Harmonic reduction for multi-bridge converters

A method for reducing the signal harmonics of the output fundamental signals of a three-phase inverter systems made up of an N number of inverter bridges achieves harmonic signal reduction by combining the outputs of immediately adjacent bridges separated by 60.degree./N relative to one another and then summing the combined sum signal with the outputs of the next immediately adjacent bridge.

BACKGROUND OF THE INVENTION 
The present invention relates to harmonic signal reduction, and more 
particularly to harmonic signal reduction in the output fundamentals of a 
multi-bridge three-phase power supply. 
Present day three-phase converter systems provide for two way conversion of 
electrical energy, selectably either from DC to AC or from AC back to DC, 
i.e. each converter functions alternately as an inverter (DC to AC) or a 
rectifier (AC to DC). As known, three-phase converters providing output 
power in excess of a few hundred kilowatts require the use of multiple 
converter bridges connected in parallel between the DC or AC sources and 
the load due to the limited power handling capability of individual 
bridges. When used as an inverter, each bridge provides at each of 
three-phase outputs, or poles, a square wave fundamental signal for each 
of the three output phases of the converter. The square wave fundamental 
signals from each bridge have a harmonic content which causes the power 
level of the bridge fundamental signals to change each time a pole 
switches. These harmonics may be determined from the Fourier series 
expansion for a square wave fundamental signal of frequency wt. as: 
##EQU1## 
where V is the signal voltage magnitude and 0 the phase angle. Only odd 
harmonics are present in the expansion, and for a square wave fundamental 
signal measured between the output poles of the three-phase system there 
is inherent cancellation of the third harmonics and multiples thereof; 
i.e. triplens, such that the signal harmonics of the fundamental signal 
between pole outputs are odd harmonics less triplens, i.e. the 5, 7, 11, 
13, 17, 19, 23, 25, 29, 31, 35, 37. . . etc. 
As known to those skilled in the art, if two signals (current or voltage) 
are added to each other at an angle 360.degree./2N=180.degree./N, the Nth 
harmonics of each signal are displaced from each other by (180.degree./N) 
N=180.degree. and will cancel if the amplitudes of each are equal. If 
pairs of signals are added from two sets of P phase signals this angle 
becomes 360.degree./2PN=180.degree./PN, or 60.degree./N for a three-phase 
system. This relationship is used in providing harmonic cancellation in a 
two-bridge three-phase inverter as disclosed by Udo H. Meier in U.S. Pat. 
No. 3,792,286, where various interconnection arrangements are illustrated 
for two-phase displaced bridges driving two equally displaced load 
windings, to provide cancellation of the 5th and 7th harmonics of the 
output fundamental. In the Meier patent the corresponding phase outputs of 
the two bridges are relatively phase displaced by 30.degree. 
(360.degree./2PN, where P=3, N=2) and the load windings are similarly 
displaced to provide a unity power factor fundamental signal to the load. 
Cancellation of the 5th and 7th harmonics occurs, in a three-phase reactor 
connected to the phase outputs of each bridge, as a direct result of the 
summation of two (N=2) sets of three (P=3) phase corresponding fundamental 
signals separated relatively displaced in phase by the angle 
360.degree./2PN=30.degree.. Cancellation for only two bridges is disclosed 
and any attempt to extend the teaching of Meier to inverters having more 
than two bridges results in the realization that the number of bridges 
must be limited to powers of two to allow for successive addition of 
pairs, then pairs of pairs and so on. Therefore, the next number of 
bridges required is four, with the signals of the second pair summed in a 
second reactor which cancels the 5th and 7th harmonics of the second pair, 
and with the outputs from each of the two reactors being summed in a third 
reactor which provides cancellation of the next two sets of higher order 
harmonics 11, 13, 17 and 19. Since it may be found practical to provide 
high power converters with as many as seven inverter bridges, Meier fails 
to teach a method or apparatus for cancelling the fundamental harmonics in 
a three, five, six or seven bridge converter system. 
A second U.S. Pat. No. 3,876,923, to A. J. Humphrey et al provides an 
extension of the Meier teaching by disclosing the use of the Meier 
arrangement for a two inverter bridge system relatively displaced at the 
interpole angle of 30.degree. and providing three-phase power through a 
similar reactor into a phase displaced load winding, which in Humphrey et 
al is disclosed as a combination of phase and auxiliary windings in a 
common magnetic circuit as opposed to the electrically isolated loads of 
Meier. As in Meier, there is no suggestion by Humphrey et al of a method 
or arrangement for cancelling the fundamental harmonics in an inverter 
system having non-power of two numbers of bridges. 
