Guidance of Speaker Network Circuit
１．Various types of Network Circuits and their property
There are various types of Network Circuits, unfortunately there is not perfect one that is superior to all
items of charactoristics. The lower table show grading of Networks. Property of 6dB/oct Network seems
to be very good, but it often needs correction for Speaker because has little attenuation in stop band.
If correction for charactoristics vs freq is performed, phase distortion appear and total voltage vs freq.
becomes worse. 18dB/oct is good except phase distortion, higher cost because of using many parts. There
is phase distortion in 12-24dB/oct, phase distortion becomes bigger so that crossover frequency is lower.
Grading of Networks		Correction	2way
A:VeryGood  B:Good		6-12dB/oct	6dB/oct	12dB/oct		18dB/oct	24dB/oct
C:NotSoGood D:Bad		-3dBcross	-3dBcross	-3dBcross	-6dBcross	-3dBcross	-3dBcross	-6dBcross
Total voltage vs Freq		−	A	D	A	A	B	A
Electric power vs Freq		−	A	A	D	A	A	D
Zin vs Freq		A	A	A	D	A	B	D
Phase distortion		C	A	C	C	C	C	C
StopBandAttenuation		C	C	B	B	A	A	A
LC Parts amount (cost)		2-24	2	4	4	6	8	8
Grading of Networks		3way					4way
		6dB/oct		12dB/oct		18dB/oct	6dB/oct	12dB/oct
A:VeryGood  B:Good		Normal	ＺｉｎConstant	Normal	ＺｉｎConstant	ＺｉｎConstant	ＺｉｎConstant	ＺｉｎConstant
C:NotSoGood D:Bad		-3dBcross	-3dBcross	-3dBcross	-3dBcross	-3dBcross	-3dBcross	-3dBcross
Total voltage vs Freq		C	A	D	D	B	A	D
Electric power vs Freq		C	A	C	A	A	A	A
Zin vs Freq		C	A	D	A	B	A	A
Phase distortion		B	A	C	C	C	A	C
StopBandAttenuation		C	C	B	B	A	C	B
LC Parts amount (cost)		4	4	8	8	12	6	12
２．Charactoristic items of Speaker Network Circuit
(1) Total output voltage curve vs frequency
Total voltage is vector sum of voltage supplied to all speakers,low tone, middle tone, high tone and etc, and
it is in proportion to sound pressure on center axis of speaker system. Accordingly total voltage curve vs
freq. need to be flat, and sound pressure level is dependent upon total voltage at low frequency because
sound pressure of low frequency is the same level to all direction in sound field.
(2) Output power curve vs frequency
Output power is sum of electric power to all speakers, it is inpropotion to sound energy per time in sound
field. Output power curve vs freq. need to be flat, and sound pressure average level is dependent upon
output power at high frequency because sound presure is not the same to any direction in sound field.
(3) Input impedance (Zin) curve vs frequency
According to relation of input apparent power P=(Input voltage Ｅ)2/(Input impedance Zin), output power
(input power) is in proportion to a reciprocal of Zin. Therefore both are the same meanings that Zin curve
vs. freq is flat, and that output power curve vs freq. is flat if network circuit has no loss. So it becomes
very important charactoristic that Zin curve vs freq. is flat. And when impedance depreciate beyond rating
limit of an audio amplifier, a big burden maydepend on the audio amplifier and can get into trouble.
(4) Phase difference in output voltage（phase distortion <= Group delay time)
If wave form changes caused by phase difference between various frequency, phase distortion occurs.
When a phase distortion is big, there can be low readability of the voice. For example, in the case of the
long distance telephone, loading coils are used to make phase distortion lower and readability higher. So
pase distortion need to be low for obtaining good quality of sound. In 6dB/oct network circuit, there is
no phase distortion, but when corrected for charactoristics					frequency	Group delay time/phase distortion
vs freq., 6dB/oct network circuit has phase distortion.						CCIR std.	P.Distortion	１８ｄＢ／ｏｃｔ
But comparing it against CCIR standard, even 18dB/oct,						m sec	degree/Hz	degree/Hz
network circuit satisfy the standard enough. Though it is					４０Ｈｚ	５５max	20.37max	cross500Hz
ideal circuit to have no phase distortion, because you can					７５Ｈｚ	２４max	8.89max	０〜0.48
not realize it, you need not be nervous. For making your					１４ｋＨｚ	８max	2.96max	cross2kHz
favorite sound quality, you don't avoid phase distortion					１５ｋＨｚ	１２max	4.44max	0〜0.12
and had better to choose freely network and correction.
3.Feature of corrective circuit for speaker
3-1.Corrective circuit (attenuator of resistor)					Attenuator of resistor
When sensitivity or effective resistance of speaker differ
from adjusting value, attenuator of resistor may be used.
