Six-port measuring circuit

A six-port measuring circuit includes only four hybrids coupling two input orts to four power measuring ports. A first hybrid is connected to one input port and to second and third hybrids; a second input port is connected to the second hybrid; the second and third hybrids are connected to a fourth hybrid; first and second measuring ports are connected respectively to the second and third hybrids; and third and fourth measuring ports are connected to the fourth hybrid. In one embodiment, the first hybrid is a 180.degree. hybrid; and the second, third and fourth hybrids are quadrature hybrids. In a second embodiment, the first three hybrids are 180.degree. hybrids and the fourth a quadrature hybrid. Another embodiment includes three quadrature hybrids as the first three hybrids and a 180.degree. hybrid as the fourth hybrid. A fourth embodiment employs four quadrature hybrids. The basic six-port circuit is useful as a vector voltmeter and may be coupled to a transmission line by means of a directional coupler. Net power and the complex reflection coefficient .GAMMA..sub.l may be computed from the power readings at the measuring ports.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to measuring systems and more particularly to 
measuring systems employing six-port measuring circuits. 
2. Description of the Prior Art 
The so-called "six-port" approach to the measurement of microwave 
parameters, such as power and complex impedance, provides an attractive 
alternative to existing automated measurement schemes, because the 
requirement for frequency conversion is eliminated. Typical prior art 
disclosures of the six-port approach are found in a number of references, 
including: 
G. f. engen and C. A. Hoer, "Application of an Arbitrary 6-Port Junction to 
Power Measurement Problems," IEEE Trans. Instrum. Meas., Vol. IM-21, pp. 
470-474, Nov. 1972; 
C. a. hoer and G. F. Engen, "Analysis of a Six-Port Junction for Measuring 
v, i, a, b, z, .GAMMA. , and Phase," presented at the Proc. IMEKO Symp. 
Acquisition and Processing of Measurement Data for Automation, Dresden, 
Germany, June 17-23, 1973; 
G. f. engen, "Calibration of an Arbitrary Six-Port Junction for Measurement 
of Active and Passive Circuit Parameters," IEEE Trans. Instrum. Meas., 
Vol. IM-22, pp. 295-299, December 1973; 
C. a. hoer, "Using Six-Port and Eight-Port Junctions to Measure Active and 
Passive Circuit Parameters," Nat. Bur. Stand. (U.S.), Tech. Note 673, 23 
pages, September 1975; 
C. a. hoer and K. C. Roe, "Using an Arbitrary Six-Port Junction to Measure 
Complex Voltage Ratios," IEEE Trans. Microwave Theory & Techniques, Vol. 
MTT-23, No. 12, pp. 978-984, December 1975; 
E. l. komarek, "An Automated Broadband System for Measurement of One-Port 
Microwave Parameters," Conference on Precision Electromagnetic 
Measurements, June 1976, Boulder, Colo., CPEM Digest, pp. 167-170; 
G. f. engen, "Determination of Microwave Phase and Amplitude from Power 
Measurements," IEEE Trans. Instrum. Meas., Vol. IM-25, No. 4, pp. 414-418, 
December 1976; and 
S. b. cohn and N. P. Weinhouse, "An Automatic Microwave Phase Measurement 
System," The Microwave Journal, pp. 49-56, February 1964. 
Moreover, preliminary results, in the case of power at least, suggest that 
the requirement for a phase-locked source is eliminated as well as 
disclosed in the Komarek reference. 
As noted (or stressed) in these prior art disclosures, the theory which has 
been developed applies to a five-or six-port junction of arbitrary 
parameters. In its present form, however, the theory provides only a 
limited amount of insight into the question of choosing the design goals 
for the five-or six-port so as to best exploit the technique. In some of 
the prior work, the six-port was considered an extension of the 
reflectometer concept. This led to six-port designs which are now 
considered obsolete. In other cases, guidelines, which were inferred from 
an incomplete analysis, have been proven to be partially in error. 
SUMMARY OF THE INVENTION 
It is the object of the invention to provide a circuit which permits 
optimum implementation of the six-port concept for the measurement of net 
power and the complex reflection coefficient (.GAMMA..sub.l) at a given 
terminal surface in a uniform transmission line, from which other terminal 
variables, such as wave amplitudes, voltage, current, impedance and the 
like, may be obtained by the use of well known formulas. 
It is a further object of the invention to provide a measuring circuit of 
this character which, moreover, may be implemented over a wide frequency 
range. 
Whereas the circuits of the prior art use at least five hybrids, it is an 
object of the invention to provide a circuit employing no more than four 
hybrids to achieve the basic response. 
Because signal power is very costly, it is another object of the invention 
to provide a circuit of this character which is substantially lossless and 
which does not require the dissipation of signal power for effecting the 
desired measurements. 
To these ends, the invention contemplates a six-port measuring circuit 
comprising only four hybrid means and having first and second input ports 
and third, fourth, fifth, and sixth measuring ports. The first input port 
is coupled to a first port of the first hybrid means. The second input 
port is coupled to a first port of the second hybrid means. A second port 
of the first hybrid means is coupled to a second port of the second hybrid 
means. A third port of the first hybrid means is coupled to a first port 
of the third hybrid means. A third port of the second hybrid means is 
coupled to a first port of the fourth hybrid means. A second port of the 
third hybrid means is coupled to a second port of the fourth hybrid means. 
The third measuring port is coupled to a fourth port of the second hybrid 
means. The fourth measuring port is coupled to a third port of the third 
hybrid means. The fifth measuring port is coupled to a third port of the 
fourth hybrid means, and the sixth measuring port is coupled to a fourth 
port of the fourth hybrid means. In a first embodiment of the invention, 
the first hybrid means is a 180.degree. hybrid; and the second, third, and 
fourth hybrid means are quadrature hybrids. In the second embodiment, the 
first, second, and third hybrid means are 180.degree. hybrids; and the 
fourth hybrid means is a quadrature hybrid. In a third embodiment, the 
first, second and third hybrid means are quadrature hybrids; and the 
fourth hybrid means is a 180.degree. hybrid. In a fourth embodiment, the 
first, second, third, and fourth hybrid means are quadrature hybrids. 
