CA1316991C - Microwave heating - Google Patents

Abstract

Abstract of the Disclosure A product comprises a shallow container and a load located therein for heating by microwave energy. This product is designed either to be used with, or itself to incorporate, a structure for generating or enhancing at least one mode of the microwave energy of an order higher than a fundamental mode that is determined by boundary conditions resulting from the lateral dimensions of either the container or the load or both. The invention resides in controlling the depth of the load in the container in such a manner that, upon irradiation of the product with the microwave energy, the power absorbed by the load from a higher order mode is at or near a maximum value, while preferably the power absorbed by the load from the fundamental mode is at or near a minimum value. Since uneven heating would ordinarily be associated with the predominance of a fundamental mode, the result of this invention is to increase the intensity of a higher order mode relative to the fundamental mode intensity, and thus provide improved microwave heating uniformity.

Description

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~ ~ Improved Microwave E-Ieating : :
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This invention relates to improvements in microwave heating, and, more particularly, to means and method Eor modifying a field of microwave energy in a load in a microwave oven, the load being a substance or article to be heated by the microwave energy. The substance or article~- will~ usually be a~foodstuff, but the invention is applicable to other~substances. ~Such field modification is or the purpose~of generating (or en~hanci~ng the existence~of~one or~more higher order~modes of microwave ener~gy in the load.
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The purpos~e of generating tor~-en~hancing) the higher 15~ order modes is to distribute the energy more evenly throughout the load, and, in particular, to avoid, or at least reduce the occurrence, of uneven temperatures in the load, especi;ally~the presence~of~cold spots at certain loca~tions in the load~, usually the center.

2~0 ~ The~te~rm "mode" i~s~used~in~the s~pecification and claims n lts ar~t-~ecognized~sens~e, as~meaning one~o~ several states of electromagnetic wave oscillation that may be -sust~ained~in a given~resonant~system~ at~a fixed ~requency, each~such state o~type of~vibration (i.e. each mode) being 25~ characterised~by~lts own particular electric and magnetic , .
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~ield configurations or patterns. The fundamental modes of a body of material to be heated, or o such body and a container in which it is located, are characterised by an electric field pattern ~power distribution) typically s concentrated around the edge (as viewed in a horizontal plane~ of the body of the substance to be heated, or around the periphery of its container when the substance is enclosed by and fills a container, these fundamental modes predominating in a system that does not include any higher order mode generating means. The funda~ental modes are thus defined either by the geometry of the container or by the geometry of the body of material to be heated, or to varying degrees by both geometries.
A mode of a higher order than that o~ the fundamental - 15 modes is a mode for which the electric field pattern (again, for convenience of description, considered as viewed in a horizontal plane) corresponds to each of a repeating series of areas smaller than that circumscribed by the electric field pattern of the fundamental modes.
Each such electric field pattern may be visualized, with some simplification but nevertheless usefully, as having maxima distributed about a closed loop in the horizontal ; plane.
The generation or enhancement of such higher order modes can provide more control over the heating of diferent regions of the substance, and, in particular, render the heating more uniform throughout the substance being heated, compared with the result that would be obtained from the fundamental modes alone.
Pri~r Art __. _ _ Methods of generating or enhancing such higher order modes are known. Richard M. Keefer Canadian Patent No.
1,239,999 issued~August 2, 1988 discloses the achievement of this objective by providing in a part of a container in which ~ ' ,.

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the substance to be heated is supported, e.g. in the bottom or lid of the container, or in both, an array of one or more conducting plates distributed across a microwave-transparent substrate.
Other methods of generating or enhancing higher order modes are disclosed in Richard M. Keefer's Canadian Patent No. 1,279,902 issued February 5, 1991 and Canadian Patent Application No. 544,007 filed August 7, 19~7 ~published in European Application 87309398.3 on June 22, 1988 under No. 0271981). In particular, this disclosure shows that the generation or enhancement of higher order modes can be achieved by stepped structures that protrude into or out of the container ~rom a surface thereof, usually a bottom surface, or by a dielectric wall structure that comprises at least two wall portions of respectively different electrical thicknesses, i.e. different spatial thicknesses or different dielectric constants.
When microwave energy is applied to a load mounted in a container made of metal, but with a microwa~e-transparent lid (or after the lid has been removed), the energy all enters the load ~hrough tbe top surface. If only the `: .

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fundamental modes were present, the field would be such that the edge regions of the load would be heated to a higher temperature than the central region. In the case of a container in which the side wall or walls are made of a ~icrowave-transparent or semi-microwave-transparent material, some of the energy also reaches the load through such side walls. This still further heats the edge regions of the load and hence aggravates the lack of uniformity of heating among the edge and central regions.
It is primarily to counteract this nonuniformity of heating (energy absorption) that the various methods of generating or enhancing higher order modes mentioned above have been developed.
Summary of_the InVQntiOn The present invention is directed to providing additional compensation for such lack of uniformity.
While the present invention is applicable to all containers, including those having metallic (reflective) side walls, it is especially suited to use with containeEs that either have no side wall structure at all or have a `
side wall structure that is at least partially microwave-transparent, i.e. fully microwave-transparent or semi-microwave-transparent, because of the higher inherent non-uniformity of heating that such containers tend to exhibit.
As indicated above, prior to the present invention, the proposals for minimising the nonuniEormity of energy absorption among regions of the load have concentrated on generating~(or~enhanclng) higher order modes of microwave ~energy by selection of the shapes and dimensions of a container or various structures mounted in a container or on a separate member.
While such stimulation of higher order modes has helped t~ some extent in~practice towards improving heating uniformity, there has been a continued presence of the fundamental modes simultaneously with the higher order modes.

