.sp 0.25i \fBTitle\fP .ce CmMode: Op Amp Bias Circuit .sp 0.25i \fBDescription\fP .P This is a simplified circuit representing the common-mode bias signal paths in a balanced operational amplifier. The circuit is of interest in our dc analysis algorithm investigation because it contains a positive feedback loop and exhibits hysteresis. The objective of the simulation is to establish the width of the hysteresis loop instead of just the solutions in one or the other stable bias point. .P The circuit arises out of real product design activities and not just from academic construction. The original full circuit, implemented in CMOS, has been reported in IEEE JSSC, V23#6, pp. 1410-1414. Here, for purposes of example, the circuit is implemented with bipolar devices. This modification does not change the functionality of the circuit. The purpose of the bias circuit is to establish an operating point at node [5]. In actual usage, the output at node [OUT] is connected to node [8] and the independent source at node [8] is absent. The circuit contains both positive and negative feedback. In normal operation the negative feedback far dominates the positive. A concern arises, however, that under some transient conditions the positive and negative gains may reverse dominance and cause the circuit to latch. To resolve this concern, the circuit is rearranged so that the positive feedback loop may be studied alone. The negative feedback loop is cut at node [8] and an independent source is inserted. This leads to the circuit in the accompanying schematic. .P Two resistors, RVA4 and RVA2, are added to control the gain of the positive feedback. .P SPICE fails to converge for this circuit for some value of V8 near VCM, even for resistor values as low as rva4 = 8e6 and rva2 = 250e6. .sp 0.25i \fPDescription of successful operating point computation, if available\fP .P By sweeping V8 around the value of VCM, the positive feedback loop may be forced from one stable state to the other. For intermediate values of V8, two solutions are possible. Simulations of this circuit with a homotopy method follow this behavior. With VCM = 2.5 V, RVA4 = 8e12, and RVA2 = 250e12, we have swept V8 from 2.50 V to 2.54 V in 0.1 V steps. All simulations converged to one or the other of the two stable operating points in the hysteresis region. .P The exact value of V8 to put the circuit in the hysteresis region will depend on modeling parameters. Perform several DC operating point analyses stepping V8 in small increments around VCM to find the limits of the hysteresis region, then set V8 to a value right in the middle. Three solutions are possible, one of which is unstable. This provides one test for DC convergence on this circuit. Another\(empossibly more difficult\(emtest is to set V8 outside of but right at the edge of the hysteresis band. In our implementation, the upper edge occurs at a value of approximately 2.540 volts for V8. Both situations are reported below. .bp .sp 0.25i \fBSpice File\fP .DS I \f(CW*-- Common-Mode Bias circuit -- * * Circuit has multiple DC solutions for * values of the parameter V8 in the * neighborhood of 2.5 volts which generate * a hysteresis region approximately 70mV wide * (not necessarily symmetric around 2.500) * * Particular difficulty obtaining an operating point * may be observed for a value of V8 which * is outside of but very close to the hysteresis band * q5b 5 8 7 pbjt 1.0 q5a 3 vcm 7 pbjt 1.0 q6b 5 5 vee nbjt 1.0 q2 12 5 vee nbjt 3.0 q8 12 0 3 pbjt 11.25 q1 3 out 2 pbjt 2.0 q4c 7 1 vcc pbjt 1.0 q3c 2 1 vcc pbjt 1.0 q2c 1 1 vcc pbjt 2.0 q1c 1 vbias vee nbjt 1.0 q4 out 1 vcc pbjt 25.0 q3 out 12 vee nbjt 50.0 q1d vbias vbias vee nbjt 1.0 * RVA4 vcc out 8e12 RVA2 12 vee 250e12 * rfb out 8 20.0e3 rb 0 vbias 107.5e3 