Knowledge of the values of the corresponding network parameters is a necessary prerequisite for quantitative calculations. The mode concept and the transmission line formulation of the field equations are introduced in Chapter 1. This chapter contains a technical treatment of the transmission line theory necessary for the description of propagating and non-propagating modes in the more important types of uniform and non-uniform waveguides.
Field structure, propagation, attenuation, etc. The characteristics of the transmission line modes thus described are collected in Chapter 2 with quantitative and pictorial details. The elements of microwave network theory necessary to analyze, represent, and measure equivalent circuits for ~-terminal microwave structures are outlined in Chapter 3; this chapter also provides a sketch of some of the field-theoretic methods used in the derivation of the equivalent circuit parameters reported in Chapters 4 through 8. The remaining chapters contain a collection of equivalent circuit parameters for various nondissipative ~-terminal microwave structures.
The continued interest and criticism of Levine and Sch\vinger since the closing of the laboratory is great. Although conceived at the Radiation Laboratory of MIT, the bulk of this book was written in the years following its closure, while the author lvas LL staff member of the Polytechnic Institute of Brooklyn.
TWNSMISSION LINES
This transmission line completely characterizes the behavior of the dominant mode everywhere in the waveguide. Expression for the field components in terms of the modes' amplitudes and functional form. The functional dependence of the parameters Ki and Z on the cross-sectional dimensions is specified in chap.
1“3 from which both the amplitude and the phase of the reflection coefficient can be obtained. The voltage and current amplitudes of the transverse electric and magnetic field intensity of an H-type regime are defined as V;' and Z;'. In terms of these functions, the solutions of the radial transmission line equations (64) for the dominant mode voltage and current can be written as.
The vector v is the outward-directed normal to s in the plane of the cross section. Spherical Transmission Lines.—The frequency and excitation of a spherical waveguide of the type illustrated in Fig. The scattering description of the nth mode on a spherical transmission line is based on the spherical Hankel function solutions.
These regions are generally evident when comparing the field distribution in the different cross-sectional images.
F!=sin:zsin
On releasing the amplitude factor V;' the components of the orthonormal vector function e; are given directly by E. In terms of the rms mode voltage V:' the total power carried by a Hm~-traveling wave in a nondispersive guide is given by. In terms of the amplitudes of the new V and Z modes, the undamped field components of the main mode are
The damping constant of the dominant mode due to dissipation in the inner and outer conductors is. The normalized e; vector functions that characterize the higher E-modes can be derived from the scalar functions. The z-dependence of the fields is determined by the transmission line behavior of the mode amplitudes V; and I;.
The power flow per unit area in the z direction can be expressed in terms of the effective voltage. The z-dependence of the E-type modes is determined by the transmission line behavior of the mode voltage V: and current I;. In terms of the dominant mode rms voltage, V is the total output power in a matched non-dissipative conductor.
The r dependence of the mode fields is determined by the spherical transmission line behavior of the mode voltage V:' and current Z:'. The attenuation constant of the dominant mode in a conical conductor is a function of r and is given by.
ZZTEZ2
An analysis of this plot using the previously considered tangent ratio in the form. Other methods of error curve analysis can be used depending on the value of -y. It is first necessary to find in the input region z < 0 a solution of the field equations (1.1) subject to the boundary conditions of.
The exchange of the order of summation and integration involved in the transition of Eqs. Evaluation of the resulting integrals in Eq. 46) then led to the estimated expression for the relative susceptance. To illustrate this procedure for the case of the capacitive window, let's display the test field in the form.
The Inieqral comparison method. The susceptance of the capacitive Ivindow can be obtained by directly solving the integral equation (48) for the aperture field E(y). 3.5] DETERMINATION OF CIRCUIT PARAMETERS 147 the eigenfunctions of the kernel considered as an integral operator in the aperture domain. Given the linearity of this integral equation, the solution E(y) can be written as.
The determination of the impedance parameters for this case first requires the solution of the integral equation (66) for n = O and n = 1. From the knowledge of these parameters, the desired discontinuity access f/V can be found by a simple solution of the network equations ( 84) subject to the terminal conditions (63a). Using the Schwartz-Christoffel transformation, the function that defines the guide perimeter in the {-plane of Fig.
The location of the reference plane is determined by the transformation method and is rigorous in the above range.
Rectangular to circular change in diameter.-The termination of a rectangular guide by a centered, infinitely long circular guide (H,o mode in rectangular guide, no propagation in circular guide). The circled points are the measured values; the solid line is the theoretical curve obtained from Eq. Since there is no justification for extrapolating the formulas to the case d > b, the theoretical curve has not been extended to this region.
Capacitive Gap Coaxial Line Termination.—The junction of a coaxial bus and a short circular bus (main mode in a coaxial conductor, no propagation in a circular conductor).
Parallel-plate guide in space, E-plane.—A semi-infinite parallel-plate guide with zero wave thickness radiating in free space (the plane wave in the parallel guide plate is incident at an angle with respect to the terminal plane normal) . 47a] PARALLEL-PLATE GUIDE RADIATING IN HALF-SPACE 183 The angular distribution of the emitted radiation is described by the power gain function. The equations for the circuit parameters are obtained by the transformation method and are rigorous in the above range.
4.6-3 as a function of b/A'. The alternative circuit parameters G'/Y~ and B'/Yo are plotted as a function of b/A' in Fig. 4.6-5 as a function of q4~vith b /A' as parameter; only positive angles are indicated because the gain function is symmetric about @ = O. Rectangular conduction to the bounded space, E-plane. - A rectangular guide with zero wall thickness radiating into the space between two infinitely parallel plates that form extensions of the guide sides (HIO mode in rectangular guide).
Parallel Plate Guide Radiating in Half Space, Plane E.—A semi-infinite guide with parallel plates terminating in the plane of an infinity.
