.sp 0.25i \fBTitle\fP .ce Cascade: Schmitt Trigger Cascade .sp 0.25i \fBDescription\fP .P This is a challenge circuit for Newton's method or for continuation methods which use VCC as a continuation parameter. This circuit consists of a cascade of three Schmitt triggers, arranged so that the complementary outputs of the "middle" circuit feed the trigger inputs of the other two copies. The independent source \f(CWVX \fP is set so that the middle circuit is \fInot\fP in its hysteresis region. This drives the outputs of the middle circuit low and high, which thus bias the other two copies out of their hysteresis regions. Thus, the circuit has a \fIunique\fP DC operating point with VCC equal to 12 volts. However, the potential for multiple solutions at other values of VCC and VX causes problems for some operating point algorithms. .P Some experimentation with the value of VX may be necessary to put the circuit in the state described above. In STB, Q41 should be conducting hard (i.e., saturated), and Q42 should be hard off. This drives Q61 hard off and Q62 on. Finally, Q51 should be on and Q52 off. Larger values of VX seem to cause more convergence difficulties. To really exercise an operating point algorithm, try VX at 3.0 volts. .sp 0.25i \fBDescription of successful operating point computation, if available\fP .P A homotopy method has been used to identify the DC solution in the state described above. .bp .sp 0.25i \fBSpice File\fP .DS I \f(CW * Schmitt Trigger Cascase * * This circuit is a cascade of three Schmitt * triggers, arranged so that the complementary * outputs of the middle circuit STB feed the trigger * inputs of the other two circuits STA and STC. * With the component values given, the circuit * should have a *unique* DC operating point * because the high output of STB drives the * trigger of STA high enough so that STA is * out of its hysteresis region, and the low output * of STB drives the trigger of STC low enough so that * STC is out of its hysteresis region. * * All the transistors are the same size, and * default npn parameters are fine. * VCC 99 0 12.0 VX 1 0 3.0 RIN 1 2 10e3 * * "Middle" circuits, STB R4C1 99 41 1.1e3 R4C2 99 42 1e3 R4B 41 43 10e3 R4E 44 0 100.0 Q41 41 2 44 nbjt Q42 42 43 44 nbjt * * STA R6BF 68 41 1e3 R6C1 99 61 1.1e3 R6C2 99 62 1e3 R6B 61 63 10e3 R6E 64 0 100.0 Q61 61 68 64 nbjt Q62 62 63 64 nbjt * * STC R5BF 42 58 1e3 R5C1 99 51 1.1e3 R5C2 99 52 1e3 R5B 51 53 10e3 R5E 54 0 100.0 Q51 51 58 54 nbjt Q52 52 53 54 nbjt \&.end \fP .DE .bp .sp 0.25i .PS Q61:[B:box ht 1.4 wid 1.4; "\f(CWQ61\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+11.007" ljust at B.ne+(-0.5,-0.03); " +1.167" ljust at B.se+(-0.5,0.05); " +1.125" ljust at B.w; "+118.77a" ljust at B.ne+(-1.1,-0.1); "-18.37a" ljust at B.se+(-1.1,0.05); "-100.41a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q62:[B:box ht 1.4 wid 1.4; "\f(CWQ62\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.234" ljust at B.ne+(-0.5,-0.03); " +1.167" ljust at B.se+(-0.5,0.05); " +1.978" ljust at B.w; "+10.77m" ljust at B.ne+(-1.1,-0.1); "-11.67m" ljust at B.se+(-1.1,0.05); "+902.86u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 11.924)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q61.e; Q41:[B:box ht 1.4 wid 1.4; "\f(CWQ41\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.125" ljust at B.ne+(-0.5,-0.03); " +1.001" ljust at B.se+(-0.5,0.05); " +1.807" ljust at B.w; " +9.89m" ljust at B.ne+(-1.1,-0.1); "-10.01m" ljust at B.se+(-1.1,0.05); "+119.35u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 82.837)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q61.s; Q42:[B:box