May 1959 Electronics World
Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
Electronics World, published May 1959
- December 1971. All copyrights hereby acknowledged.
Since I am currently planning a
loudspeaker configuration to replace the original speaker in my
1941 Crosley 03CB
floor model AM / shortwave radio set, this article made for a good refresh on audio
frequency crossover circuits. A very nice set of design charts is provided. Of course
today there is no need to design and build your own since commercial units are very good
and cost less than what I could build myself. Many moons ago while serving in the USAF
at Robins AFB, Georgia, I did actually build my own crossover circuit for use in custom
speaker cabinets I made in the base woodshop (they were sold years ago prior to a household
move, unfortunately). The speaker that came in the Crosley has a 12" cone, which is still
in good condition, but it uses an electromagnetic voice coil rather than a permanent
magnet like modern speakers use. Using it would require rigging up a DC supply for it,
which is too much trouble, and besides, the frequency response is nowhere near as good
as a trio of bass, midrange and tweeter with a crossover.
This article is Part 2, so I will try to get ahold of the first part in the April
1959 issue of Radio & TV News. This May 1959 Electronics World
is the first after the name change from Radio & TV News (April 1959 being
Hi-Fi Crossover Networks
Part 2. Constructing the Network
Advanced Acoustics Co.
By Abraham B. Cohen & Paul D. Cohen / How to design and put together home-built
precision networks for 2- and 3-way systems.
In Part 1 of this article (in April 1959 issue), the principles behind the design
of multi-speaker networks were generalized so that this article on the actual construction
of the networks would not be interrupted by some of the more general thoughts concerning
the application of networks. With the exception of the earlier reference to 6 db and
12 db attenuation per octave, a more complete treatment of the actual values involved
in construction of a network was left for this part.
Now we must deal a little more specifically with this matter of the 6 db versus 12
db roll-off characteristic of the network to determine the source of the particular values
chosen. These are not arbitrarily selected values - they are specifically related to
the values of the choke or capacitor element that will provide a given crossover point
for a given impedance.
Voltage Division at Crossover
Fig. 8 - Calculations showing voltage division across the circuit
elements as the frequency is increased. This gives rise to the common 6 db per octave
By definition, the crossover point is that frequency where the drooping output of
the low-frequency branch of the network crosses over the rising characteristic of the
high-frequency branch (as indicated in Fig. 3 of Part 1). For a 6 db-per-octave network,
the value of the capacitor in the tweeter branch and the value of the choke in the woofer
branch are chosen to provide an a.c. impedance across those two respective elements,
at the crossover frequency, which will be equal to the speaker impedance. Fig. 8 shows
a simplified circuit of a two-way network with a low-frequency branch and a high-frequency
branch, both tied across a common voltage source. Let us assume that the speakers are
both 8-ohm units and that it is desired to design a network to cross over at 2000 cps.
We will have to find an inductor and a capacitor that will each present an impedance
of 8 ohms at this frequency. Having found such components (more details later on actually
finding these) and inserting them in the network of Fig. 8A, we see that the voltage
in the low-frequency branch has been equally divided across the choke and the woofer.
In a similar manner, the voltage across the high-frequency branch has been divided equally
between the capacitor and the tweeter. Consequently, the voltage across the woofer is
equal to voltage across the tweeter. This is the crossover point where the drooping low-frequency
characteristic crosses the rising low-frequency characteristic.
6 db/Octave Attenuation
Now we come to the matter of the octave rate of attenuation of these drooping and
rising characteristics. Consider, first, the drooping woofer branch characteristic of
Fig. 8A. If it a crossover frequency of 2000 cps the inductance in the woofer circuit
is equivalent to 8 ohms, then at 4000 cps (one octave higher) this inductance will present
a 16-ohm impedance since the impedance is directly proportional to the frequency. When
this 16-ohm impedance is now considered in series with the 8-ohm woofer, Fig. 8B, then
the voltage across the choke becomes twice that across the woofer. On a db basis (db
= 20 log E2/E1) a 2 to 1 voltage ratio becomes 6 db. Thus, after
the crossover point, the voltage drop-off across the woofer progresses at a rate of 6
db-per-octave. Thus, if we go up another octave the choke impedance doubles again, going
from 16 ohms to 32 ohms, while the woofer still remains 8 ohms. The voltage in the woofer
branch, Fig. 8C, is now at a 4 to 1 ratio. On a db basis, a voltage ratio of 4 to 1 represents
a total drop of 12 db or, again, 6 db over the previous octave.