U.S. Pat. No. 4,204,264 assigned to the same assignee as the present 
invention provides harmonic signal cancellation in an inverter system 
having non-power of two numbers of bridges wherein the fundamental signals 
of each bridge are phase displaced by 60.degree./N degrees relative to the 
fundamental signals provided at another bridge. The bridges are grouped 
and fundamental signals are produced for each group which have a phase 
angle corresponding to one of the converter phases. The signal harmonics 
in one group of an order less than (6N-1) displaced 180 degrees from the 
equal order signal harmonics of another group. The fundamental signals 
having corresponding phase angles are added and provide the output 
fundamental signal in each of the converter phases with the signal having 
a first harmonic of order (6N-1). 
Each of the foregoing patents disclose methods and apparatus which attempt 
to cancel harmonic signals in the output fundamental signals of 
multi-bridge, three-phase power converters. Typically, such approaches 
require balanced circuit arrangements and equal bridge current magnitudes 
which necessitate exact ratios which are a funciton of transcendental 
functions. Thus, large turns transformers with only restricted integer 
windings can be used. These transformers are generally very expensive and 
add greatly to the cost of power converters having such harmonic signal 
cancellation circuits. In addition, it is necessary to use transformers 
that have low flux levels in order to keep power losses down. 
The transformers in high power inverters have only a few turns per winding 
despite having input voltages of several hundred volts, and windings 
having only a 1 or 2 per cent to exact ratios are feasible without 
auxiliary auto-transformers. In addition, winding unbalance may produce a 
1 to 2 per cent difference in bridge loadings. Therefore, balanced 
impedances or exact sharing is not feasible or practical in practice to 
achieve exact harmonic cancellation and bridge loading. 
It is therefore a general aim of the present invention to provide harmonic 
signal reduction for multi-bridge converters that produces an output 
voltage having an acceptable total harmonic distortion and single harmonic 
distortion for use in high power converters. 
It is a further aim of the present invention to provide apparatus for 
harmonic reduction in output fundamental signals of a multi-bridge, 
three-phase converter for any combination of odd or even numbers of 
bridges. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, harmonic signal reduction in the 
output fundamental signals of a multi-bridge, three-phase converter 
connects the outputs of the bridges to matching displaced windings on the 
output transformer through current balancing series transformers. The 
current balancing transformers provide the proper phasing of the bridge 
currents to cause them to have substantially the same power factor. The 
outputs of two adjacent bridges are combined and then the combined output 
is combined with the output of a next bridge to provide a second combined 
output which is in turn combined with the output of a next bridge. The 
combinations are expandable to cover any even or odd numbers of bridges.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
Referring now to the Figures and considering FIGS. 1 and 2, an embodiment 
of harmonic frequency reduction apparatus according to the present 
invention for a three phase, two bridge converter providing DC to AC 
conversion, i.e. inverter function is illustrated therein. The converter, 
generally designated 10, receives DC electrical power from a DC voltage 
source 12 connected positively and negatively through leads 14, 16 to 
inputs of two parallel inverter bridges functionally illustrated and 
generally designated 18, 20 respectively. Each bridge has three phase 
outputs, or pole outputs, A, B and C, relatively phase displaced in a 
closed sequence by 120.degree. (360.degree./P), each at a phase angle 
corresponding to one of the three converter output phases. In the absence 
of harmonic signal reduction circuitry, the bridge phase outputs are 
coupled directly to associated phases of an output transformer generally 
designated 22 and shown within the dashed line box 24. The transformer 22 
is of the Delta-Wye type which provides a summation of each three 
fundamental signals of the corresponding phase outputs of the bridges 18, 
20 to provide a sum fundamental signal as the output signal in each 
converter phase. In the present invention, harmonic signal reduction 
circuitry generally designated 26 within the dashed line box 28 is 
interconnected between the bridge phase outputs and the primary windings 
of the output transformer 22 to provide the harmonic signal reduction 
prior to signal transfer through the output transformer 22. 