In each of the embodiments, the six-port network, which is a vector 
voltmeter, has power responses at each of the measuring ports defined 
substantially by: 
EQU P.sub.3 = 1/2 .vertline.d.vertline..sup.2 .vertline.c/d- j 
.sqroot.2/2.vertline..sup.2 
EQU P.sub.4 = 1/4 .vertline. d.vertline..sup.2 
EQU P.sub.5 = 1/4 .vertline.d.vertline..sup.2 .vertline.c/d + (1+j) 
.sqroot.2/2.vertline..sup.2 
EQU P.sub.6 = 1/4 .vertline.d.vertline..sup.2 .vertline.c/d - (1-j) 
.sqroot.2/2.vertline..sup.2 
where c represents the wave amplitude at the second input port, d 
represents the wave amplitude at the first input port, P.sub.3 represents 
the power response at the third measuring port, P.sub.4 represents the 
power response at the fourth measuring port, P.sub.5 represents the power 
response at the fifth measuring port, and P.sub.6 represents the power 
response at the sixth measuring port. 
The input ports of the six-port network may be coupled to a transmission 
line by a directional coupler having a measurement port at which the 
emergent and incoming wave amplitudes are designated by b and a, 
respectively, and wherein, for the case of a 6 dB coupler, 
EQU c = a .sqroot.3/2 
EQU d = b .sqroot.3. 
In terms of the measurement port of the directional coupler, the power 
responses are defined by: 
EQU P.sub.3 = 3/8 .vertline.b.vertline..sup.2 .vertline..GAMMA..sub.l 
-j.sqroot.2.vertline..sup.2 
EQU P.sub.4 = 3/4 .vertline. b.vertline..sup.2 
EQU P.sub.5 = 3/16 .vertline.b.vertline..sup.2 .vertline..GAMMA..sub.l 
+(1+j).sqroot.2.vertline..sup.2 
EQU P.sub.6 = 3/16 .vertline.b.vertline..sup.2 .vertline..GAMMA..sub.l -(1- 
j).sqroot.2.vertline..sup.2 
where .GAMMA..sub.l is the complex reflection ratio between the amplitudes 
of the incoming wave a and the energing wave b. 
From the power measurements P.sub.3, P.sub.4, P.sub.5, and P.sub.6 at the 
measuring ports of the six-port, one can compute, for circuits closely 
approximating the ideal, the net power and the complex reflection 
coefficient, .GAMMA..sub.l, as follows: 
Net power = 4/3 [4 P.sub.4 - P.sub.3 - P.sub.5 - P.sub.6 ] 
and 
##EQU1## 
These and other objects, features and advantages of the invention will 
become more readily apparent from consideration of the following detailed 
description of the invention when taken in conjunction with the drawings.

DETAILED DESCRIPTION 
To begin with, the theoretical development of the invention will be 
considered. The measurement problem is illustrated in FIG. 1. The six-port 
network 20 is energized from a generator 21 through a first input port 22 
and is coupled through a second input port 27 at a terminal plane 
(indicated by the dash line) to a transmission line represented by a load 
28. The six-port has four measuring ports connected, respectively, to 
power meters P.sub.3, P.sub.4, P.sub.5, and P.sub.6. At the terminal 
plane, there are three independent parameters, some or all of which may be 
required in a given measurement. Although these may be expressed in a 
variety of ways, a convenient set is the magnitude of the emerging wave 
amplitude .vertline.b.vertline. and the complex ratio .GAMMA..sub.l 
between the amplitudes of the incoming wave a and the emerging wave b. 
Following the arguments outlined in the aforementioned article by applicant 
in IEEE Trans. Instrum. Meas., Vol. IM-22, pp. 295-299, December 1973, one 
can write the equations for the observed power meter readings P.sub.3, 
P.sub.4, P.sub.5, and P.sub.6 : 
EQU p.sub.3 = .vertline.a a + Bb.vertline..sup.2 (1) 
EQU P.sub.4 = .vertline.Ca + Db.vertline..sup.2 (2) 
EQU P.sub.5 = .vertline.Ea + Fb.vertline..sup.2 (3) 
EQU P.sub.6 = .vertline.Ga + Hb.vertline..sup.2. (4) 
Here A, B, C, D, E, F, G, and H are complex constants whose values are 
determined by the design of the six-port and which are assumed to be known 
and may be prescribed at will. It is the preliminary objective of this 
analysis to develop criteria for choosing the values A, B, C, D, E, F, G, 
and H in a way which leads to an optimal design. 
Apart from the criteria which may emerge from a study of these equations, 
there are the additional practical requirements of correcting for power 
instability in the signal source and assuring that the power levels at the 
several detectors and output port are maintained at some optimum value as 
the frequency is varied. Ordinarily, this calls for a feedback loop and, 
unless otherwise provided for, an additional directional coupler or other 
means to sample and measure the incident wave amplitude, 
.vertline.b.vertline.. The measurement of .vertline.b.vertline., however, 
represents a determination of one of the measurands of interest; thus, 
there is a double role served by designing the six-port in such a way that 
the response of one of the power meters is proportional to 
.vertline.b.vertline..sup.2. The fourth measuring port connected to power 
meter P.sub.4 is chosen for this role. Referring to Equation (2), the 
first design objective is that C = 0, and to the extent that this 
condition is realized, Equation (2) becomes 
EQU P.sub.4 = .vertline.D.vertline..sup.2 .vertline.b.vertline..sup.2 (5) 
In order to explicitly display the measurands of interest, Equations (1), 
(3), and (4) may be written 
EQU P.sub.3 = .vertline.A.vertline..sup.2 .vertline.b.vertline..sup.2 
.vertline..GAMMA..sub.l -q.sub.3 .vertline..sup.2 (6) 
EQU P.sub.5 = .vertline.E.vertline..sup.2 .vertline.b.vertline..sup.2 
.vertline..GAMMA..sub.l -q.sub.5 .vertline..sup.2 (7) 
EQU P.sub.6 = .vertline.G.vertline..sup.2 .vertline.b.vertline..sup.2 
.vertline..GAMMA..sub.l -q.sub.6 .vertline..sup.2 (8) 
where q.sub.3 = -B/A, q.sub.5 = -F/E, and q.sub.6 = -H/G. 
The parameters .vertline.b.vertline. and .GAMMA..sub.l may be considered as 
representing a point in three-dimensional space, permitting the problem to 
be discussed in terms of three-dimensional geometry. A more convenient 
approach, however, is to first eliminate .vertline.b.vertline..sup.2 from 
Equations (6), (7), and (8) by means of Equation (5). This leads to a 
problem in two dimensions. Although Equation (5) is only an approximation, 
it is convenient initially to treat it as exact and then consider the 
general case. 
