.vs 15p .EQ delim @@ .EN .EQ define vt ' V sub size -1 T ' define Vbe ' V sub { size -1 BE } ' define vo ' V sub size +1 o ' define BetA ' bold beta ' define a1 ' size +2 a sub 1 ' define a2 ' size +2 a sub 2 ' define PartiaL ' bold partial ' define DeltA ' bold delta ' .EN .sp 0.25i \fBTitle\fP .ce Hybrid: Hybrid Voltage Reference .sp 0.25i \fBDescription\fP .P This voltage regulator circuit will appear in the January 1991 ( volume 26 ) issue of the @italic "Journal of Solid State Circuits"@. The bandgap regulator can be partitioned into two sections; a primary bandgap standard and an error feedback amplifier. Transistors @Q sub 1-2@ constitute the primary bandgap voltage standard. This sub-circuit produces an error voltage @V sub os@ @=@ @ V sub size -1 C2@ @-@ @V sub size -1 C1@ which is proportional to the output voltage deviation from the ideal bandgap reference voltage @V sub bg (T)@ @approx@ 1.25V : .DS I .EQ [1] V sub os ~~approx~~{vo ~-~V sub bg (T)} over H .EN .DE .DS I .EQ H ~~=~~(^1~+~ K sup -1 ^)(^1~+~ R sub 3 over R sub 2 ^ K sup -1^) .EN .DE when the @Q sub 1-2@ base currents are negligible and |@vo@ @-@ @V sub bg@| @size -2 <@ 150mV. The ideal bandgap voltage is defined as @V sub bg (T)@ @=@ @(^ R sub 2 /^ R sub 3 ^)^K^ vt @ @+@ @V sub size -1 BE1 (^ V sub os ^=^ 0^,^ I sub ib ^=^ 0 ^) @. @K@ is related to the ratio of ideal @Q sub 1@,@Q sub 2@ emitter current densities by @K@ @=@ @ln ( a2 R sub 2 )/( a1 R sub 1 ) @, where @a1@, @a2@ are the emitter areas of @Q sub 1@, @Q sub 2@, respectively. @vt@ @==@ @k sub { size -2 B }T/ ^ q@ is the thermal voltage. @H@ is typically about 2.5. This reference circuit also has a second stable state with @V sub os@ @=@ 0 at @vo@ @approx@ 0.8V which can produce start-up problems. .P The error amplifier, consisting of differential amplifier @Q sub 3-4@, voltage follower @Q sub 8@ and current mirror preregulator @Q sub 5-7@, adjusts @vo@ so that @V sub os@ @approx@ 0 against variations in load current, temperature and supply voltage @V sub c@. The current mirror @Q sub 5-7@ stabilizes the collector voltage of @Q sub 7@ against variations in @V sub c@ when @R sub 5@ @=@ @R sub 6@. Resistor @R sub 7@ provides first order temperature compensation for @V sub size -1 C4@ when @R sub 7@ @=@ @R sub 6@ @=@ @R sub 5@, since @V sub size -1 C4@ @=@ @V sub size -1 BE7@ @+@ @V sub size -1 BE5@ @+@ @R sub 5 over R sub 7 ^(^ vo ^-^ V sub size -1 BE5 ^)@ @-@ @V sub size -1 BE8@ @approx@ @vo@. A number of factors contribute to degrade the line regulation. Analysis of the current mirror shows that .DS I .EQ {PartiaL V sub size -1 C7} over {PartiaL V sub c} ~~= mark ~~ 1 over {g sub m7 R sub 6 ^+^2} ~+~ {R sub 6 ^-^ R sub 5} over R sub 6 ~+~ {a sub 6 ^-^ a sub 5 } over a sub 6 .EN .DE .DS I .EQ lineup ~+~ {1 ^-^ R sub 6 /^ R sub 7} over {g sub m5 R sub 6 ^+^2} ~+~ 2 over BetA sup {fwd 30 2} .EN .DE The first term represents the change in @Vbe@ of @Q sub 7@ due to the current flow @d V sub c /^ R sub 5 @ in @R sub 5@. The next two terms represent resistor and effective transistor emitter area mismatch, respectively. The fourth term vanishes when @R sub 7@ @=@ @R sub 6@. The overall line regulation is .DS I .EQ {d vo } over {d V sub c } ~~=~~ H over { g sub m4 ^ R sub 6 } ~ {PartiaL V sub size -1 C7} over {PartiaL V sub c} .EN .DE .P The optimum line regulation is about 0.7mV/V. It may appear trivial to set @{PartiaL V sub size -1 C7 }/^ {PartiaL V sub c}@ @=@ 0 by chosing @R sub 5@ and @R sub 6@ so that the first three terms in Eqn. 7 cancel. However, this condition will not prevail at all operating conditions. A number of factors may prevent self-starting when @{PartiaL V sub size -1 C7 }/^ {PartiaL V sub c}@ @size -2 <@ 0 due to bistability of the basic reference. .P This circuit should have three solutions with the values given for \f(CWR5 \fP and \f(CWR6 \fP. The solutions may merge if the values of these two resistors are brought closer together. In other words, let the value of \f(CWR6 \fP be expressed as @"\f(CWR5\fP" + epsilon@. There will be a qualitative change in the behavior of the circuit at a bifurcation point as @epsilon@ is increased from zero. This is not just an academic consideration, because offsetting the values of \f(CWR5 \fP and \f(CWR6 \fP improves the performance of the circuit. However, too large a difference raises the possibility of multiple