r3c vcc 2 250.0e3 * vcc vcc 0 5.0 vee vee 0 -5.0 vcm vcm 0 2.5 * * See discussion above regarding * values for v8 * *v8 8 0 2.520 v8 8 0 2.540 * \&.end\fP .DE .bp .sp 0.25i .PS Q2C:[B:box ht 1.4 wid 1.4; "\f(CWQ2C\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 +4.359" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.359" ljust at B.w; "-27.22u" ljust at B.ne+(-1.1,-0.1); "+27.77u" ljust at B.se+(-1.1,0.05); "-555.46n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\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 +4.971" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.359" ljust at B.w; "-122.56u" ljust at B.ne+(-1.1,-0.1); "+133.85u" ljust at B.se+(-1.1,0.05); "-11.30u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 10.849)\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 Q2C.e; Q3C:[B:box ht 1.4 wid 1.4; "\f(CWQ3C\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 +4.982" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.359" ljust at B.w; "+70.32n" ljust at B.ne+(-1.1,-0.1); "+480.99n" ljust at B.se+(-1.1,0.05); "-551.31n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( -0.128)\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 Q4.e; Q4C:[B:box ht 1.4 wid 1.4; "\f(CWQ4C\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 +3.132" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.359" ljust at B.w; "-13.61u" ljust at B.ne+(-1.1,-0.1); "+13.89u" ljust at B.se+(-1.1,0.05); "-277.73n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q3C.e; Q5A:[B:box ht 1.4 wid 1.4; "\f(CWQ5A\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 +0.570" ljust at B.ne+(-0.5,-0.03); " +3.132" ljust at B.se+(-0.5,0.05); " +2.500" ljust at B.w; " -9.20u" ljust at B.ne+(-1.1,-0.1); " +9.39u" ljust at B.se+(-1.1,0.05); "-187.79n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2C.s; Q5B:[B:box ht 1.4 wid 1.4; "\f(CWQ5B\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 -4.394" ljust at B.ne+(-0.5,-0.03); " +3.132" ljust at B.se+(-0.5,0.05); " +2.520" ljust at B.w; " -4.13u" ljust at B.ne+(-1.1,-0.1); " +4.22u" ljust at B.se+(-1.1,0.05); "-84.38n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q5A.e; Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\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 +0.570" ljust at B.ne+(-0.5,-0.03); " +4.982" ljust at B.se+(-0.5,0.05); " +4.971" ljust at B.w; "-512.50a" ljust at B.ne+(-1.1,-0.1); "+506.80a" ljust at B.se+(-1.1,0.05); " +5.70a\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 .n at Q5A.s; Q8:[B:box ht 1.4 wid 1.4; "\f(CWQ8\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 -4.930" ljust at B.ne+(-0.5,-0.03); " +0.570" ljust at B.se+(-0.5,0.05); " +0.000" ljust at B.w; " -9.02u" ljust at B.ne+(-1.1,-0.1); " +9.20u" ljust at B.se+(-1.1,0.05); "-184.04n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q1.s; Q1D:[B:box ht 1.4 wid 1.4; "\f(CWQ1D\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 -4.332" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.332" ljust at B.w; "+39.90u" ljust at B.ne+(-1.1,-0.1); "-40.10u" ljust at B.se+(-1.1,0.05); "+200.49n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q8.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\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 +4.971" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.930" ljust at B.w; "+85.91f" ljust at B.ne+(-1.1,-0.1); "-81.29f" ljust at B.se+(-1.1,0.05); " -4.62f\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 Q1D.