This invention relates to electrical sheet heaters, and more particularly, to sheet heaters that include irregular heating areas and processes for making the same.

Background of Invention U. S. Patents Nos. 4,485,297, 4,633,068, 4,626,664, and 4,892,998 disclose flexible electrical sheet heaters which include a semi-conductive pattern of semi- conductive material printed on an insulating substrate. The heaters disclosed in U.S. Patents no. 4,485,297 and 4,892,998 provide uniform heat distribution over what are essentially rectangular heating areas; those disclosed in U.S. Patents no. 4,626,664 and 4,633,068 provide one level of heat (i.e., watt density) in one area, and a different heating level (i.e., watt density) in one or more other areas. As will be apparent, a relatively complicated semi-conductive pattern is required to provide different heating levels (particularly over areas that are irregular in shape) in a single heater. The difficulty of determining the required semi-conductive pattern also has limited the extent to which heaters of irregular configuration, or having an irregularly-shaped heating area, have been available.

Summary of Invention The present invention makes it possible to produce, simply and practically, electrical sheet heaters in which the heating areas have essentially any desired configuration, and which may contain a number of heating areas each of which has a different specific desired watt density.

In its first aspect, the invention provides a greatly simplified procedure for establishing the necessary conductive, typically semi-conductive, pattern. A second aspect is directed to heaters in which areas of either the same or different desired watt density are distributed over either regular or irregular areas.

Description of Drawings The drawings are plan views of electrical sheet heaters having heat-producing semi-conductor patterns made in accord with the present invention.

Description of Embodiments Figure 1 shows a portion of an electrical heater 10 including a semi-conductor pattern generally designated 20 carried on the top surface of an organic plastic insulating sheet 30. As discussed in the aforementioned U. S. Patents, the semi-conductor pattern typically is a conductive graphite ink silk-screen printed on the insulating substrate 30, and extends between and is elec¬ trically connected to pairs of spaced-apart printed silver bus-bars or electrodes 40, 42. The overall heating area of the heater 10 of Figure 1 includes three longitudinally extending, undulating areas, designated 12, 14 and 16, having respectively, watt densities of 10, 20 and 15 watts per square foot. Electrodes 40, 42 are connected across a 120 voltage power source, designated 50.

As shown in the aforementioned patents, the semi¬ conductor patterns of heaters of the type involved in the practice of the present invention comprise discrete, spaced-apart stripes of semi-conductive ink. The resistance per unit length of such stripes depends on the type of ink used, and the width and thickness of the stripe. For ease of manufacture, it is usually desirable

to print all the stripes at the same thickness using the same ink, and to vary the resistance by varying the width of the stripes.

The following description illustrates the manner in which the particular semi-conductor pattern (e.g., thickness, width, and spacing of stripes) used in heater 10 is established. The description is intended to be illustrative of the present invention, and the parameters chosen for the purposes of the description are not those of an actual product.

The first step in the procedure is to determine the size, shape and desired watt density of the area(s) to be heated. In the Figure 1 example, both the overall heating area (i.e., the area between the bus bars 40, 42), and the three heating areas of different watt densities are of continuously varying width. The overall heated area is about 22 inches wide at its widest point and 20 inches in minimum width? and areas 12, 14, and 16 vary, respectively, from 7-10, 4-8, and 5-8 inches in width.

The next step is to determine the lay-out of the semiconductor pattern. This is accomplished by dividing the entire heating area into sub-areas. In the illustrated example, the overall heater area is divided, from top to bottom, into a number of rectangular sub- areas, each of which extends across the full width of the heater. As will be recognized, the vertical height of each sub-area is somewhat arbitrary and, to some extent, may be determined by trial and error. The goal is an arrangement in which the individual sub-areas are sufficiently narrow so that the all of the sub-areas, taken together, approximate the shape of the overall heating area.

In the heater of Figure 1, the various sub-areas vary in width from 0.250 in. (sub-area A) to 0.375 in. (sub-area B). As shown, sub-area A extends across the heater at its narrowest point, and is 20 inches long

between conductors 40, 42; and sub-area B extends across at the point of greatest width, and is 22 inches long between conductors. The other sub-areas comprising the illustrated portion of the heater are shown in partial phantom.