ht 1.4 wid 1.4; "\f(CWQ42\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +7.175" ljust at B.ne+(-0.5,-0.03); " +1.001" ljust at B.se+(-0.5,0.05); " +1.125" ljust at B.w; "+14.63f" ljust at B.ne+(-1.1,-0.1); "-14.61f" ljust at B.se+(-1.1,0.05); "-27.47a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q41.e; Q51:[B:box ht 1.4 wid 1.4; "\f(CWQ51\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.562" ljust at B.ne+(-0.5,-0.03); " +1.526" ljust at B.se+(-0.5,0.05); " +2.349" ljust at B.w; "+10.44m" ljust at B.ne+(-1.1,-0.1); "-15.26m" ljust at B.se+(-1.1,0.05); " +4.83m\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 2.163)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q41.s; Q52:[B:box ht 1.4 wid 1.4; "\f(CWQ52\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+12.000" ljust at B.ne+(-0.5,-0.03); " +1.526" ljust at B.se+(-0.5,0.05); " +1.562" ljust at B.w; "+520.89a" ljust at B.ne+(-1.1,-0.1); "-422.50a" ljust at B.se+(-1.1,0.05); "-98.39a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q51.e; .PE .nf \f(CW[41]: 1.12504 [42]: 7.17470 [43]: 1.12504 [44]: 1.00057 [2]: 1.80653 [68]: 1.12504 [61]: 11.00685 [62]: 1.23425 [63]: 1.97824 [64]: 1.16686 [58]: 2.34940 [51]: 1.56224 [52]: 12.00000 [53]: 1.56224 [54]: 1.52631 .ce \fBCascade: Solution 1; signature: 367.81894; ||rho(x*,1)|| 2.364e-16\fP \&-------- PostScript ------------ %!PS-Adobe-1.0 %%Creator: HPF version 3.4 SUN4-P2 28 Feb 1990 %%CreationDate: Sun Nov 4 20:22:14 1990 %%Pages: 1 %%EndComments save /a{arc}def /c{0 360 arc}def /l{lineto}def /m{moveto}def /n{newpath}def /s{stroke}def /w{setlinewidth}def 0.240000 0.240000 scale 90 rotate 468.000000 -2325.000000 translate %%EndProlog %%Page: x0y0 1 gsave n 253 793 m [] 0 setdash 4 w 253 706 l s n 255 793 m 255 706 l s n 254 749 m 2 w 209 749 l s n 254 719 m 299 704 l 281 698 l s n 299 704 m 286 721 l s n 299 704 m 299 689 l s n 254 779 m 299 794 l 299 809 l s n 1603 793 m 4 w 1603 706 l s n 1605 793 m 1605 706 l s n 1604 749 m 2 w 1559 749 l s n 1604 719 m 1649 704 l 1631 698 l s n 1649 704 m 1636 721 l s n 1649 704 m 1649 689 l s n 1604 779 m 1649 794 l 1649 809 l s n 1003 1333 m 4 w 1003 1246 l s n 1005 1333 m 1005 1246 l s n 1004 1289 m 2 w 959 1289 l s n 1004 1259 m 1049 1244 l 1031 1238 l s n 1049 1244 m 1036 1261 l s n 1049 1244 m 1049 1229 l s n 1004 1319 m 1049 1334 l 1049 1349 l s n 796 793 m 4 w 796 706 l s n 794 793 m 794 706 l s n 794 749 m 2 w 839 749 l s n 794 719 m 749 704 l 768 698 l s n 749 704 m 763 721 l s n 749 704 m 749 689 l s n 794 779 m 749 794 l 749 809 l s n 2146 793 m 4 w 2146 706 l s n 2144 793 m 2144 706 l s n 2144 749 m 2 w 2189 749 l s n 2144 719 m 2099 704 l 2118 698 l s n 2099 704 m 2113 721 l s n 2099 704 m 2099 689 l s n 2144 779 m 2099 794 l 2099 809 l s n 1546 1333 m 4 w 1546 1246 l s n 1544 1333 m 1544 1246 l s n 1544 1289 m 2 w 1589 1289 l s n 1544 1259 m 1499 1244 l 1518 1238 l s n 1499 1244 m 1513 1261 l s n 1499 1244 m 1499 1229 l s n 1544 1319 m 1499 1334 l 1499 1349 l s n 989 984 m 1003 984 l s n 989 1056 m 1003 1056 l s n 996 1049 m 996 1063 l s n 950 1028 m 950 1016 l 959 1007 l 968 1016 l 968 1028 l s n 959 989 m 959 959 l s n 959 1049 m 959 1079 l s n 959 1019 29 360.000000 719.912109 a s n 554 899 m 569 899 l s n 491 899 m 479 899 l s n 545 917 m 4 w 554 899 l s n 515 917 m 500 881 l 491 899 l s n 545 917 m 530 881 l 515 917 l s n 1904 899 m 2 w 1919 899 l s n 1841 899 m 1829 899 l s n 1895 917 m 4 w 1904 899 l s n 1865 917 m 1850 881 l 1841 899 l s n 1895 917 m 1880 881 l 1865 917 l s n 1304 1439 m 2 w 1319 1439 l s n 1241 1439 m 1229 1439 l s n 1295 1457 m 4 w 1304 1439 l s n 1265 1457 m 1250 1421 l 