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\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 -4.930" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.394" ljust at B.w; " +9.02u" ljust at B.ne+(-1.1,-0.1); " -9.71u" ljust at B.se+(-1.1,0.05); "+687.58n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 13.115)\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 Q3.e; Q6B:[B:box ht 1.4 wid 1.4; "\f(CWQ6B\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 -4.394" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.394" ljust at B.w; " +3.43u" ljust at B.ne+(-1.1,-0.1); " -3.45u" ljust at B.se+(-1.1,0.05); "+17.24n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2.e; .PE .nf \f(CW[VBIAS]: -4.33220 [1]: 4.35871 [2]: 4.98242 [OUT]: 4.97113 [12]: -4.93040 [3]: 0.57050 [7]: 3.13151 [5]: -4.39354 \fP .fi .ce \fBCmMode V8=2.520: Solution 1; signature: -0.68992; ||rho(x*,1)|| 6.315e-16 (Stable)\fP .bp .sp 0.25i .PS Q2C:[B:box ht 1.4 wid 1.4; "\f(CWQ2C\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 +4.356" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-30.63u" ljust at B.ne+(-1.1,-0.1); "+31.26u" ljust at B.se+(-1.1,0.05); "-625.10n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\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 +4.373" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-382.88u" ljust at B.ne+(-1.1,-0.1); "+390.69u" ljust at B.se+(-1.1,0.05); " -7.81u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2C.e; Q3C:[B:box ht 1.4 wid 1.4; "\f(CWQ3C\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 +4.972" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; " -5.09u" ljust at B.ne+(-1.1,-0.1); " +5.61u" ljust at B.se+(-1.1,0.05); "-517.06n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 9.843)\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 Q4.e; Q4C:[B:box ht 1.4 wid 1.4; "\f(CWQ4C\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 +3.134" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-15.32u" ljust at B.ne+(-1.1,-0.1); "+15.63u" ljust at B.se+(-1.1,0.05); "-312.55n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q3C.e; Q5A:[B:box ht 1.4 wid 1.4; "\f(CWQ5A\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 +0.583" ljust at B.ne+(-0.5,-0.03); " +3.134" ljust at B.se+(-0.5,0.05); " +2.500" ljust at B.w; "-10.36u" ljust at B.ne+(-1.1,-0.1); "+10.57u" ljust at B.se+(-1.1,0.05); "-211.34n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2C.s; Q5B:[B:box ht 1.4 wid 1.4; "\f(CWQ5B\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 -4.386" ljust at B.ne+(-0.5,-0.03); " +3.134" ljust at B.se+(-0.5,0.05); " +2.520" ljust at B.w; " -4.65u" ljust at B.ne+(-1.1,-0.1); " +4.75u" ljust at B.se+(-1.1,0.05); "-94.96n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q5A.e; Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\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 +0.583" ljust at B.ne+(-0.5,-0.03); " +4.972" ljust at B.se+(-0.5,0.05); " +4.373" ljust at B.w; " -5.10u" ljust at B.ne+(-1.1,-0.1); " +5.20u" ljust at B.se+(-1.1,0.05); "-104.01n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q5A.s; Q8:[B:box ht 1.4 wid 1.4; "\f(CWQ8\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 -4.380" ljust at B.ne+(-0.5,-0.03); " +0.583" ljust at B.se+(-0.5,0.05); " +0.000" ljust at B.w; "-15.14u" ljust at B.ne+(-1.1,-0.1); "+15.45u" ljust at B.se+(-1.1,0.05); "-309.04n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q1.s; Q1D:[B:box ht 1.4 wid 1.4; "\f(CWQ1D\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 -4.332" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.332" ljust at B.w; "+39.90u" ljust at B.ne+(-1.1,-0.1); "-40.10u" ljust at B.se+(-1.1,0.05); "+200.49n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q8.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\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 +4.373" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.380" ljust at B.w; "+290.34u" ljust at B.ne+(-1.1,-0.1); "-291.80u" ljust at B.se+(-1.1,0.05); " +1.46u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q1D.