Elimination of .vertline.b.vertline..sup.2 between Equations (5) and (6), 
for example, leads to 
EQU .vertline..GAMMA..sub.l - q.sub.3 .vertline..sup.2 = 
.vertline.D/A.vertline..sup.2. P.sub.3 /P.sub.4. (9) 
fig. 2 represents the .GAMMA..sub.l plane. Ordinarily, the terminations to 
be measured are passive (.vertline..GAMMA..sub.l .vertline. .ltoreq. 1) 
so that .GAMMA..sub.l falls within unit circle 31 as shown. For reasons 
which will emerge, it is convenient to assume initially that q.sub.3 lies 
outside this circle. Given the measurement results P.sub.3, P.sub.4, and 
assuming q.sub.3 and .vertline.D/A.vertline..sup.2 are known, the locus of 
possible values for .GAMMA..sub.l is a circle 34 whose center is at 
q.sub.3 and whose radius 33, .vertline..GAMMA..sub.l -q.sub.3 .vertline., 
may be determined from Equation (9). 
In the same way, Equations (5) and (7) may be combined, and the radius 35 
of another circle 36, which contains .GAMMA..sub.l, whose center is at 
q.sub.5, determined. The situation is now as shown in FIG. 3. Here 
.GAMMA..sub.l is determined by the intersection of the two circles. The 
two circles, however, intersect in a pair of points 38 and 40. In this 
example, point 38 falls outside the unit circle. One is therefore able to 
choose between the two solutions on the basis .vertline..GAMMA..sub.l 
.vertline. .ltoreq. 1: point 40 thus represents the correct solution for 
.GAMMA..sub.l. 
Thus far, no use has been made of P.sub.6, and the system may be considered 
a five-port rather than as a six-port. Before introducing P.sub.6, some 
additional observations on the five-port mode are of interest. As already 
noted, the five-port mode leads to a pair of values for .GAMMA..sub.l. 
Provided, however, that a straight line 42 between q.sub.3 and q.sub.5 
does not intersect unit circle 31, one is assured that one of these roots 
will fall outside of unit circle 31 and (assuming a passive termination) 
may be rejected on this basis. 
From further inspection of FIG. 3, one notes that the angle at which the 
circles intersect is rather small; and it is easily recognized that the 
position of .GAMMA..sub.l in a direction perpendicular to line 42 between 
q.sub.3 and q.sub.5, has a high sensitivity to errors in 
.vertline..GAMMA..sub.l -q.sub.3 .vertline. or .vertline..GAMMA..sub.l 
-q.sub.5 .vertline.. In the parallel direction, the sensitivity is 
appreciably less. Over the range of possible choices for .GAMMA..sub.l, 
and in particular if .GAMMA..sub.l moves around the perimeter of unit 
circle 31, one can expect a considerable variation in these sensitivities 
or expected errors in a practical measurement system. 
At first glance, one might be tempted to relieve this problem by increasing 
the distance from q.sub.3 and q.sub.5 to the origin. For example, if 
q.sub.3 = 10 and q.sub.5 = j10, the intersection of the respective circles 
will be nearly orthogonal over the entire unit circle. Unfortunately, 
however, this superficial improvement is more than offset by other 
considerations. In the example just given, a little further study would 
show that a 1% error in measuring .vertline..GAMMA..sub.l -q.sub.3 
.vertline. or .vertline..GAMMA..sub.l -q.sub.5 .vertline. would translate 
respectively into a nominal uncertainty of 0.1 in the real and imaginary 
parts of .GAMMA..sub.l. 
On the basis of this discussion, it should be apparent that the choice of 
optimum values for q.sub.3 and q.sub.5 represents a compromise between a 
number of conflicting requirements. How one chooses to resolve this 
conflict will depend in part, for example, upon how much variation in 
accuracy at the perimeter of the unit circle one is prepared to accept in 
return for improved accuracy at the center. 
Although the five-port measurement concept is technically sound, it will be 
appreciated that there are substantial benefits from a six-port vs. a 
five-port approach. Because the improvements obtained from the six-port 
approach are substantial, the future for the five-port appears limited. 
For this reason, the question of optimum design for the five-port will not 
be considered in further detail. 
To continue, q.sub.6 is chosen as shown in FIG. 4, and 
.vertline..GAMMA..sub.l -q.sub.6 .vertline. is determined from Equations 
(8) and (5). This provides a third circle 47 of radius 46 upon which 
.GAMMA..sub.l must lie and which (ideally) must pass through the 
intersection of the other two circles as shown in FIG. 4. In practice, 
because of measurement errors, the three circles will not intersect in a 
point; and some sort of statistical weighting is called for. Although it 
is not within the scope of this disclosure to consider this aspect in 
detail, it is intuitively obvious that this additional detector has 
substantially enhanced the accuracy with which .GAMMA..sub.l may be 
determined. In particular, the position of .GAMMA..sub.l in the direction 
orthogonal to the line 42 between q.sub.3 and q.sub.5, and which was quite 
sensitive to errors in P.sub.3 and P.sub.5, may now be inferred primarily 
from .vertline..GAMMA..sub.l - q.sub.6 .vertline. and with less 
sensitivity to error. Moreover, the double root ambiquity has also been 
resolved; no longer is it required that the line connecting q.sub.3 and 
q.sub.5 lie outside the unit circle. 
Following this general approach, the system may be expanded to seven or 
more ports. With the possible exception of a seven-port, however, this 
does not ordinarily appear to be warranted. 