The converter bridges 18, 20 are of a type well known to those skilled in 
the art and a detailed description of their operation is not necessary for 
an understanding of the present invention. Reference may be had to the 
above-referenced U.S. Pat. No. 4,204,264 for a more detailed description 
of the bridges 18, 20 and which disclosure is incorporated herein by 
reference. 
In the embodiments illustrated in FIGS. 1 and 2, the bridge output signals 
are assumed not to be pulse modulated, such that the phase output 
fundamental signals are substantially square waves. This assumption 
provides a simplification of the description and analysis of the harmonic 
signal reduction of the present invention, but in no way limits the 
invention to inverters providing only square wave pole output signals. As 
is well known to those skilled in the art, pulse modulation is used to 
reduce harmonics of the fundamental as well as to provide for voltage 
regulation and may be used in combination with the harmonic signal 
reduction of the present invention and in fact may be used to reduce the 
5th and 7th harmonic components and to minimize transformer size. 
Again, referring to FIGS. 1 and 2, the corresponding phase outputs 
(A.sub.1, A.sub.2, and B.sub.1, B.sub.2, and C.sub.1, C.sub.2) are phase 
displaced to provide a relative phase displacement of 0= 
360.degree./2PN=30.degree.. 
The phase outputs of the two bridges 18, 20 are connected to the harmonic 
signal reduction circuitry 26 which includes a phase shifting transformer 
shown within the dashed 32 and 34, respectively each phase displaced from 
the other in a closed sequence by 120.degree.. The phase shifting 
transformer 28 includes a set of three windings 36, 38 and 40 on the core 
leg 30, windings 42, 44, 46 on leg 32 and windings 48, 50 and 52 on leg 
34. 
The windings 36, 42 and 48 are long windings (L) and windings 38, 40, 44, 
46, 50 and 54 are short windings (S) and each L winding is associated with 
a pair of S windings. An S winding is electrically connected in series 
opposing with another S winding as illustrated in FIGS. 1 and 2. The 
individual L and S windings are connected to selected phase outputs from 
each of the pair of bridges 18, 20 to provide zero fundamental signal 
ampere turns within the transformer three-phase core. 
In FIGS. 1 and 2, the phase outputs of the bridge 18, 20 are connected 
through the lines 56-66 to selected windings on the legs of the 
transformer 28 as illustrated. The S/L turns ratio is calculated to 
provide zero ampere turns in the transformer core for the displaced 
fundamental signals such that the leg 30 has its L winding 36 connected 
through line 56 to the corresponding phase output A.sub.1 and S windings 
38, 40 connected through lines 62, 64 respectively to the corresponding 
phase outputs A.sub.2, B.sub.2. The S winding 38 is poled to provide 
opposite phasing with respect to the windings 36 and 40 which are also 
wound on the leg 30. 
Likewise, the leg 32 has its L winding 42 connected through line 58 to the 
corresponding phase output A.sub.2 and S 
Likewise, the leg 32 has its L winding 42 connected through line 58 to the 
corresponding phase output A.sub.2 and S windings 44, 46 connected through 
lines 64, 66 respectively to the corresponding phase outputs B.sub.2, 
C.sub.2. The S winding 44 is poled to provide opposite phasing with 
respect to the windings 42 and 46 which are also wound on the leg 32. 
The leg 34 also is wound similarly with its L winding 48 connected through 
line 60 to the phase output C.sub.2 and S windings 50, 54 connected 
through lines 62, 66 respectively to the corresponding phase outputs 
A.sub.2, C.sub.2 with the S winding 54 poled to provide the opposite 
phasing. 
FIGS. 3A and 3B illustrate the displaced fundamental signals presented 
through the lines 56-66 to the transformer 28, each with a power factor of 
cos 15.degree.. The kilowatt (KW) current (I.sub.o) and voltage (V.sub.o) 
of each is equal to I cos 15.degree. and V cos 15.degree., where I and V 
are current and voltage magnitudes for a nondisplaced fundamental. 
In FIG. 3C, the voltages developed in the leg 30 of the transformer 28 are 
illustrated for the fundamental signal. The output fundamental voltage 
signal shown as the vector A.sub.11 is summed with the voltage signals 
shown as the vector -A.sub.21 (opposite phasing of winding 38) and 
B.sub.21 where the sum is illustrated as the vector 31 which is equal in 
magnitude but 180.degree. out of phase with the fundamental voltage signal 
A.sub.11 thereby passing the fundamental signal unattenuated to the output 
transformer 22. 
