.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 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