I have five operational radios
and speakers spread around my house (912 ft^{2}, BTW) and in the basement.
Only one of them is newer than 20 years old and the others are circa 1978 or earlier.
AM or FM overtheair radio is playing all day (when the el cheapo BSR turntable
isn't spinning LP and 45 vinyl). In a couple instances I feed a stereo output into
a mono speaker. With truly stereoseparated audio, listening to just the right (R)
or left (L) channel does not do an adequate job of replicating the broadcast since
often, particularly in music, the voice tends to favor one or the other of R or
L. Simply tying the right and left channels together does not do the job because
the low impedance of the speakers  typically 4 Ω or 8 Ω  causes noticeable
distortion when doing so. The only way to achieve good sound is to use a power combiner
that presents the proper impedance to each component (amplifier RL outputs and
speaker). While maybe a reactive combiner might be better, I have found that a simple
resistive combiner does the job. This article from a 1954 issue of Radio &
TV News magazine delves a little deeper into multiple speaker matching than
I need, but if you are an audio technician, the information could be useful.
"Why all the radios?" you might be asking. the answer is I like old radios and
besides, with that many radios within listening distance from anywhere in the house,
I can leave each one tuned to a different station and never have to touch the knobs,
turning on only the one I want to hear.
Impedance Matching of Multiple Speakers
By Sherman H. Hubelbank
Connecticut Telephone & Electric Corp.
Performance of multiple speaker installations can be improved if voicecoil impedances
are matched.
In setting up multiple speakers, the problem of impedance matching is a most
important one. All the speakers must be matched to the output impedance of the audio
amplifier to secure a maximum transfer of energy from the amplifier to each speaker
and to minimize the undesirable effects of distortion which are prevalent when the
system is mismatched.
Fig. 1  Simplest type of multiple speaker installation where
each speaker draws the same amount of power and is parallel wired.
Table 1  Maximum permissible highimpedance line lengths for
various installations.
Since the distribution of audio energy from the amplifier to multiple speakers
is a power distribution problem, the power desired at each speaker location must
be individually considered for proper impedance matching.
The simplest type of multiple speaker installation would be a type similar to
Fig. 1, where each speaker draws the same amount of power and is wired in parallel
without the use of matching transformers.
This type of installation, using only two speakers that have low power ratings,
works well for short distances. However, since this is a low impedance line (4 ohms
terminating resistance) it has a high current and low voltage, and since the line
loss is proportional to the square of the current, the length L (distance from amplifier
to speakers) cannot be long. In general a 15% power loss in the line is the maximum
acceptable loss. Using #22 AWG size wire for the 4ohm example of Fig. 1, the maximum
distance of L is 18 feet for this 15% line power loss. Of course, a larger size
wire would reduce the line loss and, consequently, extend the distance of the run.
A run of 30 feet may be made for this example using #20 AWG size wire. In general,
for long runs and for speakers of larger power, it becomes increasingly more economical
and efficient to use a high impedance line to obtain low current and high voltage.
The use of matching transformers or line transformers provides the necessary high
voltage.
If conditions are such that one area needs 15 watts of power for coverage, yet
another area needs only 3 watts of power for adequate coverage, connecting a 15watt
speaker and a 3watt speaker in parallel will not give the desired results.
Note: Lengths beyond those shown above for specific impedances and wire sizes
will exceed the maximum allowable power loss of 5%.
As shown in Fig. 1, with both speakers rated at 3 watts and an impedance of 8
ohms, the voltage developed across each speaker is the same, approximately 4.9 volts.
Now, since the wattage rating of a loudspeaker is only the rating of the maximum
input power that the speaker can safely handle and not necessarily the power developed
across it, two dissimilar speakers with the same impedance will develop the same
voltage and consequently the same power. To develop different power levels from
each speaker, the system should be wired as shown in either Fig. 2A or 2B, or different
speaker impedances should be used.
In Fig. 2A both speakers "A" and "B" are rated at 15 watts, however, it is desired
that the coverage of speaker "A" be 15 watts and that of speaker "B" be 3 watts.
By placing an attenuator rated at 15 watts across speaker "B" this is accomplished.
The output of the amplifier must be 30 watts to allow speaker "A" to utilize 15
watts, speaker "B" to utilize 3 watts, and the attenuator to waste 12 watts. Speaker
"B" must be rated at 15 watts even though only 3 watts output is desired, since
it is possible for the attenuator to be at an extreme position, allowing the full
15 watts to enter the speaker. The maximum distance L is still 18 feet using #22
A WG size wire.
Fig. 2  To develop different power levels from each speaker,
the system should be wired as shown. (A) If speakers "A" and "B" are both rated
the same but the coverage is to be different. an attenuator is used. (B) The use
of matching transformers is an improvement over the circuit of (A). See text for
discussion.
Fig. 3  Graphical representation of the formula for matching
various speakers of different output loads and voice coils with an amplifier of
a certain output.