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\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 -4.380" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.386" ljust at B.w; "+13.68u" ljust at B.ne+(-1.1,-0.1); "-13.75u" ljust at B.se+(-1.1,0.05); "+68.76n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q3.e; Q6B:[B:box ht 1.4 wid 1.4; "\f(CWQ6B\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 -4.386" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.386" ljust at B.w; " +4.56u" ljust at B.ne+(-1.1,-0.1); " -4.58u" ljust at B.se+(-1.1,0.05); "+22.92n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2.e; .PE .nf \f(CW[VBIAS]: -4.33220 [1]: 4.35575 [2]: 4.97219 [OUT]: 4.37278 [12]: -4.38038 [3]: 0.58346 [7]: 3.13446 [5]: -4.38641 \fP .fi .ce \fBCmMode V8=2.520: Solution 2; signature: -0.45060; ||rho(x*,1)|| 1.141e-15 (Unstable!)\fP .bp .sp 0.25i .PS Q2C:[B:box ht 1.4 wid 1.4; "\f(CWQ2C\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 +4.356" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-30.79u" ljust at B.ne+(-1.1,-0.1); "+31.42u" ljust at B.se+(-1.1,0.05); "-628.32n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\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 -0.117" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-384.85u" ljust at B.ne+(-1.1,-0.1); "+392.70u" ljust at B.se+(-1.1,0.05); " -7.85u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2C.e; Q3C:[B:box ht 1.4 wid 1.4; "\f(CWQ3C\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 +0.604" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-15.39u" ljust at B.ne+(-1.1,-0.1); "+15.71u" ljust at B.se+(-1.1,0.05); "-314.16n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q4.e; Q4C:[B:box ht 1.4 wid 1.4; "\f(CWQ4C\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 +3.135" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-15.39u" ljust at B.ne+(-1.1,-0.1); "+15.71u" ljust at B.se+(-1.1,0.05); "-314.16n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q3C.e; Q5A:[B:box ht 1.4 wid 1.4; "\f(CWQ5A\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 +0.586" ljust at B.ne+(-0.5,-0.03); " +3.135" ljust at B.se+(-0.5,0.05); " +2.500" ljust at B.w; "-10.41u" ljust at B.ne+(-1.1,-0.1); "+10.62u" ljust at B.se+(-1.1,0.05); "-212.43n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2C.s; Q5B:[B:box ht 1.4 wid 1.4; "\f(CWQ5B\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 -4.386" ljust at B.ne+(-0.5,-0.03); " +3.135" ljust at B.se+(-0.5,0.05); " +2.520" ljust at B.w; " -4.68u" ljust at B.ne+(-1.1,-0.1); " +4.77u" ljust at B.se+(-1.1,0.05); "-95.45n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q5A.e; Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\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 +0.586" ljust at B.ne+(-0.5,-0.03); " +0.604" ljust at B.se+(-0.5,0.05); " -0.117" ljust at B.w; " -6.41u" ljust at B.ne+(-1.1,-0.1); "+32.98u" ljust at B.se+(-1.1,0.05); "-26.57u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 0.241)\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 Q5A.s; Q8:[B:box ht 1.4 wid 1.4; "\f(CWQ8\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 -4.365" ljust at B.ne+(-0.5,-0.03); " +0.586" ljust at B.se+(-0.5,0.05); " +0.000" ljust at B.w; "-16.48u" ljust at B.ne+(-1.1,-0.1); "+16.82u" ljust at B.se+(-1.1,0.05); "-336.42n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q1.s; Q1D:[B:box ht 1.4 wid 1.4; "\f(CWQ1D\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 -4.332" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.332" ljust at B.w; "+39.90u" ljust at B.ne+(-1.1,-0.1); "-40.10u" ljust at B.se+(-1.1,0.05); "+200.49n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q8.