# Newbie Q: Speaker parameters mesurment?

Last response: in Home Audio

Anonymous

July 12, 2005 6:24:25 PM

Archived from groups: rec.audio.tech (More info?)

I would like to measure the parameters of speakers - T/S, impedance,

inductance, etc. but can't find very much info on the web. I have

electronics experience so I have test equipment (multimeters, signal

generator, frequency counters, etc.). I looked at the sound

card/software approach, but I'm sceptical of it, does anyone have any

info/pointers on doing it the 'old-fashioned' way?

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I would like to measure the parameters of speakers - T/S, impedance,

inductance, etc. but can't find very much info on the web. I have

electronics experience so I have test equipment (multimeters, signal

generator, frequency counters, etc.). I looked at the sound

card/software approach, but I'm sceptical of it, does anyone have any

info/pointers on doing it the 'old-fashioned' way?

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More about : newbie speaker parameters mesurment

Anonymous

July 12, 2005 6:51:20 PM

Nigel Thomson wrote:

> I would like to measure the parameters of speakers - T/S, impedance,

> inductance, etc. but can't find very much info on the web. I have

> electronics experience so I have test equipment (multimeters, signal

> generator, frequency counters, etc.). I looked at the sound

> card/software approach, but I'm sceptical of it,

Well, depending upon what "it" is, "it" can be faster, more

accurate, more repeatable and more error-free than doing it

the "old fashinoned way." I've used a number of said products

and will never measure Thiele/SMall parameters the old fashioned

way ever again. Mind you, it's oftenm the case that when I have

to measure drivers, I'll have to measure a couple of dozen of

them at one time, as a manufacturer will send me a pile of samples

to evaluate, so anything that makes it faster, more accurate, more

repeatable and less error-prone is fine by me.

But, ...

> does anyone have any info/pointers on doing it the 'old-

> fashioned' way?

Below are two articles I have published around these parts in the

past. The first is the basics of measuring impedance, and measuring

impedance is a necessary part of measuring Thiele/Small parameters

You're best reading these using a fixed-space font.

---------------------------------------------------------------

THE IMPEDANCE MEASURING FAQ

Dick Pierce

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 energy 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 negative (capacitive) or 0.

Looking at the equation for the impedance phase angle, this

means that the phase angle of the impedance will always be

inside 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 those with a more technical 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 absolutely 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, no

calculation is 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 oscillator. 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 (25 volts 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 prepared

for a little tune-up work, like cleaning and lubing dial

shafts, maybe 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 excellent frequency response to well

beyond 50 kHz on the 2.5 volt AC scale, sigh).

Equally unfortunate is the fact that many hand-held DVMs

(Digital Volt Meters) have poor high-frequency response,

often showing significant errors as low as 500 Hz.

Generally, most meters that advertise themselves as "true

RMS" have adequate frequency response.

Again, turning to the used or surplus markets, there are

treasures to be had. The Hewlett-Packard 400D has all the

needed sensitivity (1 millivolt full scale), wide

frequency response below 10 Hz to 1 MHZ), excellent

linearity and are plentiful and easy to find. Again, I

have seem them for as low as $25 in serviceable

condition, and even arrived 30 seconds too late one day

as I saw 20 of them being crushed at a local landfill!

Again, they may need new capacitors here and there and

occasional new tube, but little else is needed to keep

them going. Most of the HP 400 series are equally useful.

Look also for meters from GR, Ballantine, B&K and others.

Heath made an AC millivoltmeter that is quite useful.

3. 1 KOhm resistor

This need not be anything fancy. A noninductive carbon or

metal film, 1/2 watt 5% resistor is really all that's

needed. This will turn our oscillator into a current

source.

4. 4, 8, or 10 ohm precision non-inductive resistor

This is used to calibrate the impedometer. It can be any

value that's close to the impedance you expect to

measure. Just make sure that it's non-inductive (film

resistors work here) and that you know its resistance

accurately (a 1% or better tolerance is ideal). You'll

only need a small resistor, 1/2 watt is probably fine.

5. Frequency counter

Not essential, but considering that the frequency dial

calibration on many oscillators and function generators

can be considerably off, it's a useful thing to have.

Digital frequency counters can be had both on the new and

used market for not a lot of money. Remember that the

accuracy is directly proportional to the reciprocal of

the needed accuracy: if you want 1/10 Hz accuracy, you'll

have to wait 10 seconds to get there.

6. Oscilloscope

Not essential, but useful for several things: it can help

you verify that nothing is being distorted. Connected as

an X-Y scope, it can help you unambiguously find the

exact resonant frequency and also enable you to (via a

rather laborious procedure) estimate the phase angle of

the impedance. If you're going to get a scope, get one

that has X-Y capability with no less than 10 mV/cm on

both axes. Scopes fitting the bill can be found for

anywhere from $50 used to many tens of thousands of

dollars. Look for an old HP 130, the best audio scope for

the cheapest money around. There are some big-ass

Tektronix 500 series that are huge and cheap, also look

for 400 series, and scopes by Phillips and others.

7. Miscellaneous

If you're going to be doing this a lot, buy a metal box,

some good 5-way binding posts and some high-quality

switches, and make your life easier. Use good sized wire,

because a 1/2 ohm of parasitic resistance in your test

harness is a 1/2 ohm that WON'T be there when you connect

your crossover.

MAKING AN IMPEDOMETER

The actual connection is very simple. Let's refer to the

diagram below:

+---- 1 kOhm ----+------------+

| | |

+-----+ +------+ +---+---+

| | | | | switch

Sine wave | | AC V

Oscillator | | voltmeter o o

| | | | | |

| | Calibrated +------o

| 'X' 'Y' | resistor Driver

| | | +------o

| | | | | |

+-----+---+------+--------+-------+

If you need more signal level, you can insert an amplifier

between the oscillator and the 1 kOhm resistor.

Calibration is simple: connect the calibration resistor to

the output (via the switch, if you've constructed it that

way, or just hook the resistor where the speaker would be

connected). Adjust the output of the oscillator and the gain

of the meter until you get a reading in some convenient units

that is the same as the resistance of the calibrator. For

example, if the oscillator was putting out 1 volt into the 1

kOhm resistor, you'd probably find that the voltage across an

8 ohm calibrator was almost exactly 8 millivolts. Fine, now

you know that your impedomoter has a calibration factor of 1

mV/ohm. This is because we have calibrated our AC current

source for 1 mA output. Remember Ohms law:

E

Z = --- I = 1 mA, so Z (ohms) = E (millivolts)

I

You might want to adjust it for a higher level, like 10

mV/ohm. You see here why you might want an oscillator with a

nice high output voltage, because you might want to measure

the impedance at several different current levels. (I have a

laboratory amplifier that's capable of more than 100 volts at

100 mA into a 1 kohm load: this is very useful for measuring

drivers at reasonably high current levels).

It's a good idea to check the calibration across the entire

frequency range.

MEASURING IMPEDANCE

To actually measure the impedance, make sure your setup is

calibrated, then disconnect your calibration resistor and

connect your speaker. Dial the oscillator to the desired

frequency and then read the impedance. It's that simple.

If your want to know the impedance across the whole frequency

range, it's good to measure it at 1/3 octave intervals. This

will be enough to plot an pretty accurate graph of the

impedance curve. Here are the standard 1/3 octave

frequencies:

20 200 2000

25 250 2500

31.5 315 3100

40 400 4000

50 500 5000

63 630 6300

80 800 8000

100 1000 10000

126 1260 12600

159 1590 16900

To find a resonance, look for a frequency where the impedance

is at a maximum. In a typical loudspeaker system, or a

bass-reflex enclosure system, you'll find several such

maxima. Record them all.

Look for other "critical points" such as minima in impedance.

An oscilloscope can be useful here. Connect the X axis to the

oscillator output (shown as 'X' in the above diagram) and the

Y axis to the same place as the AC voltmeter ('Y'). Adjust

the gain of the X axis so that the trace takes up nearly the

whole width of the screen. The Y axis gain can be similarily

adjusted, but you'll have to keep changing it as the

impedance changes.

You'll notice that, over most of the range, the trace is an

ellipse aligned along a line going from the lower left to the

upper right (if it goes in the opposite direction look for a

switch on the scope called "phase invert" and push it). The

elliptical shape indicates that the impedance has both a

reactive and a resistive component. In fact, you can measure

the phase by measuring the relative "openness" of the

ellipse, though we won't go into that here.

What IS important is that at some frequencies, the ellipse

closes up into a line. This indicates the impedance is purely

reistive, and this will occur at the exact center of a

resonance, and is a reliable way of finding the resonant

frequency.

The trace can also tell you other things. If the ends of the

ellipse are flattened or distorted, it's likely that you've

exceeded the output voltage capability of your oscialltor or

amplifier. Sorry, only one way to fix it: turn it down and

recalibrate your impedometer. If the traces shows a figure-8

shape, especially near and at resonance, you're likely

looking at some non-linearity in the driver itself. Finally,

if your trace looks fuzzy or has lots of little wiggles on

it, you have an electrical inteference problem that you'll

have to cure.

CONCLUSION

The impedometer method provides a simple, inexpensive,

reliable, repeatable and reasonably accurate way of measuring

loudspeaker impedance, assuming you use reasonable

instruments and take care to check and maintain calibration.

There are certainly more steamlined methods, including new

computer based applications that are fast, very detailed and

accurate. Not everyone can afford such a solution, not

everyone has the time, and not everyone needs that level of

sophistication. The impedometer method is useful for

occasional measurements, and the equipment needed is quite

useful for an entire array of audio measurements.

----------------------------------------------------------------

Measuring Driver Thiele-Small Parameters

Dick Pierce

Assuming you have the means to measure the impedance magnitude

of a driver with reasonable accurcy, determining the

Thiele-Small smnall signal parameters of a driver requires but a

few simple measurements and some straightforward calculations.