In the discussion thus far, it has been assumed that Equation (5) was 
satisfied; at best, this is only approximately true. Unfortunately, a 
complete discussion of the more general case is lengthy, and many of the 
conclusions will be stated without detailed proof. In order to generalize 
the approach, it is convenient to ignore P.sub.4 and begin by eliminating 
.vertline.b.vertline..sup.2 between Equations (6) and (8). This leads to 
##EQU2## 
If one expands this result, it can be shown, as illustrated in FIG. 5, 
that the locus of possible values for .GAMMA..sub.l is again a circle, 
with its center somewhere on the line 48 through q.sub.3 and q.sub.6. If 
the ratio P.sub.3 /P.sub.6 is permitted to take on different values, a 
family of circles, such as circles 50-59, each corresponding to a 
different value of P.sub.3 /P.sub.6, is generated as shown in FIG. 5. It 
is of interest, and easily shown, that this family of circles is analagous 
to that used to illustrate the surfaces of constant potential associated 
with a parallel wire transmission line, where q.sub.3 and q.sub.6 
correspond to the positions of the conductors. As already noted, for a 
given value of P.sub.3 /P.sub.6, the locus of .GAMMA..sub.l is a circle, 
but unlike the previously described ideal case, the position of the 
center, as well as radius, is a function of P.sub.3 /P.sub.6. In a similar 
manner, Equations (7) and (8) may be combined, leading to another circle, 
this time with its center somewhere on the line through q.sub.5 and 
q.sub.6. As before, .GAMMA..sub.l is determined by the intersection of two 
circles, and two possible values of .GAMMA..sub. are obtained. For large 
values of .vertline.q.sub.6 .vertline., the role played by P.sub.6 
approaches that previously filled by P.sub.4 and becomes identical to it 
as .vertline.q.sub.6 .vertline. .fwdarw. .infin.. Thus, the primary 
correction to the prior description, which was based on Equation (5) is to 
recognize that the respective circles are not centered at q.sub.3 or 
q.sub.5, although this is usually a good approximation. Finally, one may 
also combine Equations (6) and (7). This also leads to a circle, this time 
with its center on the line which connects q.sub.3 and q.sub.5. It can be 
shown that this center also lies on the line which connects the centers of 
the two previously determined circles and passes through their points of 
intersection. Thus, there is no additional information to be gained by 
this exercise. Because P.sub.4 has been ignored, it will be recognized 
that this discussion pertains to a five-port. Although not its primary 
objective, the discussion has also provided insight into possible designs 
if for some reason levelling is not required. The extension to a six-port 
follows along the lines already presented. 
As noted earlier, and referring again to Equation (2), the first design 
objective ordinarily is that C = 0. This leads to Equation (5). Although 
nothing has been said, thus far, about the choice of 
.vertline.D.vertline., .vertline.A.vertline., .vertline.E.vertline., and 
.vertline.G.vertline., it is immediately evident from inspection of 
Equations (5), (6), (7), and (8) that these are scale factors, which for a 
given signal at the output port, determine the power levels at the several 
power meters. Ordinarily, these parameters are chosen so that these levels 
are compatible with the power meter characteristics. 
The major design question centers around the choice of q.sub.3, q.sub.5, 
and q.sub.6. One representative set of values is shown in FIG. 4. However, 
it is appropriate to ask if a better choice would be to place one of the 
q's, say q.sub.3, at the center of the unit circle. If this is done, one 
has one response P.sub.4 which measures the incident wave 
.vertline.b.vertline., while P.sub.3 now measures the reflected wave 
.vertline.a.vertline.. In this case, the six-port incorporates the 
reflectometer, a device which has played a substantial role in the prior 
art. There are several considerations, however, which argue against this 
choice for q.sub.3. Assuming one could obtain the condition q.sub.3 = 0, 
the prospect of achieving a direct measure of the reflection coefficient 
magnitude is indeed attractive. In actual fact, in the current state of 
the art, even with this as a design goal, the expected deviations of 
q.sub.3 from zero are such as to largely negate potential advantages. A 
more serious objection arises from dynamic range vs. measurement precision 
considerations. This point is perhaps best illustrated by a specific 
example. 
In FIG. 4, let q.sub.3 be moved to the center of the diagram, and let 
q.sub.5 = 2 and q.sub.6 = j2. If bolometric type power meters are assumed, 
typical performance specifications include: upper power limit -- 10 mW., 
error -- 0.1% .+-.1.mu.W. Next, the value of .vertline.A.vertline. is 
chosen so that P.sub.3 = 10 mW. (the upper limit) when 
.vertline..GAMMA..sub.l .vertline. = 1. If now one wishes to measure a 
termination for which .vertline..GAMMA..sub.l .vertline. .about. 0.01, 
P.sub.3 will be approximately 1.mu.W., and the signal-to-noise ratio has 
dropped to unity. By contrast if .vertline.E.vertline. and 
.vertline.G.vertline. are porperly chosen, P.sub.5 and P.sub.6 will be 
operating at approximately 50% of their maximum expected value 
(.vertline..GAMMA..sub.l .vertline. .ltoreq. 1). Thus, the 0.1% error 
will be the dominating term in this probable error. Since this applies to 
power, the voltage error will be half of this. On the other hand, the 
distance from q.sub.5 and q.sub.6 is 2, so that the uncertainty with which 
a point in the neighborhood of the origin is located is .+-. 0.001, which 
corresponds to a 10% error when .vertline..GAMMA..sub.l .vertline. = 
0.01. This represents a nominal ten-fold improvement in accuracy. The 
interesting and unexpected conclusion is that, if one requires operation 
over the entire range .vertline..GAMMA..vertline. .ltoreq. 1, a point in 
the neighborhood of the orgin can be located more precisely in terms of 
its distances from points which are somewhat removed, than from a point in 
its immediate neighborhood. Returning to the example just given, the 
response of P.sub.3 is virtually useless in inferring the value of 
.GAMMA..sub.l when .vertline..GAMMA..sub.l .vertline. is small; it appears 
that a better choice of q.sub.3 would be as shown in FIG. 4. Although the 
foregoing arguments do not necessarily hold for all choices of power 
meters, they do appear valid for the immediate candidates which include 
the bolometric and diode types. 
Having disposed of the question of placing one of the q's at the center of 
the unit circle, it now appears, from considerations of symmetry, that 
q.sub.3, q.sub.5, and q.sub.6 should be located at the vertices of an 
equilateral triangle whose center is at the origin. If one accepts this 
proposition, this calls for .vertline.q.sub.6 .vertline. = .vertline. 
q.sub.5 .vertline. = .vertline. q.sub.3 .vertline., while the arguments 
differ by .+-. 120.degree.. Thus, the only remaining choice is the value 
of .vertline.q.sub.3 .vertline.. 
Before addressing this question, several additional practical 
considerations should be noted. One of these concerns the power 
requirement at the input to the six-port. To the extend that this can be 
minimized, the power output requirements on the signal source may be 
reduced. This calls for a design where all of the input power is 
ultimately delivered to the several detectors rather than being dissipated 
in other internal terminations. A further consideration pertains to the 
ratio of the signal amplitudes which appear at the detectors as contrasted 
with that at the measurement port. For example, if one is interested in 
calibrating bolometer mounts, and one is also using bolometric detectors 
for P.sub.3 --P.sub.6, the range of signal levels at the different ports, 
including the measuring port, are nominally equal. Finally, although 
calibration procedures will not be considered here, one of the more 
promising techniques, which is based on sliding shorts and loads, is 
better conditioned for certain choices of .vertline.q.sub.3 .vertline. 
than others. 