1241 1439 l s n 1295 1457 m 1280 1421 l 1265 1457 l s n 1409 944 m 2 w 1409 929 l s n 1409 1007 m 1409 1019 l s n 1391 953 m 4 w 1409 944 l s n 1391 983 m 1427 998 l 1409 1007 l s n 1391 953 m 1427 968 l 1391 983 l s n 509 524 m 2 w 509 509 l s n 509 587 m 509 599 l s n 491 533 m 4 w 509 524 l s n 491 563 m 527 578 l 509 587 l s n 491 533 m 527 548 l 491 563 l s n 749 974 m 2 w 749 959 l s n 749 1037 m 749 1049 l s n 731 983 m 4 w 749 974 l s n 731 1013 m 767 1028 l 749 1037 l s n 731 983 m 767 998 l 731 1013 l s n 299 974 m 2 w 299 959 l s n 299 1037 m 299 1049 l s n 281 983 m 4 w 299 974 l s n 281 1013 m 317 1028 l 299 1037 l s n 281 983 m 317 998 l 281 1013 l s n 1859 524 m 2 w 1859 509 l s n 1859 587 m 1859 599 l s n 1841 533 m 4 w 1859 524 l s n 1841 563 m 1877 578 l 1859 587 l s n 1841 533 m 1877 548 l 1841 563 l s n 2099 974 m 2 w 2099 959 l s n 2099 1037 m 2099 1049 l s n 2081 983 m 4 w 2099 974 l s n 2081 1013 m 2117 1028 l 2099 1037 l s n 2081 983 m 2117 998 l 2081 1013 l s n 1649 974 m 2 w 1649 959 l s n 1649 1037 m 1649 1049 l s n 1631 983 m 4 w 1649 974 l s n 1631 1013 m 1667 1028 l 1649 1037 l s n 1631 983 m 1667 998 l 1631 1013 l s n 1259 1064 m 2 w 1259 1049 l s n 1259 1127 m 1259 1139 l s n 1241 1073 m 4 w 1259 1064 l s n 1241 1103 m 1277 1118 l 1259 1127 l s n 1241 1073 m 1277 1088 l 1241 1103 l s n 1499 1514 m 2 w 1499 1499 l s n 1499 1577 m 1499 1589 l s n 1481 1523 m 4 w 1499 1514 l s n 1481 1553 m 1517 1568 l 1499 1577 l s n 1481 1523 m 1517 1538 l 1481 1553 l s n 1049 1514 m 2 w 1049 1499 l s n 1049 1577 m 1049 1589 l s n 1031 1523 m 4 w 1049 1514 l s n 1031 1553 m 1067 1568 l 1049 1577 l s n 1031 1523 m 1067 1538 l 1031 1553 l s n 959 1124 m 2 w 959 1109 l s n 959 1187 m 959 1199 l s n 941 1133 m 4 w 959 1124 l s n 941 1163 m 977 1178 l 959 1187 l s n 941 1133 m 977 1148 l 941 1163 l s n 209 824 m 2 w 209 809 l s n 209 887 m 209 899 l s n 191 833 m 4 w 209 824 l s n 191 863 m 227 878 l 209 887 l s n 191 833 m 227 848 l 191 863 l s n 347 809 m 2 w 341 815 l s n 329 824 m 329 815 l 335 809 l 341 809 l 347 815 l 347 824 l 341 830 l 335 830 l 329 824 l s n 371 830 m 356 830 l 353 827 l 353 812 l 356 809 l 368 809 l 371 812 l 371 818 l 368 821 l 356 821 l 353 818 l s n 383 827 m 386 830 l 386 809 l s n 380 809 m 392 809 l s n 1547 809 m 1541 815 l s n 1529 824 m 1529 815 l 1535 809 l 1541 809 l 1547 815 l 1547 824 l 1541 830 l 1535 830 l 1529 824 l s n 1571 830 m 1553 830 l 1553 821 l 1568 821 l 1571 818 l 1571 812 l 1568 809 l 1556 809 l 1553 812 l s n 1583 827 m 1586 830 l 1586 809 l s n 1580 809 m 1592 809 l s n 1097 1319 m 1091 1325 l s n 1079 1334 m 1079 1325 l 1085 1319 l 1091 1319 l 1097 1325 l 1097 1334 l 1091 1340 l 1085 1340 l 1079 1334 l s n 1121 1325 m 1103 1325 l 1118 1340 l 1118 1319 l s n 1133 1337 m 1136 1340 l 1136 1319 l s n 1130 1319 m 1142 1319 l s n 797 809 m 791 815 l s n 779 824 m 779 815 l 785 809 l 791 809 l 797 815 l 797 824 l 791 830 l 785 830 l 779 824 l s n 821 830 m 806 830 l 803 827 l 803 812 l 806 809 l 818 809 l 821 812 l 821 818 l 818 821 l 806 821 l 803 818 l s n 845 809 m 827 809 l 827 812 l 833 818 l 842 818 l 845 821 l 845 827 l 842 830 l 830 830 l 827 827 l s n 2147 809 m 2141 815 l s n 2129 824 m 2129 815 l 2135 809 l 2141 809 l 2147 815 l 2147 824 l 2141 830 l 2135 830 l 2129 824 l s n 2171 830 m 2153 830 l 2153 821 l 2168 821 l 2171 818 l 2171 812 l 2168 809 l 2156 809 l 2153 812 l s n 2195 809 m 2177 809 l 2177 812 l 2183 818 l 2192 818 l 2195 821 l 2195 827 l 2192 830 l 2180 830 l 2177 827 l s n 1547 1349 m 1541 1355 l s n 1529 1364 m 1529 1355 l 1535 1349 l 1541 1349 l 1547 1355 l 1547 1364 l 1541 1370 l 1535 1370 l 