LOUDSPEAKERS 4, 2012.

TESTING RESPONSE AND IMPEDANCE.

Unless loudspeakers are tested and measured adequately during their manufacture or repair work,
there is NO CHANCE that the result will ever sound very good. So the first item for this page on
DIY speakers manufacture deals with testing, because its most important, and nobody can ever
fully trust their ears.
Many people use an enormous amount of time to make wooden boxes for "normal" front radiating
dynamic drive units and some even make complex horn structures for horn loaded drivers hidden
from view, and all without real understanding of the electronics or maths involved or any use of
adequate testing procedures, so they end up constructing what I call noisy expensive firewood.
But at least good measuring gear allows anyone to see their own shortcomings, if they are not the
type who thinks he cannot ever make a mistake or cannot be any better.

I built my own very adequate test equipment to analyse what is right or wrong with the F response
of any speaker. It is all analog and rather old fashioned. There is perhaps no doubt that modern
PC based programs used with a sound card with built in pink noise source and a decent calibrated
microphone will enable even fairly inexperienced diyers to measure their own speakers.

I have not found I have any need to use a fully computer aided test method. I would have to set up
a PC in my listening room and have yet another table full of clunky dust gathering junk always in
my way when I am not testing speakers. Those with laptops will cope better. The computer
program approach has major advantages. The filter can have a higher number of bands, filtering is
all done digitally, so Q could be higher, and measurement is achieved much faster, because what I
do manually is done automatically. Just whether its more accurate and useful is a moot point.

There were plenty of expensive and well manufactured speakers made before any computers were
used during design and manufacture. There are now very many very poor quality speakers made
even though manufacturers have access to very cheap computing power.
I guess if I did have a PC with sound card and an analysis program, I could check it against my old
fashioned test gear I show here, and then see which seemed to be telling the truth or not.
Fig 1. Speaker testing set up.

The above diagram shows a power amp, microphone and a typical speaker arranged for response testing.
The pink noise test signal, microphone amp, and 34 band filter is in one metal box about the size of a large
shoe box and powered from a mains transformer and rectifier giving + / - 14Vdc supply rails for the
op-amps, transistors, diodes, switches, analog meter, and active and passive filter circuits with R&C
elements. There are no inductors used anywhere.

Fig 2. Pink Noise Generator.

Electronic "white" noise is generated using a single transistor Q1 with a low amount of current flow in the
backward or reverse direction to normal operation. The white-noise from such a simple device is a small
signal containing randomly varying frequencies, with randomly varying amplitudes, phase, and the amplitudes
rise at 3dB/octave over the audio band and beyond, and limited in rise at RF because of stray capacitance.

An op-amp U1 amplifies the noise. The op-amp has NFB and attenuation of HF above 25kHz. There is a
following R&C filter network giving attenuation of -3dB per octave so that the peak amplitude remains
constant to 20kHz, and thus white-noise is converted to pink-noise. A second op-amp U2 amplifies the
noise slightly, and its following R&C network shapes the noise amplitude contour to be flat because the initial
transistor does not produce an ideal noise signal with equal energy in an equal spaced range of F.

U3 is a unity gain buffer to power a 20k log pot allowing level of pink noise to be adjusted.Bandwidth of the
pink noise is 16Hz to 23kHz, -3dB points. Such a noise signal is excellent for testing loudspeakers.

The equalizing circuit is extremely important so that when any band is selected using a bandpass filter with 36
switchable bands, the average amplitude is the same for each band, where the Q of each band is between say
5 and 12. I have not tried having a BPF with Q of say 24, and with many more switchable bands. Having 36
bands is probably enough to capture the average level of each band. In any speaker, it would be unusual for a
peak or valley in the acoustic response to have a Q of more than 5. For example, say there was a sharp peak
in response of +6dB at say 47Hz, then the readings of energy in bands at 43Hz and 52Hz would both be
pushed up about +3dB. Very sharp response peaks or valleys cannot usually be compensated by LCR
crossover networks, but they can't be ignored either, but arranging the crossover to have a -3dB cut in the
2 bands of 43Hz and 52 Hz is feasible, and will lessen the effect of a peak.  Having a 72 band BPF may just
drive the speaker designer mad, because he is made aware of problems he may not be able to cure.
A suitable bandpass filter is best explained to you all by starting with basics.