To return to the problem of choosing .vertline.q.sub.3 .vertline., an 
earlier paragraph has commented on the errors which result from making 
this too large. Although the use of four detectors has eliminated the 
ambiguity problem, and thus permits one to choose .vertline.q.sub.3 
.vertline. &lt; 1, there are easily recognized similar problems if 
.vertline.q.sub.3 .vertline. becomes too small. In particular, since 
.GAMMA..sub.l is determined from its distances from q.sub.3, q.sub.5, and 
q.sub.6, it is evident that an ill-conditioned situation will result if 
these distances become large in comparison with the distances between 
q.sub.3 and q.sub.5, q.sub.3 and q.sub.6, or q.sub.5 and q.sub.6. On the 
basis of these last considerations, it appears that an optimum value for 
.vertline.q.sub.3 .vertline. might be expected to lie in the range 0.5 - 
1.5. However, the calibration techniques referred to earlier become poorly 
conditioned if .vertline.q.sub.3 .vertline. .perspectiveto. 1. Moreover, 
an experimental study with the aid of a computer shows a decrease in the 
measurement accuracy when .vertline..GAMMA..sub.l .vertline. 
.perspectiveto. .vertline. q.sub.3 .vertline.. Since there is usually a 
substantial interest in values of .GAMMA..sub.l with nominal magnitude of 
unity, there is a double reason for avoiding .vertline.q.sub.3 .vertline. 
.perspectiveto. 1. Apart from values close to unity, the other region of 
primary interest is .vertline. .GAMMA..sub.l .vertline. .ltoreq. 0.3. In 
order to provide the largest possible band-width, a fairly loose tolerance 
on the performance of the individual components from which the six-port is 
constructed is desirable. This now reduces the choices for 
.vertline.q.sub.3 .vertline. to values in the neighborhood of 0.5 or 1.5. 
As will be shown in what follows, the former generally calls for a larger 
power input to the six-port, and where this is a potential problem, one is 
left with 1.5 as the design objective for .vertline.q.sub.3 .vertline.. 
These principles are incorporated in the six-port measuring circuit of the 
present invention. As means of illustration, it is convenient to consider 
a specific problem. Let is be required that the six-port circuit be used 
for calibrating balometer mounts and measuring reflection coefficient, 
where the detectors P.sub.3, P.sub.4, P.sub.5, and P.sub.6 are also of the 
bolometric type, and be inherently lossless and broadband. 
In today's art, the broadest frequency coverage is afforded by stripline 
components. Here bandwidths of 10:1 are not uncommon. The basic circuits 
thus available include quadrature hybrids, 180.degree. hybrids, and 
directional couplers. In waveguide parlance, a quadrature hybrid is a 3dB 
(four-port) directional coupler, while an 180.degree. hybrid is an E-H 
tee. These two hybrids and the relationships which exist among the 
incident and emergent wave amplitudes are as shown in FIGS. 6A and 6B. In 
FIG. 6A, a quadrature hybrid 60 has two input ports 61 and 62, receiving 
signals a.sub.1 and a.sub.2 respectively. Two output ports 63 and 64 
provide the respective signals (a.sub.1 - ja.sub.2) / .sqroot.2 and 
(a.sub.2 - ja.sub.1) / .sqroot.2. In FIG. 6B, a 180.degree. hybrid 70 
receives signals a.sub.1 and a.sub.2 on input ports 71 and 72, while 
signals (a.sub.1 + a.sub.2)/.sqroot.2 and (a.sub.1 - a.sub.2)/.sqroot.2 
appear on output ports 73 and 74. Ideally, these devices are lossless and 
matched at all ports. 
In the existing art, a broadband circuit which yields a 120.degree. phase 
shift is unknown. However, one is able to achieve a broadband 90.degree. 
phase shift by means of quadrature hybrid. This suggests some compromises 
in the design goals outlined above. 
A preferred embodiment of the six-port measuring circuit of the invention 
is shown in FIG. 7. The basic six-port 100 has input ports 101 and 102. 
Four hybrids at positions, I, II, III, and IV are employed. A 180.degree. 
hybrid 110 at postion I has a port 111 terminated by resistive termination 
115. A port 112 is connected to input port 102. As described below, ports 
113 and 114 of hybrid 110 are connected to ports of hybrids at positions 
II and III, respectively. A quadrature hybrid 120 is at position II with a 
port 121 connected to input port 101. A port 122 of hybrid 120 is 
connected to port 113 of hybrid 110. A port 123 of hybrid 120 serves as a 
measuring port of six-port 100 and is connected to a power meter P.sub.3, 
and port 124 is connected to the hybrid at position IV. A quadrature 
hybrid 130 at position III has a port 131 connected to port 114 of hybrid 
110, while a port 132 is connected to resistive termination 135. A port 
133 of hybrid 130 is connected to the hybrid at position IV. The fourth 
port 134 of hybrid 130 is a measuring port of the six-port 100 and is 
connected to power meter P.sub.4. At position IV, quadrature hybrid 140 
has ports 141 and 142 connected respectively to ports 124 and 133 of 
hybrids 120 and 130. The remaining two ports 143 and 144 of hybrid 140 
serve as measuring ports of six-port 100 and are connected, respectively, 
to power meters P.sub.5 and P.sub.6. 
Six-port 100 is coupled to a transmission line 156 by means of a four-port 
directional coupler 150, which in the example being considered is a 6 dB 
directional coupler. A first port 151 of directional coupler 150 is 
connected to a signal generator 155. Second and third ports 152 and 153 of 
the directional coupler are connected, respectively, to input ports 101 
and 102 of six-port 100. The fourth port 154 of the directional coupler is 
connected to transmission line 156 where a terminal plane indicated by the 
vertical line establishes a measurement port. 
In analyzing the operation of the circuit of FIG. 7, ideal components are 
assumed. Consistent with the notation used in Equations (1), (2), (3), and 
(4), the emergent and incoming wave amplitudes at the measurement port 
(terminal plane) are designated by b and a, respectively. As indicated on 
FIG. 7, the wave amplitude at input port 101 of six-port 100 will be 
a.sqroot.3/2, and the wave amplitude at input port 102 of six-port 100 
will be b.sqroot.3. The power responses at the respective power meters 
will be 
EQU P.sub.3 = 3/8 .vertline.b.vertline..sup.2 .vertline..GAMMA..sub.l 
-j.sqroot.2.vertline..sup.2 (11) 
EQU P.sub.4 = 3/4 .vertline.b.vertline..sup.2 (12) 
EQU P.sub.5 = 3/16 .vertline.b.vertline..sup.2 .vertline..GAMMA..sub.l + 
(1+j).sqroot.2.vertline..sup.2 (13) 
EQU P.sub.6 = 3/16 .vertline.b.vertline..sup.2 .vertline..GAMMA..sub.l - 
(1-j).sqroot.2.vertline..sup.2 (14) 
These values are confirmed by comparison with the hybrid characteristics as 
shown in FIGS. 6A and 6B. Note, however, that no attempt has been made to 
keep track of the phase of a and b or even their phase differences in an 
absolute sense. The only question of importance in this context is: How 
does the phase difference between a and b at the measuring port connected 
to P.sub.3 compare with that which exists at the measuring ports connected 
to P.sub.5 and P.sub.6 ? 
The power responses also may be considered in terms of the wave amplitudes 
at input ports 101 and 102 of six-port 100 itself, which will function as 
a vector voltmeter. Designating the wave amplitude at input port 101 as c 
and the wave amplitude at input port 102 as d, it follows from FIG. 7 that 
EQU c = a .sqroot.3/2 (15) 
EQU d = b .sqroot.3 (16) 
In terms of c and d, the responses are 
EQU P.sub.3 = 1/2 .vertline.d.vertline..sup.2 .vertline.c/d - j 
.sqroot.2/2.vertline..sup.2 (17) 
EQU P.sub.4 = 1/4 .vertline.d.vertline..sup.2 (18) 
EQU P.sub.5 = 1/4 .vertline.d.vertline..sup.2 .vertline.c/d + (1+j) 
.sqroot.2/2.vertline..sup.2 (19) 
EQU P.sub.6 = 1/4 .vertline.d.vertline..sup.2 .vertline.c/d - (1-j) 
.sqroot.2/2.vertline..sup.2 (20) 
In a practical application the complex ratio c/d is almost always of 
interest; the value .vertline.d.vertline..sup.2 may or may not be of 
interest. This is the motivation behind expressing the equations in this 
particular form. Given the observation of of P.sub.3, P.sub.4, P.sub.5, 
and P.sub.6 one can solve for both .vertline.d.vertline..sup.2 and c/d. 
The unique feature of this circuit lies in the terms -j .sqroot.2/2, (1+j) 
.sqroot.2/2 and -(1-j) .sqroot.2/2 which are added to c/d in these 
equations. Although there is some interest in vector voltmeter 100 on a 
"stand alone" basis, more often it is connected to other microwave 
circuitry. FIG. 7 may be regarded as a typical application. In this 
application, the ultimate interest is in .vertline.b.vertline..sup.2 and 
a/b. As already noted, however, in this particular case c = a .sqroot.3/2 
and d = b .sqroot.3 so that if .vertline.d.vertline..sup.2 and c/d are 
known, this leads easily to .vertline.b.vertline..sup.2 and a/b. In a more 
general application, there may be a different functional relationship 
between c and d and the parameters a and b; e.g., one may have 
EQU c = Ka + Lb (21) 
EQU d = Ma + Nb (22) 
where K, L, M, and N are complex constants. Again, however, if K, L, M, and 
N are known, a measurement of .vertline.d.vertline..sup.2 and c/d suffices 
to determine .vertline.b.vertline..sup.2 and a/b. 
The measurements made by power meters P.sub.3, P.sub.4, P.sub.5, and 
P.sub.6 of FIG. 7 may be used for computing the net power and the complex 
reflection coefficient .GAMMA..sub.l at the terminal surface (measurement 
port) to uniform transmission line 156. These parameters may be computed 
from the equations: 
EQU Net power = 4/3 [4 P.sub.4 - P.sub.3 - P.sub.5 - P.sub.6 ] (23) 
and 
##EQU3## 
It is to be noted that other terminal variables such as wave amplitudes, 
voltage, current, impedance, etc., may be obtained from these computed 
parameters by the use of well-known formulas. In practice, Equations (23) 
and (24) are useful when the quadrature and 180.degree. hybrids and the 
directional coupler, from which the circuit is constructed, closely 
approximate the ideal. When this is not the case, the circuit continues to 
be useful, even when constructed of components whose performance differs 
substantially from the ideal. For this non-ideal case, however, a more 
general approach to the utilization of the circuit is preferred. The 
manner in which the more general approach may be applied will be readily 
apparent to the skilled worker in the art from a number of papers 
published in the prior art, including the aforementioned publications of 
G. F. Engen and C. A. Hoer in IEEE Trans. Instrum. Meas., Vol. IM-21, 
November 1972; C. A. Hoer and G. F. Engen in Proc. IMEKO Symp. Acquisition 
and Processing of Measurement Data for Automation, June 17-23, 1973; G. F. 
Engen in IEEE Trans. Instrum. Meas., Vol. IM-22, December 1973; C. A. Hoer 
in Nat. Bur. Stand. Tech. Note 673, September 1975; and C. A. Hoer and K. 
C. Roe in IEEE Trans. Microwave Theory and Techniques, December 1975, all 
of which publications are incorporated by reference herein. 
When the circuit of FIG. 7 is compared with the previously discussed design 
goals, it is first noteworthy that resistive terminations 115 and 135 are 
used at two different locations. Ideally, however, none of the signal 
power reaches these terminations, so the circuit is inherently lossless. 