In FIG. 3D, the voltages developed in the leg 32 are illustrated for the 
fundamental signal. The output fundamental voltage signal shown as the 
vector B.sub.11 is summed with the voltage signals shown as the vectors 
-B.sub.21 (opposite phasing of winding 44) and C.sub.21 where the sum is 
illustrated as the vector 33 which is equal in magnitude but 180.degree. 
out of phase with the fundamental voltage signal B.sub.11 thereby passing 
the fundamental signal unattenuated to the output transformer 22. 
In FIG. 3E, the voltages developed in the leg 34 are illustrated for the 
fundamental signal. The output fundamental voltage signal shown as the 
vector C.sub.11 is summed with the voltage signals shown as the vectors 
-C.sub.21 (opposite phasing of winding 54) and A.sub.21 where the sum is 
illustrated as the vector 35 which is equal in magnitude but 180.degree. 
out of phase with the fundamental voltage signal C.sub.11 thereby passing 
the fundamental signal unattenuated to the output transformer 22. 
FIGS. 4A and 4B illustrate the displaced fifth harmonic signals presented 
through the lines 56-66 to the transformer 28. In FIG. 4C, the voltages 
developed in leg 30 of the transformer 28 are illustrated for the fifth 
harmonic signal. The output fifth harmonic voltage signal is shown as the 
vector A.sub.15 summed with the voltage signals shown as the vectors 
-A.sub.25 and B.sub.25 where the sum is illustrated as the vector 37 which 
is substantially equal to and in phase with the fifth harmonic signal such 
that substantially all of the fifth harmonic voltage signal is dropped 
across the transformer 28 rather than passed to the output transformer 22. 
In FIG. 4D, the voltages developed in leg 32 of the transformer 28 are 
illustrated for the fifth harmonic signal. The output fifth harmonic 
voltage signal is shown as the vector B.sub.15 summed with the voltage 
signals shown as the vectors -B.sub.25 and C.sub.25 where the sum is 
illustrated as the vector 39 which is substantially equal to and in phase 
with the fifth harmonic voltage signal such that substantially all of the 
fifth harmonic voltage signal is dropped across the transformer 28 rather 
than passed to the output transformer 22. 
In FIG. 4E, the voltages developed in the leg 32 of the transformer 28 are 
illustrated and as above, the output fifth harmonic voltage signal is 
shown as the vector C.sub.15 summed with the voltage signals shown as the 
vectors -C.sub.25 and A.sub.25 where the sum is illustrated as the vector 
41 which is substantially equal to and in phase with the fifth harmonic 
signal such that substantially all of the fifth harmonic voltage signal is 
dropped across the transformer 28 rather than passed to the output 
transformer 22. 
The voltages developed in the transformer 28 for the seventh harmonic 
voltage signal are illustrated in FIGS. 5A-5E. As in the case of the fifth 
harmonic voltage signals described above, the seventh harmonic voltage 
signals are also attenuated with the harmonic reduction apparatus of the 
present invention. 
The eleventh and thirteenth harmonic signals are, as is the fundamental 
frequency voltage signal, passed unattenuated to the output transformer 
22. FIGS. 6A-6B illustrate the output eleventh harmonic voltage signals 
and FIGS. 6C-6E illustrate as vectors the eleventh harmonic voltage 
signals developed across the legs of the transformer 28. FIGS. 7A-7B 
illustrate the output thirteenth harmonic voltage signals and FIGS. 7C-7E 
illustrate as vectors the thirteenth harmonic voltage signals developed 
across the legs of the transformer 28. 
It can be shown that the 17, 19, 29, 31, etc. harmonic voltage signals are 
reduced as demonstrated above for the fifth and seventh harmonic voltage 
signals. It can also be shown that the 23, 25, 35, 37, etc. harmonic 
voltage signals are passed unattenuated as demonstrated above for the 
fundamental, eleventh and thirteenth harmonic voltage signals. 
Referring to FIGS. 8 and 9, the harmonic reduction apparatus embodying the 
present invention is illustrated as used with a three bridge configuration 
wherein the phase outputs of two adjacent bridges are combined and then 
combined with the output of the third bridge. Again, the bridge output 
signals are assumed not to be pulse modulated such that phase output 
fundamental signals are substantially square waves. 