The same analysis may be applied to the tweeter branch and it may be shown, in identical
fashion, that the tweeter circuit capacitor, when necessarily chosen to be equal in impedance
at the crossover frequency to the tweeter impedance will, below the crossover point,
continue to roll-off at the gradual rate of 6 db-per-octave. So it is seen that the automatic
6 db rate of this type of network arises from the simple necessity of choosing reactive
elements in the two branches to divide the voltages equally across the various elements
in the circuit so that the individual speaker terminal voltages will be the same at the
12 db/Octave Attenuation
In Part 1 we discussed the general method of pairing off a capacitor with an inductance
in each speaker circuit to convert a 6 db-per-octave network into a 12 db system. While
"pairing off" is the general procedure, the values to be used in converting from a 6
db to a 12 db network need some modification. Thus, if a choke had been originally selected
to have an impedance of 8 ohms at the crossover frequency (and equal to the. speaker
impedance), then it would have to be multiplied by a factor of 1.41 when the systems
were changed to a 12 db-per-octave network as indicated in Fig. 7 of Part 1. Similarly,
the capacitance of the component which had been originally chosen for the tweeter circuit
of the 6 db-per-octave network would have to be divided by a factor of 1.41 when the
conversion is made. Once these new values have been determined by modifying the 6 db
values, they may then be paired off to provide the 12 db network. Calculations similar
to those in Fig. 8 may be made when using these revised values to plot out the network
branch voltage which will drop at the rate of 12 db-per-octave after the crossover point
when going in either direction.
It may seem that we put the "cart before the horse" in giving details on how to convert
from a 6 db to a 12 db-per-octave network before we had discussed how to select the simple
values for the 6 db network. However, since we had treated such conversion last month
as part of the general philosophy of network design, it was deemed logical to carryover
that discussion in terms of "numbers" so that a transition might be made to the problem
of selecting real values of inductances and capacitances for a particular network.
Of the basic elements found in the common network, the components such as capacitors
and volume controls may be readily purchased, with the inductors not so widely available.
However, this should prove no obstacle to the man who wants to build his own network.
Invariably all instructions for building these chokes are predicated on "air-core" (non-magnetic
core) design, for two reasons: first, air-core chokes completely eliminate distortion
due to iron saturation and, second, laminations of a quality good enough for audio chokes
are not easily obtained by the average home constructor. Wooden dowels, Masonite, and
wires are, however, readily available.
Easy as it is to build a choke, the initial design is far from simple. We cannot simply
say that so many turns of wire constitute a given inductance. As a matter of fact, a
given number of turns may yield widely different values of inductance depending upon
the manner in which the turns are wound. The total inductance of a coil depends on the
geometry of the coil. A long one-layer solenoid will have a far different inductance
than a flat pancake coil of the same number of turns simply because the flux linkages
of the various turns in one case are completely different than in the other. Even after
having started with one given coil configuration, it is not a simple matter to guess
what inductance a similar coil of more turns would be. It is true that, in general, the
inductance is proportional to the square of the number of turns, but there are additional
factors involved that determine the final inductance of the coil. For the purpose of
this discussion, the inductance formula as derived by Maxwell was used in calculating
the inductance characteristic of the coil.
Building the Coil
The practical reader need not become discouraged nor distressed at this point. The
calculations have all been accurately carried out and checked on an actual model so the
constructor may use these inductance values "as is." All he need be concerned about is
the desired crossover frequency and the speaker impedance of his system. Chart 1 (on
the fold-out page) supplies the basic details he needs to know about building the coil.
