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Design Considerations for Microwave Oven Cavities 74 IEEE TRANSACTIONS ON INDUSTRY AND GENERAL APPLICATIONS, VOL. IGA-6, NO. 1, JANUARY/FEBRUARY 1970 Design Considerations for Microwave Oven Cavities HAROLD S. HAUCK, MEMBER, IEEE Abstract-The heating mechanism in a microwave oven results z DIRECTION OF from the interaction of a high-frequency electromagnetic field and ENERGY PROPAGATION the food within it. In most ovens the field is generated by a magne- tron which converts dc energy to high-frequency energy at approx- imately 2450 MHz. This energy is then propagated into the oven 71 chamber which is, in reality, a multimode resonant cavity where the is IT- energy reflected from the walls to create standing wave patterns. I To properly design a microwave oven, one must consider not only Ll- MICROWAVE CAVITY the magnetron but also the dimensions and resonant properties of b-- II II the oven cavity. The designer must strive for a uniform energy II density within the cavity for uniform cooking of the food and must I be sure the cavity presents the proper load to the magnetron. These objectives are discussed, and a procedure for obtaining them is outlined. MODES WITHIN AN OVEN CAVITY Fig. 1. Waveguide with two shorting plates JF WE HAVE a waveguide with the wave propagating to form microwave cavity. 'along the Z axis as shown in Fig. 1, and then construct two shorting plates as shown, we have created a micro- wave cavity. This cavity is resonant at a particular set z of frequencies. For instance, if the E field varies as shown TE232 MODE in Fig. 2, where we have two half-waves in the width direction, three half-waves in the depth direction, and two half-waves in the height direction, the cavity would HEIGHT be resonating in the TE232 mode. X1IHy J 'Y The wavelength at which the resonance can occur is given by 2 + (N/D)2 + (P/H)2 Fig. 2. Microwave cavity formed in Fig. 1 with schematic portrayal \VI(MIW)2 of E-field variation for the TE232 mode. where X is the wavelength of the resonant frequency; M, N, and P are the wavenumbers or half-waves of variation of E field in the W, D, and H directions, respec- Because of the field variations due to these modes, tively; and W, D, and H are the width, depth, and height areas of high and low energy density will occur in the of the cavity. cavity. If food were placed in such a cavity, it is possible Since energy in a waveguide can propagate in both TE that it may not be cooked uniformly. We have found and TM modes, we can have TE and TM resonant that cooking uniformly can be increased by, first, choosing modes in a cavity. Thus we will also have a TM232 mode, dimensions which give the largest number of resonant given by the same equation. Since both modes can occur modes within the frequency limits of the magnetron (2425- at the same frequency but have different field configura- 2475 MHz); and second, adding a field stirrer to constantly tions, they are called degenerate modes. All modes for change the energy pattern within the oven. which the equation holds true can be excited in the cavity CALCULATION OF MODES except for configurations which violate boundary condi- tions. These are the TEMNO modes, the TEoop modes, the A computer program can be written to compute cavity TMONP modes, and the TMMop modes. Since waveguides dimensions which have a large number of resonant modes. will not propagate the TEM mode, this mode is also Essentially, the equation is solved for all combinatiorns impossible to sustain in a cavity of this geometry. of M, N, and P for small increments of the dimensions, and the combinations which result in a resonant frequency within the desired frequency limits are retained. Two Paper 69 TP 64-IGA, approved by the Domestic Appliance Committee of the IEEE IGA Group for presentation at the IEEE nomographs are also available to facilitate the calculation 20th Annual Appliance Technical Conference, Detroit, Mich., of modes and cavity dimensions. These nomographs are April 29-30, 1969. Manuscript received August 28, 1969. The author is with the Amperex Electronic Corporation, Hicks- shown in Figs. 3 [1] and 4 [2] and are described in detail ville, N. Y. 11802. in Appendices I and II. The first nomograph is better for HAUCK: DESIGN MICROWAVE OVEN CAVITIES 75 WiDTH 2 (W2H J HEIGHT) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 p=89 FREQUENCY: 2425-2475 MHz P = 6 WAVE LENGTH: 12.12-12.37 cm. P=5 P= 4 P2 P= 1 17 1a76 15 14 13 .70 12 , 11 10 60 19 i8 i7 ,50 i6 i5 4o04 i3 .3o2 2011 00 (w)2 041 * e61 0 *A * *21 * *01 *82 042 * *22 * *02 (w)2 (WIDTH)2 S63 S *43 0 *23 *g03 924* 04 - .84 64*6 *0 .44 a 0 * .005 (HEIGHT) H 68 L * 567 * * * em 0 *68 * .68* .0.08 8at * .69 * 4*49. S09 0.5 1.0 1.5 2.0 2!.5 3.0 3.5 .I (W) = WIDTH)2 Fig. 3. Nomograph for resonant modes of rectangular microwave oven. TM AND TM AND TM AND TM AND TE3N TM AND TE4N TM AND TE5N TE6, TE7N TE8N MODES MODES MODES MODES MODES MODES 46 28 V\/ 37 38 47 V 56 57 66 \75 TEO9 TM AND TEM8 MODES TE08 TM AND TEM7 MODES TE07 TM AND TEM6 MODES TE06 (2 WIDTH) TM AND TEMO MODES TE05 3 7 898 f t N A _ t ~~~~~~~~~~~~~~~~~~~6 TM AND TEM4 MODES TE04 TM AND TEM3 MODES TE03 TE30 ~~~~~~~~~~~~~~~~~~~~~~TE40 TE50 TE60 TE70 TE80 TE90N (2 DEPTH) Fig. 4. Mode contours for rectangular cavity; TEMNp and TMMNP modes. 76 IEEE TRANSACTIONS ON INDUSTRY AND GENERAL APPLICATIONS, JANUARY/FEBRUARY 1970 of the ratio of reflected to incident energy. The outpuT LEVELER VERT. HOR.I from the ratiometer can be fed into either an oscilloscope I ; VERT. + MOMM-11 or an X-Y recorder. Fig. 6 shows the results using an X-Y recorder. At a I resonant frequency, energy will be absorbed by the cavity and will not be reflected. At a frequency which is not resonant, the energy will be reflected. As seen in the L figure, we have resonances occurring at approximately the calculated frequencies for the 431, 243, 342, and 252 modes. We do not see the 333 mode, and we have a I slight trace of the 060 mode. We do have evidence of 2 additional modes near 2500 M\IHz. Possibly these are due to resonances within the coupling system, or thev might be the appearance of higher frequeincy modes Fig. 5. Sweep frequency test circuit. caused by our errors in measuring the cavity. The figure shows that most, but not necessarily all, of the calculated modes will appear in the cavity. Whether or not a mode appears is largely determined by the manner in which the energy is coupled into the cavity. z FIELD STIRRER Lu p The mode pattern within the cavity can be continually z disturbed by adding a field stirrer, which is a bladed device similar to a -j fan and which rotates at a frequency a: which should be asynchronous with the 60-Hz power frequency. The effect of a stirrer can be seen in Fig. 7, w which shows the heating pattern for an oven cavity with and without a stirrer. The patterns were obtained by placing a layer of moistened silica gel in the cavity and operating the miagnetron to see how uniformly the silica FREQUENCY - MHz gel dries. Silica gel is normally used as a desicant and is Fig. 6. Voltage reflection coefficient versu s frequency showing light pink when moist but turns various shadesaif blue as resonant modes in oven cavity with width 29.7 cm, depth 36.6 cm, and height 30.2 cm. it becomes dry. The light areas in the figure show areas which were not being heated by the energy within the oven. As seen in the figure, the uniformity of heating was calculating modes in a cavity of known dimensions, while improved by the field stirrer. the second nomograph is better for calculating dimensions As a demonstration of what is actually happening in which will have a large number of modes. the cavity as the stirrer rotates, we took pictures of To verify the existence of these modes, we calculated the the heating pattern for six consecutive 2-degree incre- modes for a cavity with width of 29.7 cm, depth of 36.6 ments of rotation of the stirrer. These are shown in Fig. 8. cm, and height of 30.2 cm. A close examination of the figure will show that the areas of high and low energy density appear and disappear, Frequency and that, at the same time, the areas appear to move Mode (MHz) around slightly within the oven. A further demonstration 431 2415 of what is happening is given in Fig. 9, showing X-Y 243 2430 recorder traces of voltage reflection coefficient versus 342 2441 333 2453 frequency for the 2-degree increments of stirrer rotation. 060 2462 The figure shows the modes appearing and 252 disappearing, 2488 and at the same time, changing frequency slightly. The changes in frequency suggest that the stirrer changes the The cavity was then tested using the circuit of Fig. 5. effective dimensions of the cavity as it rotates. In the system we used the sweep oscillator to vary the frequency from 2400 to 2500 MHz; a dual directional LOAD PRESENTED TO THE MAGNETRON coupler to sample the energy coming from the oscillator Fig.
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