Impedance Matching of Multiple Speakers, April 1954 Radio & Televsion News

I have five operational radios and speakers spread around my house (912 ft², 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 over-the-air 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 stereo-separated 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 R|L 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.

Performance of multiple speaker installations can be improved if voice-coil 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 high-impedance 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 4-ohm 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 15-watt speaker and a 3-watt 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_aZ_a)/W_s

Z_a = amplifier output transformer secondary impedance (line impedance) , in ohms

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.

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 3-watt 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 constant-voltage 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 per-cent 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 70-volt 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 117-volt 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:

For simplification, the value of E₂ 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 primary-to-secondary 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.

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 with-in 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 over-driven. 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 in-phase, 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 hum-bucking 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 70-volt constant voltage output tap, to allow for ease in expansion. Under the conventional method if additional speakers are desired it is necessary to re-compute the values of all the matching transformers, because the total power has changed. The RETMA 70-volt tap allows for continued expansion until the output of the amplifier is reached, without re-computing 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.

"Impedance Matching and Power Distribution In Loud Speaker Systems," Jensen Technical Monograph No.2, Jensen Mfg. Co.

Impedance Matching of Multiple SpeakersApril 1954 Radio & Television News

Impedance Matching of Multiple Speakers
April 1954 Radio & Television News