, by Ohms law:

E
Z = ---
I

However, this poses some problems. As mentioned above, it
requires a hefty amount of current to get enough of a reading to
be dependable. Most commonly available meters that measure AC
current at all well aren't very sensitive. There is also the
issue of having to go through the calculation for each and every
frequency being measured.

Another method that seems to have escaped many peoples'
attention is the "impedometer." This is nothing more that a
calibrated constant current source. When properly set up, there
is no calculation required and it is reasonably accurate over a
wide range of impedances. Another advantage is that it requires
less equipment than other methods. It is the impedometer method
that we will discuss here.

TEST INSTRUMENTS

Very little is required for a properly working impedometer.
We'll enumerate the requirements here.

1. AC sine wave generator

This can either a function generator (usually meaning an
instrument that has the capability of sine, square, and
triangle waves, and often has pulse output as well) or a
Wein-bridge or twin-T audio oscillator. The major
requirements are stable AC output, stable frequency,
reasonably low distortion (less than 1%), flat frequency
response over the audio bandwidth, and reasonable voltage
output (10 volts or more into 1 kOhm is good).

There are a lot of new instruments that are acceptable,
funtions generators by B&K, Tenma, Leader and others can be
had, but often cost several hundred dollars new. Their
performance is generally more than good enough, and they are
versatile instruments for other purposes as well. Often they
have frequency ranges far in excess of what's needed, like
0.02 Hz to 2 MHz, but that's okay, too.

On the other hand, you can often find used equipment that is
very serviceably as well as inexpensive. I have seen
excellent units from the likes of Wavetek an Krohn-Hite for
under $100. In working order, they have superb
specificationa and are ideal for this sort of use. Their
distortion is not the lowest (because, like other function
generators, they synthesize the square wave frm the triangle
output), but, for impedance and frequency response
meaasurements, they are superbly accurate for audio use.

One of the all-time best sine generators is the venerable HP
200 audio ooscillator. I have seen them at swap meets and
even at yard sales for as low as 5 dollars. The have good
frequency response, good stability and high output voltage
(5 vots into 600 ohms). There are several variants, the 200
AB and 200 CD are the most common and both are equally good.
Look for examples from General Radio or GR as well. The
GR1309 can often be had for $50 and can be tuned to have
very low distortion, under 0.05%, while 1304 will do 20-20
kHz without range sweeping and has high ouput voltage as
well. Be preapred for a little tune-up work, like cleaning
and lubing dial shafts, amybe replacing a tube and an
electrolytic capacitor or two. Otherwise, these units last
absolutely forever. I cannot recommend them too highly.

2. AC voltmeter

This can either be an analog or digital unit. Ideally, it
must be capable of reading down to about about 10 mV full
scale with reasonable accuracy. It must also have flat
frequency response over the audio range.

Unfortunately, the sensitivity requirement eliminates most
"passive" VOMs (volt-ohm-milliammeters), including the
ubiquitus and venerable Simpson 260 (which is truly
unfortunate, because the 3 I have here of different vintages
all have
...
read more »

Why not be simple? Speakers typically come in specific flavors, 2ohm, 4ohm, 8ohm, 16ohm.

Measure the dc resistance with your cheapo radio-shack ohm-meter, and round up to the nearest reasonable value. if you measure 14ohms, that's a 16 ohm speaker. If you measure 3 ohms, that's a 4 ohm speaker.

An electrical engineer with access to a signal generator and the knowhow to set up a full accurate test bench isn't going to be asking how to measure speaking impedance on a diy website...

Really don't understand why people like to make simple things complex, I see so many examples.
1. of course you need sine wave because the impedance is a function of frequency. But the speaker shall have min power so that it is all most in sleep.
2. add a know resistor in series with the speaker, thus the resistor and impedance makes a voltage divider, Vo=Vi(R/(R+Z)), meaasure Vi,Vo and calculate Z.

In <6se5ku$2i.net at 02:43 PM, "Eirik Andreassen" <
Using your multimeter to measure the current and voltage may be a problem
because very few multimeters have a frequency response that is good enough
for audio work. Check the meter's specs. You may find that it is rated for
60 to 400 Hz.

Always know the accuracy of your meter. Digital meter specs are
interesting. There is a percentage and a digit spec. While you may have a
0.5% or better basic accuracy, they'll also throw in a "digit" spec. which
says that the least significant digit can't be trusted within "n" digits.
I've seen the digit spec. as high as seven -- which means that the last
digit can't be trusted!

In any case don't use a mutimeter to directly measure the current because
you will be using a sweep of frequencies and you don't know the impedance
of the meter.

A standard trick for this measurement is to use a constant current source
-- a resistor in series with the generator and the speaker. If you use a
resistor value that is much larger than the expected speaker impedance,
the current won't change enough over a range of frequencies to bother the
measurement. Calculate a few typical values and satisfy yourself that this
trick works.

Pick a resistor value (don't use a wirewound resistor) and generator
output that yields a convenient current -- 1 or 10 mA. Measure the voltage
drop across the speaker, shift the decimal point, and you're done! Keep in
mind that you don't need three or four digits of precision for your
results. Also, since you will be dealing exclusively with a single
frequency sine wave at each data point, you can use an RMS or average
responding (but RMS calibrated) voltmeter.

Conceptually it is possible to use your sound card and some programming to
make the measurement. If you attempt the feat, be sure that your sound
card has a decent frequency response at the frequencies of interest.


(Barry Mann)

Just bought an LCR meter.... soooooooo simpleeeeeee

Http://www.mitedu.freeserve.co.uk/Theory/inzoz.htm

I like innovation when you are designing quality assurance tests.
If you want a professional test you have the option of looking up ASTM tests which are developed by the engineering community or else using software - some is free like ARTA if you have a computer. I assume you want something handheld and accurate. The previous posts pointed out that it is harder to come by than you may think. I have found that low currents like speaker coil movement output (the actual output impedance, not the input impedance being assumed by other posts) is probably best approximated by vibrating the cone at 1000 herz (a standard) and using a handheld RF meter - I perfer UHF as digital has gone UHF instead of VHF. The new digital ones run about $50 but the used coil needle older types run about $20. The point is that that type of instrument is sensitive enough to pick up the speaker output.
Then there are other concers about quality. Thicker coil wire makes current stick to the inside of the wire because of shorter path length around the inside of the wire. The center of the coils also is worst because of coils next to it. But when doing engineering DIY - its ALWAYS best to start low cost and work up to better measurement equipment and quality methods.