solutions, which is undesirable. One of the three solutions is electronically unstable. .sp 0.25i \fBDescription of successful operating point computation, if available\fP .P A homotopy method has been used to identify all three DC solutions of this circuit. .bp .sp 0.25i \fBSpice File\fP .DS I \f(CW * * Voltage reference with potential for multiple DC solutions * r5 and r6 are deliberately offset to improve the regulation * however, if offset too much, the circuit will exhibit * multiple solutions * The value of r5 given below should generate 3 solutions; * if not, try making it a bit smaller. * * A default NPN model is adequate, but note the scaling factors for * q2 and q4 . * * bandgap core q1 1 1 0 npn q2 2 8 3 npn 3.33 * error amp q3 4 2 0 npn q4 50 4 6 npn 3.33 q7 7 8 0 npn *active load q5 4 7 5 npn q6 5 5 0 npn q8 9 5 0 npn *vaf compensation q9 7 7 9 npn *start up q10 7 7 6 npn * * resistors * r1 6 1 948 r2 6 2 2844 r3 3 0 362 * * See above * r5 50 7 3100 r6 50 4 3280 * r7 6 5 3200 r8 1 8 362 * vcc 50 0 5.0 \&.end \fP .DE .bp .sp 0.25i .PS Q9:[B:box ht 1.4 wid 1.4; "\f(CWQ9\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 +1.503" ljust at B.ne+(-0.5,-0.03); " +0.752" ljust at B.se+(-0.5,0.05); " +1.503" ljust at B.w; " +1.11m" ljust at B.ne+(-1.1,-0.1); " -1.11m" ljust at B.se+(-1.1,0.05); " +5.56u\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;]; Q5:[B:box ht 1.4 wid 1.4; "\f(CWQ5\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 +1.227" ljust at B.ne+(-0.5,-0.03); " +0.751" ljust at B.se+(-0.5,0.05); " +1.503" ljust at B.w; " +1.15m" ljust at B.ne+(-1.1,-0.1); " -1.16m" ljust at B.se+(-1.1,0.05); " +5.78u\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 Q9.e; Q10:[B:box ht 1.4 wid 1.4; "\f(CWQ10\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 +1.503" ljust at B.ne+(-0.5,-0.03); " +0.646" ljust at B.se+(-0.5,0.05); " +1.503" ljust at B.w; "+75.17m" ljust at B.ne+(-1.1,-0.1); "-75.55m" ljust at B.se+(-1.1,0.05); "+377.75u\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 Q5.e; 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 +5.000" ljust at B.ne+(-0.5,-0.03); " +0.646" ljust at B.se+(-0.5,0.05); " +1.227" ljust at B.w; " +4.03u" ljust at B.ne+(-1.1,-0.1); " -4.05u" ljust at B.se+(-1.1,0.05); "+20.27n\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 Q5.e; 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 +0.752" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.751" ljust at B.w; " +1.11m" ljust at B.ne+(-1.1,-0.1); " -1.12m" ljust at B.se+(-1.1,0.05); " +5.58u\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 Q9.s; Q6:[B:box ht 1.4 wid 1.4; "\f(CWQ6\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 +0.751" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.751" ljust at B.w; " +1.11m" ljust at B.ne+(-1.1,-0.1); " -1.12m" ljust at B.se+(-1.1,0.05); " +5.58u\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 Q8.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 +0.636" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.636" ljust at B.w; "+11.07u" ljust at B.ne+(-1.1,-0.1); "-11.12u" ljust at B.se+(-1.1,0.05); "+55.61n\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 +1.227" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.574" ljust at B.w; "+943.82n" ljust at B.ne+(-1.1,-0.1); "-948.56n" ljust at B.se+(-1.1,0.05); " +4.74n\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 Q1.e; Q7:[B:box ht 1.4 wid 1.4; "\f(CWQ7\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 +1.503" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.636" ljust at B.w; "+11.04u" ljust at B.ne+(-1.1,-0.1); "-11.09u" ljust at B.se+(-1.1,0.05); "+55.47n\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 Q1.s; 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 +0.574" ljust at B.ne+(-0.5,-0.03); " +0.009" ljust at B.se+(-0.5,0.05); " +0.636" ljust at B.w; "+25.40u" ljust at B.ne+(-1.1,-0.1); "-25.53u" ljust at B.se+(-1.1,0.05); "+127.63n\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 Q7.e; .PE .nf \f(CW[1]: 0.63575 [2]: 0.57420 [3]: 0.00924 [4]: 1.22691 [5]: 0.75098 [6]: 0.64646 [7]: 1.50280 [8]: 0.63568 [9]: 0.75195 \fP .fi .ce \fBHybrid: Solution 1; signature: 20.81636; ||rho(x*,1)|| 7.588e-17 (Stable)\fP .bp .sp 0.25i .PS Q9:[B:box ht 1.4 wid 1.4; "\f(CWQ9\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 +1.502" ljust at