These details include not only the number of turns, but the number of layers of wire,
and, most important, the weight of the wire. It is discouraging to go out and buy a quantity
of wire for an inspired evening of coil winding and then discover that you are short
Hi-Fi Crossover Network Design Charts
Although Chart 1 provides all of the practical details for making the coil for any
given impedance and for any given crossover frequency, we have included another chart
for the purist who still wants to know the inductance of his coil. If one were truly
ambitious, he could wind one master coil with several taps along the depth for experimental
purposes. Charts 1 and 3 give the actual curves of an experimentally checked master coil
wound of #18 enamel wire on the coil form shown on the chart page. Along the abscissa
are four scales: first, the number of layers, then the number of turns, then the pounds
of wire that are necessary for a given inductance, and finally the coil depth. The coil
form is made with a 1" wooden dowel as the core and the end pieces of hard 1/4" Masonite.
A series of 1/8" holes were drilled along a radius of one of these end pieces so taps
could be brought out anywhere along the depth of the coil.
It is recommended that care be taken to insure that the coil is layer wound rather
than random wound. Not only will there be considerable satisfaction in seeing a job well
done but, what is more important, the final value of the coil will be more nearly correct
for a given number of turns. Layer winding of the coil will be facilitated if separators
of heavy fish paper or several layers of masking tape or sealing tape are interposed
between every two layers of windings. Thus there will always be a comparatively smooth
surface for the subsequent layers. It is suggested that the end Masonite pieces be secured
to the center dowel by means of a brass bolt at least 2" long. This will permit the end
of the bolt to be inserted in the chuck of a hand drill. The drill may then be held secure
in a vise and the coil form slowly turned while the wire is guided onto the form by the
Using Chart 1
Chart 1 gives the details of the coil configuration for any desired frequency and
speaker impedance. Choose the speaker impedance on the vertical scale, move over horizontally
to the curve which represents the desired crossover frequency, and then move down to
the horizontal scale which gives all the vital statistics on the coil for the conditions
selected for a 6 db-per-octave network.
To use Chart 1 for 12 db-per-octave networks multiply the value of the speaker impedance
by 1.41 and proceed as above. This, in effect, increases the inductance value by 1.41
times, a requirement for a 12 db-per-octave network.
The corresponding capacity to go along with the chosen inductance is easily determined.
One may make a simple calculation of capacity by using the formula: C = 1/2πfXc.
where f is the crossover frequency and Xc represents the reactance
of the capacitor chosen to be equal to the speaker impedance at the crossover frequency.
C will be the capacity required for the tweeter branch. Alternately, Chart 2 may be used
to pick off the actual capacitor value for a given impedance at a given frequency. Here,
again, as in the case of the coil, the value found for the capacitor is for a 6 db-per-octave
network. For a 12 db-per-octave crossover, divide the capacitance value obtained by 1.41.
Typical Three-Way Network Parts
The very important matter of the type of capacitor to use deserves individual treatment,
but consideration of this point will be deferred to the last so that we may illustrate
the actual selection of component values for a typical three-way system. Let us assume
an 8-ohm system with a crossover at 300 cps between the woofer and the mid-range and
an upper crossover at 5000 cps between the mid-range and the tweeter. This system was
shown in Fig. 7 of Part 1. The choke for the woofer is selected from Chart 1 by coming
in from the 8-ohm point (speaker impedance) on the vertical scale to the 300 cps curve
and then down to the horizontal scale where it is indicated that very nearly 16 layers
(or 500 turns) of wire will be required on the coil form, that just under one pound of
wire will be needed, and the coil depth will be approximately 3/4". This is all the information
required for winding this woofer circuit coil.
Now, the low-frequency blocking capacitor of the mid-range circuit will have to be
equivalent in impedance to the speaker at the 300 cps crossover frequency. From Chart
2 the value of this capacitor turns out to be 65 μfd.