Referring to FIGS. 8 and 9, a three bridge converter providing DC to AC 
conversion is illustrated therein and generally designated 70. A DC 
voltage source 72 is connected positively and negatively through leads 74, 
76 to inputs of three parallel inverter bridges functionally illustrated 
and generally designated 78, 80 and 82, respectively. The corresponding 
phase outputs (A.sub.1, A.sub.2, A.sub.3 and B.sub.1, B.sub.2, B.sub.3 and 
C.sub.1, C.sub.2 and C.sub.3) are phase displaced to provide a relative 
phase displacement of 0=360.degree./2PN=20.degree.. 
The phase output of the two bridges 78, 80 are connected to a phase 
shifting reduction transformer shown within the dashed line box 84 and 
which is part of the harmonic reduction circuitry generally designated 86 
embodying the present invention. The phase outputs of the bridges 78 and 
80 are connected through the lines 112-122 to the selected windings on the 
legs of transformer 84 as illustrated. The transformer 84 has a 
three-phase core of X, Y and Z legs, 88, 90 and 92 respectively, each 
phase displaced from the other in a closed sequence by 120.degree.. The 
phase shifting transformer 84 includes a set of three windings 94, 96 and 
98 on the core leg 88, windings 100, 102 and 104 on the leg 90 and 
windings 106, 108 and 110 on the leg 92. The transformation ratio of the 
windings of the transformer 84 are 7 to 5 to 3 as illustrated. 
The outputs of the transformer 84 on the leads 124-134 are connected to a 
second phase shifting reduction transformer shown within the dashed line 
box 136 and which transformer has a three phase core of X, Y and Z legs, 
138, 140 and 142 respectively, each phase displaced from the other in a 
closed sequence by 120.degree.. The phase shifting transformer 136 
includes a set of four windings 144, 146, 148 and 150 on the leg 138, 
windings 152, 154, 156 and 158 on the leg 140 and windings 160, 162, 164 
and 166 on the leg 142. The transformer 136 combines the outputs from the 
transformer 84 and the phase outputs on the leads 168-172 of the bridge 
82. The transformation ratio of the windings on each leg of the 
transformer 136 is 7 to 7 to 8 to 8. 
The output signals from the transformer 136 are coupled to the associated 
phases of an output transformer generally designated 174 and is shown 
within the dashed line box 176. The transformer 174 is of the Delta-Wye 
type which provides a summation of each three fundamental signals of the 
corresponding phase outputs of the bridges 78, 80 and 82 to provide a sum 
fundamental signal as the output signal in each converter phase. 
FIGS. 10A, 10B and 10C illustrate the displaced fundamental signals 
presented through the lines 112-122 and 168-172 to the transformer 84 and 
136 respectively each with a power factor of cos 20.degree.. In FIG. 10D, 
the voltages developed in leg 88 of the transformer 84 are illustrated for 
the fundamental signal. The output fundamental voltage signal shown as the 
vector A.sub.11 is summed with the voltage signals shown as the vector 
-A.sub.21 (opposite phasing of winding 96) and B.sub.21 where the sum is 
illustrated showing that the fundamental signal is passed unattenuated to 
the transformer 136. Likewise, FIGS. 10E and 10F show respectively that 
the fundamental voltage signals represented by the vector B.sub.11 and 
C.sub.11 are likewise passed unattenuated to the transformer 136. FIGS. 
10G, 10H and 10I illustrate the voltages developed in the legs 138, 140 
and 142 respectively of the transformer 136 for the fundamental signal. 
The output fundamental voltage signal shown as the vectors A.sub.11 and 
A.sub.21 are summed with the voltage signals shown as the vectors 
-A.sub.31 (opposite phasing of winding 148) and B.sub.31 and illustrates 
that the fundamental signal is passed unattenuated to the output 
transformer 174. Likewise, the output fundamental voltage signals 
B.sub.11, B.sub.21, C.sub.11 and C.sub.21 are passed unattenuated to the 
output transformer 174. 