The advantages of using the matching transformers shown in Fig. 2B to accomplish
the same end result as the circuit of Fig. 2A are evident from the following comparison:
Fig. 2A, audio amplifier  30 watts; speakers "A" and "B"  15 watts each; maximum
distance using #22 wire  18 feet; Fig. 2B, audio amplifier  18 watts; speakers
"A" and "B"  15 and 3 watts respectively; maximum distance using #22 wire  400
feet.
Therefore, as the multiple speaker requirements become more complex, i.e., different
wattages, voice coil impedances, longer runs of line, etc., it becomes much more
economical to use matching transformers.
The problem of how to properly match the various speakers of different output
loads and voice coils with the amplifier can be approached using the formula: Z_{t}
= (W_{a}Z_{a})/W_{s}
where:
Z_{t} = matching transformer primary impedance, in ohms
W_{a} = total amplifier power required, in watts
Z_{a} = amplifier output transformer secondary impedance (line impedance)
, in ohms
W_{s} = desired input power to speaker, in watts
Note: This formula will only give the matching impedance of a single speaker
in a group of parallel speakers. In using this formula it should be remembered that
the sum of all the desired speaker input powers must equal that of the output power
of the amplifier.
Since the formula is a proportional type it can be transposed to a simple graph
(see Fig. 3).
In using either the formula or the graph, the value of Z_{a}, the impedance
of the secondary of the amplifier's output transformer, must be arbitrarily chosen.
If upon computing the values of the matching transformers they are either not readily
available types or odd values, try another output transformer tap value.
To use the graph, the following steps should be taken:
1. Assume a value for Z_{a} the impedance of the secondary of the output
transformer.
2. Using the value decided upon for the desired speaker power, W_{s}
(Fig. 3  15 watts or 3 watts) draw a vertical line to the intersection of the horizontal
line from the transformer impedance Z_{a}.
3. Draw a diagonal line from the origin of the graph (point "0") to the point
of intersection of the transformer impedance line and the individual speaker watts
line.
4. Continue this diagonal line until it intersects a vertical line drawn from
W_{a} the amplifier output in watts.
5. The impedance value of the primary of the matching transformer is at this
intersection point.
6. Repeat the procedure for each speaker until the total watts to be dissipated
equals the total available at the amplifier.
The following example (see Fig. 4) covers a more complex installation, one that
is fairly typical for a small factory which uses voice paging and intermission music.
It has been decided that 30 watts will adequately cover the machine shop, 15
watts the general factory, 10 watts the shipping room, and 3 watts each of the two
offices. The total power needed is 61 watts. A 70 watt or larger amplifier should
be chosen not only to allow for future expansion, but also to allow for losses in
the lines, speakers, transformers, etc. However, in using the formula or graph to
compute the matching transformer impedances, the amplifier wattage should be 61
in the formula to balance the total needed to cover the necessary factory departments.
Where individual volume level must be controlled at each speaker area, "T" pad
attenuators should be used. These present a constant source impedance as well as
a constant load at all settings. The attenuator should be chosen to match the impedance
of the speaker and should be rated to dissipate the entire wattage of the speaker.
In the example shown in Fig. 4 the volume level of the speaker in one office needed
to be individually controlled as did the speaker in the general factory. Consequently,
a "T" pad attenuator was inserted in front of each of the two speakers.
Since the two offices were located close to each other and they each had low
wattage requirements, it was decided they should be parallel connected to one matching
transformer. If they were individually connected to the line each would require
a matching transformer with an impedance ratio of 5000 to 8 ohms. However, by wiring
the speakers in parallel the total wattage is 6 watts, therefore the matching transformer
needed requires an impedance ratio of 2500 to 4 ohms. The reason that the impedance
ratio for the two cases remains the same is that the ratio is determined by the
computed primary value and the impedance of the voice coils of the loudspeakers
for the secondary. Therefore, one less transformer was needed when the two 3watt
speakers were wired directly in parallel.
Fig. 4  A more complex installation typical for a small factory
or shop.
Fig. 5  Same installation as Fig. 4 but using transformer constantvoltage
tap.
It should be noted that in Fig. 4, the maximum distance of "L" using #20 A WG
size wire, for a line power loss of 5% is 750 feet. Five percent is the maximum
allowable line loss for high impedance lines for maximum efficiency, since there
are other losses in the matching transformers. See Table 1.
The output impedance of many amplifiers will be found to be rated in ohms and
also have either a 70 volt (70.7 constant voltage) tap or a 140 volt (141.4 constant
voltage) tap. The 70volt tap will be found on audio amplifiers that are rated under
100 watts; the 140 volt tap on those rated over 100 watts. This is the new RETMA
method for multiple loudspeaker matching to allow multiple loudspeakers to be connected
with the same ease as electric lights are connected across a 117volt a.c. system.
The same requirement that holds for electric lights, that the total power consumed
must be less than or equal to the total power available, also holds for loudspeakers.