Moving to the upper crossover frequency of 5000 cps, the high-frequency limiting choke
in the mid-range circuit should have an impedance of 8 ohms at this frequency. Again
from Chart 1, we select 8 ohms on the vertical scale, move horizontally to the curve
representing 5000 cps, then vertically down the horizontal scale where we find that the
coil will consist of 5 layers of wire (160 turns), will utilize approximately 1/4 pound
of wire, and will be about 1/4" thick. The corresponding tweeter branch capacitor at
this crossover frequency point will also have to have an impedance of 8 ohms and from
Chart 2 this turns out to be 4.2 μfd. (call it 4). Thus all the details for winding
the coils and choosing the right capacitor values are readily available if you know the
speaker impedances and the desired crossover frequencies.
To convert this network into the 12 db system shown in Fig. 7D, Part 1, the inductance
values of the chokes should be multiplied by 1.41 and the capacities divided by 1.41
and then paired off as previously described.
Type of Capacitors
Fig. 9 - Transmission curves of back-to-back or non-polarized (A)
and polarized (B) electrolytic capacitors for maximum undistorted power transfer. Refer
to the text.
We must now discuss the controversial question of the type of capacitor to be used
in audio dividing networks. It has been generally conceded that one can't go wrong if
he uses good oil-filled or paper capacitors. However, there is the matter of cost for
such units. A 60 μfd. capacitor, even one rated at comparatively low voltage, may
not fit one's pocketbook as well as it does the network data. This problem has been overcome
in commercial equipment by using non-polarized electrolytic types where large capacities
are required. These are comparatively cheap but they do have their shortcomings. In practice
it has been found that the actual capacity of a batch of electrolytics, all rated the
same but measured at the higher frequencies, may vary by as much as 25 to 30% from the
rated value. In some instances it has also been found that the impedance of the non-polarized
electrolytic may climb at the very high frequencies causing a tweeter loss.
This latter loss may be easily overcome by shunting the electrolytic with a small
paper capacitor, 1 μfd., for example, which will serve to keep the impedance of the
capacitor section of the tweeter branch low at the high frequencies. The earlier question
of the capacity variations is a more ticklish one. It is not generally possible to measure
capacity before the capacitors are purchased. The next best thing is to buy two or three
capacitors of the nominal rating and to select from these the one that comes nearest
to the required impedance at the desired frequency. To make such a selection means, of
course, the use of an audio oscillator, a voltmeter, and a potentiometer. With these
items, an impedance substitution test may be made to determine which capacitor comes
closest to the required value. It is desirable to choose one that is a little low in
value since, if required, the value may be brought up to the proper capacity by shunting
it with a small additional capacity which will aid the very high frequencies.
Such closely controlled electrolytics have been successfully used in commercially
available networks for many years and they have withstood the element of time very well.
They have, however, been of the non-polarized variety, such as the motor-starting type.
The hobbyist has had equivalent success by putting two electrolytics of the polarized
type "back-to-back" to provide a non-polarized capacitor.
Recently there has been discussion on the use of the simple polarized type of electrolytics
for these audio networks and the writer approached the problem with some trepidation.
On the surface, it seemed heretic to use a polarized element in an audio circuit that
was to pass alternating waveforms unmarred and untarnished. However, in view of the fact
that all these doubts could be resolved by definitive measurements, an analysis was made
of the operation of polarized electrolytics and non-polarized electrolytics from the
standpoints of reactance change, waveform distortion, and power transfer. The basic facts
that were being sought were those concerned with the manner in which the waveform was
passed through either type of electrolytic, the voltage rating of the capacitor, and
the power to be passed on to the load by the capacitor. Tests were made at both low-level
power and at high-level power with waveform and amplitude distortion observed on a scope
over the entire audio spectrum.
The non-polarized variety, made by backing up two standard polarized 8 μfd., 450-volt
electrolytics, was tested first. A test run was made from 100 to 20,000 cps feeding this
combination into an 8-ohm load resistor. Since these two 8 μfd. capacitors were connected
in series back-to-back, their resulting capacity was 4 μfd. This value of capacity
has a reactance of 8 ohms (to match the load at crossover point) at approximately 5000
cps. Under these conditions a frequency run was made of the maximum undistorted voltage
that appeared across the 8-ohm load resistor, starting at 100 cps and proceeding to
20,000 cps. The output voltage of the amplifier was continually adjusted to give the
maximum amplitude clean waveform at the load resistor, as seen on the scope. The plot
of this run is shown in Fig. 9A. At the approximate crossover point, 5000 cps, there
was the equivalent of 30 clean watts delivered to the load resistor, while at 20,000
cps this figure was 50 watts. This comes very close to expectations in that, at the crossover
point, the power should be 3 db down from maximum.