1529 1364 l s n 1571 1355 m 1553 1355 l 1568 1370 l 1568 1349 l s n 1595 1349 m 1577 1349 l 1577 1352 l 1583 1358 l 1592 1358 l 1595 1361 l 1595 1367 l 1592 1370 l 1580 1370 l 1577 1367 l s n 485 857 m 488 860 l 488 839 l s n 482 839 m 494 839 l s n 518 857 m 503 842 l 503 857 l 506 860 l 518 860 l 521 857 l 518 857 l s n 503 842 m 506 839 l 518 839 l 521 842 l 521 857 l s n 527 851 m 536 851 l 536 848 l 545 839 l s n 527 839 m 527 860 l s n 536 851 m 545 860 l s n 479 929 m 479 950 l 494 950 l 497 947 l 497 941 l 494 938 l 479 938 l s n 497 929 m 488 938 l s n 521 950 m 506 950 l 503 947 l 503 932 l 506 929 l 518 929 l 521 932 l 521 938 l 518 941 l 506 941 l 503 938 l s n 527 929 m 542 929 l 545 932 l 545 938 l 542 941 l 530 941 l s n 527 950 m 542 950 l 545 947 l 545 944 l 542 941 l s n 530 929 m 530 950 l s n 1835 857 m 1838 860 l 1838 839 l s n 1832 839 m 1844 839 l s n 1868 857 m 1853 842 l 1853 857 l 1856 860 l 1868 860 l 1871 857 l 1868 857 l s n 1853 842 m 1856 839 l 1868 839 l 1871 842 l 1871 857 l s n 1877 851 m 1886 851 l 1886 848 l 1895 839 l s n 1877 839 m 1877 860 l s n 1886 851 m 1895 860 l s n 1829 929 m 1829 950 l 1844 950 l 1847 947 l 1847 941 l 1844 938 l 1829 938 l s n 1847 929 m 1838 938 l s n 1871 950 m 1853 950 l 1853 941 l 1868 941 l 1871 938 l 1871 932 l 1868 929 l 1856 929 l 1853 932 l s n 1877 929 m 1892 929 l 1895 932 l 1895 938 l 1892 941 l 1880 941 l s n 1877 950 m 1892 950 l 1895 947 l 1895 944 l 1892 941 l s n 1880 929 m 1880 950 l s n 1235 1397 m 1238 1400 l 1238 1379 l s n 1232 1379 m 1244 1379 l s n 1268 1397 m 1253 1382 l 1253 1397 l 1256 1400 l 1268 1400 l 1271 1397 l 1268 1397 l s n 1253 1382 m 1256 1379 l 1268 1379 l 1271 1382 l 1271 1397 l s n 1277 1391 m 1286 1391 l 1286 1388 l 1295 1379 l s n 1277 1379 m 1277 1400 l s n 1286 1391 m 1295 1400 l s n 1229 1469 m 1229 1490 l 1244 1490 l 1247 1487 l 1247 1481 l 1244 1478 l 1229 1478 l s n 1247 1469 m 1238 1478 l s n 1271 1475 m 1253 1475 l 1268 1490 l 1268 1469 l s n 1277 1469 m 1292 1469 l 1295 1472 l 1295 1478 l 1292 1481 l 1280 1481 l s n 1277 1490 m 1292 1490 l 1295 1487 l 1295 1484 l 1292 1481 l s n 1280 1469 m 1280 1490 l s n 1325 917 m 1328 920 l 1328 899 l s n 1322 899 m 1334 899 l s n 1343 911 m 1352 911 l 1352 908 l 1361 899 l s n 1343 899 m 1343 920 l s n 1352 911 m 1361 920 l s n 1289 1019 m 1289 1040 l 1304 1040 l 1307 1037 l 1307 1031 l 1304 1028 l 1289 1028 l s n 1307 1019 m 1298 1028 l s n 1331 1040 m 1313 1040 l 1313 1031 l 1328 1031 l 1331 1028 l 1331 1022 l 1328 1019 l 1316 1019 l 1313 1022 l s n 1337 1019 m 1352 1019 l 1355 1022 l 1355 1028 l 1352 1031 l 1340 1031 l s n 1337 1040 m 1352 1040 l 1355 1037 l 1355 1034 l 1352 1031 l s n 1340 1019 m 1340 1040 l s n 1361 1019 m 1361 1040 l 1379 1040 l s n 1361 1031 m 1370 1031 l s n 545 527 m 548 530 l 548 509 l s n 542 509 m 554 509 l s n 578 527 m 563 512 l 563 527 l 566 530 l 578 530 l 581 527 l 578 527 l s n 563 512 m 566 509 l 578 509 l 581 512 l 581 527 l s n 602 527 m 587 512 l 587 527 l 590 530 l 602 530 l 605 527 l 602 527 l s n 587 512 m 590 509 l 602 509 l 605 512 l 605 527 l s n 539 569 m 539 590 l 554 590 l 557 587 l 557 581 l 554 578 l 539 578 l s n 557 569 m 548 578 l s n 581 590 m 566 590 l 563 587 l 563 572 l 566 569 l 578 569 l 581 572 l 581 578 l 578 581 l 566 581 l 563 578 l s n 605 569 m 587 569 l 587 590 l 605 590 l s n 587 581 m 596 581 l s n 785 977 m 788 980 l 788 959 l s n 782 959 m 794 959 l s n 803 971 m 812 971 l 812 968 l 821 959 l s n 803 959 m 803 980 l s n 812 971 m 821 980 l s n 779 1019 m 779 1040 l 794 1040 l 797 1037 l 797 1031 l 794 1028 l 779 1028 l s n 797 1019 m 788 1028 l s n 821 1040 m 