Fig 3. Response of bandpass filter ( BPF ) and the basic schematic :-

Fig 3 shows a basic active BPF schematic on LHS which uses a "bridged T R&C notch filter"
for a negative feedback network applied between the low Ro output of an op-amp to the high
Rin inverting terminal of an op-amp. At very low F or very high F the op-amp voltage gain = 1.
But at Fo, op-amp gain becomes high because the NFB signal applied is much lower
than at op-amp Vo, because the filter network produces a null in the response at Fo.
The op-amp input circuit shows VR1 to set input level from any noise signal
source such as an amplified microphone signal picking up sound from a speaker driven with
pink-noise. C1 & R1 and R2 form a HPF to keep extremely low F out of the op-amp, with
R2 biasing the non-inverting op-amp input at 0V. R3 and R4 form a positive FB network
which about doubles the gain of the op-amp and increases the Q of the filter.
The bridged T RC filter has two R labelled Rb, and these are equal value R. But
each can be changed in value to alter the Fo to a desired F.
The actual BPF I have used has three selectable F ranges with each having 12 selectable
bands, so there are a total of 36 bands which can be tested.........

Fig 4. 36 band BPF schematic.

Fig 4 shows the bandpass filter consisting of a "bridged 'T' RC filter" in a series NFB loop around an op-amp.
This gives Q = 5 for each band of F. Adding about 6dB of positive FB viaR3 18k0 and R4 2M0 increases
Q to about 12, and although there are "gaps" between pass bands, the F response recorded seemed better
than if the PFB had been left out and Q of 5 used.
The Q is calculated as Q = Centre F / ( F2 - F1 ) where F1 is the LF -3dB cut off, and F2 is the HF -3dB cut off.
For example, Fig 3 shows a response for F0 = 52Hz. F1 = 47Hz and F2 =57Hz, so the bandwidth
= 57 - 47 = 10Hz, and Q = 52 / 10 = 5 approximately. It is unusual that peaks and dips in the speaker response
will have sharper Q or higher rates of attenuation in speaker speaker than any one filter pass band, so usually the
truth about a response can be measured using the filter as I have it. Fig 4 shows a bandpass filter with 36
switchable bands from 24Hz to 20kHz.
Bass band, Hz, :- 24, 29, 35, 43, 52, 63, 76, 92, 112, 136, 165, 200.
Midrange band, Hz, :- 240, 290, 350, 430, 520, 630, 760, 920, 1,120, 1,360, 1650, 2,000.
Treble band, kHz, :- 2k4, 2k9, 3k5, 4k3, 5k2, 6k3, 7k6, 9k2, 11k2, 13k6, 16k5, 20k0.

To achieve the centre F of each pass band, there are two series strings of resistors soldered around a 12
position 2 pole wafer switch, which was new old stock made in about 1950, and still very reliable after 12
years of use. The R values were carefully worked out to give bands as listed above, and accurate within
+/-3% of the nominal F. To achieve all the values of R11 to R34, you should use parallel and/or series
connected arrangements of 1% x 1/4 Watt metal film resistors which are quite cheaply purchased in resistor
packs containing say 10 R of all standard values between 10ohms and 1Meg-ohm.

Accuracy of the final values should be within +/- 3% as calculated. Don't rely on trials of parallel R using an
ohm meter, so you need to be able to calculate or access a calculator program which tells you what R to
use to make up each of the values needed above.
For example, to make up R11 = 1,695r,
Go to http://www.sengpielaudio.com/calculator-paralresist.htm

There is a table down the page where you can choose two standard resistance values to get close to the wanted
total.
Example :- Find 2 parallel R to give slightly under 1,695r, = 2k2 // 6k8 = 1,662r.
Then, 1695r - 1662r = 33r.
So you could use ( 2k2 // 6k8 ) + 33r = 1,695r total. The Resistance Calculator allows entering the total
wanted R plus some other value R1 above the wanted value, and then the needed R2 parallel value is calculated.
So you get 2k2 // 7k384 to make 1,695r.

But 7k384 is not near a standard value except 7k5 which isn't included in resistor packs, usually just 5k6 and 6k8.
So try final value = 7k384, and let R3 = 10k0, and it calculates R4 = 28k, and final R = 1,694r. Now 27k is a
standard value closest to 28k, and if you use 2k2 // 10k0 // 27k0, you get 1,690r, and error is 0.3% and quite OK.
Using only paralleled R means their leads may be all twisted up and soldered with only one lead at each end left
long so the compound R is easy to fit and solder neatly around the switch lugs.
There are THREE frequency ranges, with each determined by a switched pair of capacitors using a 2 pole x 3
position wafer switch. Some sort of press button switch could be used for changing cap values. 
The capacitor values are :-
Bass 4.7uF + 47nF, Midrange 0.47uF + 4n7, Treble 47nF + 470pF.

