of the TE10 mode as illustrated in figure 1. While the cutoff frequency of the TE10 mode is simply calculated from

the cutoff frequencies of the TE01 mode are much more involved and have been calculated by many workers [1,2,3,4] as shown in figure 2. Let us consider, for example, a typical 50% TEM cell having a width of a = 1 m, a height of b = 0.6 m, and a width of inner conductor of s = 0.72m. While the cutoff frequency of the TE10 mode is 150 MHz, the cutoff frequency of the TE01 mode is approximately 135 MHz according to figure 2. It can also be shown that the cutoff frequencies of all TM modes of a TEM cell are always higher than those of their hollow waveguide counterparts. Thus, the dominant cutoff frequency (i.e., the lowest) is either the TE01 mode or the TE10 mode. It is interesting to note that the cutoff frequency of the TE01 mode decreases as the gap between the inner conductor and the wall of the TEM cell becomes narrower. This phenomenon has also been observed in a ridge waveguide [5] and is associated with the infinite gap capacitance.

In the EMC measurements, an object under test is placed inside of a TEM cell. The field from the TEM mode incident upon the scattering object is identical to that of a plane wave in a free space. However, the scattered field produced by the object in the TEM cell is different from the scattered field produced by the object in a free space because of multiple reflections from the TEM cell walls, or equivalently, the mutual coupling between the object and the TEM cell.

Placing a test object in a TEM cell is equivalent to introducing a capacitive discontinuity. For low frequencies, where the transverse dimensions of the object are negligible compared to the wavelength, the discontinuity due to the object is a pure capacitive reactance, and may be regarded as the fringing capacitance of the corresponding electrostatic problems. Under this assumption, the ratio of the electric field strength near the metal object in the TEM cell to the unperturbed electric field strength at the same location in a pure TEM mode has been calculated by G. Meyer [6] and is shown in figure 3.

The purpose of this paper is to discuss the loading effects, i.e., the electromagnetic field distortion caused by an object under test in a TEM cell. In the theoretical analysis, the frequency domain integral equation for the magnetic field, or equivalently, the current density on the surface of a perfectly conducting cylinder in a parallel plate waveguide is solved by the method of moments to predict the degree of mangetic field distortion. For the purpose of mathematical tracta

bility, a parallel plate waveguide is used to model a TEM cell structure. The results given in the paper are for the magnetic field intensity on the surface of the cylinder. Other related quantities, such as the electric field intensity and the poynting vector, can be readily derived from the surface current by use of Maxwell's equations.

II. THEORY

The problem of determining the electromagnetic field scattered by a perfectly conducting rectangular cylinder has been studied by many

workers [7,8,9]. The coordinate system used to analyze the current density on the surface of the rectangular cylinder in a parallel plate waveguide is shown in figure 4. The source of the TEM wave is a delta function voltage source of the form

where Vo is the magnitude of an equivalent voltage source located at the source location Z。. Since there is no variation in the y direction and the voltage source has only a y-component, we will have a scalar wave

and k is the free space wave number. The boundary

condition is that the normal field be zero on all of the reflecting

The solution of equation (3) may be found through the Green's

Function technique,

(4)

v2 G(r,r') + k2 G(r,r')

=

-ε(x-x') ɗ(z-z').

(5)

Multiplying eq. (3) by G (r,r'), eq. (5) by Hy, subtracting the two results and integrating over the free space volume V,

=

↓↓ [G(r,r') v2 Hy (r') - Hy (r') v2 G(r,r')] dv'

jwe ↓↓ G(r,r') M↓ (r') dv' + √ √ Hy (r') 8(x-x') ô(z-z') dv'.

My

(6)

Evaluating the integration of the right hand side of eq. (6) and using

On the perfectly conducting surface, s, of the plates, we set the

Hy(r) = -Jwc {yG(r2r') Myr') dv' - Jsc Hy(r') a G(n,r) ds', (9)

an

where so indicates the surface of the rectangular cylinder. The first term on the right hand side of eq. (9) corresponds to the incident

field, and the second term to the scattered field. The known incident

Equation (9) is an integral equation which can be solved for Hy(r) once Green's function G (r,r') is obtained.

The Green's function is the solution of eq. (5). By imposing the proper boundary condition for the parallel plate waveguide, i.e.

Once the Green's function is obtained and the source is specified, eq.

(9) can be solved by the method of moments. The technique used is discussed briefly below. A detailed discussion on this subject is given