This 70.7 volt rating allows the speaker transmission line to conform to the
National Electric Code and the Underwriter's standard and not require the use of
"BX" cable.
It should be pointed out that this condition of 70 or 140 constant voltage exists
only when the amplifier is delivering its exact rated output. At lower signal levels,
the output voltage is less than 70 or 140 volts and if the amplifier is driven beyond
the rated output, the voltage is higher than 70 or 140 volts. This standardization
method means that the amplifier output voltage is the same for a low power amplifier
as for a high power amplifier if the output of both amplifiers is rated under or
above the dividing line of 100 watts.
Fig. 5 shows the same installation as Fig. 4 using the constant voltage tap on
the output transformer of the amplifier. The desired power at each speaker site
is the same as the previous example, however the amplifier now has a 70 volt tap.
To calculate the needed primary impedance of the matching transformer the following
formula should be used:
Z_{t} = E_{2}/W_{s} where:
Z_{t} = matching transformer primary impedance, in ohms
E_{2} = output voltage 702 or 1402
W_{s} = desired input power to speaker, in watts
For simplification, the value of E_{2} for a 70 volt tap is rounded off
to 5000. Since the amplifier power does not enter into the calculations, it must
be remembered that the desired power of all the loudspeakers cannot exceed the total
amplifier power available.
The primary impedance for speaker "A" should be 166 ohms. Since this is not a
conventional value, a transformer having a primary of 150 ohms and the proper secondary
was chosen. In the event no substitute can be found, any transformer having the
correct primarytosecondary impedance ratio may be used.
For speaker "B," 333 ohms was computed and a transformer with a primary of 333
ohms and secondary of 16 ohms was found. An alternate method would be to consider
the attenuator dissipating an extra 5 watts and therefore allow 20 watts to be the
desired wattage. Then the transformer would require a primary of 250 ohms.
Speaker "C" did not require any manipulation in matching transformers.
Speakers "D" and "E" require a matching transformer of approximately 833 ohms.
A transformer having a 1000 ohm primary and a secondary of 4 ohms would not present
too great a mismatch.
How much of a mismatch is permissible depends upon whether or not the speaker
will be overdriven, whether there is still adequate power to give sufficient coverage,
and whether the increase in power level at each speaker (if any) exceeds the total
power available.
Before using an alternate matching transformer, substitute the new transformer
primary value in the formula and solve for the desired power. If this figure satisfies
the requirements, a permissible substitution has been found.
In general, a transformer of ±10% mismatch may be chosen without any appreciable
disruption of power levels. However, if there is no matching transformer available
with a tap within tolerance use the larger value tap, especially if the speaker
is rated exactly or close to the desired wattage, so that the speaker will not be
overdriven. In all cases the figures should be recomputed to check that the speaker
will not be overdriven.
Another important consideration in proper loudspeaker matching is that each speaker
be properly phased with respect to each other. If the speakers are not properly
phased, the sound from one may cancel the sound from the other, resulting in "dead"
spots when two or more speakers are used in the same room. When the speakers are
wired inphase, the sound from one speaker will reinforce the other and provide
maximum coverage with a minimum output.
Phasing may be checked by placing a flashlight battery (1.5 volts) across the
speaker. Mark the polarity of the battery on the speaker terminals when the cone
goes inward. Repeat for all the speakers. When wiring, connect the like terminals
together, except when wiring a series circuit, then connect the positive terminal
of one speaker to the negative terminal of the other speaker. If a humbucking coil
is used in a speaker, it should be temporarily shorted out for this phasing check.
Where the speakers are connected in parallel, if one breaks down the power is
distributed over the others. This could cause the remaining speakers to break down
shortly thereafter especially if all the speakers are operating close to their maximum
power ratings. However, this disadvantage can readily be overcome by operating the
speakers at about 75% of their continuous load rating.
The major disadvantages of connecting the speakers in series are similar to the
general objections to series circuits; that is, if the voice coil of one speaker
opens up, all the speakers are out of service and the fact that surge voltages become
greater, hastening breakdowns. In the event that a series connection is required,
it is advisable to electrically insulate the speaker cluster, by insulating each
speaker mounting bracket individually.
If a choice is available in amplifiers it would be advisable to choose one with
a 70volt constant voltage output tap, to allow for ease in expansion. Under the
conventional method if additional speakers are desired it is necessary to recompute
the values of all the matching transformers, because the total power has changed.
The RETMA 70volt tap allows for continued expansion until the output of the amplifier
is reached, without recomputing any transformer values; since the formula is not
dependent upon the total power in use.
By carefully matching the various loudspeakers using either the RETMA method
or the conventional method a judicious saving of necessary power will be obtained
allowing for a more flexible and inexpensive amplifier.
References
"Impedance Matching and Power Distribution In Loud Speaker Systems," Jensen Technical
Monograph No.2, Jensen Mfg. Co.
Read, Oliver: "The Recording and Reproduction of Sound" Howard Sams & Co.,
Inc.
Posted March 19, 2020