It will be noted that, like the overall heating area, each of sub-areas A and B includes three blocks of different length and watt density. For example, the block of sub-area A within heater area 12, designated A- 12, is 7 inches long and has a watt density of 10 watts per square foot; the block A-14 within heater area 14 is 8 inches long and has a watt density of 20 watts per square foot; and the block A-16 within heater area 16 is 5 inches long and has a watt density of 15 watts per square foot. Similarly, blocks B-12, B-14 and B-16 of sub-area B are, respectively, 10, 4 and 8 inches long and have respective watt densities of 10, 20 and 15 watts per square foot.

The next step is to determine first, the number of watts in each block of each sub-area, and, then, (i) the total watts, (ii) the total required resistance (ohms) per watt, and (iii) the total resistance in each rectangular sub-area. The number of watts in each block, and the total watts, ohms per watt and total resistance in each sub-area, may be calculated using the following formulae:

(1) watts in block = (block watt density) x (block area)

(2) total sub-area watts = sum of watts in blocks of sub-area

(3) total sub-area ohms/watt = voltage- watts ²

(4) total sub-area resistance = total ohms _x total watts watt

Since the sub-areas are all connected in parallel across power source 50, the voltage drop across each sub-area is the same, i.e., 120 volts.

The area and number of watts in each block of sub- areas A and B, and the total area, total watts, total number of watts, ohms/watt and total resistance in each of sub-areas A and B are set forth in Tables 1 and 2 below:

It is important to note that the ohms per watt is the same throughout each respective sub-area, e.g., the ohms per watt in each of blocks B-12, B-14 and B-16 of sub- area A is 23593.

The resistance per inch of a "stripe" of conductive ink depends on the particular ink, and on the thickness and width of the "stripe." Typically, the entire semi¬ conductor pattern of heater is printed in a single pass, so that the pattern is formed with a single ink printed

at a single, and substantially constant, thickness. The controlled variables are the conductivity of the ink, the thickness at which a stripe is printed, and the stripe width. The conductive stripes are typically printed at a constant thickness of about 0.0005 in. When printed at such a thickness, the range of resistivity (ohms per square) obtainable from commercially available inks ranges from about 0.025 to 20,000, but more usually is in the range of about 0.25 to 1000 ohms per square. The lower resistivities are usually obtained from silver inks; resistivities above about 40 ohms per square are obtained using carbon inks.

The choice of the particular ink is to some extent a matter of trial and error, based on experience. The general procedure followed is to select a particular trial resistivity (e.g., 100 ohms per square), and use this selected value to calculate a trial number of squares and bar width in each block of each sub-area, using the following formulae:

(5) No. of squares = Ohms in block

Ink resistivity (ohms/square)

(6) Bar width = Block length

No. of squares

If, throughout the entire heater, the trial ink resistivity results in bars having the desired width (e.g., each bar in each block is more than about 1/16 inch and not over about 1 inch wide, and the width of each sub-area in a single bar is located not more than about two inches but also is at least 1/16 inch greater than the widest bar in the particular sub-area), the trial calculations can be used to lay-out the semi¬ conductor pattern. If it does not, the procedure is repeated using different ink resistivities, or if necessary changing also such things as the sub-area width or total sub-area length (in a manner discussed with

reference to the embodiment of Figure 3 discussed hereinafter), until a satisfactory arrangement is obtained.

In the heater of Figure 1, the resistivity of ink eventually used was 162 ohms/square, and the resulting number of squares and bar width in each of the blocks of sub-areas A and B are as follows:

It will be noted that each bar is more than 0.0625 in. wide, and that in each of sub-areas A and B the overall sub-area width, 0.375 and 0.250, respectively, is more than 0.625 in. wider than the widest bar in the sub-area. It should also be noted that the number of watts per square is the same in all the blocks of any particular sub-area; e.g. , there are about .00318 watts per square in each of blocks A-12, A-14 and A-16, and about .00686 watts per square in each of the three blocks of sub-area B.

Figure 2 illustrates a modified heater, designated 100, of the type intended for use as a thermal target, and includes a 5 square foot circle 102 (watt density 17 watts/ft ² ) in the center of a 5 ft. by 5 ft. square (watt density 3 watts/ft ² ). It will be noted that the total wattage of the target is 145 watts (85 watts in the circle 102 and 60 watts in the area surrounding the cir¬ cle). The entire conductive pattern 110 extends between a single pair of parallel copper electrodes 140 that

extend along the opposite sides of the square, and the electrodes are connected to a 100 volt power source, designated 150.