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The improvement in heating uniformity resulting from the generation of higher order modes would be further enhanced if it were possible to increase the intensity of the higher order modes relative to the fundamental modes.
It has now been discovered that this objective can be achieved by proper control of the depth dimension of the load itself.
More specifically, it has been found possible by such control to ensure that the power absorbed by the load from a higher order mode is substantially at or at least near a maximum value relative to the fundamental mode. Prefer-ably, the depth control is also such as simultaneously to arrange for the power absorbed by the load from the fundamental mode to be less than that absorbed by the load from the higher order mode and indeed Eor such power absorbed from the fundamental mode to be at or near a minimum value.
; Thus, the invention consists of a product comprising a container and a loaa located therein or thereon for heating by micxowave energy, said product being for use with means for generating at least one mode of said energy of an order higher than a fundamental mode determined by boundary conditions defined by lateral dime~sions of at least one of said container and said load, wherein the depth of the load ~in the container is such that, upon irradiation of the product with microwave energy, the power absorbed by the load from said higher order mode is at or near a maximum ~value.
The invention also consists of an assembly comprising (a) a container for mounting~a load in a microwave oven, for use with means for generating at least one mode of microwave energy of an order higher than a fundamental mode determined by boundary conditions defined by lateral dimensions of at least one of said container and said load, and (b) means for indicating a depth of the load in the container such that the power absorbed by the load from said higher ordex mode will be at or near a maximum value, ~3~ ~3~ ~

The invention also provides a method of heating a load in a container by microwave energy, lateral di~ensions of at least one of said container and said load defining boundary conditions that determine a fundamental mode of said energy, said method comprising the steps of (a) generating at least one mode of said energy of an order higher than said fundamental mode, and (b) so controlling the depth of said load that the power absorbed by the load from said higher order mode is at or near a maximum value relative to the fundamental mode.
rief Description of the Drawings Figu.re 1~ is a top plan view of a product consisting of a circular container with a load therein, for heating in a microwave oven;
lS Figure lB is a similar view of a container with elliptical geometry;
Figure lC is a similar view of a container with rectangular geometry;
Figure lD is a similar view of a container with complex geometry;
; Figure 2 is a cross-section on each of lines 2a-2a;
: 2b-2b; 2c-2c; and 2d-2d in Figures lA-lD;
Figures 3-8 depict in an idealized way various : distributions of power absorp~ion tha~ may exist in the product;
Figures 9 and 10 respectively depict in an idealized : form characteristics of fundamental and higher order modes ~:: of microwave~energjy in a circular container having a microwave-transparent side wall; :
: 30 Figures 11 and 12 are respectively a plan and a perspective view of a container fitted with a lid for : generating higher order modes;
Figure 13 depicts an electrical field that exists in ~: the construction of Figures 11 and 12;
~ 35: Figure 14 is a sectional view of an alternative : ~ construction;
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Figure 15 is a plan view of Figure 14;
Figures 16 and 17 respectively depick in an idealized form characteristics of fundamental and higher order modes of microwave energy in a circular container having a reflective side wall; and Figures 18 and 19 are plan views of alternative constructions.
~etailed Description of the Preferred Embodiments In accordance with the present invention, selection of lo the depth of the load creates a condition in which the ratio of the energy existing as the higher order mode (or modes) to the energy present in the fundamental mode (or modes) is maximized, or is at least increased over the value that it would have in the absence of such depth control.
Figures lA, lB, lC and lD show top plan views of containers o~ circular, elliptical, rectangular and ~; complex geometry, respectively. Corresponding to each of these views are the cross-sectional views taken across 20~ lines 2a-2a, 2b-2b, 2c-2c and 2d-2d, all represented by ~igu~e 2. Each of the containers lla, llb~ llc and lld is comprised of a base portion 12 and sidewall portion 13 enclosing a microwave energy absorptive load 10. If the load 10 is a solid or semi-solid article or assemblage of articles, the sidewall 13 may not be necessary for containment o~ the load, and therefore may optionally be omittedr in which event the containers lla, llb, llc and lld will be understood to consist~essentially of a sheet ~` ~ or plate bottom portion l2.
Hence the term "container" as used herein (including the claims) includes a simple~support for the load without necessarily having a restraining sidewall structureO
The container lla o~ circular geometry shown in Figures lA and 2 is also representative of containers of nearly circular plan; that is, a container having a small ~ 3 ~

departure from circularity in plan will behave essentially as a circular container for the purpose of this invention.
Likewise, the container llb of elliptical plan shown in Figures lB and 2 is for the purpose of this invention representative of elliptical containers of greater or lesser eccentricity than that shown, and also of containers whose plan approximates to the elliptical. Recognizing that a circle is merely an ellipse of zero eccentricity, the circular container lla may be regarded notionally as belonging to the more general family of elliptical containers. While a theoretical structure with an eccentricity of exactly unity must have zero volume, containers having nearly unity eccentricity will ~ssume a rod-like plan suitable for the heating of elongated loads.
Thus, at a ratio of elliptical major--axis to minor-axis lengths of as low as 5, the corresponding eccentricity will approach O.g8, and at a ratio of 10, the eccentr;city will exceed 0.~9. Elliptical containers may therefore be defined as having eccentricities within the range o just less than unity, and greater than or nearly zero.
Similarly, the container llc of rectangular plan shown in Figures lC and 2 is for the purpose of this invention ; representative of square containers and of containers of greater or lesser aspect ratio, and also oE containers whose plan approximates to the rectangular (e.g.
rectangular, but with rounded corners).
The container l~id of complex geometry depicted in Figures lD and 2 is representative of container plan geometries not readily describable as belonging to the famiLies`of circular, elliptical, and rectangular container geometries as hereinabove set out. The container plan geometries herein referred to as complex may also include, without limitation, triangular~ trapezoidal (of which rectangular and square plans are special cases), ~ 35 pentagonal,~ hexagonal, and other polygonal geometries, : ~