Good quality polypropylene caps should suffice, but to ensure the values are close to those nominated, the C
should be measured first. When the bandpass filter is completed, it must be tested to ensure your work is done
correctly. To check the capacitor values for each F range, use a sine wave signal generator with variable F but
fixed amplitude to apply signal to the lowest and highest F able to be selected. The signal is varied to "tune" for
highest amplitude of Fo.

A frequency meter must be use to record the frequency. If you get say 20Hz instead of the wanted 24Hz,
the C pillar of 4u7 must be made smaller, so use multiple smaller paralleled capacitors to achieve the wanted F.
If you get say 30Hz for the lowest Fo, you need to add parallel C to 4u7 until you have 24Hz. At the high end
of the band, the 47n may need adjustment to get the wanted 200Hz. Once that is done, you should get all the
other Fo I have listed.

The bandpass profiles of all 36 bands and their centre frequency can be plotted and recorded. You should be
able to record the F1 and F2 for each band where the response is -3dB, ie, if Vout = 1V at Fo, you need to
record F where Vout = 0.7V.

What you should find :-
All Vout for 36 bands have the same amplitude at Fo, except for 24Hz and 20kHz, which may be slightly
down because of the pink noise pass band contouring.
Fo where maximum Vout occurs should be within +/- 5% of the bands listed above, and Q of all bands
should be equal. I have Q = 12 with some slight positive FB around the BPF opamp.
Without PFB, the Q should be about 5.0
A low Q below 4 or a high Q above 15 wouldn't be useful.
When your BPF passes all tests using sine waves, it should be used to test your pink-noise signal to ensure an
equal amount of energy exists in each F band. After applying pink-noise to the BPF, the meter Vout should be
equal for each band. The response for all 36 bands can be plotted as a graph and the response should show
some reduction in level at 24Hz and 20kHz, but for all other F the response should be no more than +/- 1dB
above or below a reference level at say 920Hz It takes awhile to get used to levels needed to get above noise
but below overload of any part of the circuit. What you will find is that the meter amp as I have it will not give
a rock steady voltage reading.
This is because the amplitudes of all bands of signals vary at a random rate which includes LF rates which
tend to get past the time constants of peak detector circuit and meter circuit. The time constants should not
be any slower, ie, C3 and C4 in Fig 4 should not be higher values because you need the meter to be able to
swing to a different amplitude at a different Fo without having to wait too long. So when reading the meter,
it is normal to see the meter needle wobbling +/- 2dB around a centre value and you have to estimate the
reading.

THE METER should have a nice big meter face. Mine is 100mm wide, and maybe 40 years old. I removed
the glass face and attached a new cardboard blank dial to accept calibration markings with blank ink pen.
Setting up the meter takes some doing, because you have to figure out how much signal is needed to swing
the meter fully, and then you need to apply an adjusted fixed Vdc across the meter, maybe similar to how I have
mine with R8, R9, R10. The reason for the slight negative voltage at the negative meter terminal is because you
want the meter to read lowest reading -20dBV with say 0.01Vac signal, 0.1Vac at center reading, 0.0dBV, and
1Vac at the maximum reading, +20dBV. The dc op-amp U3 has a diode in a shunt NFB loop and it is
LOGARITHMIC amplifier. How I have it allows easy readings of voltages varying over a 100 fold value,
something quite impractical if the meter amp was a linear type. The meter face can be calibrated in 3dB steps,
and you will find all to be about equally spaced so thus can be divided up to give you even 1dB spacings.

CALIBRATING the meter is done using a sine wave applied to the peak detector input and while measuring
its Vac input value. The range of Vac produced at the input to the peak detector should be well above circuit
noise but below any overloading. Such matters take days and days to get correct.

