Toward an Engineering Method for Calculating Smoothing Chokes
Abstract Generated abstract
This paper addresses the practical calculation of smoothing chokes for a specified voltage drop when standardized magnetic cores are used. It outlines an engineering approach based on selecting a core size from the coefficient defined by core cross section, window area, and mean turn length, then using tabulated geometric parameters to determine winding and technical-economic characteristics. The main contribution is a set of computer-calculated reference tables for standardized ShL, PL, and OL cores, including dimensions, magnetic path and turn lengths, window and core areas, selection coefficients, and related products useful for estimating weight, volume, active material use, and cost.
Full Text
Toward an Engineering Methodology for Calculating Smoothing Chokes
A. K. Mayer
(Presented by the scientific-technical seminar of the Department of Instruments and Devices of Automatic-Control Systems)
When calculating smoothing chokes for a specified voltage drop and using standardized cores, the choice of size is made according to the calculated value of the coefficient
\[ N=\frac{Q_c^2\cdot Q_0}{l_0}. \]
When counting the number of turns, the values of the window area \(Q_0\) and the mean turn length \(l_0\) for the selected size of magnetic core are used.
Table 1
| Size | \(x\) | \(y\) | \(z\) | \(l_0\cdot 1^{-3}\times 10^{-3}\), m | \(l_c \times 10^{-3}\), m | \(Q_0\times 10^{-4}\), m² | \(Q_c\times 10^{-4}\), m² | \(\dfrac{Q_c^2\cdot Q_0}{l_0}\times 10^{-10}\), m⁵ | \(Q_c\cdot Q_0\cdot 10^{-8}\), m⁴ |
|---|---|---|---|---|---|---|---|---|---|
| ShL 6×6.5 | 1.08 | 1.0 | 2.5 | 43.8 | 51 | 0.9 | 0.38 | 0.0297 | 0.34 |
| 8 | 1.38 | 46.8 | 0.48 | 0.0443 | 0.43 | ||||
| 10 | 1.67 | 50.9 | 0.6 | 0.0636 | 0.54 | ||||
| 12.5 | 2.08 | 55.8 | 0.75 | 0.0907 | 0.68 | ||||
| ShL 8×8 | 1 | 1.0 | 2.5 | 57.1 | 68 | 1.6 | 0.64 | 0.1145 | 1.02 |
| 10 | 1.25 | 61.1 | 0.80 | 0.1675 | 1.28 | ||||
| 12.5 | 1.56 | 66.1 | 1.0 | 0.242 | 1.6 | ||||
| 16 | 2.0 | 73.2 | 1.28 | 0.358 | 2.04 | ||||
| ShL 10×10 | 1 | 1.0 | 2.5 | 71.4 | 85 | 2.5 | 1.0 | 0.35 | 2.5 |
| 12.5 | 1.25 | 76.4 | 1.25 | 0.511 | 3.12 | ||||
| 16 | 1.6 | 83.4 | 1.6 | 0.741 | 4.0 | ||||