806 1040 l 803 1037 l 803 1022 l 806 1019 l 818 1019 l 821 1022 l 821 1028 l 818 1031 l 806 1031 l 803 1028 l s n 845 1022 m 842 1019 l 833 1019 l 827 1025 l 827 1034 l 833 1040 l 842 1040 l 845 1037 l s n 869 1019 m 851 1019 l 851 1022 l 857 1028 l 866 1028 l 869 1031 l 869 1037 l 866 1040 l 854 1040 l 851 1037 l s n 365 977 m 368 980 l 368 959 l s n 362 959 m 374 959 l s n 389 959 m 386 959 l 386 962 l 389 962 l 389 959 l s n 413 977 m 416 980 l 416 959 l s n 410 959 m 422 959 l s n 431 971 m 440 971 l 440 968 l 449 959 l s n 431 959 m 431 980 l s n 440 971 m 449 980 l s n 359 1019 m 359 1040 l 374 1040 l 377 1037 l 377 1031 l 374 1028 l 359 1028 l s n 377 1019 m 368 1028 l s n 401 1040 m 386 1040 l 383 1037 l 383 1022 l 386 1019 l 398 1019 l 401 1022 l 401 1028 l 398 1031 l 386 1031 l 383 1028 l s n 425 1022 m 422 1019 l 413 1019 l 407 1025 l 407 1034 l 413 1040 l 422 1040 l 425 1037 l s n 437 1037 m 440 1040 l 440 1019 l s n 434 1019 m 446 1019 l s n 1895 527 m 1898 530 l 1898 509 l s n 1892 509 m 1904 509 l s n 1928 527 m 1913 512 l 1913 527 l 1916 530 l 1928 530 l 1931 527 l 1928 527 l s n 1913 512 m 1916 509 l 1928 509 l 1931 512 l 1931 527 l s n 1952 527 m 1937 512 l 1937 527 l 1940 530 l 1952 530 l 1955 527 l 1952 527 l s n 1937 512 m 1940 509 l 1952 509 l 1955 512 l 1955 527 l s n 1889 569 m 1889 590 l 1904 590 l 1907 587 l 1907 581 l 1904 578 l 1889 578 l s n 1907 569 m 1898 578 l s n 1931 590 m 1913 590 l 1913 581 l 1928 581 l 1931 578 l 1931 572 l 1928 569 l 1916 569 l 1913 572 l s n 1955 569 m 1937 569 l 1937 590 l 1955 590 l s n 1937 581 m 1946 581 l s n 2135 977 m 2138 980 l 2138 959 l s n 2132 959 m 2144 959 l s n 2153 971 m 2162 971 l 2162 968 l 2171 959 l s n 2153 959 m 2153 980 l s n 2162 971 m 2171 980 l s n 2129 1019 m 2129 1040 l 2144 1040 l 2147 1037 l 2147 1031 l 2144 1028 l 2129 1028 l s n 2147 1019 m 2138 1028 l s n 2171 1040 m 2153 1040 l 2153 1031 l 2168 1031 l 2171 1028 l 2171 1022 l 2168 1019 l 2156 1019 l 2153 1022 l s n 2195 1022 m 2192 1019 l 2183 1019 l 2177 1025 l 2177 1034 l 2183 1040 l 2192 1040 l 2195 1037 l s n 2219 1019 m 2201 1019 l 2201 1022 l 2207 1028 l 2216 1028 l 2219 1031 l 2219 1037 l 2216 1040 l 2204 1040 l 2201 1037 l s n 1535 977 m 1538 980 l 1538 959 l s n 1532 959 m 1544 959 l s n 1559 959 m 1556 959 l 1556 962 l 1559 962 l 1559 959 l s n 1583 977 m 1586 980 l 1586 959 l s n 1580 959 m 1592 959 l s n 1601 971 m 1610 971 l 1610 968 l 1619 959 l s n 1601 959 m 1601 980 l s n 1610 971 m 1619 980 l s n 1529 1019 m 1529 1040 l 1544 1040 l 1547 1037 l 1547 1031 l 1544 1028 l 1529 1028 l s n 1547 1019 m 1538 1028 l s n 1571 1040 m 1553 1040 l 1553 1031 l 1568 1031 l 1571 1028 l 1571 1022 l 1568 1019 l 1556 1019 l 1553 1022 l s n 1595 1022 m 1592 1019 l 1583 1019 l 1577 1025 l 1577 1034 l 1583 1040 l 1592 1040 l 1595 1037 l s n 1607 1037 m 1610 1040 l 1610 1019 l s n 1604 1019 m 1616 1019 l s n 1145 1067 m 1148 1070 l 1148 1049 l s n 1142 1049 m 1154 1049 l s n 1178 1067 m 1163 1052 l 1163 1067 l 1166 1070 l 1178 1070 l 1181 1067 l 1178 1067 l s n 1163 1052 m 1166 1049 l 1178 1049 l 1181 1052 l 1181 1067 l s n 1202 1067 m 1187 1052 l 1187 1067 l 1190 1070 l 1202 1070 l 1205 1067 l 1202 1067 l s n 1187 1052 m 1190 1049 l 1202 1049 l 1205 1052 l 1205 1067 l s n 1139 1109 m 1139 1130 l 1154 1130 l 1157 1127 l 1157 1121 l 1154 1118 l 1139 1118 l s n 1157 1109 m 1148 1118 l s n 1181 1115 m 1163 1115 l 1178 1130 l 1178 1109 l s n 1205 1109 m 1187 1109 l 1187 1130 l 1205 1130 l s n 1187 1121 m 1196 1121 l s n 1565 1517 m 1568 1520 l 1568 1499 l s n 1562 1499 m 1574 1499 l s n 1583 1511 m 1592 1511 l 1592 1508 l 1601 1499 l s n 1583 1499 m 