Building my "box of tricks" took weeks of full time work with many late nights. If you only get 4 hours each
Saturday afternoon, expect to never ever finish any hand crafted electronics including any amplifiers or
speakers. If you were extremely keen, you could use a 2 pole x 24 position rotary switch to change the
resistance values. This means you could have 72 F bands, with 24 F in each band.
F band Hz numbers would then be :-
22, 24, 26, 29, 32, 35, 39, 43, 47, 52, 57, 63, 69, 76, 84, 92, 101, 112, 123, 136, 150, 165, 181, 200.
Q would need to be higher.

2 pole x 24position switches are available for constructing stereo switched attenuator volume controls.
But the switch needs to be very good quality to avoid intermittent contacts and perplexing variations and
annoyances during measurement.
High Pass Filter.
If you look closely, you can see a switchable high pass filter after the microphone amp. This filters out
large stray LF signals the microphone may have picked up below 300Hz, and which may affect the
measurement of frequencies above 300Hz by causing excessive meter needle movement.
This can be a useful thing when trying to measure midrange and treble units in an environment where there
is extraneous LF noise such as traffic. The whole unit I made is portable, and I have been asked to check
systems in homes of other people, and this is all usually just as easy as testing speakers here.
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Microphone and amp.
In about 1996, I made 3 microphones.
I use pre-tested and calibrated electret mic inserts from Hi-Q International in Melbourne in my home built
microphones. They cost less than $2 each. Such inserts are about 10mm in dia and two wires can be
soldered to the rear and then the mic "button insert" is fitted to a 300mm long length of 12mm copper
water pipe.
The mic is padded in cotton wool where it is flush with the pipe end to prevent hard contact with the pipe.
An RCA socket is fitted to the far end of the pipe, and the cost of such a good mic is $10 and some time.
I use an old heavy stage mic stand and clamp to alter mic height and position. I occasionally a change
mics to check on each other for drift, but after several years there has not been much change and I
continue to be able to build new speakers of reform older speakers and have them sing very well.

Behringer electret microphone.
A friend provided me with a new Behringer Calibrated Microphone which cost about $150 in 2007
and I tested a pair of speakers I was reforming at that time using both my own hand made microphones
and the swish looking Behringer. Mics were set up 150mm apart and at the 3 metre distance from the
speakers in my shed which is so cluttered that it is fairly non resonant. The response graphs plotted
from meter readings and for 20Hz to 20kHz varied less than +/- 1dB and after a moving mics a little
but keeping them close to each other, the variations when averaged became less than +/- 1dB.
I figured my homemade mics were just as good as the factory made "professional" microphones.

Measuring acoustic signal levels.
I set up speakers as they may be used in most hi-fi listening situations in a normal lounge room.
Small floor standers should be raised off the floor so the tweeter is about 1 metre above floor level.
My lounge-room is also cluttered, but carpeted and with enough soft furnishings to damp most HF and
it has sloping ceilings and irregular wall layout and a volume all up of 200 cubic metres.
Most people very much like my lounge room's acoustic properties. If I get a pair of speakers to
sound well and measure well in my room, then they usually "travel well" and sound very well in anyone
else's home. When pink noise is used for a test signal the rooms resonant behaviour is much avoided.
If pure steady F sine waves are used to test speakers in a normal room, one will get a graph with perhaps
15 peaks and troughs of up to +/- 15dB across the whole audio band and the measurement of speaker
output for narrow F bands is entirely ruined by the resonant behaviour. Anechoic chambers are needed
for sine wave response measurements, and such chambers or rooms are large, and only available at huge
expense. But by using pink noise which resembles the sound of a huge nearby waterfall, the phase of any
one frequency within the noise varies so much that an outgoing wave at say 1kHz cannot much excite
the resonant waves which exist in a normal echoic room, ie, a normal lounge room. The effects of the
worst resonances of a room are limited to 3dB variation in voltage measurements from the microphone.

The 4 mic positions are usually at 3.5M +/- 0.5M from a speaker and nearly on axis and between 0.7M
and 1.2M above floor level. The response will vary slightly with each of the 4 mic positions because even
with randomly varying test signal frequency and phase shift and level there is still some effect from room
resonances and reflections. I usually set up the pink noise generator level to give a healthy sound level
which is loud enough to drown out other noises in the environment.
SPL is roughly equal to an 88dB SPL reading from an SPL meter one might buy. Having mentioned such
meters, don't be tempted to use one for response checks, they are too inaccurate, and you must apply
signal to the speaker using a filtered band of frequencies from the pink noise. I find it better to apply the
whole band of pink noise 20Hz to 20kHz, and then filter the recovered and amplified microphone signal.
The best time to measure speakers is late at night when LF traffic rumble is at a minimum, and you can
turn off any noisy devices, and rumble from passing traffic or lawn mowers is at a minimum.
The graphs you may wish to plot for speakers may be drawn on printed paper copies of :-
Fig 5 blank F response graph sheet.