| 20 | 2.0 | 91.4 | 2.0 | 1.06 | 5.0 | ||||
| ShL 12×12.5 | 1.04 | 1.0 | 2.5 | 86.6 | 102 | 3.6 | 1.5 | 0.909 | 5.4 |
| 16 | 1.33 | 93.5 | 1.9 | 1.38 | 6.9 | ||||
| 20 | 1.67 | 101.8 | 2.4 | 2.04 | 8.7 | ||||
| 25 | 2.08 | 111.5 | 3.0 | 2.83 | 10.8 | ||||
| ShL 16×16 | 1.0 | 1.0 | 2.5 | 114.3 | 136 | 6.4 | 2.6 | 3.62 | 16.6 |
| 20 | 1.25 | 122.2 | 3.2 | 5.22 | 20.5 | ||||
| 25 | 1.56 | 132.1 | 4.0 | 7.52 | 25.6 | ||||
| 32 | 2.0 | 146.2 | 5.1 | 11.11 | 32.6 | ||||
| ShL 20×20 | 1 | 1.0 | 2.5 | 142.8 | 171 | 10 | 4.0 | 10.9 | 40 |
| 25 | 1.25 | 152.5 | 5.0 | 16.2 | 50 | ||||
| 32 | 1.6 | 166.8 | 6.4 | 23.85 | 64 | ||||
| 40 | 2.0 | 182.3 | 8.0 | 34.6 | 80 | ||||
| ShL 25×25 | 1 | 1.0 | 2.5 | 178.3 | 213 | 15.6 | 6.25 | 33.6 | 98 |
| 32 | 1.28 | 192.5 | 8.0 | 51.2 | 125 | ||||
| 40 | 1.6 | 208 | 10.0 | 73.5 | 156 | ||||
| 50 | 2.0 | 228.1 | 12.5 | 104.5 | 195 |
Continuation of Table 1
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| ShL 32×32 | 1 | 1,0 | 2,5 | 228 | 273 | 25,6 | 10,2 | 115,9 | 261 |
| ShL 32×40 | 1,25 | 1,0 | 2,5 | 244 | 273 | 25,6 | 12,8 | 126 | 328 |
| ShL 32×50 | 1,56 | 1,0 | 2,5 | 264 | 273 | 25,6 | 16,0 | 246 | 410 |
| ShL 32×64 | 2,0 | 1,0 | 2,5 | 292,1 | 273 | 25,6 | 20,4 | 360 | 523 |
| ShL 40×40 | 1 | 1,0 | 2,5 | 283,5 | 342 | 40,0 | 16,0 | 358 | 640 |
| ShL 40×50 | 1,25 | 1,0 | 2,5 | 305,9 | 342 | 40,0 | 20,0 | 510 | 800 |
| ShL 40×64 | 1,6 | 1,0 | 2,5 | 333,8 | 342 | 40,0 | 25,6 | 776 | 1025 |
| ShL 40×80 | 2 | 1,0 | 2,5 | 365 | 342 | 40,0 | 32,0 | 1110 | 1280 |
Table 2
| Standard size | $x$ | $y$ | $l_0 \cdot 10^{-3}$, m | $l_c \cdot 10^{-3}$, m | $Q_0 \cdot 10^{-4}$, m² | $Q_c \cdot 10^{-4}$, m² | $\dfrac{Q_c^2 \cdot Q_0}{l_0} \cdot 10^{-10}$ m⁵ | $\dfrac{Q_0 \cdot Q_c}{l_0} \cdot 10^{-8}$ m⁴ |
|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| OL 10/16--4 | 1,33 | 3,3 | 24,9 | 40 | 0,78 | 0,12 | 0,00281 | 0,09 |
| OL 10/16--5 | 1,67 | 3,3 | 27 | 40 | 0,78 | 0,15 | 0,00439 | 0,12 |
| OL 10/16--6,5 | 2,16 | 3,3 | 29,9 | 40 | 0,78 | 0,2 | 0,0078 | 0,16 |
| OL 10/16--8 | 2,67 | 3,3 | 33 | 40 | 0,78 | 0,24 | 0,01123 | 0,19 |
| OL 12/20--5 | 1,25 | 3,0 | 31,1 | 50 | 1,1 | 0,2 | 0,0088 | 0,22 |
| OL 12/20--6,5 | 1,62 | 3,0 | 34,1 | 50 | 1,1 | 0,26 | 0,0149 | 0,29 |