Both of them are corrected by attenuator simultaneously.
The correction is designed so that all speakers may have
same sensitivity and resistance. Because the correction
by attenuatorof resistor do not make phase distortion,
phase distortion of speaker do not increase at all.
3-2.Corrective circuit (charactoristics vs frequency)
One of the reasons for what correction is needed, is uneven sound pressure curve vs freq. High pass type
corrective circuit is used to improve decreasing lowrange of a speaker that has highrange down-sloped.
The second of the reasons,quantity of decrement of stop band becomes small for a rise of Zin of the
speaker. When woofer and tweeter sound in squawker range greatly, corrective circuit are necessary.
There are series type and parallel type of corrective circuits. The input impedance may often be high
at highrange of speaker. As Zin of the woofer may often be high at high freq., quantity of decrement is
higher at series type than at parallel type in 6dB/oct, and at parallel type than at series type in 12dB/oct.
Because phase changes when used corrective circuit, you must check polarity again and must judge
which is better to connect in order or reverse.  It need to be judged whether speaker is corrected or not
comparing extent improved by correction and extent toturn worse,because phase distortion increases when
used corrective circuit. When correcting the highrange and lowrange of a speaker at the same time, you
can use band pass type circuit. The corrective circuit of high pass type or low pass type is arranged from
2way network circuit, and it of band pass type is arranged from 3way network circuit. Input impedance is
Rio, as they are Zin constant type in both case. Supposing an equivalent circuit of the woofer is series of
R and L, a method to correct an impedance rise of highrange by R and C is attempted, but had better to
consider to be a simple method as it is not right theoretically. An impedance rise is corrected in the lowest
resonance frequency of the woofer paralleled with series circuit of RLC. Because it takes three parts for
means that is not effective on output, there is the feeling to be extra. But there may be a meaning at the
point whether can consider the input impedance of the speaker system to be pure resistance or not.
Corrective circuit (6dB/oct)					Corrective circuit (12dB/oct)
Series type		Parallel type			Series type		Parallel type
4.Feature of Network Circuit					2way 6dB/oct network circuit diagram
4-1.Network Circuit for 2way
(1) 6dB/oct Network
There are parallel  and series type of 6dB/oct network.
The output voltage, output power, the input impedance
in both types are good characteristics becoming constant
regardless of frequency. Because there is the fault that
each impedance influences mutually in a series type, the
parallel type is usually used. The output are connected to
speakers in the same aspect, and has no phase distortion.
But phase distortion of about 0.12 degree/Hz maximum					6dB/oct parallel type		6dB/oct series type
occurs when corrective circuit is used.
(2) 12dB/oct Network					2way 12dB/oct network circuit diagram
There are parallel  and series type of 12dB/oct network.
All of output voltage, power and Zin vs freq. are not flat.
By -3dB crossover output power and Zin are constant
regardless of frequency, by -6dB crossover output voltage
is constant regardless of frequency. By any quantity of
decrement at crossover, all charactoristics vs frequency
are not flat too. To get the good result, when frequency
is highly set as the design of crossover frequency 2-3kHz
by decrement -3dB, 12dB/oct network circuit becomes
to have the flat characteristics audibly. Both output voltage					12dB/octParallelType		12dB/octSeriesType
and power seem to be equivalent with flatness, because
the peak of 3dB of the output sound pressure become flat within angle range of about 8.5 degrees up
and down for a center axis. The reverse aspect connection is adapted because there is phase difference
of 180 degrees at crossover. The phase distortion size becomes maximum about 0.05-0.10 degree/Hz
without correction, and maximum about 0.17 degree/Hz with correction.
(3) 18dB/oct Network					2way 18-24dB/oct network circuit
Voltage, power, Zin are becoming constant regardless of
frequency same as 6dB/oct. Different points from 6dB/
oct are that phase distortion occurs and that quantity of
decrement in stop band is big. There is phase difference
of 270 degrees at crossover. The both aspect connections
are adapted. Phase distortion is about 0.24 degree/Hz.
(4) 24dB/oct Network
The output voltage has a peak of about 1.1dB at cross
over, but the characteristic is good generally. It is rare
to be adopted because they are inferior to 18dB/oct in					18dB/octParallelType		24dB/octParallelType
characteristics. There is phase difference of about 286
degrees at crossover. The both aspect connections are adapted. Phase distortion is about 0.22 degree/Hz.
4-2.Network Circuit for 3way
Regular speaker system can be built from very low tone					3way 6dB/oct network circuit diagram
to high tone by 3way system. In the case of 2way, very
low tone is omitted, because frequency range to take
charge of a speaker is too wide, but 3way system can
cover from very low tone to high tone easily.
(1) 6dB/oct Network
The normal type network has not a flat characteristic vs
frequency, in which output voltage, output power, input
impedance make a small mountain and valley at crossover.