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\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 -0.117" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.365" ljust at B.w; "+543.29u" ljust at B.ne+(-1.1,-0.1); "-546.02u" ljust at B.se+(-1.1,0.05); " +2.73u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q1D.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\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 -4.365" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.386" ljust at B.w; "+13.75u" ljust at B.ne+(-1.1,-0.1); "-13.82u" ljust at B.se+(-1.1,0.05); "+69.12n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q3.e; Q6B:[B:box ht 1.4 wid 1.4; "\f(CWQ6B\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 -4.386" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.386" ljust at B.w; " +4.58u" ljust at B.ne+(-1.1,-0.1); " -4.61u" ljust at B.se+(-1.1,0.05); "+23.04n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2.e; .PE .nf \f(CW[VBIAS]: -4.33220 [1]: 4.35562 [2]: 0.60353 [OUT]: -0.11750 [12]: -4.36471 [3]: 0.58558 [7]: 3.13459 [5]: -4.38628 \fP .fi .ce \fBCmMode V8=2.520: Solution 3; signature: -16.00105; ||rho(x*,1)|| 3.753e-16 (Stable)\fP .bp .sp 0.25i .PS Q2C:[B:box ht 1.4 wid 1.4; "\f(CWQ2C\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 +4.356" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-30.79u" ljust at B.ne+(-1.1,-0.1); "+31.42u" ljust at B.se+(-1.1,0.05); "-628.32n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\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 -0.137" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-384.85u" ljust at B.ne+(-1.1,-0.1); "+392.70u" ljust at B.se+(-1.1,0.05); " -7.85u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2C.e; Q3C:[B:box ht 1.4 wid 1.4; "\f(CWQ3C\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 +0.591" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-15.39u" ljust at B.ne+(-1.1,-0.1); "+15.71u" ljust at B.se+(-1.1,0.05); "-314.16n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q4.e; Q4C:[B:box ht 1.4 wid 1.4; "\f(CWQ4C\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 +3.139" ljust at B.ne+(-0.5,-0.03); " +5.000" ljust at B.se+(-0.5,0.05); " +4.356" ljust at B.w; "-15.39u" ljust at B.ne+(-1.1,-0.1); "+15.71u" ljust at B.se+(-1.1,0.05); "-314.16n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q3C.e; Q5A:[B:box ht 1.4 wid 1.4; "\f(CWQ5A\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 +0.574" ljust at B.ne+(-0.5,-0.03); " +3.139" ljust at B.se+(-0.5,0.05); " +2.500" ljust at B.w; "-12.55u" ljust at B.ne+(-1.1,-0.1); "+12.81u" ljust at B.se+(-1.1,0.05); "-256.16n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2C.s; Q5B:[B:box ht 1.4 wid 1.4; "\f(CWQ5B\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 -4.402" ljust at B.ne+(-0.5,-0.03); " +3.139" ljust at B.se+(-0.5,0.05); " +2.540" ljust at B.w; " -2.53u" ljust at B.ne+(-1.1,-0.1); " +2.59u" ljust at B.se+(-1.1,0.05); "-51.72n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q5A.e; Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\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 +0.574" ljust at B.ne+(-0.5,-0.03); " +0.591" ljust at B.se+(-0.5,0.05); " -0.137" ljust at B.w; " +2.11u" ljust at B.ne+(-1.1,-0.1); "+33.03u" ljust at B.se+(-1.1,0.05); "-35.14u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( -0.060)\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 Q5A.s; Q8:[B:box ht 1.4 wid 1.4; "\f(CWQ8\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 -4.364" ljust at B.ne+(-0.5,-0.03); " +0.574" ljust at B.se+(-0.5,0.05); " +0.000" ljust at B.w; "-10.24u" ljust at B.ne+(-1.1,-0.1); "+10.44u" ljust at B.se+(-1.1,0.05); "-208.89n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 49.