1. Background

The microwave art is characterized by the fact that a typical dimension of the associated apparatus, if measured in wavelengths of the attendant electromagnetic radiation, is of the order of unity. Because of this, retardation can no longer be neglected, and the usual circuit concepts, which are extensively employed at lower frequencies, are no longer completely valid.

There is, however, a type of circuit or network theory which retains its usefulness, and which finds widespread application in microwave problems. For example, it would be difficult, if not impossible, in the immediate context, to assign a meaningful "equivalent circuit" to a slab of resistive material. However, if this slab is mounted in a uniform section of waveguide, it now becomes possible to assign an equivalent circuit in such a way that if this two-port device is incorporated in a given system, the net result on the operation is predictable.

A sufficient condition for the validity of such a circuit representation is that the different components be interconnected by ideal (lossless and uniform) waveguide, and of such length that the interaction is only via single mode.2

Notwithstanding the formal similarity between microwave and low frequency circuit representations, the field of microwave measurements remains distinct for at least two reasons. First, the lower frequency concepts of voltage and current lose much of their practical significance in the microwave region and the measurement of power assumes a fundamental role. Second, the other measurement objectives are usually limited to a determination (many times only in part) of the equivalent circuit parameters. This includes measurements of both impedance and attenuation.

Because the uniform waveguide requirement is implicit in the usual microwave circuit representation, it is not surprising that a review of the existing art finds this requirement deeply enmeshed in current measurement practice. The "standing wave machine," for example, includes a moving probe

*Based on the thesis "A New Concept in Microwave Measurement Techniques" in partial fulfillment of the requirements for the degree of Ph. D., University of Colorado, Boulder, Colorado, 1969.

**Radio Standards Engineering Division, Microwave Circuit Standards, NBS Laboratories, Boulder, Colorado 80302.

See for example reference [1].

"The extension to multimode interaction is straightforward, however this type of operation is avoided in much of the current practice.

which samples the field at different longitudinal positions in a uniform line. The reflectometer, on the other hand, measures reflection coefficient and, in particular, gives a null output when terminated by a matched (reflectionless) load. The matched load plays an important role in the adjustment or design of such devices, and the existing methods of recog nizing matched loads include motion within a uniform piece of waveguide. Finally, the usual definition of attenuation is tied to the reduction in power which results when the two-port device is inserted in a matched (reflectionless) system. The realization of a "matched" system, in turn, calls for the already cited impedance measurement techniques.

In brief, the field of microwave measurements represents a highly developed art, and the waveguide uniformity requirement, upon which microwave circuit theory is based, is strongly reflected in the existing measurement practice. Indeed, it is difficult to imagine how it could be otherwise. at least while attention continues to focus on the usual microwave circuit theory.

Another feature of the existing art which warrants consideration is the usual description of a microwave system which often starts (sometimes implicitly) with a model in which a match (reflectionless) is assumed for the different components. Then, in order to extend its validity, mismatch corrections are introduced, and here the circuit concepts come into full play.

Unfortunately, however, the mathematical descriptions which usually emerge from such an approach are often complicated in appearance, and provide little physical insight into the phenomena they describe. As a result, the subject of mismatch errors and corrections is but little appreciated, even by many practicing engineers. In addition, there is a considerable amount of permissible arbitrariness in interpreting the mismatch correction. This is reflected by the proliferation of terminology which exists. In a mismatched system, for example, what is the most meaningful way to characterize the generator power? Should it be (a) the power which would be delivered to a reflectionless load, (b) the power actually delivered to the given load, (c) the power associated with the emergent wave amplitude when the generator is terminated by the given load, or (d) the available power (which is obtained under conditions of conjugate impedance match)? All of these concepts (and perhaps more) are in current

use. The term "matched load" has at least three meanings: (a) reflectionless, (b) equal to another load, and (c) complex conjugate of another load (such that maximum power transfer is effected). (In this dissertation the term "matched" is limited to the first of these.) This is only the beginning, however; a recent survey (which was by no means complete) indicates the existence of at least seventeen different terms for expressing the loss characteristics of a two-port device.

It must be recognized that this proliferation has been generated, in part, by the need for precision on the one hand, and on the other the desire to limit the number of terms required to describe a particular system. This has been achieved, but at the virtual expense of inventing a different language for each system.

In summary, the existing measurements art is characterized by a circuit theory which imposes (or at least does not relax) certain uniformity requirements upon the associated waveguide. The corollary precision connector requirement results from the recurrent need to separate this uniform waveguide into two (or more) parts. Perhaps the greatest application for this circuit theory is in connection with mismatch corrections or other attempts to sharpen the existing descriptions, but unfortunately there is no consensus of opinion on how best to do this, and a wide variety of competing descriptions are in current use. Finally, the inevitable deviations from the assumed uniformity, in any physically realizable apparatus, represents a limitation on the accuracy with which the performance or other characteristics may be evaluated.

2. Introduction

The "new" concept, which is to be developed in this dissertation, begins by observing that many of the microwave measurement objectives are, of themselves, quite independent of the assumed waveguide uniformity. Perhaps the best example is power which carries the same physical meaning in a system confined within irregular boundaries as in regular waveguide. In other cases, as will be developed, it is possible to substitute new measurement objectives, for old ones, such that the uniformity concept is avoided and yet retain a meaningful system evaluation. Traditionally, attenuation and impedance measurements have played a major support role in extending the dynamic range and evaluating mismatch corrections. However, since these quantities are tied to the uniformity concept, they will be replaced by others for which uniformity is not required. In particular this implies that the matched load, which plays a central role in much of the existing practice, is no longer required.

As a consequence, a more meaningful set of criteria, as to which are the important parameters in a mismatched system, will emerge, together with a new a model, for describing the system, in which

the emphasis is on power transfer rather than traveling waves, and which provides improved insight into the mismatch corrections. Finally, the uniform waveguide and precision connector requirement will be greatly relaxed for the class of problems under consideration.

Throughout the development of this concept, it will prove convenient to retain the existing circuit descriptions as a working tool, and then examine the final techniques for their independence from uniformity considerations. The development will proceed with the consideration of specific measurement

areas.

3. Microwave Power Measurement

Because power represents a basic parameter in the microwave art, it is appropriate to apply the new concept first to power measurement problems.

A large percentage of the microwave power meters in current use, especially at low power levels, are of the "terminating type." This means that they (ideally) terminate the waveguide or transmission line in its characteristic impedance and indicate the power which they absorb. The practical application of such devices calls for their connection to the signal source, in place of the load, to which the power input is required. Provided that the power meter and load are of identical impedance, the power meter reading will correctly indicate the power delivered to the load.

In the more general case, where the load and power meter are of different impedances, it is necessary to multiply the power meter reading by an appropriate "mismatch" factor [2]3:

where Pg and Pgm are the powers delivered to the load and power meter and г, гt, гm are the reflection coefficients of the generator, load and power meter. The coefficient of Pgm in eq (1) is a mismatch factor, whose determination calls for the measurement of three complex reflection coefficients and the indicated computation. Fortunately, in many measurement applications (such as the transfer of calibration between power meters) the parameters of the generator are at one's disposal, and a substantial simplification in the mismatch factor is effected by adjusting the generator impedance such that г=0. In the more general application, this is not possible, and in many cases the mismatch factor represents an error because of the practical problems in its evaluation.

The application of the new concept to this measurement problem begins with the system shown in figure 1 where that portion to the left of the arbitrarily chosen (and not necessarily plane) terminal surface is, by definition, the generator; that to the right is the load. The entire system,

3 Figures in brackets indicate the literature references at the end of this paper.