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rounded polygonal geometries, and epitrochoidal, multi-foil (e.g. trefoil) and other lobed geometries Hence, the plan view of the container lld is intended to be broadly representative of these and other geometries in showing that the p~esent invention is not specific to a particular container plan geometry.
Figures 3-8 serve to demonstrate graphically the problems of nonuniformity of heating of a load lO to be heated by microwave energy in containers of circular elliptical, rectangular or complex (as hereinbefore defined) plan geometry.
Microwave heating of the load, also referred to as its power absorption, can be described by the relation:
P ~[ae (E E~ + am-(H.~*l]
In this relation, the power absorption P is expressed in units of watts per cubic meter. The term ~eis the conductivity o~ the load, in units of coulomb per (volt meter second) or (coulomb)2 per ~joule meter second).
In the absence o~ e~ectrical conduction by the load, ae will have the value 2~-f en ;~0~ where f is the microwave oven operating frequency, ~ is the complex part of the relative dieIectric constant giving rise to dielectric ~losses, and eO is the free-space (electric) permittivity, having a value of nearly 8.8541878 10 12 expressed in ~` coulomb per (volt meter) or (coulomb)2 per (joule-meter).
The vector E describes the electric field intensity, in units of ~olt per meter or joule per (coulomb meter), and ) E* is its complex conjugate. The vectorial dot product E-E* may be expressed as the vectorial square magnitudelEl2 The term am gives rise to magnetic losses, and ; 30 ~ is expressed in units of (joule-second) per (meter-(coulomb) ). The vector ~ is~the magnetic field intensit~, in units of coulomb per ~meter second), H* is its complex conjugate, and the vector dot product H-H* is ~- ; equivalent to tne squared magnitude 1 H¦2-~, ' ' :

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For such non-magnetic loads as foods, the term ~m will have a value approaching zero, so that the contri-bution of the magnetic field to power absorption may then be ignored. For these loads, power absorption may be taken as essentially proportional to ¦E¦2, or it may be described by the expression:
P = ~-f ~" ~O ¦E ¦ 2.
The vector ~ from which ¦~2 is obtained can be represented in the generalized form:
~ = Eu u + Evv + Ez~z.
where û, v and z are unit vectors parallel to the corres-ponding axes making up the coordinate system. The magnitude of these vectors is 1.
The unit vectors û and v are directed in the horizontal plane 14 of the load parallel to the container plan views of Figures lA, lB, lC and lD, and the unit vector z is - orthogonal to this plane. For the circular, elliptical and rectangular container geometries of Figures lA, lB and lC~ the horizontal plane unit vectors û and v may be listed in the more familiar notation:
Horizontal PIane _ Unit Vectors Coordinates ?
Container Geometry û v u v Circular p ~ P
Elliptical ~ n ~ n Rectangular x y x y The p and ~ coordinates of the circular geometry are -~ radial and angular, and the p and ~ unit vectors designate ~ radial and angular components, respectively. The unit - ~ 30 vector p is directed normally to the sidewall 13 of the circular container lla and the vector ~ is directed tangentially to this sidewall. Unit vector ~ is directed normally to sidewall 13 of elliptical container A
llb and vector n is directed tangentially to the sidewall.

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The x and y coordinates of the rectangular geometry are parallel to the flat sidewall portions of a rectangular container, and the unit vectors x and y are parallel to the corresponding x and y axes, respectively. Unit vector x is directed normally to the sidewall parallel with the y-axis, and tan~entially to the sidewall parallel with the x-axis; y is directed normally to the sidewall parallel with the x-axis, and tangentially to the sidewall parallel with the y-axis. The generalized unit vector û is chosen to be directed normally to a region of sidewall 13 of the container lld of complex geometry, and the unit vec~or v is directed tangentially to the same region of sidewall 13.
If the sidewalls 13 of the containers lla, llb, llc and lld approximate to the vertical, the vertical component 1~ of the vector E with the unit vector z will be orthogonal to the components having unit vectors generalized as û and v, directed in the horizontal plane of the containers. In differentia form, Maxwells's equations governing E and H
; may be expressed as:
V x (V x E) = 4(~/~o)2~ E
V x (V x H3 = 4(~/~O) (~ jE ) H-~3~ 20 ~ In these equations, the vectors (V x E) and ~V x H~
~ may also be written as their equivalents curl E and curl i ~ H. The term ~O is the free-space wavelength (approxi-` mately that in air~ at the microwave~oven operating frequency, ~' is the real part of the relative dielectric constant, and j has the usual value ~ . For the circuIar-cylindrical, elliptical-cylindrical, rectangular or generalized cylindrical coordinate systems describing, respectively, the circular, elliptical, rectangular and complex conta ner geometries, orthogonality of the vertical component of E with respect to the û v plane allows separation of variables in the solution of Maxwell's equat ons. Hence, the Eollowing relation is obtainedO
- ~ k - p = 4(~/~O) .(~

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The terms k and p are separation constants, in units of reciprocal meters. The constant k allows separation of the parts of a solution dependent on the norizontal plane coordinates (generalized as u and v), and p is the separation constant for the parts of the solution dependent on the coordinate z of the vertical axis.
When the sidewalls 13 of the containers lla, llb, llc and lld are strongly reflective te.g. metallic), the term ae determining power absorption by the load 10 principally affects the vertical parts of the solution, so that k is constrained to be real and p complex. The vertical separation constant p may thus be written as:
P ~ ~
The terms a and ~ are also in units of reciprocal meters, and are then defined by the relations:

) (' (k~ /27r)2~+((~l-(k~o/2~)2)~+~l2)~ and [+(~l-(k~o/2~2)+((Fl- (k~o/2~)2~2+~2)~ (la) The corresponding vertical dependence of the solutions is then essentially proportional to the factor D(z), ~iven by the equation: ~
D(z) - (e PZ + r ePZ). ~ (lb) The symbol e is used in its~usual sense to denote exponential functions. The coordinate z refers to vertical depth in the load 10 (lts upper surface being at z=0~, with the first part e PZ describing downward propagation from the upper surface of the load, and the second part ePZ
referring to propagation upwardly from the lower surface.
The upward propagation of this second part may be due to to reflections at the container bottom 12, or if the container bottom is at least partially microwave-transparent, a portion of the upwardly propagating energy will result from transmission through the bottom surface (assuming the micro-wave oven and any utensils used with it are so designed as ~ '''"~' .
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to supply energy to that surface). The term r then serves to described multiple reflections occurring between the upper and lower surfaces of the load, which may be expressed as phase shifts. Just as the solutions of Maxwell's equations for these containers in ~ and H will depend on the vertical part of the solutions determined by the factor D(z), the power absorption P will be essentially proportional to the square magnitude of this part, through the dependence of P on the squared magnitude ¦E¦2.
From the separation of variables previously discussed, the parts of the solutions dependent upon the horizontal plane coordinates u and v may now be examined, independently of the vertical part of the solutions. Since the power absorption P may be treated as essentially proportional to the squared magn;tude o~ the vertical part, (this vertical part being independent of the coordinates u and v), the power P may also be regarded as essentially proportional to the squared magnitude of the horizontal parts expressed in the variables u and v (independently of the vertical variable z).
In circular, elliptical and rectangular geometries, the vectors û and v are orthogonal, and the horizontal part~with coordinates u and v may be further separated into u- and v-parts (the u-part being independent of the variable v, and vice versa). For these geometries, the power P can there-fore be further taken as essentially proportional to the squared magnitude tor square) of each of its u- and v-parts.
When u;and v are orthogonal, the power P may also be expressed as:
~ e [¦EU¦ + ¦E 12 +IE 12]
~ . , ~ In this expression, each of the components of the power ~ ¦EU¦2 ¦EV¦2 and ¦EZ¦2 will also be essentially proportional to its u-, v- and z-parts.
The sidewall portions 13 of the containers lla, llb, llc :: :
and lld may be made of metallic, microwave-transparent or .

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semi-microwave-transparent (e.g. suscepting) materials;
alternatively, the sidewall may be omitted, in which event the term "sidewall" will be understood to refer to the exterior surface of the load 10. If the sidewall 13 is a good electrical conductor (e.g. metallic or containing a metallic layer), the laws of electromagnetics require that the component of the electric field directed tangentially to the sidewall be small or disappear at the sidewall.
Hence, in virtue of the aependence of power P on ¦E¦ , ; 10 that portion of the power depending on the tangential component of ~he electric field must also disappear at the sidewall. At a boundary between two dielectrics, the laws of electromagnetics also require that:
Ef En f = ~O En,o~ hence ~n f = (o/~; En,o).
The term ~f 4 is the relative dielectric constant oE the load 10. The relative dielectric constant ~O applies to an adjacent portion of a microwave-transparent container or to surrounding air. If the container is thin and made of a material having a low dielectric constant, ~O may be taken as approaching the free-space value of unity.
The electric field components En f and En O are directed normally to the surface of ~he load. For such loads as foods, the relative dielectric constant ~f may have values exceeding 70. Consequently, the normal component En f will be small in relation to En Ol and will be forced to assume a minimum at the boundary.
Accordingly, in containers having microwave-transparent sidewalls 13 (or in which the sidewalls are omitted), the portion of power P depending on the norm~l component of the electric field will also approach a minimum at the container sidewalls.
Figures 3 and 4 show the variation of the various horizontal plane components of the power P taken at the - depth h of plane 14 in Figure 2. In its minima oE power , ~ ~

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P shown as corresponding to sidewall portions 13, Figure 3 may be used to describe the variation along lines 2a-2a, 2b-2b, 2c-2c and 2d-2d of the components of power associated with tangential components of the electric S Eield in a container with electrically conductive walls, or the variation along these lines of t:he component of power due to the normal component of the electric field in a microwave-transparent container. For a circular container lla as shown in Figure lA, the angular and vertical components of the power ¦E~2 and ¦E~ 2 corresponding to the tangential unit vectors ~ and z, respectively, will thus disappear at sidewall 13 when the sidewall is metallic (Figure 3); alternatively, wit'n a microwave-transparent sidewall 13,.the radial component ¦EP¦~ corresponding to the unit vector p will approach a minimum at the sidewall tFigure 4). In a complementary manner, the maxima of power shown in Figure 4 as corres-ponding to the sidewall portions 13 may be used to describe ~ the variation.along lines 2a~2a, 2b-2b~ 2c-2c and 2d-2d o~
; 20 the component of power associated with the normal componen.t : of the electric field in a container with electrically conductive sidewalls, or the variation along these lines of the components of power due to the tangential components of the electric field in a microwave-transparent container.
- 25 The curves of power absorption shown in Figures 3 and 4 are intended to depict lower order or fundamental modes within ~: a load. Fundamental modes will typ;cally give rise to a concentration of power absorption or héating in regions oE
the load that are displaced outwardly from the central 30 ~ region, and hence the centr~al~region tends to be a cold spot.
In addition to the power entering the load in a vertical sense, power may also penetrate the edge portions of the load through the sidewalls 13 of microwave-transparent or semi-microwave-transparent containers. Figure 5 shows a . :
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smoothed curve of the variation of this power absorption P
along the lines 2a-2a, 2b-2b, 2c-2c and 2d-2d of the various container geometries. In less absorptive loads, this power absorption may also show quasi-periodic variations resembling those of a damped periodic function (as its magnitude). Figuxe 6 shows how the additivity of power entering vertically and through the sidewalls of a microwave-transparent or semi-microwave-transparent container causes the low level of relative heating of the central region to become even more pronounced. The power absorption curves of Figures 7 and 8 show the effect of higher order modes in yielding maxima of heating that are nearer to each other, which represents a somewhat more uniform distribution of energyO It must be realised that these illustrations depict idealized situations, and that, in practice, the fundamental modes will continue to exist concurrently with the higher order modes in relation to improving heating uniformity.
Recapitulating, the vertical dependence of power absorption by the load was seen to be essentially proportional to the squared magnitude of the factor D(z) given in equation (lb) r containing exponential functions of argument +pz, and with the complex term p = ~ . These Eunctions may also be expressed in their equivalent form:
e+PZ = e+ ~.(cos~z ~ jsin~z).
Since the dependence of power absorption on these functions operates through the squared magnitude of the factor D(z), power absortion by the load may be seen to have maxima and minima repeating on a period approximated by:
~ ~ ~ Qm = ~, whence ~ Qm - n/~ c~
The term Qm may therefore be used to describe ~he vertical ; interval separating maxima of power absorption or heating, or between minima. If ~ is in units of reciprocal meters, ~ then Qm will be measured in meters, or if ~ is in - 35 reciprocal centimeters or millimeters, Qm will be in ~ centimeters or millimeters, respectively.
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Because of the effects described above, it has been found that by varying the value of d (the depth of the load), it becomes possible to promote power minima or power maxima for specific modes. A typical curve for the power P
versus depth d, showing such maxima 25 and minima 26 (at intervals Qm) for a fundamental mode in a fully microwave-transparent container is depicted in an idealized and not dimensionally accurate form in Figure 9~ while a similar curve with maxima 25' and minima 26' for a typical higher order mode is shown in Figure 10. The curves for the fundamental mode and for each higher order mode will have different values for the intervals Qm and Qm'. By locating a value for d, such as the value a~, where the fundamental curve is substantially at a minimum 26 while the higher order curve is substantially at a maximum 25', the desirable condition described above can be achieved, namely a high ratio of the energy embodied in the higher order mode to that embodied in the Eundamental mode.
However, it will not always be possible to select a depth such that a minimum 26 and a maximum 25' will coincide.
In such cases the depth should be chosen to achieve the highest possible~ratio of energy embodied in the higher order mode to that embodied in the fundamental mode.
Each minimum 26 of the fundamental mode will occur when ~ 25 d is given by - (2K + i) ~ d-= - Q