This blank sheet may be printed off by anyone wanting to plot F responses of speakers.
There are TWO frequency scales. One is arranged so there is even spacing of F bands along the audio band but
the rate of F increase is actually LOGARITHMIC, and there is a log scale at the bottom, for those who need to
plot F which are not equal to the even spaced F bands.

To draw a response graph, the gear is all set up with pink noise levels sounding loud enough to drown out most
other noise. A level measuring about 85dB on a cheap SPL meter should be OK. The bandpass filter is set for
the reference frequency of 1kHz, and output of the mic amp is adjusted to give a meter reading of what is 0.0dB
with meter needle in the centre needle REFERENCE position.

Some slight change in metered level will be seen to occur because the level of the filtered noise centered around
1kHz varies in amplitude at varying rates between very low F and much higher F. The peak detector circuit
produces a Vdc which floats on the peaks in the noise and the diode plus RC deector circuit cannot have a time
constant that is too high lest the meter take to long to settle at a value which best describes the average peak levels.
So one has to get used to a meter needle hovering around a centre reading position.

But it is easy to adjust the reference level so that the needle appears to hover around the 0.0 center meter position.
The bandpass filter may then be switched up or down along the audio band and at each selected F the meter needle
will hover around a center value which can be read off easily despite meter needle hovering maybe +/- 1 dB.
I take about 15 minutes to switch along all frequency bands and place a dot on the graph with a pencil at a given
dB level within +/- 0.5dB. The use of the above method becomes easy to use with practice without measuring
any actual voltage levels in volts. One only has to set up the meter to read the 0.0dB meter level for 1kHz,
then just plot where the needle goes along the band. Response testing of each speaker in a stereo pair should be
done with each in the same room position relative to the microphone. In an ideal world, the two speakers should
have very close responses, regardless of whether the response is very flat or not. Where large peaks and troughs
are measured exceeding +/-3dB, or that bass levels are poor in comparison to MF and HF bands, big one may
find that the crossover filters and the relative phase of drivers must be investigated for shortcomings.
It is extremely rare to find that any mass marketed speaker will give an ideal response. If there a response graph
shown in a user manual or shown on the rear panel of a speaker, I am usually led to believe how well the makers
have lied about their product. It is not uncommon for speakers to have a "loudness" characteristic with boosted
bass and treble so that people in shops will be well impressed.

The speaker impedance at all F should also be tested and graphed, but that operation uses a completely different
technique to be described elsewhere. Faults with crossovers or driver units may be discovered by measuring the
impedance.

The response measuring method may be used to improve a given pair of speakers or while producing a new pair
of speakers.

Testing each driver.
The response of each driver should be separately plotted during work to build new speakers or reform old speakers.
This must be done without any crossover present and at low enough levels to not damage tweeters with LF signals.
Dome tweeters are very easily damaged, yet it is important to plot their unfiltered response at least down
to 1kHz, when the intended crossover point is to be say 3kHz. To avoid damage, a capacitor of 47uF can be
used in series with a 4r0 tweeter which acts as a high pass filter with pole at 845Hz. For 8r0,
use 22uF. From the responses measured, one will begin to see what is possible to achieve with crossover filters.
The individual driver response with driver mounted within the intended enclosures and when powered by an amp
with Rout < 1.0 ohms may give puzzling variations in response levels. Bass, midrange and treble drivers may
show quite large variations of average levels.

The measured impedance for each driver in its intended enclosure must always be measured carefully, but this
 is not done using pink noise signals and will be discussed elsewhere. Once the response graphs for all drivers is
plotted without X-over filters, the amount of attenuation measured in dB which is required for each driver to
attain a flat response may read from the acoustic response graphs. Usually the bass will begin to roll off
somewhere below 100Hz. The -1dB level of bass response will set the levels of all frequencies above.
Depending on how well the bass driver suits its ported or closed box, one may be lucky to find the -1dB
bass response extends down to say 25Hz, and this may be 6dB lower than midrange response at 1kHz.
In fact the bass driver itself may produce a fairly flat response from 30Hz to 100Hz, then show a rise in
response level of 6dB between 100Hz and 1kHz, and between 500Hz and 3kHz, bass response may have
a number of peaks and troughs to +/- 9dB, caused by "cone breakup" where the cone deforms dynamically
to produce very odd behaviour. It is for this reason I don't like 2 way speakers with just a bass plus midrange
driver with a tweeter handling all F above 1kHz. The LOW bass frequencies is usually where speaker sensitivity
is at its very worst, but for a flat response the low bass should set the reference levels for all other frequencies.