The semi-conductor pattern in the "hotter" area inside circle 102, and in the "cooler" area in the rest of the square, is designed by dividing the entire heater (both "hotter" and "cooler" areas) into a number of generally rectangular sub-areas each of which extends transversely the full width of the heater between electrodes 140. Some of the resulting sub-areas include portions of different desired watt densities; i.e., some sub-areas include both part of the "hotter" circle 102 and parts of the "cooler" area outside the circle) . These sub-areas are in turn sub-divided into blocks of which includes an area having only a single watt density.

Thus, and as shown in Figure 2, the portion of heater 100 including circle 102 is divided into five rectangular sub-areas 120, 122, 124, 126, 128, each of which is approximately 6 inches (0.5 feet) wide and extends the full width of the heater. Rectangular sub- area 160, centered on the diameter of the circle, in¬ cludes a 2.5 foot long block 120a within circle 102, and a 1.25 foot long block 120b, 120c on either side of the circle. Rectangular sub-areas 122, 124, respectively above and below area 120, each include an about 2.1 foot long block, designated 122a, 124a, respectively, within circle 102, and outside of the circle a pair of 1.45 foot blocks 122b, 122c, 124b, 124c outside the circle. In rectangular sub-areas 126, 128, the length of the blocks within the circle is about 1.5 feet, and that of the blocks outside the circle is about 1.75 feet. Above and below the circle 102, rectangular blocks 130, 132, each five feet long and 1.25 feet high, extend the full with of the heater 100.

As discussed with reference to heater 10 of Figure 1, the next step is to determine (a) the total watt output in each rectangular sub-area; and (b) the amount of resistance (ohms) required per watt in the sub-area. For example, the area within each of blocks 120b and 120c produces about 1.875 watts (0.625 sq.ft. at 3 watts/ sq.ft.), and the area of block 120a produces about 21.25 watts (1.25 sq.ft at 17 watts/sq.ft) ; the total wattage of sub-area 120 is thus 22.3 watts. Since the voltage drop across the entire sub-area 120 (and also across each of the other sub-areas) is 100 volts, the required number of ohms/watt in sub-area 120 is about 16. Note that the ohms/watt is constant in a portion or sub-area, regardless of variations in watt density in different blocks of the sub-area.

In tabular form, the various wattages and required ohms/watt in the various blocks and sub-areas of heater 100 are as follows:

Once the required ohms per watt for each block and sub-area is determined, the conductive ink (which is usually printed at a thickness of 0.0005 in.) is chosen to establish the specific resistance (ohms/square) of each semi-conductor stripe. The total required width of the "stripe" in each block of each sub-area is then determined, in the manner as previously discussed. In tabular form, the total resistance, resistance per inch and total required stripe width in each block are as fol¬ lows:

T A B L E 5

The total stripe width assumes that the conductive ink, printed at a thickness of 0.0005", has a specific resistance of 11.5 ohms/square.

Neither the distance between adjacent stripes in a block or sub-area, nor the width of each stripe itself, should be too great. In each sub-area of the heater 100 of Figure 2, the total required stripe width is in some cases longer than desired, so it is divided to provide a number of narrower stripes, which will actually be printed on the substrate. The widths of the narrower stripes in each block of the different sub-areas are as follows:

T A B L E 6

Normally, and as shown in Figure 2A, the portion of each stripe in a higher watt density "a" block is narrower than the portion of the stripe in the lower watt density "b" or "c" blocks of the same sub-area. Moreover, in each block, the sum of the widths of the narrower stripes is equal to the desired total stripe width in the block. All of the narrower stripes in the sub-area extend the full width of the sub-area, and at the opposite ends of each sub-area are connected in parallel to electrode/bus bars 140, 142.

The final number of stripes in each block is based principally on the widths of the narrower stripes and associated heating area. In the final heater, it is desirable that each stripe not be more than about one inch or less than about 1/16 inch wide, and it also is desirable that the elongated heating area associated with each stripe be at least 1/16 inch wider than the stripe within it but not more than about two inches wide overall. In heater 100, each of sub-areas 120, 128 is divided into one inch wide strips each containing a "narrower" stripe, and the 30 stripes in each of sub- areas 130, 132 are placed on 1 inch centers. For clarity, the drawing shows fewer stripes in each sub- area.