Warning: make sure that you use consistent units throughout. I

highly recommend you use straightforward metric units of meters,

kilograms, seconds and derived units of newtons and so forth.

Here's how to proceed:

* Measure the DC resistance of the driver to test. This gives

you Re. [Let's say it's 6.5 ohms]

* Replace the calibration resistor with the driver to test. Do

not change the voltage from the generator!

* Adjust the frequency in the region of the specified

resonance until the voltage across the driver is at a

MAXIMUM. Record the frequency. This is Fs, the resonant

frequency [let's say it's 32 Hz]. Also, measure the voltage

across the driver. This is Re+Res. [let's say it's 42 ohms].

(using an oscilloscope set for phase measurement, Fs will

also be where the phase is 0).

* Calculate the ratio between the DC resistance (Re) and the

maximum impedance (Re+Res), call it Rc. [In this case, it

will be 42/6.5 or 6.46]

* Find the two frequencies on either side of the resonant

frequency f1 and f2 where the impedance is Re * sqrt(Rc) [in

this example, that impedance will be 6.5 * sqrt(6.46) = 16.5

ohms, and let's say that occurs at f1 = 22.6 Hz and f2 =

45.3 Hz].

* Calculate Qms as:

Fs sqrt(Rc)

Qms = -----------

f2 - f1

[in the example, it will be:

32 sqrt(6.46) 32 * 2.54 81.3

Qms = ------------- = ----------- = ---- = 3.58

45.3 - 22.6 22.7 22.7

* Calculate Qes as:

Qms

Qes = --------

(Rc - 1)

[in this example, it will be:

3.58 3.58

Qes = --------- = ------ = 0.66

6.46 - 1 5.46

* Calculate Qts as:

Qes * Qms

Qts = ---------

Qes + Qms

[here, it would be:

0.66 * 3.58 2.36

Qts = ----------- = ------ = 0.56

0.66 + 3.58 4.24

So, you have derived Fs, Res, Qms, Qes, Qts for the driver.

* Repeat the measurements in a sealed, leak-free, unlined test

box, and determine the equivalent values of Fc, Qmc, Qec,

and Qtc (use a box whose volume, Vb, is close to the

expected Vas for maximum accuracy). [In our example, Vb =

20L, Fc = 80 Hz, Qec = 0.95]

* calculate Vas as follows:

Fc Qec

Vas = Vb [ -------- - 1 ]

Fs Qes

[In our example:

80 * 0.95

Vas = 20 [ ----------- - 1 ]

32 * 0.66

76

= 20 [ ---- - 1 ]

21

= 20 * 2.62 = 52L

Our Vas is 52 liters].

You now have Fs, Re, Qms, Qes, Qts and Vas for the driver. From

these figures, with knowledge of the effective emissive area of

the driver (Sd), you can derive the electromechanical parameters

Mms (moving mass), Cms (mechanical compliance), Rms (mechanical

suspension losses) and Bl (transduction ratio).

Sd, as mentioned, is the emissive area of the driver: that part

of the driver which actually contributes to the total volume

velocity of the driver. You can get a very good approximation of

Sd by taking the diameter d of the driver, including about half

the width of the suspension:

Sd = pi (d/2)^2

The last bit of information we need is about the air around us:

p0 = 1.18 kg/m^3 density of air at STP

c = 341 m/s speed of sound at STP

>From there, the electromechanical parameters can be derived:

Mechanical compliance Cms can be derived directly from the

equivalent valume of compliance, Vas:

Vas

Cms = ------------

p0 c^2 Sd^2

Mechanical mass Mms is derived knowing the compliance and the

resonant frequency. Since:

1

Fs = ------------------

2 pi sqrt(Mms Cas)

then

1

Mms = ---------------

4 pi^2 Fs^2 Cms

The mechanical resistance, Rms, is what determines the

mechanical damping, Qms, thus:

1

Rms = -----------------

2 pi Fs Cms Qms

Finally, the Bl product can be derived using Fs, Qes, Mms and

Re:

2 pi Fs Mms Re

Bl = sqrt( ---------------- )

Qes

Finally, the reference efficiency, n0 is:

4 pi^2 Fs^3 Vas

n0 = -------- ----------

c^3 Qes

Copyright (c) 1993-2005 by Dick Pierce.

Permission given for one-time no-charge electronic

distribution with subsequent followups.

All other rights reserved.

-----------------------------------------------------------------

Anonymous

July 26, 2005 12:36:45 PM

"Nigel Thomson" <unknown@unknown.net> wrote in message

news:q228d15ko0s6s5to0kju424praudf91c4k@4ax.com...

> I would like to measure the parameters of speakers - T/S, impedance,

> inductance, etc. but can't find very much info on the web. I have

> electronics experience so I have test equipment (multimeters, signal

> generator, frequency counters, etc.). I looked at the sound

> card/software approach, but I'm sceptical of it, does anyone have any

> info/pointers on doing it the 'old-fashioned' way?

The Loudspeaker Design Cookbook by Vance Dickason has a section on measuring

speaker parameters.

Tim

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