| OL 12/20--8 | 2,0 | 3,0 | 37,1 | 50 | 1,1 | 0,32 | 0,0225 | 0,35 |
| OL 12/20--10 | 2,5 | 3,0 | 41,2 | 50 | 1,1 | 0,4 | 0,0352 | 0,44 |
| OL 16/26--6,5 | 1,3 | 3,2 | 41,8 | 65 | 2,0 | 0,33 | 0,0335 | 0,66 |
| OL 16/26--8 | 1,6 | 3,2 | 44,8 | 65 | 2,0 | 0,4 | 0,0492 | 0,80 |
| OL 16/26--10 | 2,0 | 3,2 | 48,9 | 65 | 2,0 | 0,5 | 0,077 | 1,0 |
| OL 16/26--12,5 | 2,5 | 3,2 | 53,9 | 65 | 2,0 | 0,68 | 0,142 | 1,36 |
| OL 20/32--8 | 1,33 | 3,33 | 50,1 | 81 | 3,1 | 0,48 | 0,142 | 1,50 |
| OL 20/32--10 | 1,67 | 3,33 | 54,18 | 81 | 3,1 | 0,60 | 0,198 | 1,86 |
| OL 20/32--12,5 | 2,08 | 3,33 | 59,1 | 81 | 3,1 | 0,75 | 0,284 | 2,32 |
| OL 20/32--16 | 2,67 | 3,33 | 66,18 | 81 | 3,1 | 0,96 | 0,423 | 3,0 |
| OL 25/40--10 | 1,33 | 3,33 | 62,6 | 102 | 4,9 | 0,75 | 0,43 | 3,67 |
| OL 25/40--12,5 | 1,67 | 3,33 | 67,7 | 102 | 4,9 | 0,94 | 0,619 | 4,6 |
| OL 25/40--16 | 2,13 | 3,33 | 74,6 | 102 | 4,9 | 1,2 | 0,923 | 5,9 |
| OL 25/40--20 | 2,67 | 3,33 | 82,7 | 102 | 4,9 | 1,5 | 1,283 | 7,35 |
| OL 25/40--25 | 3,33 | 3,33 | 92,6 | 102 | 4,9 | 1,87 | 1,806 | 9,18 |
| OL 32/50--16 | 1,78 | 3,55 | 85,68 | 128 | 8,0 | 1,44 | 1,895 | 11,5 |
| OL 32/50--20 | 2,22 | 3,55 | 93,6 | 128 | 8,0 | 1,8 | 2,7 | 14,4 |
| OL 32/50--25 | 2,78 | 3,55 | 108,7 | 128 | 8,0 | 2,25 | 3,82 | 18,0 |
| OL 32/50--32 | 3,55 | 3,55 | 117,54 | 128 | 8,0 | 2,88 | 5,54 | 23,0 |
| OL 40/64--20 | 1,67 | 3,33 | 108,36 | 163 | 12,6 | 2,4 | 6,18 | 30,0 |
| OL 40/64--25 | 2,08 | 3,33 | 118,2 | 163 | 12,6 | 3,0 | 9,4 | 38 |
| OL 40/64--32 | 2,67 | 3,33 | 132,4 | 163 | 12,6 | 3,8 | 13,6 | 48 |
| OL 40/64--40 | 3,33 | 3,33 | 148,2 | 163 | 12,6 | 4,8 | 19,0 | 60 |
| OL 50/80--25 | 1,67 | 3,33 | 136,0 | 204 | 19,6 | 3,8 | 20,39 | 75 |
| OL 50/80--32 | 2,13 | 3,33 | 149 | 204 | 19,6 | 4,8 | 29,8 | 94 |
| OL 50/80--40 | 2,67 | 3,33 | 165,5 | 204 | 19,6 | 6,0 | 42,1 | 118 |
| OL 50/80--50 | 3,33 | 3,33 | 185,3 | 204 | 19,6 | 7,5 | 58,9 | 148 |
| OL 64/100--32 | 1,78 | 3,55 | 171,4 | 258 | 32,2 | 5,8 | 61,9 | 187 |
| OL 64/100--40 | 2,22 | 3,55 | 187,2 | 258 | 32,2 | 7,2 | 88,1 | 232 |
| OL 64/100--50 | 2,78 | 3,55 | 207,4 | 258 | 32,2 | 9,0 | 124,2 | 290 |
| OL 64/100--64 | 3,55 | 3,55 | 235 | 258 | 32,2 | 11,5 | 178,1 | 370 |