Reference is now made to Figure 3 which illustrates a third heater, generally designated 200, embodying the present invention. Heater 200 is designed for use in a refrigerator to prevent freezing and/or water condensation on, and in various areas around, an automatic ice-dispenser. As will be seen, the outer periphery of the heater 200 is quite irregular, and the area within the heater periphery includes one circular opening 202 and three generally rectangular openings 204, 206 and 208. The heater 200 is connected to a 117.5 volt source of power (not shown) by a female connector 210 which is in turn connected by wires 212 to the conduc-

tors, generally designated 214 (shown as a dark solid line) and 216 (shown as a dark dashed line) on the heater substrate 218.

The total heat output of heater 200 is 7 watts. The portion of the heater (including areas Gl, HI and II has a total output of 1 watt; the portion including areas C, C2, Dl and D2 has a total output of 2 watts, the portion including areas Bl, B2, El and E2 has a total output of 2 watts, and the remaining portion including areas Fl, F2, G2, H2, 12, 13, Al and A2) has a 2 watt output.

The semi-conductor pattern carried on the heater substrate to provide the desired different watt outputs in the various different areas is also irregular. As shown, it includes nine heating sub-areas, designated A through I, each of which extends between electrodes 214 and 216. For convenience, the portion of each electrode connected to a particular heating sub-area is designated by the number of the electrode and, as a suffix, the heating sub-area designation. Thus, for example, heating sub-area C is connected between electrodes 214-C and 216- C. It will be noted that four of the heating sub-areas, i.e., sub-areas A and F-H each include two "blocks" connected in series; and that heating sub-area I includes three serially connected blocks. In each of heating sub- areas A and F, the two blocks are connected by intermedi¬ ate electrodes 218-A and 218-F (both shown as dark short dashed lines), respectively; in each of heating sub-areas G-H, the "stripes" in the two blocks of the sub-area are continuous and connect directly to each other; in heating sub-area I, blocks Ij. and I2 are contiguous, and blocks 12 and I3 are connected by an intermediate electrode 218- I.

Each of conductors 214 and 216 comprises a relatively conductive "bar" (typically printed on the substrate using a conductive silver ink) extending in a generally serpentine path from the point at which it is connected to one of wires 212 to one end of each of

heating sub-areas A-I. Printed semi-conductor "barlets" (designated 215A-I and 217A-I) at the opposite ends of each heating sub-area connect the "stripes" of the respective heating sub-areas in parallel. Silver conductor bar 214 is printed over barlets 215; conductor bar 216 is printed over barlets 217.

Semi-conductor barlets 219 also are provided at the adjacent ends of "blocks" Ai and A2 of heating sub-area A, Fi and F2 of heating sub-area F, and I2 and I3 of heating sub-area I. In each instance, a barlet connects the adjacent ends of the stripes in a respective heating sub-area block in parallel, and the pair of barlets in each heating sub-area are in turn electrically connected by a printed conductive silver conductor 218 which extends between and overlies the respective barlets. As discussed in aforementioned U.S. 4,485,297, barlets 215, 217 and 219 provide extra interface area and thus help eliminate potential "hot spots."

The procedure used to design the semi-conductor portion of the heater of Figure 3 is generally the same as that discussed earlier, but with some modifications.

The 2 watts total output required in areas C and D was divided, somewhat arbitrarily, equally between the two areas; and each of the two stripes in each area was designed to produce 0.5 watts output. As noted in Table 9 below, the two stripes in the two blocks of sub-area area C are generally semi-circular and of equal length. In sub-area D, the stripe in block D2 is straight; that in block Dl is slightly longer, and is bowed to provide more even heat throughout areas C and D.

In a similar manner, each of the four stripes in areas B and E was designed to produce a 0.5 watt output, thereby providing the desired 2 watts total output. In each of areas B and E, one of the stripes is straight; the other is slightly longer and includes a slight jog at the end joining conductor 214-B/E.

In designing the remaining portions of the heater, the general location of the silver bus bars 214, 216 was first determined (it will be noted that, generally, one bus bar extends down one side of the remaining area and the other down the other side) ; and the watt densities of the to-be-heated areas then calculated. In making the watt density calculations, it was assumed that all the total watts required would be produced from the area (i) between bus bars and (ii) omitting openings 206 and 208. Additionally, the rectangular sub-areas in the to-be- heated area were tentatively laid-out as half-inch wide areas extending between bus-bars.