FIGS. 11A-11F illustrate the displaced fifth harmonic signals presented 
through the lines 112-122 and 168-172 to the transformers 84 and 136 
respectively. In FIG. 11A, the voltages developed in the leg 88 of the 
transformer 84 are illustrated for the fifth harmonic signal. The output 
fifth harmonic voltage signal is shown as the summation of vectors 
A.sub.15 -A.sub.25 (opposite phasing of winding 96)+B.sub.25 where the sum 
is illustrated as the vector 91 and which illustrates the fifth harmonic 
signal is dropped across the transformer which substantially attenuates 
any fifth harmonic voltage signal passed to the output transformer. 
Likewise, FIGS. 11B and 11C also illustrate that the fifth harmonic 
voltage signals are dropped across the transformer 84 and are 
substantially attenuated rather than being passed to the output 
transformer 174. 
FIGS. 11D-11F illustrate the displaced fifth harmonic signals presented 
through the lines 124-134 as attenuated by the transformer 184 and through 
the lines 168-172 from bridge 82 and which signals are summed in the 
transformer 136. In FIG. 11D, the voltages developed in leg 138 of the 
transformer 136 are illustrated for the fifth harmonic signal. The output 
fifth harmonic voltage signal is shown as the summation of the vectors 
A.sub.15 +A.sub.25 -A.sub.35 (opposite phasing of winding 148)+B.sub.35. 
From FIG. 11D, it is seen that the transformer leg 138 supports a 
substantial portion of the fifth harmonic voltage signal and reductions of 
95% or greater can be expected. FIGS. 11E and 11F also illustrate that the 
displaced fifth harmonic voltage signals are supported by the transformer 
legs 140 and 142 respectively such that any fifth harmonic signal reaching 
the output transformer 174 is significantly attenuated. 
FIGS. 12A-12F illustrate the displaced seventh harmonic voltage signals 
presented through the lines 112-122 and 168-172 the transformers 84 and 
136 respectively. In FIG. 12A, the voltages developed in leg 88 of the 
transformer 84 are illustrated for the seventh harmonic signal. The output 
seventh harmonic voltage signals is shown as the summation of the vectors 
A.sub.17 +B.sub.27 -A.sub.27 (opposite phasing of winding 96) where the 
sum is illustrated as the vector 93 demonstrating that the transformer leg 
88 supports a substantial portion of the seventh harmonic voltage signal. 
FIGS. 12B and 12C likewise illustrate that the transformer legs 90 and 92 
respectively of the transformer 84 support the displaced seventh harmonic 
voltage signal sums. 
FIGS. 12D-12F illustrate the displaced seventh harmonic voltage signals 
presented to the transformer 136 through the lines 124-134 of the 
transformer 84 and lines 168-172 of the bridge 82. The output seventh 
harmonic voltage signal is shown as the summation of the vectors A.sub.17 
+A.sub.27 -A.sub.37 (opposite phasing of winding 148)+B.sub.37. From FIG. 
12D it is seen that the seventh harmonic output voltage from the third 
bridge 82 is combined with the seventh harmonic voltage signals presented 
by the bridges 78 and 80 and are supported in the leg 138 of the 
transformer 136 thus, significantly attenuating any seventh harmonic 
voltage signal presented to the output transformer 174. FIGS. 12E and 12F 
likewise show the displaced seventh harmonic voltage signals supported in 
the respective legs 140, 142 of the transformer 136. 
It can be shown that the voltage outputs due to the 11, 13, 23, 25, 29, 31 
and higher harmonic multiples of [.(6m) (+/-) 1] harmonic pairs are 
significantly reduced by the harmonic reduction apparatus illustrated in 
FIGS. 8 and 9. It can also be shown that in addition to passing the 
fundamental signal unattenuated to the output transformer, the 17, 19, 35, 
37 and higher harmonic multiples of the [(18m) (+/-) 1] harmonic pairs are 
also passed unattenuated. 
The harmonic reduction apparatus described above and disclosed as embodied 
in a two and three bridge inverter configuration may be extended to any 
numbers of odd or even bridge configurations. In contrast to prior known 
designs, the present invention does not require the use of a balanced 
structure for equal inverter bridge loading. From a practical standpoint, 
balanced impedances or exact current sharing is not feasible and 
therefore, substantial size and cost savings are realized through harmonic 
signal reduction rather than exact cancellation and equal bridge loading. 
The number of windings on the phase shifting transformers and output 
transformers are minimized as is the size of the transformers. Therefore, 
the invention has been described by way of illustration rather than 
limitation.