| OL 80/128--40 | 1,67 | 3,33 | 216,7 | 326 | 50,2 | 9,6 | 210 | 482 |
| OL 80/128--50 | 2,08 | 3,33 | 236,4 | 326 | 50,2 | 12 | 302,2 | 603 |
| OL 80/128--64 | 2,67 | 3,33 | 264,7 | 326 | 50,2 | 15,4 | 445 | 775 |
| OL 80/128--80 | 3,33 | 3,33 | 296,4 | 326 | 50,2 | 19,2 | 618 | 965 |
Table 3
| Size designation | $x$ | $y$ | $z$ | $l_c\cdot10^{-3}$ m | $l_o\cdot10^{-3}$, 1 layer, m | $l_o\cdot10^{-3}$, 2 layers, m | $Q_o\cdot10^{-4}$ m$^2$ | $Q_c\cdot10^{-4}$ m$^2$ | $\dfrac{Q_c^2\cdot Q_o}{l_o}\cdot10^{-10}$, m$^5$ | $\dfrac{Q_c^2\cdot Q_o}{l_o}\cdot10^{-10}$, m$^5$ | $Q_c\cdot Q_o\cdot10^{-8}$ m$^4$ |
|---|---|---|---|---|---|---|---|---|---|---|---|
| PL 6.5×8 | 1,92 | 1,23 | 1,23 | 52 | 63,1 | 50,5 | 0,64 | 0,81 | 0,0665 | 0,083 | 0,52 |
| 10 | 1,92 | 1,23 | 1,54 | 56 | 63,1 | 50,5 | 0,8 | 0,81 | 0,0831 | 0,1037 | 0,65 |
| 12.5 | 1,92 | 1,23 | 1,92 | 61 | 63,1 | 50,5 | 1 | 0,81 | 0,1037 | 0,1297 | 0,81 |
| 16 | 1,92 | 1,23 | 2,46 | 68 | 63,1 | 50,5 | 1,28 | 0,81 | 0,133 | 0,166 | 1,04 |
| PL 8×12.5 | 1,56 | 1,25 | 1,56 | 69 | 72,4 | 46,6 | 1,25 | 1 | 0,172 | 0,221 | 1,25 |
| 16 | 1,56 | 1,25 | 2,0 | 76 | 72,4 | 46,6 | 1,6 | 1 | 0,221 | 0,283 | 1,6 |
| 20 | 1,56 | 1,25 | 2,5 | 84 | 72,4 | 46,6 | 2 | 1 | 0,276 | 0,353 | 2 |
| 25 | 1,56 | 1,25 | 3,13 | 94 | 72,4 | 46,6 | 2,5 | 1 | 0,345 | 0,442 | 2,5 |
| PL 10×20 | 1,25 | 1,25 | 2,0 | 96 | 84,5 | 64,6 | 2,5 | 1,25 | 0,45 | 0,586 | 3,1 |
| 25 | 1,25 | 1,25 | 2,5 | 106 | 84,5 | 64,6 | 3,1 | 1,25 | 0,565 | 0,639 | 3,9 |
| 32 | 1,25 | 1,25 | 3,2 | 116 | 84,5 | 64,6 | 4 | 1,25 | 0,724 | 0,947 | 5 |
| 40 | 1,25 | 1,25 | 4,0 | 136 | 84,5 | 64,6 | 5 | 1,25 | 0,912 | 1,19 | 6,3 |
| PL 12.5×25 | 1,28 | 1,28 | 2,0 | 120 | 107,24 | 82,5 | 4 | 2 | 1,465 | 1,905 | 8 |
| 32 | 1,28 | 1,28 | 2,56 | 134 | 107,24 | 82,5 | 5,1 | 2 | 1,870 | 2,425 | 10,2 |
| 40 | 1,28 | 1,28 | 3,2 | 150 | 107,24 | 82,5 | 6,4 | 2 | 2,35 | 3,06 | 12,8 |
| 50 | 1,28 | 1,28 | 4,0 | 170 | 107,24 | 82,5 | 8,0 | 2 | 2,94 | 3,82 | 16 |
| PL 12.5×30 | 2,0 | 1,6 | 2,4 | 138 | 137,8 | 106,4 | 6 | 3,1 | 4,17 | 5,43 | 18,7 |
| 40 | 2,0 | 1,6 | 3,2 | 158 | 137,8 | 106,4 | 8 | 3,1 | 5,59 | 7,19 | 25 |
| 50 | 2,0 | 1,6 | 4,0 | 178 | 137,8 | 106,4 | 10 | 3,1 | 6,91 | 8,93 | 31 |