The crossover filters have to flatten the acoustic response within the intended band for wach driver, and
eliminate some unwanted peaks, and make average levels for all drivers flat between say 70Hz and 20kHz.
The crossovers may also need to have resistance attenuation networks to lower midrange and treble output
levels, yet provide enough resistance termination to damp resonant behaviour of LC filters.

Combined effects of crossover filters must not present impedance that is too for an amplifier to safely drive.
So there are suddenly very many things to consider after making response tests. As testing proceeds,
the evidence about the real nature of the speakers is accumulated to be taken into consideration when designing
the Xovers.

Testing Speaker Impedance. This requires a power amplifier, 1k x 5Watt resistance, CRO, ie, oscilloscope,
and good wide band millivolt meter. DMM are useless above 2Khz to measure signal voltages.
Good voltmeters able to measure between 2Hz and 200kHz and all levels from 1mV to 1,000Vac, but
are difficult to find, and the CRO may be used to measure voltages well enough once it is adjusted for a
reference level at 1kHz. The signal generator must have variable F and be fairly well calibrated for F between
10Hz and 50kHz at least, and once adjusted for level, must give a flat response of sine wave within +/- 0.25dB.
Most good signal generators have Rout at 600 ohms, and have several ranges between 2Hz and at least 200kHz.
One might easily make such an oscillator with a Wien Bridge circuit using a single opamp and a good double
gang log pot of 50k, lamp globe used for Vo stability, and with THD < 0.5%, which is adequate for all
speaker tests.

Fig 6. Measuring Speaker Impedance.

The above shows a set up for measuring speaker Z. The power amp is fed by a signal gene to produce
a flat response signal of 10Vrms at the output. This is fed to a 1k0 series R to the speaker under test.
A CRO may be used to measure relative impedance levels. Actual impedance ohms may be calculated
well enough by measuring the voltage across speaker and x 100.

So if VLS = 0.08Vrms, then Z = 8 ohms. One can use a DMM to measure all voltages below 1kHz,
but most DMM become unaccurate above 1kHz. The CRO trace height may be set for
1 graticle = 0.08Vrms, or at frequency below 1kHz speaker has Z = 8 ohms, which is usually easy to
find with an 8r0 speaker which often has Z at 8r0 somewhere between 200Hz and 1 kHz.
If one moves to another F and trace height = 2 graticles, then voltage = 0.16Vrms and Z at the new
F = 16r0.

Most speaker impedances measured will be between 2r0 and 50r0.

Measuring Crossover Response.
So far we have dealt with measuring a complete speaker's acoustic response, or acoustic response of
an individual driver. We have also dealt with the method of measuring the impedance of complete speaker
or a driver.
But we also may need to measure the frequency response of the signal applied to speaker drive units
when the crossover filter is in place. If the speaker is one we are to repair or upgrade, the schematic of
the existing X-over filters must be plotted carefully by reading all L, C and R values on the X-over filter
boards,
and then figure out all track connections. Its sometimes not easy when tracks are hidden from view, and
where those absoluely attrocious variable driver level potentiometers or switches plus R have been used.
All speaker midrange and treble attenuators of any kind are best removed from all crossovers, but we will
still need to know what exists before moving in with soldering iron and long nose pliers.

Most good 3 way hi-fi speakers will have a separate X-over filter for LF, MF and HF drivers.
Where attenuators have been used, set them all for their mid position wherethe manufacturer was hopeful
that the acoustic response would be flat. The Z for the whole speaker can be measured and then for
each driver with X-over in place, then for each driver with no X-over.The test set up above may be
used for plotting speaker voltage responses after the X-over.

The amplifier output must be adjusted right down to maybe 0.2Vrms. The 1k0 series resistance is
shunted with a strap. Loud Sound will be heard from the speaker, and we might need ear plugs if annoying.
The CRO must be set up to read the voltage applied to each driver and for this some access is needed to the
X-over filters which are buried inside the speaker enclosure. To gain access, usually the bass driver is removed,
and a coax lead with aligator clips to outer shield and inrrer wire is threaded through low bass port hole and
to wherever we wish to measure on the X-over board, rather than to each driver whose terminals may be
inaccessable while drivers are screwed to the box. It is probably that wires to drivers from X-overs may need
some insulation removed to clip onto suitable bare metal. One way or another, suitable connections must be
found. Care must be used to ensure the 0V line from CRO to connect to the 0V line of LS and amplifier.
Once access is made to speaker driver signals, the bass driver may be screwed back in with just two screws.
This is OK for testing bass units. Once bass units have been tested, the bass unit may be left removed
because mid and treble will have their own small enclosures and be unaffected by the presence of bass
speakers and the bass X-over filter. This assumes though than the X-over for each driver is an entirely
stand alone type, and not a series type where mid + treble unts are fed with signal across an inductor in
series with bass, and bass is fed with a signal across a shunt capacitor.

The Series Type of X-over is a veritable nightmare to ever try to optimise. The only reason it is has ever
been used is because fewer L,C&R parts are required, and company accountants dictate such rubbish
be used to save costs of production. Usually when a speaker becomes a 3 way, nobody ever bothers
with series X-overs, and what is mostly used are individual X-over filters which are wired in parallel to
the amplifier.
Once the connection to a X-over speaker terminals has been made, the voltage maybe monitored on the
CRO. A dual trace CRO is handy, and the amplifier signal of 0.2Vrms can be displayed on one trace so
it takes up 1/2 the screen.The other trace is also pre-set to the same amp voltage before connection
to a driver voltage. When this lead is connected to a driver, the attenuation by X-over and series
resistance by the driver can immediately be read by comparing the two traces. Any strange distortion
or peaks in response may be easily plotted on a graph in 3 dB steps while the F at the sig gene is
adjusted.

The sig gene with pot F adjustment is infinitely variable, and peaks in response may be "tuned".
Such peaks in response often correspond with a drop in the impedance "looking into" the filter especially
if is an LC second order type which requires adequate terminating R at filter output lest the L and the C
act as a very low Z resonant shunt circuit at the Fo, resonant frequency which is also usually the wanted
crossover F pole. Peaks in signal response giving low Z are an unwanted tradgedy, and are often the
reason for "difficult to drive" speakers which can kill amplifiers. If crossovers for 6r0 bass and 6r0
midrange both have poles at say 250Hz using 2nd order LC filters, Z at Fo may fall to 4r0 or lower for
both filters. Thus the total Z at 250Hz could become 2r0 and where most audio energy exists, and such
an arrangement will kill some amps. Therefore the X-over responses and total impedance character must
be carefully measured out and many sheets of notes and graphs be made lest we waste our time to get
good sound. I laugh at people trying to build speakers by guessing LC&R values, and using only their
ears to monitor their results.
Sometimes they get their nose involved - smoke has that certain aroma indicating serious shortcomings in
their methods.
From what I have said so far, there are many mass produced speakers which may benefit from complete
re-engineering of crossovers and the method is no different to building a new set of speakers.

In the 2 years up to the end of 2011, I re-engineered several sets of speakers including smaller sized 3 way
Magnat speakers which had fused 5 out of 6 drivers including both 9" bass drivers and both. X-over filters
had burnt and melted inductor coils where wire size was far too small. I also re-engineered a pair of large
1975 AR9 4 way floorstanders which had extremely insensitive 3.6 ohm 11" twin bass drivers, but with
all other drivers being much more sensitive and of uneven impedance.

In the case of the Magnat speakers, all drivers and crossover parts were put out with the recyclables,
and all that was used from the original speakers was the rear, sides and top panels of the box.
A new front baffle was cut from 33mm thick MDF and painted to match original colours. A 3 way design
using Peerless 200mm LF, 120mm MF and 25mm HF all made in Denmark were used. I made up new
crossovers with coild having thick wire and I better capacitors througout. The crossovers were built using
plywood panels with 16mm x 4g brass plated wood screws used for terminals for solid copper wire
"tracks" or links between components. X-overs are easily removed as they are held in by wood screws
to the rear of the box with a layer of foam to stop vibration. Such X-overs are vanished well and all parts
well mounted, yet easy to service. I don't use crummy tag strips or printed circuit boards.
The AR9 were also done the same way after ditching the attrocious 1975 engineering.
To summarize the re-engineering, I can list the procedures :-

(1) Decide what parts if any are worth re-using.