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where K is a posl~ive integer.
To coincide a maximum 25' oE the higher order mode with such a fundamental minimum 26, it is necessary ~o choose a mode that has a value for Qm' such that d = K ~' = 2 m ~ (2) where R' is also a positive integer. In the example shown in Figures 9 an~ 10, K and K' have both been taken as 2.
Hence, in designing a produc~, i.e. a container and load combination, the first parameter to select will be the most desirable higher order mode. The order of the mode should preferably not be too high, because the higher the order, (a) the more difficult it will be to excite and propagate the mode, and the more complicated the structure to do ~o;
` ~ (b) the greater the likelihood of interference from other modes; and (c) the more severe the cut-o~f limitation and hence the probability of evanescent propagation.
~ ~ As~indicated above~in equation l(c), theory shows that ; ~ the value of Qm is~given by the expression ., :
m = ~
While the values for Qm (and Qm') will vary to some ex~tent with the overall size of the container (becoming larger with smaller containers), it has been found that, 25~ ~ with a circular container~of 10 cm inside diameter and a food load havi~g a typical diele~tric constant relative to air ~') of appro~ximately 60 (determined chiefly by the water constant of ~ the load), and a typical dielectric loss characteristic ( ~ o~approximately 12, for circular ; 30 ~modes wherein ~
j ~:
.: ~: : ~
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:~ 3 ~ ' g in,m/ o where k is the separation constant mentioned above, in m is the mth zero of an nth order Bessel function, and rO is the container radius, the fundamental modes will have the following values of Qm:
[0, 1] Qm = 0.7919 cm [1, 1] Rm = 0.8009 cm [3/2, 1~ Qm = 0.8067 cm The latter mode will occur only in a container partitioned into three sections by radial vanes at 120 to each other.
High order modes in the same circular container will have the following values of ~m':
[0, 2] Qm' = 0.8177 cm [1, 2] Qm' = 0.8390 cm [3/2, 2] Qm' = 0.8517 cm [0.3] Qm' = 0.8711 cm [1, 3] Qm' = 0.9144 cm 13/2, 3] ~Qm' = 0.9355 cm [1, 4]~ Qm' = 1~0479 cm ~ ~
If~the principal fundamental mode is taken as the 11,1]
mode with Qm~= 0.8009 cm, and K is taken as 1, then the right hand te}m of equation (l) becomes 2 1/2 Qm = 2.0023 cm.
;To obtain a high field strength in the central region of a sircular container with~a ~0, 1] fundamental mode, it S desi~rable~to select a ~l,n] higher o~rder mode.
If~n is chosen to be~j i.e.~the [1, 4~mode with ; 30~ Qm' - 1.047~9~cm,~ is~selected, then the~ value for the middle ; term~of equation ~ becomes 2Qm' - 2.0958 cm. While this value~for a~higher order maximum is not exactly equal to the value ~2.002:3~cm) for~a~fundamental minimum, they are very close.~ I~t follows that, if the load depth d is 3s ~ s`elected within the range of approximately 2.0 to 2.1 cm, ~,.,~ ., .
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the ratio of power embodied in the higher order mode [1,4]
to that embodied in the fundamental mode [l,l] will be significantly increased over that ob~ained with a randomly chosen depth. Since a high (but not necessarily the theoretically highest) value for thi~ ratio will represent a significant improvement, and, since there will likely in practice be some unevenness to the top surface of the load and hence some nonuniformity to its depth across its - lateral dimensions, the preEerred range of 2.0 to 2.1 cm applicable in these circumstances can be extended to a range of approximately l.9 to 2.2 cm, while still obtaining benefits from the invention.
The values for Qm and ~m' will be determined ~efore making a final choice Eor the ideal value of d, and the lS acceptable range of values straddling such ideal value, since ~m and Qm' will vary with the values of ~' and ~" for ; each particular load. Nevertheless, it has been found experimentally that, for a large number of typical food . loads, a value for d of approximately 2.0 to 2.1 cm. affords substantially improved results ~in terms of heating uniformity) over loads of other depths.
One way of creating the [1,4]~mode having the characteristic shown in ~igure l0, is illustrated in Figures ll and 12 which show a microwave-transparent lid 30 for the container lla, the lid 30 haviny an inner circle 31 of foil (microwave-reflective material) centrally located thereon, and an annulus 32 of foil symmetrically surrounding the central circle 3I~ To achieve~the 11,4] mode the : diame~ers for a l0 cm container should be approximately 30 : D4 (the inside diameter of the container and : hence the outside diameter of the load) = l0 cm D3 (the outside diameter of the foil : annulus 32) = 7.64 cm : D2 (the inside diame~er of the foil annulus 32) = 5.27 cm ~: Dl (the diameter of the foil circle 31) - 2.88 cm , . , .~
,, ~,,, ~ , .