| 60 | 2,0 | 1,6 | 4,8 | 198 | 137,8 | 106,4 | 12 | 3,1 | 8,38 | 10,8 | 37,6 |
| PL 16×40 | 2,0 | 1,56 | 2,5 | 180 | 174,17 | 135 | 10 | 5,1 | 14,7 | 19,3 | 51 |
| 50 | 2,0 | 1,56 | 3,12 | 200 | 174,17 | 135 | 12,5 | 5,1 | 18,5 | 24,0 | 64 |
Continuation of Table 3
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 65 | 4.06 | 230 | 16.3 | 24 | 31.4 | 83 | |||||
| 80 | 5.0 | 260 | 20 | 29.5 | 38.5 | 102 | |||||
| PL 20×50 | 2.0 | 1.6 | 2.5 | 227 | 220.4 | 170.2 | 16 | 8.0 | 45 | 59.4 | 128 |
| 60 | 2.0 | 1.6 | 3.0 | 247 | 220.4 | 170.2 | 19.2 | 8.0 | 55.7 | 71.4 | 154 |
| 80 | 2.0 | 1.6 | 4.0 | 287 | 220.4 | 170.2 | 25.6 | 8.0 | 73.5 | 95 | 205 |
| 100 | 2.0 | 1.6 | 5.0 | 327 | 220.4 | 170.2 | 32 | 8.0 | 91.6 | 118.5 | 256 |
| PL 25×65 | 2.0 | 1.6 | 2.6 | 288 | 275.5 | 212.2 | 26 | 12.5 | 145.5 | 188.3 | 325 |
| 80 | 2.0 | 1.6 | 3.2 | 318 | 275.5 | 212.2 | 32 | 12.5 | 179.2 | 232 | 400 |
| 100 | 2.0 | 1.6 | 4.0 | 358 | 275.5 | 212.2 | 40 | 12.5 | 224.2 | 290 | 500 |
| 120 | 2.0 | 1.6 | 4.8 | 398 | 275.5 | 212.2 | 48 | 12.5 | 269 | 348 | 600 |
| PL 32×80 | 2.0 | 1.56 | 2.5 | 360 | 348.8 | 270 | 40 | 20.5 | 475 | 615 | 820 |
| 100 | 2.0 | 1.56 | 3.12 | 400 | 348.8 | 270 | 50 | 20.5 | 595 | 768 | 1025 |
| 130 | 2.0 | 1.56 | 4.06 | 460 | 348.8 | 270 | 65 | 20.5 | 770 | 996 | 1330 |
| 160 | 2.0 | 1.56 | 5.0 | 520 | 348.8 | 270 | 80 | 20.5 | 949 | 1230 | 1640 |
| PL 40×100 | 2.0 | 1.6 | 2.5 | 453 | 440.8 | 340.4 | 64 | 32 | 1470 | 1919 | 2050 |
| 120 | 2.0 | 1.6 | 3.0 | 490 | 440.8 | 340.4 | 77 | 32 | 1775 | 2289 | 2460 |
| 160 | 2.0 | 1.6 | 4.0 | 573 | 440.8 | 340.4 | 102 | 32 | 2349 | 3060 | 3260 |
| 200 | 2.0 | 1.6 | 5.0 | 653 | 440.8 | 340.4 | 128 | 32 | 2961 | 3848 | 4100 |
In determining the technical-and-economic indicators of a smoothing choke (weight, overall volume, volume of active materials, and cost of active materials), the values of the relative parameters of the choke geometry \(x\), \(y\), and \(z\) are used.
To reduce the time required for calculating a smoothing choke when developing a simple engineering methodology for designing smoothing filters, the author used a digital computer to calculate the above quantities for standardized cores of the ShL, PL, and OL types. The results are summarized in Tables 1, 2, and 3.