Last modified: 11-10-2019

#### Abstract

A Rieke diagram [1] is a magnetron characteristic that visualizes the dependence of the generated frequency *f _{g}* and the net delivered power

*P*on the load reflection coefficient G

_{L}*. G*

_{R}*is defined in a specific magnetron-to-waveguide coupling structure called the*

_{R}*standard*or

*reference launcher*(Fig. 1). The diagram is plotted as a family of isolines of constant

*f*and of constant

_{g}*P*in the polar diagram of G

_{L}*. Rieke diagrams are essential in the design of applications without isolators, such as domestic or professional microwave ovens.*

_{R}Constructing Rieke diagrams is tedious, time-consuming and equipment-demanding [2], [3], preventing systematic studies of their dependence on operating conditions, such as anode voltage and its ripple, filament current, mounting repeatability, etc.

We have devised a procedure, centering around a high-power automatic impedance matching device (autotuner), which enables fully automatic measurement and plotting of the stated dependences. A block diagram of the setup is shown in Fig. 1. The autotuner, when terminated in a match (waterload), can accomplish a task inverse to impedance matching: realizing any desired reflection coefficient G* _{R}*. The measurement consists of stepping through a grid of

*n*suitably chosen reflection coefficients G

*=*

_{R}*x*+

_{R}*jy*, covering a desired area of the polar diagram. Each G

_{R}*is measured accurately by the autotuner, along with the corresponding*

_{R}*f*and

_{g}*P*. Thus, raw data for constructing a Rieke diagram are obtained, the data consisting of a collection of

_{L}*n*points {G

*,*

_{R}*f*,

_{g}*P*}

_{L}*,*

_{i}*i*= 1…

*n*, with G

*, in general, irregularly scattered in the complex plane. A dedicated MATLAB routine then reads the data, sorts them out to create tabulated functions*

_{R}*f*=

_{g}*f*(

*x*,

_{R}*y*),

_{R}*P*=

_{L}*f*(

*x*,

_{R}*y*), approximates these by a 2D spline, and uses the splines to plot smoothed isocontours for chosen constant values of

_{R}*f*and

_{g}*P*, completing thus the desired Rieke diagram construction. We will present details of this procedure as well as real-life examples.

_{L}**Fig. 1.** Rieke diagram measurement setup.

**References**

- Meredith, R. J.,
*Engineers' Handbook of Industrial Microwave Heating*, London: The IEE, 1998, 250–270. - Takahashi, H., I. Namba, K. Akiyama,
*J. Microwave Power*, 1979,**14**, 261–267. - Yixue, W., Z. Zhaotang,
*Proc. ICMMT'98*, 1998, 795–798.