As indicated in Fig. 9A, the actual measured crossover point for these two electrolytics
in series turned out to be 700 cps low (from 5000 cps) which would indicate that the
electrolytic combination was about 13% off from rated value.
What is of major importance is the fact that a full 50 watts could be delivered through
such a back-to-back configuration of polarized electrolytics. Just to be contrary, the
back-to-back direction was reversed so that where in the first case, the positive terminals
were tied together, in the second case the negative terminals were connected. There was
no change in performance. There is apparently no reason why non-polarized electrolytics
cannot be used in crossover networks.
But, now, how about the polarized type? With the same test setup as described previously,
a test run was made on only one of the 8 μfd. units of the previous test. Again during
the run the amplifier was adjusted to give the maximum undistorted waveform at the load
resistor. The results were exactly the same as in the case of the non-polarized combination.
There was no waveform distortion at a full 50 watts input to the load resistor and at
the crossover point (in this case 2500 cps for 8 μfd. for 8 ohms) there was a clean
25 watts which was the expected 3 db down.
To tie the matter down even more firmly, a test was made on three different 50 μfd.
polarized electrolytics rated at 150, 50, and 25 volts respectively. No differences in
performance could be observed as far as waveform at maximum output was concerned (50
watts). They were all clean, as observed on a scope.
The last question that was to be resolved was the matter of the rising impedance of
a large value of electrolytic at the higher frequencies, which would have the effect
of reducing the voltage at the tweeter terminals. Fig. 9B is the curve of maximum undistorted
waveform voltage at the load resistor from which it will be seen that for this 50 μfd.
capacity, there is a drooping voltage characteristic at the load. When, however, this
capacity was shunted by a small paper capacitor, the voltage characteristic was respectably
Looking prejudice squarely in the eye, there would seem to be no reason as yet for
not using electrolytics, polarized or non-polarized, for network construction. This,
along with Chart 1 should make the matter of collecting the necessary components for
a home-built network a fairly simple and straightforward operation.
Chart 1 (Above). A master chart giving all physical winding data for crossover network
chokes based on speaker impedance and desired crossover frequency. Choose the speaker
impedance on the vertical scale, move over horizontally to the curve which represents
the desired crossover frequency, and then move down to the horizontal scale which gives
all the vital statistics of the coil needed for the chosen conditions for a 6 db per
octave network, shown in circuit (A) to right. To use chart for 12 db per octave network,
circuit (B), simply multiply speaker impedance by 1.41 and proceed as above. The physical
make-up of the choke coil that is employed must be as shown at the center of this page.
Chart 2 (Left). Auxiliary chart to be used in conjunction with Chart 1 for determining
the value of capacity needed to cross over at a given speaker impedance. To use chart,
simply lay a straight edge between the point on the first column representing the impedance
of the speaker and the point on the last column representing the crossover frequency
desired. The point where the straight edge crosses the center column is the value of
capacity required. Be sure to use the two columns marked "A" together, or the two columns
marked "B" together. This chart is to be used for a 6 db per octave network only. In
order to obtain capacity values for a 12 db per octave network it is only necessary to
divide the value of capacity obtained by. 1.41. For the lower values of capacitance,
oil-filled capacitors are preferred. For the higher values, electrolytics are employed.
Chart 3 (Below). The actual inductance values of network chokes used in the master
Chart 1 are given here. This chart makes it possible to wind coils of given inductance
if the construction details shown along the bottom axis and in the drawing at the center
of this page are followed. Inductance values from about 0.03 up to 20 millihenrys are
Posted July 3, 2018