31 3~6~

The cross-sectional energy profile of the [1,4~ mode in the structure of Figures ll and 12 is shown in Figure 13.
As an alternative, a more general version of equation (2) can be employed, namely d = ~ + K~'m = t2K ~ l)Q (2A) where ~ is the helght of a step 33 in the bottom 12' of a container 11l ~Figure 14)o While in Figures 9 through 13, the container has been assumed to have a flat, unstepped bottom 12 (Figure 2), resulting in a constant depth d o~
the load 10 throughout, i.e. ~ = 0, which arrangement simplifies the manufacture of the container, use of the step 33 affords a wider choice of higher order mode to ~- satisfy equation (lA). For example, if, with the Figure 14 construction, the ~1,2] mode is selected as the higher order mode, the value of 2Qm' becomes 1.6780 cm, and hence ~should be equal to 2.0023 - 1.6780 = 0.3243 cm. In practice, values of d = approximately 2.0 cm and ~=
approximately 0.3 can be chosen.
To achieve t'ne [1,2] mode the structure of the li~ 30' ~ 20 shown in Figures 14 and 1~ can be used, with the diameter `~ Dl of a foil circle 31' being 5.46 cm, assuming that the diameter D4 of the load remains at lO cm. The annulus 32 is omitted.
This latter construction is essentially that described in Figure 8 o~ the Canadian patent No. 1,239,999 cited above.
Alternatively, if its lateral dimensions are properly ~` chosen, i.e. in the present example a diameter of 5.46 cm for the ~imension ~x, the step 33 can itself be used at least in part to generate the ~1,2] higher order mode, in the manner explained in the Canadian patent No. 1,279,902 ~` ; cited above, in which case the foiI circle 31' on the lid could be dispensèd with, although there would be an advantage in retaining it,~ since the assembly would then '' : ~
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have similar higher order generating means both top and bottom and the result would be a more uniform distr;but;on of the energy oE such mode in the vertical direction.
Figures 9 and 10, on which equations (2) and (2A) are based, show conditions in a microwave transparent container.
If, on the other hand, the bottom 12 oE the container ;s electrically conductive (e.g. metallic or containing a metallic layer) the fundamental mode would have the characteristics shown in Figure 16, and the higher order mode would have the characteristics shown in Figure 17. In the case of a container with a semi-microwave-transparent wall, the conditions will be intermediate between those of F;gures 9 and 10 and those of F;gures 16 and 17.
Changes o composition of the container bottom 12 can be visualized as g;ving rise to displacement of the maxima and minima of power absorpt;on ;n the vertical axis shown in Figures 9 and 10. When electric fields with components of equal magnitude are appl;ed to the upper and lower surfaces oE a load 10 placed in a container having a ~20 microwave-transparent bottom 12, then for a container depth d, the term ~ and the factor D(z) of equation (lb) may be written as:
~ r = e pd, and D~Z)I 2 = 2e ~d.~cosh2~z - 1/2d) + cos2~(z - 1/2d)] _ ~ld) tm;crowave-transparent bottom) For a container w;th~an electrically conductive bottom 12 (e.g. a container made of aluminum~foil), the components of the electric f;eld~directed tangentially to the inner surface o the container bottom will have a negligible ;ntensity at this surface, and hence the term r and the factor D(z) may~be~taken as:
r = e 2pd,~ and ~ D (Z ) I :2 = 2e 2 ~ ~COSh2~ ( Z -~d) +~cos2~z - d)] (le) (electr;cally conductive bottom) ~ When the depth d is an integral mul~t;ple R of the vertical ",............ ~

~ 3 ~

interval Qm given by equation tlc), equations ~ld) and (le) become, respectively:
¦ D (Z)I 2 = 2e ~CQm-[cosh2~(z - 1/2R ~ + t-1)X.cos2~]~
and S ¦D(Z)I Z = 2e2 ~ m [cosh2~(z - RQm) + cos2~z]

For odd-integral values of K, the sign of the periodic part of these equations changes sign depending on whether the container bottom 12 is microwave-transparent or electrically conducting. A relative minimum of power absorption in the vertical axis oE a container having a microwave-transparent bottom will correspond to a relative maximum for a container with an elec~rically conducting bottom, and vice versa~
Hence, the term r may be considered notionally as resulting in a phase shift in the location of maxima and Ininima of power absorFtion in the vertical axis, this phase shift being determined by the composition of the container bottom, that is, in whether it is electrically conducting, ~` microwave-transparent, or even semi-microwave-transparènt.
In the case of a container with a re~lecti~ve side wa~l, to achieve substantial coincidence between a fundamental minimum 26a and a hi~her order maximum 25a at the same value of d, i~e. d'~, it would be necessary to satisfy the equation `: :
d = X ~ _ (2K +-1)Qm 25~ or in the more gener-al case d = RQm :a (2K~ +: 1) Ql ~ (3A) Figures~16 and 17 assume that~K is taken as 2, and Rl as 1, although these values can~be chosen to best fit the values of~Qm and Qm~ available for the selected ~fundamental and hi~her order modes.