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q1.s; Q1D:[B:box ht 1.4 wid 1.4; "\f(CWQ1D\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 -4.332" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.332" ljust at B.w; "+39.90u" ljust at B.ne+(-1.1,-0.1); "-40.10u" ljust at B.se+(-1.1,0.05); "+200.49n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q8.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\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 -0.137" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.364" ljust at B.w; "+553.81u" ljust at B.ne+(-1.1,-0.1); "-556.59u" ljust at B.se+(-1.1,0.05); " +2.78u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q1D.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\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 -4.364" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.402" ljust at B.w; " +7.45u" ljust at B.ne+(-1.1,-0.1); " -7.49u" ljust at B.se+(-1.1,0.05); "+37.45n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q3.e; Q6B:[B:box ht 1.4 wid 1.4; "\f(CWQ6B\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 -4.402" ljust at B.ne+(-0.5,-0.03); " -5.000" ljust at B.se+(-0.5,0.05); " -4.402" ljust at B.w; " +2.48u" ljust at B.ne+(-1.1,-0.1); " -2.50u" ljust at B.se+(-1.1,0.05); "+12.48n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); 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 Q2.e; .PE .nf \f(CW[VBIAS]: -4.33220 [1]: 4.35562 [2]: 0.59131 [OUT]: -0.13655 [12]: -4.36423 [3]: 0.57366 [7]: 3.13927 [5]: -4.40160 \fP .fi .ce \fBCmMode V8=2.54: Solution 1; signature: -16.14774; ||rho(x*,1)|| 1.105e-17\fP .ce \s+4Single solution obtained outside, but at edge of hysteresis region\s-4 \&-------- PostScript ------------ %!PS-Adobe-1.0 %%Creator: HPF version 3.4 SUN4-P2 28 Feb 1990 %%CreationDate: Sun Nov 4 20:23:33 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 488.000000 -2325.000000 translate %%EndProlog %%Page: x0y0 1 gsave n 2249 1049 m [] 0 setdash 2 w 2249 1019 l s n 2231 1004 m 4 w 2267 1004 l s n 2240 989 m 2258 989 l s n 2219 1019 m 2279 1019 l s n 29 539 m 2 w 29 509 l s n 11 494 m 4 w 47 494 l s n 20 479 m 38 479 l s n 0 509 m 59 509 l s n 1199 809 m 2 w 1199 779 l s n 1181 764 m 4 w 1217 764 l s n 1190 749 m 1208 749 l s n 1169 779 m 1229 779 l s n 1649 1139 m 2 w 1649 1109 l s n 1631 1094 m 4 w 1667 1094 l s n 1640 1079 m 1658 1079 l s n 1619 1109 m 1679 1109 l s n 2279 1074 m 2 w 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2324 1229 m 2315 1229 l 2315 1247 l 2324 1247 l s n 2333 1238 m 2333 1232 l 2336 1229 l 2348 1229 l 2351 1232 l 2351 1238 l 2348 1241 l 2336 1241 l 2333 1238 l s n 2336 1241 m 2333 1244 l 2333 1247 l 2336 1250 l 2348 1250 l 2351 1247 l 2351 1244 l 2348 1241 l s n 2360 1229 m 2369 1229 l 2369 1247 l 2360 1247 l s n 2024 929 m 2015 929 l 2015 947 l 2024 947 l s n 2051 950 m 2033 950 l 2033 941 l 2048 941 l 2051 938 l 2051 932 l 2048 929 l 2036 929 l 2033 932 l s n 2060 929 m 2069 929 l 2069 947 l 2060 947 l s n 1514 1289 m 1505 1289 l 1505 1307 l 1514 1307 l s n 1523 1310 m 1523 1298 l 1532 1289 l 1541 1298 l 1541 1310 l s n 1565 1292 m 1562 1289 l 1553 1289 l 1547 1295 l 1547 1304 l 1553 1310 l 1562 1310 l 1565 1307 l s n 1571 1289 m 1571 1310 l 1580 1301 l 1589 1310 l 1589 1289 l s n 1598 1289 m 1607 1289 l 1607 1307 l 1598 1307 l s n 749 1499 5 0.000000 359.912109 a fill s n 2249 1439 m 2249 1499 l s n 1979 1499 m 2249 1499 l s n 1379 1499 m 1919 1499 l s n 749 1499 m 1319 1499 l s n 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1649 l 530 1652 l 533 1652 l 533 1649 l s n 566 1667 m 551 1652 l 551 1667 l 554 1670 l 566 1670 l 569 1667 l 566 1667 l s n 551 1652 m 554 1649 l 566 1649 l 569 1652 l 569 1667 l s showpage grestore %%Trailer restore .