In addition C = 0 for this circuit, thus satisfying the requirements of 
Equation (5), while the values of q.sub.3, q.sub.5, q.sub.6, except for an 
unknown phase shift introduced, for example, by a phase difference in 
lines 101 and 102, are as shown in FIG. 8, where 163, 165, and 166 
represent the values of the parameters q.sub.3, q.sub.5, and q.sub.6, 
respectively. As compared with the 120.degree. design objective, the angle 
between 165 and 166 is 90.degree.; the angle between 165 and 163 is 
135.degree.; and the angle between 163 and 166 is 135.degree.. Whereas the 
design objective required that .vertline.q.sub.3 .vertline. = 
.vertline.q.sub.5 .vertline. = .vertline.q.sub.6 .vertline., the circuit 
of FIG. 7 provides .vertline.q.sub.5 .vertline. = .vertline.q.sub.6 
.vertline. and .vertline.q.sub.3 .vertline. = .vertline.q.sub.5 
.vertline./.sqroot.2. Although this result falls somewhat short of the 
design objectives, the design goals are more nearly achieved by this 
circuit than by any other which has been devised to date. Moreover, it 
appears that the theoretical loss in performance between the circuit of 
FIG. 7 and the design ideal may be small in comparison with the 
performance degradation which results from the use of non-ideal 
components. 
If one assumes 20 mW. of power at the input 151, 5mW. or 1/4 of this 
reaches the measurement port at 156. If the termination at the measurement 
port is a matched load, this power will be absorbed, while the remaining 
3/4 of the power is divided equally among the power detectors P.sub.3, 
P.sub.4, P.sub.5, and P.sub.6, resulting in a power level of 3.75 mW. for 
each. If now P.sub.4 is stabilized at this value, and a sliding short is 
connected to the measurement port at 156, the value at P.sub.3 will reach 
approximately 11 mW. for certain short positions, while the maximums at 
P.sub.5 and P.sub.6 will be approximately 8.5 mW. The maximum dynamic 
range excursion at any detector is a nominal 15 dB which occurs at 
P.sub.3. 
The circuit of FIG. 7 thus provides a reasonably optimal set of values for 
.vertline.A.vertline., .vertline.D.vertline., .vertline.E.vertline., and 
.vertline.G.vertline., which in turn determine the distribution of the 
available signal power among the several detectors and the measurement 
port. 
Perhaps the most distinctive feature of the circuit of FIG. 7 is in the 
ratios q.sub.5 /q.sub.3 and q.sub.6 /q.sub.3 which it yields. Apart from a 
constant multiplier, the "q" values are determined entirely by the basic 
six-port 100. Taken alone, basic six-port 100 may be considered as "vector 
voltmeter" which, more generally, has been the subject of the earlier 
paper of C. A. Hoer and K. C. Roe in IEEE Trans. Microwave Theory & 
Technique, Vol. MTT-23, No. 12, December 1975. As a vector voltmeter, 
circuit 100 has certain advantages for some applications. In particular, 
if it is stipulated that one of the four outputs be proportional to one of 
the input signals, this circuit requires fewer components. Moreover, as 
previously noted, the circuit is inherently lossless, and thus makes more 
efficient use of the power input. Finally, the "q" spacing is 90.degree., 
135.degree., 135.degree., rather than 90.degree., 90.degree., 180.degree., 
as is usually the case in circuits of the prior art. 
In addition to the ratios between the q's, the ratios among 
.vertline.A.vertline., .vertline.D.vertline., .vertline.E.vertline., and 
.vertline.G.vertline. are also determined by the vector voltmeter portion 
100 of the circuit. By contrast, and except as subsequently noted, the 
absolute magnitudes of all of these terms are determined by that portion 
of the circuit external to vector voltmeter 100. 
Returning again to FIG. 7, one notes that the input levels to vector 
voltmeter 100 are b.sqroot.3 and a.sqroot.3/2. Basically, the parameters 
at one's disposal in adjusting the magnitudes of q or A, D, E, and G are 
the coefficients of b and a. Let these be designated by .beta. and .alpha. 
so that in FIG. 7, .beta. = .sqroot.3 and .alpha. = .sqroot.3/2. It is 
possible to adjust .alpha. and .beta. by a variety of methods, but first 
it should be noted that the .vertline.q.vertline.'s are proportional to 
.beta./.alpha. while .vertline.A.vertline., .vertline.D.vertline., 
.vertline.E.vertline., and .vertline.G.vertline. are proportional to 
.beta.. In principle, .alpha. and/or .beta. can be made small by the use 
of attenuation in the respective lines. (This attenuation could also be 
placed at various positions inside vector voltmeter 100). Moreover, .beta. 
can be made arbitrarily large by changing 6 dB coupler 150 to 10 dB, 20dB, 
etc. At the same time, .alpha. also increases but, in contrast to .beta., 
approaches unity as a limit. Moreover, it is not hard to recognize that 
this must also be the limit for any passive circuit. This limit on .alpha. 
indirectly imposes an upper limit of perhaps 2 or so on .beta., since 
otherwise the .vertline.q.vertline. terms would become larger than 
desired. This, in turn, leads to an upper limit on .vertline.A.vertline., 
.vertline.D.vertline., .vertline.E.vertline., and .vertline.G.vertline. 
and thus on the signals at the power detectors. 
If one removes the lossless restriction, and assumes a surplus of input 
power, one could, as already noted, realize a small increase in .alpha. by 
going to a 10- or 20-dB coupler. The resulting increase in .beta., 
however, would need to be offset by an attenuator in the line which feeds 
180.degree. hybrid 110. As an alternative to this attenuation, one might 
insert another directional coupler or power divider at this point and use 
some of the surplus signal to obtain a substantially larger value for 
P.sub.4. In either case, however, the increase in P.sub.3, P.sub.5, and 
P.sub.6 would only be a nominal 5% or 10%, which makes this modification 
of doubtful practical interest. 
If, in addition to assuming a surplus of signal input power, one removes 
the restriction on the signal level at the measurement port, or assumes 
that it is substantially larger than that required at P.sub.3, P.sub.4, 
P.sub.5, and P.sub.6, this eliminates the requirement to make .alpha. as 
large as possible. Ordinarily, in this mode, the connections at the left 
side of the coupler should be reversed, and the desired signal levels and 
values of .vertline.q.vertline. realized through the choice of coupling 
values and possibly attenuators. 
In addition to obtaining a numerical output, to which the various 
corrections have been applied, it is frequently useful to have a real time 
oscilloscope display of the results, even at a substantially reduced 
accuracy. For the ideal circuit of FIG. 7, one has 
##EQU4## 
while 
##EQU5## 
where Re (.GAMMA..sub.l) and Im (.GAMMA..sub.l) represent the real and 
imaginery parts of the reflection coefficient .GAMMA..sub.l. Thus, if 
P.sub.3, P.sub.4, P.sub.5, and P.sub.6 are available in analogue form, and 
assuming the system is leveled so that P.sub.4 is constant, one can obtain 
signals proportional to the real and imaginary parts of .GAMMA..sub.l by 
simple addition. These signals may then be applied to an oscilloscope to 
provide a visual display of the reflection coefficient. 