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Comparing equations (2A) and ~3A) tnere will be seen to be a generic equation covering both situations, namely d = ~ + AQl = (2B2+-l) Q2 _ (4) where ~ is the height of the step (zero in a flat bottom container), A and B are positive integers, ~l is the spacing between minima (a~d between maxima) of one of (i) the fundamental mode selected, and (ii) the higher order mode selected, and is the spacing between minima (and between maxima) of the other of such selected modes.
When the side wall is at least partial microwave-transparent, Qlis ~m' (higher order mode spacing) and Q2 is Qm (fundamental mode spacing) t while, when the side - wall is reflective, Ql is Qm and Q2 is Qm'7 While the step 33 has been shown in Figure 14 as projecting into ~he container lll r which for manufacturing p~rp~ses will normally be the more convenient arrangement as explained;in the Canadian patent No. 1,279,90~ cited above,~such step can achieve a similar higher order mode generating effect when pro]ecting out of the container, or both into and out of the container simultaneously. It follows that, in addition to being zero (fIat bottomed ~ container), the value of ~ can be either positive or negative,~both to accommodate either such alternative direction of projection~of the step (or steps) 33, an~d to locate~ a;positive~value of ~ on the appropriate side of equation~;~4),~ i.e. to~render equation (4) more clearly a generalised version of equations (~A) and (3A).
The descrip~ion so~far has assumed a container with a vertical si~e~wall. In practice, the side wall will often have sQme u-ward and outward slope, whlch will mean that : ~ ..
, " ~
".~
: ~ :
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v ~3~ rJll the diameter of the top surface of the load will be greater than that of its bottom surace. The foregoing calculations will nevertheless be sufficiently accurate in practice to provide a significant improver.lent in heating uniformity, even though equation ~4) may not always be fully satisfied at all levels in the load.
In fact, equation (4) represents an ideal situation for which i~ i5 not always necessary in practice to aim fully.
Equation (4) represents the situation in which the selected higher order mode is theoretically at maximum power while the selected fundamental mode is theoretically at minimum power. It is important to realise that the former criterion is more impsrtant than the latter criterion. In other words, provided the hi~her order mode power is at or near its maximum, ensuring that the undamental mode power is at or near its minimum is less critical. While keeping the fundamental mode power at a minimum theoretically affords an optimum value of the ratio of the intensity of the higher order mode relative to the intensity of the fundamental mode r there are circumstances in which a less ~; than optimum such value can be tolerated. ~ence coincidence of the minima 26 and 26a on the depth related curves ~; (Figures 9 and 16~ for the fundamental mode with the maxima 25' and 25a on the corresponding curves (Figures 10 and 17) for the chosen higher order mode, i.e. full satisfaction of equation (4), is not an essential feature of the present invention in its broadest scope. What is essential is that the depth d be so chosen that the higher order mode power is at or near one of its maxima 25' or 25a.
Essentially the same practical considerations as for a circular container also apply to the elliptical container llb~(Figure 18) which exhibits similar modes. Indeed, since a circle is merely a special form of an eIlipse, i.e.
with zero eccentricity; the term "elliptical" will be used in thls speciflcation and the claims that follow to include ::

1 3 ~

a circle. If an elliptical container with a positive eccentricity has a sloping side wall, the construction should ideally be such that the smaller ellipse defined by the bottom surface of the load should be confocal or conformal with the larger ellipse defined by the top surface of the load. Also, if structures such as those shown in Figures 11, 14 and 15 are used to generate a higher order mode in an elliptical container with a positive eccentricity, the foil portion (5) e~g. 31a, or stepts) of these structures should hav0 inner and outer edges that are pre~erably confocal or at least conformal with the load surface(s).
If the container is rectangular so that rectangular modes are involved, the calculations for the values of Qm and Qm' are different ~rom those given above.
Specifically, for fundamental modes in a square container the value for k is ~2 = ~ (m2 ~ n2 ~ ' '` ~ ., where L is the length of each sideO and the terms m and n originate as separation constants in the x and y coordinates and determine the order of the mode (taken as ~m, nl).
If L is taken as equal to 11 cm, the following values of Qm apply:
[0, 1] Qm = 0.7882 cm [1, 0] Qm = 0.7882 cm 11, 11 Qm = 0.7902 cm ~; For higher order modes, the following values for Qm' ~apply:
[2, 0] Qm~ = 0.7943 cm - Eo, 2] Qm' = 0.7943 cm - [2, 1] Qm' = 0~7963 cm [1, 2] Qm~ = 0.7963 cm ~ [2, 2] Qm~ = 0.8026 cm .,:;i~' ~ .
, . .
[3, 0] Qm' = 0.8047 cm [0~ 3~ Qm' = 0.8047 cm [3, 3] Qm' = 0.8246 cm In a rectangular container, if a structure such as shown in Figure l0A or l0B of the Canadian patent cited above is employed to generate the higher order ~ode, the structure of Figure l0B of such prior patent (foil islands in an area of microwave-transparent material) would gener-ate modes [0, 3], [3, 0] and ~3, 31, while the structu~e of Figure l0A of such prior patent (apertures in a sheet of foil) would generate the [3, 3] mode. Figure l9 shows an example of foil islands 31b in microwave-transparent material 30b forming the lid of the generally rectangular container llc.
The above considerations, including equation (4), will be appllcable to a rectangular container, provided that the value for k is given by ~ .
k2 = ~2 ~(m/LX)2 + (n/~y)21 (6) where Lx and Ly define the rectangular dimensions.
20 ~ ~ ~ As will be~clear from the foregoing aescription, the present invention can employ any structure by which at least one higher order mode is generated (or enhanced).
In the~claims that foll:ow the;term "generated" is intended to~include the~enhancing of existing modes. While the ~; 25 foregoing description has~assumed~that the higher order mode gènerating means will~be embodied in the container [lid, bottom or both), i~t is possible to~use an unmodified~container with separate~higher order mode generating means,~such as described`in the Canadian patent 30~ ; ~ and various Canadlan patent applications cited above.
An importan~t use of the present invention is believed to reside in~the manufacture of produc~s that consist of disposable containers containing food, usually in the Erozen~stateO However, the advantages of the invention can also be taken advantage of in the manuacture o~ reusable ' :,....