Phase distortion is almost zero, maximum 0.02degree/Hz.
For the squawker raising a bit of resistance, and reducing
sensitivity about 2dB lower, it is improved but is not flat.
As for the Zin constant type, these problems are improved,
and the output voltage, output power, input impedance are					Normal (resonace)		Zin constant type
becoming constant regardless of frequency, they are very					3way 12dB/oct network circuit diagram
good property.There is no phase distortion, but quantity of
decrement in stop band is small, so if corrective circuit is
used, phase distortion(about 0.34degree/Hz) occurrs.
Sound quality can not be considered deteriorating by phase
distortion, when collated with a standard value of CCIR
(2.96-20.37degree/Hz). All speakers are the same aspect
connection without correction, but polarity check is
necessary with correction for improving characteristics.
(2) 12dB/oct Network
In all types of 12dB/oct commonly, there is a peak of
about 3dB to the output voltage at crossover. There is
unevenness on output power and input impedance curve					Normal type		Zin constant type
in normal type, the resonance type is an approximately
flat, and the Zin constant type is completely flat. It is pretty					3way 6&12dB/oct scrambled network
improved, if outputpower curve is flat, and if peak of output
voltage in highrange is left, and if peak of output voltage
in lowrange is changed flat by a low pass type corrective
circuit for woofer. There is not any problem because phase
distortion can be reduced less than about 0.28 degree/Hz
even with correction. Because there is phase difference
of about 180 degrees between each speakers, squawker
is connected in the reverse aspect. Polarity check is
necessary with correction for characteristic vs frequency.
(3) 6&12dB/oct scrambled Network
The input impedance becomes equal to speaker resistance,
If Zin constant type are connected in cascade, and when
using not only 6dB/oct or 12dB/oct but also scrambled.					Zin constant type		Zin constant type
When crossover of 12dB/oct is selected higher, it hears
a peak of the output voltage in audibly flat. The output is					3way 12-18dB/oct network circuit
connected at the part of 6dB/oct in the same aspect,
and at the part of 12dB/oct in the reverse aspect. It is
controlled in low value of phase distortion by designing
lower crossover as 6dB/oct circuit. When correction is
used at low frequency, phase distortion increase.
(4) 18dB Network
The voltage, output power, Zin are approximately constant
regardless of freq. but undulation of the characteristic
become large when two crossover frequency come close.
Sqawker is adapted to the same or reverse aspect and
phase distortion is maximum about 0.52 degree/Hz.
4-3.Network Circuit for 4way
(1) 6dB/oct Network					12dB/octResonance		18dB/octResonance
Because it is Zin constant type, voltage, power, input
impedance are constant regardless of frequency. There is					4way 6-12dB/oct network circuit
no phase distortion without correction, but phase distortion
(about 0.63 degree/Hz) occurs with correction because
quantity of decrement of stop band is small. Without
correction, all speakers are same aspect, but need to
check polarity when correction is used.
(2) 12dB/oct Network
There is a peak of about 3dB to output voltage at the
vicinity of crossover in all type of 12dB/oct. Because
it is Zin constant type, output power and the input
impedance are perfectly flat. When the speakers connect
with reverse aspect in turn, peak voltage of +3dB at
crossover occur. Because the first crossover frequency
is lower than 3way, phase distortion becomes big, about
0.58 degree/Hz, and about 1.1 degree/Hz with correction.					6dB/octZinConstant		12dB/octZinConstant
5.Wiring
The wiring from an audio amplifier to a network circuit has conductor resistance and a self-inductance.
Let us consider these influence and examine measures for improving.
5-1.Influence of conductor resistance
The output voltage of an audio amplifier is wave which has various voltage and various frequency, but
voltage will descend in all frequency equally by conductor resistance of the wiring if Zin is pure resistance.
It is enough to select suitable rating wire, as AWG22 in the case of 2m, AWG18 in the case of 10m, and
AWG14 in the case of 50m. Making input impedance to pure resistance is more simple than performing
multi-wiring for multi-way speakers. Because network impedance of each speaker is not pure resistance
in the case of the multi-wiring, I think that the voltage at crossover makes a peak. However, there is not
any problem because it is only about 0.3dB of the output voltage into which such a wiring is converted.
5-2.Influence of self-inductance
When there is inductance in wiring, a voltage drop may occur at high frequency. As for the output
voltage of 20kHz, it is about -0.002dB at 2m, -0.05dB at 10m, -1.05dB at 50m in length of the wiring,
when it assumed that impedance of the speaker is 6 ohms, inductance of the wiring is 1.0 microH at 2m,
5.0 microH at 10m, 25 microH at 50m. Therefore, it is smaller level than error until 10m in length of the
wiring, and we can understand that it is not necessary to correct.