1583 1520 l s n 1592 1511 m 1601 1520 l s n 1559 1559 m 1559 1580 l 1574 1580 l 1577 1577 l 1577 1571 l 1574 1568 l 1559 1568 l s n 1577 1559 m 1568 1568 l s n 1601 1565 m 1583 1565 l 1598 1580 l 1598 1559 l s n 1625 1562 m 1622 1559 l 1613 1559 l 1607 1565 l 1607 1574 l 1613 1580 l 1622 1580 l 1625 1577 l s n 1649 1559 m 1631 1559 l 1631 1562 l 1637 1568 l 1646 1568 l 1649 1571 l 1649 1577 l 1646 1580 l 1634 1580 l 1631 1577 l s n 905 1517 m 908 1520 l 908 1499 l s n 902 1499 m 914 1499 l s n 929 1499 m 926 1499 l 926 1502 l 929 1502 l 929 1499 l s n 953 1517 m 956 1520 l 956 1499 l s n 950 1499 m 962 1499 l s n 971 1511 m 980 1511 l 980 1508 l 989 1499 l s n 971 1499 m 971 1520 l s n 980 1511 m 989 1520 l s n 899 1559 m 899 1580 l 914 1580 l 917 1577 l 917 1571 l 914 1568 l 899 1568 l s n 917 1559 m 908 1568 l s n 941 1565 m 923 1565 l 938 1580 l 938 1559 l s n 965 1562 m 962 1559 l 953 1559 l 947 1565 l 947 1574 l 953 1580 l 962 1580 l 965 1577 l s n 977 1577 m 980 1580 l 980 1559 l s n 974 1559 m 986 1559 l s n 839 1169 m 839 1190 l 854 1190 l 857 1187 l 857 1181 l 854 1178 l 839 1178 l s n 857 1169 m 848 1178 l s n 866 1169 m 878 1169 l s n 866 1190 m 878 1190 l s n 872 1169 m 872 1190 l s n 887 1169 m 887 1190 l 905 1172 l s n 905 1169 m 905 1190 l s n 845 1127 m 848 1130 l 848 1109 l s n 842 1109 m 854 1109 l s n 878 1127 m 863 1112 l 863 1127 l 866 1130 l 878 1130 l 881 1127 l 878 1127 l s n 863 1112 m 866 1109 l 878 1109 l 881 1112 l 881 1127 l s n 887 1121 m 896 1121 l 896 1118 l 905 1109 l s n 887 1109 m 887 1130 l s n 896 1121 m 905 1130 l s n 89 869 m 89 890 l 104 890 l 107 887 l 107 881 l 104 878 l 89 878 l s n 107 869 m 98 878 l s n 131 890 m 116 890 l 113 887 l 113 872 l 116 869 l 128 869 l 131 872 l 131 878 l 128 881 l 116 881 l 113 878 l s n 137 869 m 152 869 l 155 872 l 155 878 l 152 881 l 140 881 l s n 137 890 m 152 890 l 155 887 l 155 884 l 152 881 l s n 140 869 m 140 890 l s n 161 869 m 161 890 l 179 890 l s n 161 881 m 170 881 l s n 95 797 m 98 800 l 98 779 l s n 92 779 m 104 779 l s n 113 791 m 122 791 l 122 788 l 131 779 l s n 113 779 m 113 800 l s n 122 791 m 131 800 l s n 2189 704 m 2180 704 l 2180 722 l 2189 722 l s n 2216 725 m 2198 725 l 2198 716 l 2213 716 l 2216 713 l 2216 707 l 2213 704 l 2201 704 l 2198 707 l s n 2222 722 m 2225 725 l 2237 725 l 2240 722 l 2240 719 l 2237 716 l 2228 716 l s n 2222 707 m 2225 704 l 2237 704 l 2240 707 l 2240 713 l 2237 716 l s n 2249 704 m 2258 704 l 2258 722 l 2249 722 l s n 2009 824 m 2000 824 l 2000 842 l 2009 842 l s n 2036 845 m 2018 845 l 2018 836 l 2033 836 l 2036 833 l 2036 827 l 2033 824 l 2021 824 l 2018 827 l s n 2060 824 m 2042 824 l 2042 827 l 2048 833 l 2057 833 l 2060 836 l 2060 842 l 2057 845 l 2045 845 l 2042 842 l s n 2069 824 m 2078 824 l 2078 842 l 2069 842 l s n 1529 899 m 1520 899 l 1520 917 l 1529 917 l s n 1556 920 m 1538 920 l 1538 911 l 1553 911 l 1556 908 l 1556 902 l 1553 899 l 1541 899 l 1538 902 l s n 1568 917 m 1571 920 l 1571 899 l s n 1565 899 m 1577 899 l s n 1589 899 m 1598 899 l 1598 917 l 1589 917 l s n 1844 704 m 1835 704 l 1835 722 l 1844 722 l s n 1871 725 m 1853 725 l 1853 716 l 1868 716 l 1871 713 l 1871 707 l 1868 704 l 1856 704 l 1853 707 l s n 1895 710 m 1877 710 l 1892 725 l 1892 704 l s n 1904 704 m 1913 704 l 1913 722 l 1904 722 l s n 1484 704 m 1475 704 l 1475 722 l 1484 722 l s n 1511 725 m 1493 725 l 1493 716 l 1508 716 l 1511 713 l 1511 707 l 1508 704 l 1496 704 l 1493 707 l s n 1517 713 m 1517 707 l 1520 704 l 1532 704 l 1535 707 l 1535 713 l 1532 716 l 1520 716 l 1517 713 l s n 1520 716 m 1517 719 l 1517 722 l 1520 725 l 1532 725 l 1535 722 l 1535 719 l 1532 716 l s n 1544 704 m 1553 704 l 1553 722 l 1544 722 l s n 149 689 m 140 689 l 140 707 l 149 707 l s n 176 710 m 161 710 l 158 707 l 158 692 l 161 689 l 173 689 l 176 692 l 176 698 l 173 701 l 161 701 l 158 698 l s n 182 698 m 182 692 l 185 689 l 197 689 l 200 692 l 200 698 l 197 701 l 185 701 l 182 698 l s n 185 701 m 182 704 l 182 707 l 185 710 l 197 710 l 200 707 l 200 704 l 197 701 l s n 209 689 m 218 689 l 218 707 l 209 707 l s n 1004 1094 m 995 1094 l 995 1112 l 1004 1112 l s n 1019 1112 m 1022 1115 l 1022 1094 l s n 1016 1094 m 1028 1094 l s n 1040 1094 m 1049 1094 l 1049 1112 l 1040 1112 l s n 854 1259 m 845 1259 l 845 1277 l 854 1277 l s n 881 1259 m 863 1259 l 863 1262 l 869 1268 l 878 1268 l 881 1271 l 881 1277 l 878 1280 l 866 1280 l 863 1277 l s n 890 1259 m 899 1259 l 899 1277 l 890 1277 l s n 1019 1025 m 1019 1013 l 1028 1004 l 1037 1013 l 1037 1025 l s n 1043 1004 m 1043 1007 l 1061 1025 l s n 1043 1025 m 1061 1007 l 1061 1004 l s n 404 689 m 395 689 l 395 707 l 404 707 l s n 431 710 m 416 710 l 413 707 l 413 692 l 416 689 l 428 689 l 431 692 l 431 698 l 428 701 l 416 701 l 413 698 l s n 455 695 m 437 695 l 452 710 l 452 689 l s n 464 689 m 473 689 l 473 707 l 464 707 l s n 914 779 m 905 779 l 905 797 l 914 797 l s n 941 800 m 926 800 l 923 797 l 923 782 l 926 779 l 938 779 l 941 782 l 941 788 l 938 791 l 926 791 l 923 788 l s n 947 797 m 950 800 l 962 800 l 965 797 l 965 794 l 962 791 l 953 791 l s n 947 782 m 950 779 l 962 779 l 965 782 l 965 788 l 962 791 l s n 974 779 m 983 779 l 983 797 l 974 797 l s n 644 959 m 635 959 l 635 977 l 644 977 l s n 671 980 m 656 980 l 653 977 l 653 962 l 656 959 l 668 959 l 671 962 l 671 968 l 668 971 l 656 971 l 653 968 l s n 695 959 m 677 959 l 677 962 l 683 968 l 692 968 l 695 971 l 695 977 l 692 980 l 680 980 l 677 977 l s n 704 959 m 713 959 l 713 977 l 704 977 l s n 344 869 m 335 869 l 335 887 l 344 887 l s n 371 890 m 356 890 l 353 887 l 353 872 l 356 869 l 368 869 l 371 872 l 371 878 l 368 881 l 356 881 l 353 878 l s n 383 887 m 386 890 l 386 869 l s n 380 869 m 392 869 l s n 404 869 m 413 869 l 413 887 l 404 887 l s n 1124 1229 m 1115 1229 l 1115 1247 l 1124 1247 l s n 1151 1235 m 1133 1235 l 1148 1250 l 1148 1229 l s n 1175 1235 m 1157 1235 l 1172 1250 l 1172 1229 l s n 1184 1229 m 1193 1229 l 1193 1247 l 1184 1247 l s n 1694 1349 m 1685 1349 l 1685 1367 l 1694 1367 l s n 1721 1355 m 1703 1355 l 1718 1370 l 1718 1349 l s n 1727 1367 m 1730 1370 l 1742 1370 l 1745 1367 l 1745 1364 l 1742 1361 l 1733 1361 l s n 1727 1352 m 1730 1349 l 1742 1349 l 1745 1352 l 1745 1358 l 1742 1361 l s n 1754 1349 m 1763 1349 l 1763 1367 l 1754 1367 l s n 1394 1499 m 1385 1499 l 1385 1517 l 1394 1517 l s n 1421 1505 m 1403 1505 l 1418 1520 l 1418 1499 l s n 1445 1499 m 1427 1499 l 1427 1502 l 1433 1508 l 1442 1508 l 1445 1511 l 1445 1517 l 1442 1520 l 1430 1520 l 1427 1517 l s n 1454 1499 m 1463 1499 l 1463 1517 l 1454 1517 l s n 914 1409 m 905 1409 l 905 1427 l 914 1427 l s n 941 1415 m 923 1415 l 938 1430 l 938 1409 l s n 953 1427 m 956 1430 l 956 1409 l s n 950 1409 m 962 1409 l s n 974 1409 m 983 1409 l 983 1427 l 974 1427 l s n 1844 1139 m 1835 1139 l 1835 1157 l 1844 1157 l s n 1853 1139 m 1868 1139 l 1871 1142 l 1871 1157 l 1868 1160 l 1856 1160 l 1853 1157 l 1853 1151 l 1856 1148 l 1868 1148 l 1871 1151 l s n 1877 1139 m 1892 1139 l 1895 1142 l 1895 1157 l 1892 1160 l 1880 1160 l 1877 1157 l 1877 1151 l 1880 1148 l 1892 1148 l 1895 1151 l s n 1904 1139 m 1913 1139 l 1913 1157 l 1904 1157 l s n 1244 1619 m 1235 1619 l 1235 1637 l 1244 1637 l s n 1253 1619 m 1268 1619 l 1271 1622 l 1271 1637 l 1268 1640 l 1256 1640 l 1253 1637 l 1253 