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cookware vessels. Such a vessel would be accompanied by instructions to the user regarding the optimum depth to which it should be filled to achieve the most uniform heating. Such instructions may take the form of a separate chart (different depths for different foods) or of one or more marks inscribed on the wall structure o~ the vessel and indicating optimum fill depths.
It will be understood that the various references to "vertical", "upper", "lower", "depth" and other words suggesting a particular orientation of the product are used for convenience only and that the interactions of the container and its load with the microwave energy are not specific to any particular inclination or orientation.

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Claims (24)

1. A product comprising a container and a load located therein or thereon for heating by microwave energy, said product being for use with means for generating at least one mode of said energy of an order higher than a fundamental mode determined by boundary conditions defined by lateral dimensions of at least one of said container and said load, wherein the depth of the load in the container is such that, upon irradiation of the product with microwave energy, the power absorbed by the load from said higher order mode is at or near a maximum value relative to the fundamental mode.

2. A product according to claim 1, wherein said container embodies said means for generating at least one higher order mode.

3. A product according to claim 2, wherein said depth is such that the power absorbed by the load from said fundamental mode is less than the power absorbed by the load from said higher order mode.

4. A product according to claim 3, wherein said depth is such that the power absorbed by the load from said fundamental mode is at or near a minimum value.

5. A product according to claim 4, wherein the load is a food load consisting mainly of water, the container is elliptical (including circular), the fundamental mode is the [0, 1] mode, and the higher order mode is the [1, 4] mode.

6. A product according to claim 5, wherein said depth is in the range of approximately 1.9 to 2.2 cm.

7. A product according to claim 6, wherein said depth is in the range of approximately 2.0 to 2.1 cm.

8. A product according to claim 4, wherein the load is a food load consisting mainly of water, the container is elliptical (including circular) and has a substantially centrally located step in a bottom surface thereof, the fundamental mode is the [1, 1] mode, the higher order mode is the [1, 2] mode, the depth of the load in the portion of the container not over said step is approximately 2 cm and the height of the step is approximately 0.3 cm.

9. A product according to claim 8, wherein said step constitutes at least part of said means for generating the higher order mode.

10. A product according to claim 4, wherein the load is a food load consisting mainly of water, the container is generally rectangular, the fundamental mode is the [1, 1] mode and the higher order modes is selected from.
the modes [0, 3], [3, 0] and [3, 3].

11. A product according to claim 4, wherein said depth (d) is substantially uniform throughout the lateral dimensions of the load and is given by d = A?1 = wherein A and B are positive integers, ?1 is the spacing between minima (and between maxima) of one of (i) the fundamental mode selected, and (ii) the higher order mode selected, and ?2 is the spacing between minima (and between maxima) of the other of such selected modes.

12. A product according to claim 11, wherein the container has a side wall structure that is at least partially microwave-transparent, and wherein said depth (d) is given by d = = wherein K and K' are positive integers, ?m is the spacing between power minima of the fundamental mode, and ?? is the spacing between power maxima of the higher order mode.

13. A product according to claim 11, wherein the container has a side wall structure that is microwave-reflective, and said depth (d) is given by d = K?m = wherein K and K' are positive integers, ?m is the spacing between power minima of the fundamental mode, and ?m' is the spacing between power maxima of the higher order mode.

14. A product according to claim 4, wherein the container has a substantially centrally located step of height .delta. in a bottom surface thereof, the upper surface of the load being substantially uniform throughout the container, whereby the depth (d) of the load in the portion of the container not over said step is modified by the height .delta. over said step, said depth being given by d = .alpha. + A?1 = wherein A and B are positive integers, ?1 is the spacing between minima (and between maxima) of one of (i) the fundamental mode selected, and (ii) the higher order mode selected, and ?2 is the spacing between minima (and between maxima) of the other of such selected modes.

15. A product according to claim 14, wherein the container has a side wall structure that is at least partially microwave-transparent side wall, said depth (d) being given by d = = wherein K and K' are positive integers, ?m is the spacing between power minima of the fundamental mode, and ?m' is the spacing between power maxima of the higher order mode.

16. A product according to claim 14, wherein the container has a side wall structure that is microwave reflective, said depth (d) being given by d = K?m = wherein K and K' are positive integers, ?m is the spacing between power minima of the fundamental mode, and ?m' is the spacing between power maxima of the higher order mode.

17. A product according to claim 16 wherein said step constitutes at least part of said means for generating at least one higher order mode.

18. An assembly comprising a) a container for mounting a load in a microwave oven, for use with means for generating at least one mode of microwave energy of an order higher than a fundamental mode determined by boundary conditions defined by lateral dimensions of at least one of said container and said load, and (b) means for indicating a depth of the load in the container such that the power absorbed by the load from said higher order mode will be at or near a maximum value relative to the fundamental mode.

19. An assembly according to claim 18, wherein said indicating means comprises a mark inscribed on the container.

20. An assembly according to claim 18, wherein said indicating means comprise a chart for use with the container.

21. An assembly according to claim 18, wherein said container includes means for generating said higher order mode.

22. In a method of heating a load in a container by microwave energy, lateral dimensions of at least one of said container and said load defining boundary conditions that determine a fundamental mode of said energy, the steps of (a) generating at least one mode of said energy of an order higher than said fundamental mode, and (b) so controlling the depth of said load that the power absorbed by the load from said higher order mode is at or near a maximum value relative to the fundamental mode.

23. A method according to claim 22, wherein said depth is such that the power absorbed by the load from said fundamental mode is less than the power absorbed by the load from said higher order mode.

24. A method according to claim 22, wherein said depth is such that the power absorbed by the load from said fundamental mode is at or near a minimum.