As a variant to FIG. 7, one may replace 6-dB directional coupler 150 with a 
3-dB directional coupler. If this is done, the power level at the 
measurement port is doubled, but at the expense of the power levels at 
P.sub.3, P.sub.4, P.sub.5, and P.sub.6. In addition the 
.vertline.q.vertline. terms are multiplied by .sqroot.2/2, so that 
.vertline.q.sub.3 .vertline. = 1. Fortunately, in this case the ill 
conditioning associated with the calibration procedure can be avoided 
since .vertline.q.sub.5 .vertline. = .vertline.q.sub.6 .vertline. = 
.sqroot.2. Because 3-dB directional couplers are more readily available 
than 6-dB directional couplers, this alternative may often be preferred. 
A number of other variants and embodiments of vector voltmeter six-port 100 
may be adopted. As shown in FIG. 9, the hybrids at positions II and III 
may be changed from quadrature to 180.degree. hybrids 220 and 230, 
respectively. The connections to these hybrids are identical to those made 
to the hybrids at the same positions in FIG. 7. Thus, input port 201 of 
six-port 200 is connected to a port 221 of hybrid 220, and input port 202 
of six-port 200 is connected to port 112 of 180.degree. hybrid 110. Port 
113 of hybrid 110 is connected to port 222 of hybrid 220, while port 114 
of hybrid 110 is connected to port 231 of hybrid 230. Measuring port 223 
of hybrid 220 is connected to power meter P.sub.3, and port 224 of hybrid 
220 is connected to port 141 of quadrature hybrid 140. As for hybrid 230, 
port 232 is connected to termination 235; port 233 is connected to port 
142 of quadrature hybrid 140; and measuring port 234 is connected to power 
meter P.sub.4. The connections of the embodiment of FIG. 9 are otherwise 
identical to those of FIG. 7 as indicated by the use of like reference 
numerals. 
As shown in FIG. 10, the quadrature and 180.degree. hybrids at positions I 
and IV of FIG. 7 may also be interchanged. The resulting vector voltmeter 
six-port 300 has quadrature hybrid 310 at position I and 180.degree. 
hybrid 340 at position IV. Input ports 301 and 302 of a six-port 300 are 
connected, respectively, to port 121 of quadrature hybrid 120 and port 312 
of quadrture hybrid 310. Port 311 of hybrid 310 is connected to 
termination 315; port 313 is connected to port 122 of quadrature hybrid 
120; and port 314 of hybrid 310 is connected to port 131 of quadrature 
hybrid 130. Turning to 180.degree. hybrid 340, measuring ports 343 and 344 
are connected respectively to power meters P.sub.5 and P.sub.6. Port 341 
is connected to port 124 of quadrature hybrid 120, and port 342 is 
connected to port 133 of hybrid 130. The connections are otherwise the 
same as in FIG. 7 as indicated by the use of like reference numerals. 
A variant of FIG. 7 is shown in FIG. 11. Here, the connections at the 
inputs of the hybrids 120 and 130 at positions II and III are interchanged 
as compared to the connections used in the embodiment of FIG. 7. Thus, 
six-port 400 has an input port 401 connected to port 122 of quadrature 
hybrid 120 and an input port 402 connected to port 112 of 180.degree. 
hybrid 110. Port 113 of hybrid 110 is connected to port 121 of hybrid 120, 
and port 114 of hybrid 110 is connected to port 132 of quadrature hybrid 
130. The termination 135 for hybrid 130 is connected to port 131. The 
remaining connections are the same as those shown in FIG. 7. 
Similarly, in the embodiment shown at 500 in FIG. 12, the output 
connections from quadrature hybrids 120 and 130 at positions II and III 
are interchanged from those used in FIG. 7. Power meters P.sub.3 and 
P.sub.4 are connected, respectively, to port 124 of hybrid 120 and port 
133 of hybrid 130. Ports 141 and 142 of hybrid 140 are connected, 
respectively, to ports 123 of hybrid 120 and port 134 of hybrid 130. The 
connections are otherwise the same as in the circuit of FIG. 7. Thus, 
input port 501 of six-port 500 is connected to port 121 of hybrid 120, 
while input port 502 is connected to port 112 of hybrid 110. 
Another embodiment is shown at 600 in FIG. 13. Here, all hybrids are of the 
quadrature type. Thus, a quadrature hybrid 610 is substituted at position 
I for the 180.degree. hybrid 110 of FIG. 7. The four ports 611, 612, 613, 
and 614 of hybrid 610 are connected, respectively, to termination 615, 
input port 602 of six-port 600, port 122 of hybrid 120, and port 132 of 
hybrid 130. Port 131 of hybrid 130 is connected to termination 135. The 
other input port 601 of six-port 600 is connected to port 121 of hybrid 
120. The connections are otherwise the same as in FIG. 7. 
A variant of the embodiment of FIG. 13 is shown at 700 in FIG. 14. The same 
components are used as in FIG. 13, as indicated by the use of like 
reference numerals, but with different interconnections between hybrid 
ports and terminations as shown. Input port 702 of six-port 700 is 
connected to port 611 of hybrid 610, while port 612 of this hybrid is 
connected to termination 615. Input port 701 of six-port 700 is connected 
to port 121 of hybrid 120. Port 614 of hybrid 610 is connected to port 131 
of hybrid 130, the port 132 of which is connected to termination 135. 
Power meter P.sub.3 is connected to port 124 of hybrid 120, while port 123 
of hybrid 120 is connected to port 141 of hybrid 140. The connections are 
otherwise the same as those used in FIG. 13. 
In another variant of the circuit of FIG. 7, the input connections to 
hybrid 110 at position I are interchanged. Thus, input port 102 of the 
six-port is connected to port 111 of hybrid 110, while termination 115 is 
connected to port 112 of hybrid 110. 
As compared with the six-port circuits of the prior art, each of the 
embodiments and variants of the six-port measuring circuit of the present 
invention requires fewer components and is inherently lossless. This, in 
turn, reduces the power input requirements. Moreover, the "q" values 
provided more nearly approach the design ideal. 
While particular embodiments of the invention have been shown and 
described, it will be readily apparent to those skilled in the art that 
changes and modifications may be made without departing from the spirit 
and principles of the invention the scope of which is defined in the 
appended claims.