FIGURE 1. Basic circuit involved in the application of a terminating type power meter.

including both energy sources and sinks, is enclosed in a metal envelope, a substantial portion of which, in practice, is in the form of waveguide. The object of the experiment is to replace the load by the power meter and from the power meter indication, predict the power delivered to the load. It is assumed that the input cross section of the power meter, while not necessarily the same as that for the load or generator, is such that the continuity of the metallic envelope is preserved, (i.e., the power meter mates with the generator in such a way that there are no "holes" or "gaps" in the system which would permit the electromagnetic energy to escape).

Of the several ways of characterizing the generator power, which were noted in a previous paragraph, only one satisfies the conditions of being (1) characteristic of the generator alone, (2) independent of the uniformity concept, and (3) independent of the choice of terminal surface (within the indicated lossless region). This is the available power, Pg, which is, by definition, the physically determined, maximum power that can be delivered to a passive load by the given generator.

In general, the conditions for maximum power transfer will not be satisfied, thus it is appropriate

where the reflection coefficients Tg, I have been previously defined.

It is to be emphasized that while the uniformity concept and choice of terminal surface is implicit in the definition of the reflection coefficients, Mgt is independent of both, 5,6 and, in fact, retains its physical significance in applications where the usual definitions of reflection coefficient break down completely. In order to make these points more explicit, it is useful to consider the system shown in figure 2. As indicated, it is possible to consider the irregular region as part of the load, part of the generator, or divided between the two in an arbitrary way. Within the uniform portions of guide, existing theory permits the specification of Py, and Mg in terms of circuit parameters. On the other hand, P, and Myl have been selected to characterize the system because they have a precise physical meaning which is independent of the choice of terminal surface. The replacement of the load by the power meter is indicated by substitution of the subscript "m" for ""

This is largely a matter of convenience for the discussion to follow. If the termination is an antenna it may in principle be replaced by an equivalent load whose charac teristics are such that the relationship between the electric and magnetic fields, E, H, at the terminal surface is unchanged.

* The validity of this may be recognized in several ways. First, if the conditions for maximum power transfer are satisfied for one choice of terminal surface within the lossless region it must be satisfied for all choices, since if by any means it were possible to increase the power flow across one surface, energy conservation would require a similar increase at all surfaces within the lossless region. In a similar manner if Mat 0.9 in a given combination, this suggests that by a suitable deformation of the load (or generator) boundary (e.g., a waveguide tuning transformer), an additional 10 percent in power could be realized. This argument is evidently true for any choice of terminal surface within the lossless region.

Alternatively, the power Pg, given by eq (2) cannot depend upon an arbitrary division of the system into generator and load. Thus, if P, is invariant to the choice of terminal surface, the same must be true of Mgt.

It is instructive to demonstrate this formally for a uniform system using conventional circuit theory. This is done in appendix 1.

If, for example, the bolometric technique is used, the bolometer mount should be calibrated in terms of "effective efficiency" rather than "calibration factor."

352-570 O-69-2

LOSSLESS REGION

Uniform Waveguide

FIGURE 2. A microwave system which includes nonuniform waveguide.

so that the mismatch factor introduced in eq (1) is the ratio of Mg to Mgm. The evaluation of the mismatch correction in the use of a terminating type power meter has thus been reduced to the measurement of the two terms, Mg and Mgm, which are independent of the uniformity concept. Thus, if a method can be devised for measuring My directly, instead of relying upon the usual reflection coefficient measurements, it may be anticipated that such a technique might be independent of the waveguide uniformity requirement.

Before proceeding with a description of the technique for measuring these terms, it is desirable to briefly review the prior art.

3.1. Summary of Prior Art

For measurement purposes, one of the most useful of waveguide devices is the directional coupler. A pair connected as shown in figure 3,

coefficients are given in the cited references but will not be needed here.)

If the two couplers have perfect directivity, and are free of internal reflections, both B and C vanish and b and b4 become proportional, respectively, to a and b2. This is the required condition for a reflectometer. In general, the couplers do not satisfy these conditions, but the introduction of tuning transformers, Tr, Ty, shown in figure 4 b4

4

3

63

where P3 and P4 are the powers measured at arms 3 and 4, and K1, K2 are constants of the system whose value may be determined by a suitable calibration or measurement procedure. Equations (8-10) may be given a simple interpretation: the (net) power emerging from arm 2 is given by the difference of the powers carried by the emergent and incident traveling waves.

Although the uniform waveguide concept was implicit in the derivation of this result, it was also recognized [4] that if the output port is extended by perfectly conducting boundaries of arbitrary geometry, and if the enclosed dielectric is lossless, the (net) power flow across any arbitrary terminal surface within this region is also given by eq (10). This conclusion follows, quite simply, from energy conservation. This result, in turn, implies that it should be possible to obtain eq (10) under a set of conditions which is less restrictive than B = C = 0. In particular, let the boundaries be extended by means of the (lossless) two-port device of figure 2. The resulting structure is shown in figure 5. If the terminal surface is shifted from the unprimed to

where (*) represents the complex conjugate, this is both necessary and sufficient for the output power to be expressible in the form of eq (10). In addition, this equation is also satisfied by the primed variables A' . . D'.

8

The usual method of achieving eq (11) is by means of tuner Ty, a moving short at port 2, and observation of the effect of the motion upon the ratio P 3/P4. Provided that Ty has been adjusted such that this ratio remains constant, it can be shown that eq (11) is satisfied. Although the moving short is usually provided with a uniform waveguide section, the only necessary conditions are that the device be free of loss and that the phase angle of the reflection be adjustable. Waveguide uniformity is obviously not required to achieve these conditions.

Having shown that the relationship of interest (eq 10), once established, continues to give the (net) power, irrespective of changes in terminal surface, even in a nonuniform region, it is thus significant that a method, which is also independent of the uniformity concept, exists for recognizing the proper adjustment of Ty which leads to eq (10).

In the usual reflectometer application, the only place, where a uniform section of waveguide is required, is at the output port (2).9 Nominal deviations from this ideal, in other parts of the structure, may cause some change in the elements of the equivalent circuit, but these are accounted for in the tuning and calibration procedure. If, however, the device is to be used as a feed through power meter, the above arguments indicate, in addition, that the uniform section is not required in the neighborhood of the output port.10 This provides

See appendix 2. "See appendix 3.

Note however that single mode operation was implicit in the derivation of eq (10) and that whereas the output cross section at arm 2 may be such as to permit multimode operation, it is, in general, necessary to postulate the existence of a "mode filter" at some point in arm 2 in order to insure the validity of eq (10). In practice this may be achieved by including a length of guide whose cross section permits only single mode operation.

"To the extent that T, may be considered lossless, this will not affect the adjustment of T, which provides the BD - AC*=0 condition. In general, it is desirable to use an alternative procedure to be described in a following paragraph.

In general, this condition may be realized by adjustment of the tuner Ty. This assumes that the couplers meet certain minimum conditions, which are well satisfied by available components, as to minimum directivity, etc.

It is next instructive to consider the equivalent generator which obtains at port 2 of the "reflectometer" in figure 5, if the power, P4, measured by the detector on arm 4 is assumed to be constant or independent of the load on port 2, the actual generator parameters, etc. (In practice this may be achieved by means of a servo controlled attenuator between arm 1 and the actual generator.) This problem has been treated by the author in a prior paper [6]; the important result in the present context is that there exists an equivalent generator, at port 2, whose impedance is independent of the actual source of microwave energy.

Following the results obtained in the cited reference, it will prove useful temporarily to replace the actual generator on port 1 by an adjustable passive load, and excite the junction via arm 2. The passive load on arm 1 is first adjusted such that a null obtains at arm 4, and tuner T is next adjusted such that the input impedance at port 2 is equal to the impedance 11 of the generator of figure 1. (For the present, the various components are assumed to have uniform waveguide.) The condition imposed upon the "reflectometer," by this adjustment, may be obtained from eqs (6) and (7) by letting b1 = 0, b2/a2g, whence: b2/a2 =

Equations (16), (17), and (18), thus provide an experimental method of measuring Mgt. The measurement of Mgm obviously requires the substitution of the power meter in place of the load.