As shown, the portions of the heater including areas G and H (blocks Gl, G2, HI and H2), include eight elongated rectangular sub-areas, each one-half inch wide and in each of which a single stripe is centered. In each of these half-inch sub-areas, the required width of the portion of each stripe in each block was determined in the manner previously discussed. The watt density and total watts in each block of the sub-area, and the total watts, total ohms, and ohms per watt of the sub-area as a whole, were calculated; and the number of squares and bar width in each block were then determined.

The portions of the heater including areas A and F each include five one-half wide elongated rectangular sub-areas. The initial design attempt provided five stripes, connected in parallel between the input and output bus bars, in each of these two areas. However, when the trial calculations were made it became apparent that the stripes would be narrower than desirable. Accordingly, the lay-out was changed to divide each of areas A and F into two serially-connected blocks (e.g., Al and A2, and Fl and F2, and eventually to provide three stripes in one block (e.g., those in, respectively, blocks A2 and F2) connected in series (e.g., by

electrodes 218-A and 218-F) with a set of two stripes in the other (e.g., those in, respectively, blocks Al and Fl) .

The desired width of the individual stripes in blocks Al and A2 was calculated by (i) determining the necessary widths of a "test" single stripe in block Al connected in series with a "test" single stripe in block A2, and (ii) dividing the width of the "test" single stripe in block Al in half and that in block A2 in thirds to obtain the widths of the stripes eventually printed. For example, the "test" single stripes in blocks Al and A2 were 0.840 in. and 0.539 in. wide, respectively; the widths of each of the printed stripes in the two blocks are, respectively, 0.420 in. and 0.180 in.

It will be noted the total ohms of, and ohms per watt throughout, the serially connected "test" single stripes in blocks Al and A2 are, respectively, 20545 ohms and 30573 ohms per watt; and that the total watts produced in block Al is 1.5 times that of the watts produced in block A2.

The widths of the stripes in blocks Fl and F2 were calculated in the same manner. The total watts produced by the "test" single stripe in block Fl is 1.5 times that of the watts produced by the "test" single stripe in block F2; the total ohms of and ohms per watt throughout the serially connected "test" single stripes in block Fl and F2 are, respectively, 26398 ohms and 50475 ohms per watt. The respective total widths of the "test" single stripes in blocks Fl and F2 are 0.637 and 0.427 in.; those of the narrower stripes actually printed are 0.318 in. and 0.142 in.

In each of blocks II and 12, there are four rectangular sub-areas laid out on half-inch centers. However, in block 13, a better arrangement was to provide three such sub-areas even though the total area to be heated was about 2 in. high. Accordingly, the layout in blocks II, 12 and 13 was calculated by determining the

widths of serially connected portions of a "test" single stripe required to produce the desired watt densities in the three areas - i.e., the "test" stripe portions widths in blocks II, 12 were divided into four narrower, serially connected stripe portions, and the test stripe portions width was divided into three narrower stripes in block 13. The total ohms of and ohms per watt throughout the serially connected "test" single stripe portions in blocks II, 12 and 13 are, respectively, 21273 ohms and 32778 ohms per watt; and the respective total widths of the "test" single stripe portions in blocks II, 12 and 13 are 0.327, 0.456 and 0.625 inches. Each partial stripe portion in blocks II, 12 and 13 has the width specified in Table 9.

In all of the heating sub-areas, the "stripes" were silk screen printed at a nominal thickness of .0005 in. and have a resistance of 990 ohms per square. The total watts, total ohms, and ohms/watt in each of the sub-areas is shown in Table 8. Table 9 sets forth the length, width, number of watts, ohms and squares of each stripe or stripe portion in each block of the various sub-areas. It should be noted that not all of the stripes are straight lines; the two stripes in sub-area C (one in block Cl and the other in block C2) are semi-circular (and together form a circle around opening 200); the stripe in block D2 is bowed to provide more even overall heating, and thus is slightly longer than that in block D2; and there is a slight "jog" in the stripes in blocks Bl and E2 of sub-areas B and E make them slightly longer than the stripes in blocks B2 and El. If desired (e.g., to provide more even heat in an area), the shapes of the various conductive stripes in the blocks of a sub-area can be even more irregular or radical.

T A B L E

Other embodiments will be within the scope of the following claims.

What is claimed is: