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 Dividing network is another
name for a crossover network used to separate and direct parts of the audio frequency
band to specific speakers - bass, midrange, and tweeter, for example. It is the
audio equivalent of a diplexer or multiplexer filter in the RF and microwave realm.
As with many other aspects of consumer electronics, there was a time when many audiophiles
chose to design and/or build their own crossover networks for home-built speakers.
Although never really a bona fide audiophile, I did design and build my own custom
speaker cabinets and the crossover network. The woodwork was done at the
woodshop at Robins Air Force Base while
I was serving in the USAF as an Air Traffic Control Radar Repairman (not an air traffic controller).
I don't know if it is still the case, but back then most large bases had hobby and
craft establishments for woodworking and metalworking, ceramics, artistic painting,
and even electronics benches. To the left is the only photo I have of one of the
speakers, which have since been sold (my son, Philip, is retrieving his Easter basket
which was hidden behind it - circa 1988 - while attending
U. of Vermont and living
in a trailer park). My units each had three speakers and a homemade L-C crossover
network. Admittedly, no real science went into the electrical design; I adjusted
the inductor and capacitor values until everything sounded "about right." All the
components, including the individual speakers and speaker cloth, were purchased
at the downtown Radio Shack. See also "Loudspeaker
Crossover Design" in the July 1952 issue of Radio-Electronics.
Dividing Networks
By Harold Renne
Technical Editor. Radio & Television News
This is an interior view of an RCA type of dividing network for
theater use. The crossover frequency is 400 c.p.s.
A two-speaker system using a tweeter and a woofer has many advantages over a
single speaker system.
Because of the difficulty in manufacturing a speaker with a single cone assembly
which will satisfactorily reproduce both the extreme low and extreme high audio
frequencies, it has become rather common practice to use a dual speaker system for
high-quality installations. In such installations, a low-frequency speaker, or woofer,
is used which is designed primarily to satisfactorily reproduce low frequencies,
and a high frequency speaker, or tweeter, is used which is designed for the high
frequencies.
It is desirable in systems of this nature to "sort out" the low frequencies from
the high frequencies and apply each to the proper speaker. A network for performing
this function is called a dividing network, and the point at which the frequency
division takes place is called the crossover frequency. This is the frequency at
which the two speakers receive equal amounts of energy.
Fig. 1 - Schematic of a simple dividing network which will
operate quite satisfactorily.
Experience has indicated that a dividing network should have an attenuation beyond
the crossover frequency of from 6 to 12 db. per octave. This may be accomplished
with fairly simple networks. Two types of circuits may be used: the filter network
and the constant-resistance network. Both have advantages and disadvantages, and
both will be discussed.
Fig. 2 shows parallel and series filter dividing networks, made up of half-section
elements of the so-called m-derived type. Full section elements could be
used, giving an attenuation of 18 db. per octave beyond the crossover frequency,
but the slight improvement in operation is not worth the additional cost and losses
involved. With extreme care in design, a dividing network may introduce as little
as 0.5 db. power loss, but even this can become appreciable when high powers are
involved. For example, at a power level of 100 watts, a 0.5 db. loss represents
a power loss of about 11 watts.
The equations in Fig. 2 indicate how the condenser and inductance values
may be determined. The value of Ro indicates the impedance of each of
the speakers and the input impedance to the network. The crossover frequency
fc is determined by the speakers used and should be as low as possible.
Each speaker should be able to contribute appreciably to the sound output at least
one-half octave beyond the cross-over frequency.
The filter-type dividing network is somewhat more versatile than the constant-resistance
type and has slightly better transmission characteristics in both the transmission
and attenuation bands. It does not lend itself readily to mass-production techniques,
however, as two different values of inductance and capacity are required.
Some typical commercial dividing networks. (A) RCA network with
400 cycle crossover for theater use. (B) Brociner Electronics constant-resistance
network with 500 cycle crossover and an attenuation of 12 db. per octave. (C) Circuit
used by Stephens Mfg. Co. to give an attenuation of 12 db. per octave and a crossover
of 600 cycles. (D) University Loudspeakers. Inc., network with 600 cycle crossover
frequency.
Both the parallel and series type of networks are effective, but listening tests
seem to favor the series type (Fig. 2B).
It might be instructive to calculate a typical dividing network on the basis
of the circuit and equations given in Fig. 2. For the reasons given before,
we will choose the series type for our calculations. A typical value for the speaker
and input impedances would be 8 ohms, and the crossover frequency will be chosen
as 800 cycles. Substituting these values in the proper equations gives the following
constants for the network:
L2 = 1.6 mhy.
C3 = 40 μfd.
L3 = 1.0 mhy.
C1 = 25 μfd.
The inductances should be wound with fairly heavy wire on a nonmagnetic coil
form, such as wood. An inductance bridge is very helpful in obtaining the correct
values. The coils should be mounted with their axes perpendicular to avoid mutual
coupling. The condensers must not be of the electrolytic type, but they may be paper
or oil-filled. Some condensers available on the surplus market would be suitable.
Observers report that the calculated values of inductance and capacity may be varied
as much as 25% without any appreciable effect on reproduction as judged by listening
tests.
The constant-resistance type of dividing network is shown in Fig. 3. It
will be noted that for a given network, the values of the two inductances and the
two condensers are the same, making this unit easier and cheaper to build on a production
basis. When properly designed, this network is equally as effective as the filter
type. It has the theoretical advantage of presenting a constant load to the source
at all frequencies, but the wide variation in impedance of the voice coils with
frequency tends to defeat this advantage.
Either of the networks shown will give an attenuation of about 12 db. per octave
beyond the crossover frequency and will introduce a power loss of between 0.5 and
1 db. An attenuation of 18 db. per octave may be obtained by the use of π or
T sections instead of L sections, but such attenuation is not essential, and, as
with the filter type, the additional power loss resulting from introducing the additional
components more than outweighs any advantage that might be obtained.
Fig. 2 - (A) Parallel and (B) series filter dividing networks
made up of half-section elements.
As an example of a typical series-type constant resistance dividing network (Fig. 3B)
let us take the same conditions as before, namely, Ro = 8 ohms, fc
= 800 cycles. This gives values for L2 of 1.1. mhy. and C2
of 31 μfd.
A much simpler dividing network than those described above is frequently used.
This network is shown in Fig. 1 and consists simply of a 2 μfd. condenser
in series with the voice coil of the tweeter. The inductance of the woofer voice
coil is appreciable, and its impedance rises with frequency. The inductance of the
tweeter voice coil is relatively small, so the impedance of the condenser-voice-coil
series combination decreases as the frequency increases. These two effects tend
to cancel each other, giving a fairly constant impedance.
In the above discussion, we have ignored the fact that the tweeter speaker is,
in general, more efficient than the woofer. This would tend to give an unbalanced
output with excessive high frequencies. For this reason, an attenuator is usually
placed in the tweeter circuit to compensate for this increased efficiency.
We have assumed in our dividing network calculations that the voice coil impedance
of the tweeter and of the woofer were' the same. If such is not the case, the problem
is considerably more complicated. If the tweeter voice coil impedance is higher,
it may be shunted by a resistor, within limits, to bring the impedance down to the
correct value. For example, if the woofer has an 8 ohm impedance and the tweeter
is rated at 16 ohms, a 16 ohm resistor may be connected in parallel with the tweeter
to bring the total impedance down to 8 ohms. Half of the high-frequency power is
lost in this resistor, but the higher tweeter efficiency may make up for this loss.
Fig. 3 - (A) Parallel and (B) series constant resistance
dividing networks made up of L sections.
The above discussion has assumed that the dividing network is placed between
the output transformer and the speakers. It is entirely possible to place this network
in the center of the amplifier and then use separate power amplifier stages for
the low and high frequencies. The network may be somewhat simplified since the value
of Ro may be greatly increased and since power loss in the network is
no longer a vital consideration. These advantages may be overcome by the additional
cost and complexity of the two separate power amplifier channels, but this system
has been used with marked success in a commercial amplifier manufactured in England.
Another possibility is to place the dividing network in the plate circuit of
the output stage, and then to use separate matching transformers for the high and
low frequency speakers. This permits matching the network to any speaker impedance,
and because the network is in a high impedance portion of the circuit, more convenient
values of inductance and capacity are possible. At least one company using this
latter system reports highly satisfactory results.
With good woofer and tweeter speakers, proper enclosures, and a suitable dividing
network, frequency response from 50 to 15,000 cycles can be readily achieved.
Posted February 15, 2023
(updated from original post on 1/11/2017)
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