1631 l 1256 1628 l 1268 1628 l 1271 1631 l s n 1277 1619 m 1292 1619 l 1295 1622 l 1295 1637 l 1292 1640 l 1280 1640 l 1277 1637 l 1277 1631 l 1280 1628 l 1292 1628 l 1295 1631 l s n 1304 1619 m 1313 1619 l 1313 1637 l 1304 1637 l s n 464 1139 m 455 1139 l 455 1157 l 464 1157 l s n 473 1139 m 488 1139 l 491 1142 l 491 1157 l 488 1160 l 476 1160 l 473 1157 l 473 1151 l 476 1148 l 488 1148 l 491 1151 l s n 497 1139 m 512 1139 l 515 1142 l 515 1157 l 512 1160 l 500 1160 l 497 1157 l 497 1151 l 500 1148 l 512 1148 l 515 1151 l s n 524 1139 m 533 1139 l 533 1157 l 524 1157 l s n 1334 479 m 1325 479 l 1325 497 l 1334 497 l s n 1358 497 m 1343 482 l 1343 497 l 1346 500 l 1358 500 l 1361 497 l 1358 497 l s n 1343 482 m 1346 479 l 1358 479 l 1361 482 l 1361 497 l s n 1370 479 m 1379 479 l 1379 497 l 1370 497 l s n 1499 1409 5 0.000000 359.912109 a fill s n 1049 1379 5 0.000000 359.912109 a fill s n 1409 1229 m 1379 1199 l s n 1409 1409 m 1409 1229 l s n 1499 1409 m 1409 1409 l s n 1409 1169 m 1379 1199 l s n 1409 1019 m 1409 1169 l s n 1409 929 m 1409 749 l s n 2099 1049 m 2099 1109 l s n 1649 1049 m 1649 1109 l s n 2159 1109 m 4 w 2099 1109 l s n 1619 1109 m 1649 1109 l 2099 1109 l s n 1649 1289 m 2 w 1649 1439 l s n 1589 1289 m 1649 1289 l s n 2099 809 m 2099 959 l s n 149 1109 m 4 w 299 1109 l s n 749 959 m 2 w 749 809 l s n 1499 1499 m 1499 1409 l 1499 1349 l s n 1559 749 m 1409 749 l s n 209 1139 m 179 1109 l s n 209 1379 m 209 1139 l s n 1049 1379 m 209 1379 l s n 209 1079 m 179 1109 l s n 1259 959 5 0.000000 359.912109 a fill s n 959 959 m 1259 959 l s n 2129 899 m 2249 899 l s n 2099 929 m 2129 899 l s n 2069 899 m 2099 929 l s n 1919 899 m 2069 899 l s n 1649 899 m 1829 899 l s n 1499 1649 5 0.000000 359.912109 a fill s n 1049 1649 5 0.000000 359.912109 a fill s n 2099 1109 5 0.000000 359.912109 a fill s n 1649 1109 5 0.000000 359.912109 a fill s n 749 1109 5 0.000000 359.912109 a fill s n 299 1109 5 0.000000 359.912109 a fill s n 1859 449 5 0.000000 359.912109 a fill s n 1259 449 5 0.000000 359.912109 a fill s n 509 449 5 0.000000 359.912109 a fill s n 1499 1589 m 1499 1649 l s n 1049 1589 m 1049 1649 l s n 299 1049 m 299 1109 l s n 749 1049 m 749 1109 l s n 959 1649 m 4 w 1049 1649 l 1499 1649 l 1589 1649 l s n 299 1109 m 749 1109 l 779 1109 l s n 1259 1049 m 2 w 1259 959 l 1259 449 l s n 509 509 m 509 449 l s n 1859 509 m 1859 449 l s n 149 449 m 4 w 509 449 l 1259 449 l 1859 449 l 2249 449 l s n 479 899 m 2 w 299 899 l s n 299 899 5 0.000000 359.912109 a fill s n 509 659 5 0.000000 359.912109 a fill s n 749 929 m 779 899 l s n 899 749 m 839 749 l s n 899 899 m 899 749 l s n 779 899 m 899 899 l s n 719 899 m 749 929 l s n 569 899 m 719 899 l s n 299 959 m 299 899 l 299 809 l s n 509 599 m 509 659 l s n 749 659 m 749 689 l s n 299 659 m 509 659 l 749 659 l s n 299 689 m 299 659 l s n 1649 899 5 0.000000 359.912109 a fill s n 1859 659 5 0.000000 359.912109 a fill s n 2249 749 m 2189 749 l s n 2249 899 m 2249 749 l s n 1649 959 m 1649 899 l 1649 809 l s n 1859 599 m 1859 659 l s n 2099 659 m 2099 689 l s n 1649 659 m 1859 659 l 2099 659 l s n 1649 689 m 1649 659 l s n 1229 1439 m 1049 1439 l s n 1049 1439 5 0.000000 359.912109 a fill s n 1259 1199 5 0.000000 359.912109 a fill s n 1499 1469 m 1529 1439 l 1649 1439 l s n 1469 1439 m 1499 1469 l s n 1319 1439 m 1469 1439 l s n 1049 1499 m 1049 1439 l 1049 1379 l 1049 1349 l s n 1259 1139 m 1259 1199 l s n 1499 1199 m 1499 1229 l s n 1049 1199 m 1259 1199 l 1499 1199 l s n 1049 1229 m 1049 1199 l s n 959 1079 m 959 1109 l s n 959 1199 m 959 1289 l s n 209 749 m 209 809 l s n 209 899 m 209 1079 l s showpage grestore %%Trailer restore .