A review of these equations shows that if г=0, the procedure leads to the usual reflectometer adjustment B=C=0 and thus to the value of T2; in addition, if Tg=0, Mgt is given by 1-2. The measurement procedure outlined above may thus be regarded as a generalization of the reflectometer technique, where instead of |T|2, the measurement yields |г-F„*|2/|1 — F„á|2.

In order to clarify the terminology it appears desirable to reserve the term "reflectometer" for a junction which has been so adjusted as to measure reflection coefficients. The same general combination of couplers and tuners, but with a different adjustment (one example of which has just been described) will be called a "generalized reflectometer" or "g-reflectometer" for brevity.

This measurement procedure will next be examined for its dependence upon the uniformity concept.

3.3. Examination for Dependence Upon Uniformity

The measurement procedure outlined in the preceding paragraphs calls first for the adjustment of T and then T. However in order to avoid interaction between the two adjustments an alternate form of the g-reflectometer, in which the order

12 In practice there is often substantial isolation between the actual source of microwave energy and the generator output terminal such that the generator "impedance" is essentially independent of the energy source. In any case, however, it is not within the scope of this dissertation to consider all of the practical questions which may be suggested by the prescribed measurement procedures.

13 Although Tuner T, was also used in obtaining the previous adjustment, it can be shown (see appendix 4) that the C + DI,= 0 condition is invariant to the adjustment of Ty

14 In actual practice it is usually desirable to observe P/P, with a high quality fixed short, rather than a sliding one.

of the couplers is reversed, is required. Before evaluating the dependence upon uniformity it is desirable to carefully outline the exact measurement procedure.

Referring to figure 6, the items to be considered include the original generator (1) and load (2) (for which P, and Mg are required), the g-reflectometer (3), an auxiliary directional coupler, tuner (Ta), and signal source (4), a sliding short (5), and power meter (6). These items are identified by the corresponding numbers in figure 6.

I

The first step in the procedure is the adjustment of T such that the generalized reflectometer will simulate the behavior of the actual generator (1). The desired adjustment may be recognized with the help of the auxiliary directional coupler, tuner (Ta), and signal source (4). In particular, the actual source of microwave energy in the generator (1) is turned off,12 the generator (1) is then connected to the auxiliary directional coupler and signal source (4), and tuner Ta adjusted for a sidearm null. The generator (1) is next replaced by the g-reflectometer (3), the input port (arm 1) of which is terminated in an arbitrary passive load. The tuner Ty is next adjusted for a null in arm 4 (P1=0) and tuner Tr is adjusted for a null in the sidearm of the auxiliary directional coupler. The g-reflectometer parameters now satisfy eq (14), and this completes the adjustment of tuner Tr

I

4

A signal source is next connected to the input (arm 1) of the g-reflectometer and the output port (arm 2) is connected to the sliding short (5). Tuner Ty is then adjusted such that the ratio P3/P1 remains constant for all positions of the short. The g-reflectometer parameters now satisfy eq (11).13 This completes the adjustment procedure.

The measurement consists of observing the ratio P3/P4 with the sliding short,14 load (2), and power meter (6) connected in turn. This provides a measure of Mgt and Mgm as already described using eqs (16), (17), (18). Finally, the power meter (6) is connected to the generator (1), Pym is measured, and Pt calculated using eq (5). Note that the available power, Pg, may now be obtained from eq (3), while Mgt indicates what fraction of the available power is actually delivered to the load.

Returning to figure 6, it will now be assumed that the generator (1) and g-reflectometer (3) outputs only are of uniform rectangular waveguide. When connected to the auxiliary coupler (4) there may be a discontinuity (in guide cross section) at the mating surface; if so, the discontinuity is assumed to be identical for the generator (1) and g-reflectometer (3). Within the immediate vicinity of the mating terminal surface a complete description of the waveguide fields will usually require a number of modes, while at a greater distance the higher modes will have decayed (exponentially) to negligible amplitudes and the field may be completely described by the wave amplitudes of the lowest order forward and reverse traveling waves. Corresponding to the auxiliary coupler (4) sidearm