(2) Usually the enclosure is in good enough condition to allow an effective outcome. But in some cases
the enclosure has begun to fall apart if made pine based particle board with plastic false veneer covering.
Such speakers are condemned, and the owner advised he is wasting my time.

(3) If a total rebuild is required, A set of Peerless drivers available from http://www.wescomponents.com.au
is considered. The range made in Denmark are remarkably good, and offer very good quality between the
poor quality cheap asian made drivers and the overly expensive hi-end drivers made by Scanspeak or others.
While the exotic hi-end drivers are nicely made I doubt the huge cost is justified. But I will use whatever
high priced drivers anyone is willing to pay for if they ask for them. Nobody ever does does though.
I believe the sonic outcome is mainly determined by the man who designs and instals correctly rather than
by the exotic quality and high prices of divers.

(4) Once the selection of drivers has been made and the set received from the supplier, the front baffle is
prepared or at least altered for new drivers to be installed. A typical driver set would be 200mm cone LF,
125mm cone MF, and 25mm dome HF. A separate new sealed enclosure for the rear of the MF is usually
needed to allow the MF to work down to 200Hz. rear enclosure usually may be from 2 litres to 5litres,
may be a simple box using plywood, or a PVC tube cramped between rear panel and front panel all screwed
and glued, and well stuffed with acoustically absorbant polyester wool. The enclosure is assessed for a suitable
match for a ported reflex design. The 200mm Peerless give excellent bass response with enclosure volume as
low as 50 litres, or less than 2 Cu.ft. ( 28L per Cu.Ft. )

(5) Before deciding on a bass speaker driver, the box volume is measured, and the probable outcome is
explored using a box matching program WINISD. I find the program does predict the bass response well,
even with sub-woofer designs using the rugged 300mm XLS Peerless sub woofer driver.

(6) Following the fitting of all drivers, the impedance of each driver is graphed to include whatever resonant
modes may be present, and to detect what may be the best crossover frequencies. Usually I shall choose bass
cut off at 300Hz, midrange cut off at 200Hz and 3kHz, and treble cut off at 3kHz. The bands of F chosen will
easily be by the chosen drivers. The mid band impedance for each driver is noted.
 
(7) From the impedance curves drawn for each driver, the F where Z has increased +3dB due to the series
inductance of the voice coil is noted. It is very desirable that the speaker driver act as a resistor at in its
upper band region thus ensuring predictable attenuation with L and C filter elements. To neutralise the effect
of voice coil inductance, a Zobel R&C network should be connected across each driver. Such a network
helps to damp the oscillatory speaker behaviour. Suppose a bass speaker has a flat region of Z between 150hz
and 300Hz, and is 6r5. Suppose the Z rises to 1.4 times the 6r5 value at 600Hz. To calculate the Zobel R&C
values needed, R = the nearest standard R value above the mid band Z, in this case it will be 6r8.
This resistance will at least be a 10W wire wound type.
The C value in uF = 159,000 / ( 1.41 x Z x Fo ) where 159,000 and 1.41 are constants for all equations,
Z is the midband speaker Z, and Fo is the F where Z has risen to 1.4 x lower midband Z, In this case we get
C = 159,000 / ( 1.4 x 6.5 x 600 ) = 29uF. This is an awkward non standard value, but a 30uF polypropylene
motor start cap rated for 250V would be fine. Alternatively, 2 x 10uF NP electrolytics could be used with
an 8 uF or 10uF polypropylene all in parallel. When connected across the bass speaker, the impedance
should remain at 6r5 for all F above the 6r5 mid band value at 200Hz.
The procedured of placingf Zobel networks across each driver is known as "impedance equalising".
It is often ommited where 2nd oder or 3rd order filters are used, but I always use such Zobels.
 
(8) Following  connection of Zobels, the unfiltered response of each driver is measured using a pink noise
test from a power amp. The responses are drawn on the same page as each driver is tested separately,
so that it is fairly easy to see what attenuation is required for the most sensitive speakers, and if the
band response may be optimally flattened, without lowering Z excessively.
 
(9) Crossover values are chosen. I have found the chart below indicates what is required. Fig 7, Crossover LCR values.

TO
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