B.ne+(-0.5,-0.03); " +0.751" ljust at B.se+(-0.5,0.05); " +1.502" ljust at B.w; " +1.09m" ljust at B.ne+(-1.1,-0.1); " -1.09m" ljust at B.se+(-1.1,0.05); " +5.45u\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;]; Q5:[B:box ht 1.4 wid 1.4; "\f(CWQ5\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 +1.344" ljust at B.ne+(-0.5,-0.03); " +0.751" ljust at B.se+(-0.5,0.05); " +1.502" ljust at B.w; " +1.11m" ljust at B.ne+(-1.1,-0.1); " -1.12m" ljust at B.se+(-1.1,0.05); " +5.60u\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 Q9.e; Q10:[B:box ht 1.4 wid 1.4; "\f(CWQ10\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 +1.502" ljust at B.ne+(-0.5,-0.03); " +0.694" ljust at B.se+(-0.5,0.05); " +1.502" ljust at B.w; "+10.86m" ljust at B.ne+(-1.1,-0.1); "-10.91m" ljust at B.se+(-1.1,0.05); "+54.56u\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 Q5.e; 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 +5.000" ljust at B.ne+(-0.5,-0.03); " +0.694" ljust at B.se+(-0.5,0.05); " +1.344" ljust at B.w; "+65.60u" ljust at B.ne+(-1.1,-0.1); "-65.93u" ljust at B.se+(-1.1,0.05); "+329.66n\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 Q5.e; 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 +0.751" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.751" ljust at B.w; " +1.09m" ljust at B.ne+(-1.1,-0.1); " -1.10m" ljust at B.se+(-1.1,0.05); " +5.48u\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 Q9.s; Q6:[B:box ht 1.4 wid 1.4; "\f(CWQ6\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 +0.751" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.751" ljust at B.w; " +1.09m" ljust at B.ne+(-1.1,-0.1); " -1.10m" ljust at B.se+(-1.1,0.05); " +5.48u\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 Q8.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 +0.662" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.662" ljust at B.w; "+32.24u" ljust at B.ne+(-1.1,-0.1); "-32.41u" ljust at B.se+(-1.1,0.05); "+162.03n\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 +1.344" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.549" ljust at B.w; "+342.29n" ljust at B.ne+(-1.1,-0.1); "-344.01n" ljust at B.se+(-1.1,0.05); " +1.72n\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 Q1.e; Q7:[B:box ht 1.4 wid 1.4; "\f(CWQ7\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 +1.502" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.662" ljust at B.w; "+32.05u" ljust at B.ne+(-1.1,-0.1); "-32.21u" ljust at B.se+(-1.1,0.05); "+161.05n\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 Q1.s; 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 +0.549" ljust at B.ne+(-0.5,-0.03); " +0.019" ljust at B.se+(-0.5,0.05); " +0.662" ljust at B.w; "+50.89u" ljust at B.ne+(-1.1,-0.1); "-51.15u" ljust at B.se+(-1.1,0.05); "+255.73n\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 Q7.e; .PE .nf \f(CW[1]: 0.66248 [2]: 0.54884 [3]: 0.01851 [4]: 1.34376 [5]: 0.75051 [6]: 0.69359 [7]: 1.50155 [8]: 0.66233 [9]: 0.75117 \fP .fi .ce \fBHybrid: Solution 2; signature: 21.31448; ||rho(x*,1)|| 1.404e-15 (Unstable!)\fP .bp .sp 0.25i .PS Q9:[B:box ht 1.4 wid 1.4; "\f(CWQ9\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 +1.473" ljust at B.ne+(-0.5,-0.03); " +0.734" ljust at B.se+(-0.5,0.05); " +1.473" ljust at B.w; "+691.48u" ljust at B.ne+(-1.1,-0.1); "-694.96u" ljust at B.se+(-1.1,0.05); " +3.47u\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;]; Q5:[B:box ht 1.4 wid 1.4; "\f(CWQ5\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 +1.880" ljust at B.ne+(-0.5,-0.03); " +0.739" ljust at B.se+(-0.5,0.05); " +1.473" ljust at B.w; "+564.70u" ljust at B.ne+(-1.1,-0.1); "-567.54u" ljust at B.se+(-1.1,0.05); " +2.84u\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 Q9.e; Q10:[B:box ht 1.4 wid 1.4; "\f(CWQ10\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 +1.473" ljust at B.ne+(-0.5,-0.03); " +1.169" ljust at B.se+(-0.5,0.05); " +1.473" ljust at B.w; "+19.08p" ljust at B.ne+(-1.1,-0.1); "-19.18p" ljust at B.se+(-1.1,0.05); "+95.89f\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 Q5.e; 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 +5.000" ljust at B.ne+(-0.5,-0.03); " +1.169" ljust at B.se+(-0.5,0.05); " +1.880" ljust at B.w; "+751.68u" ljust at B.ne+(-1.1,-0.1); "-755.45u" ljust at B.se+(-1.1,0.05); " +3.78u\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 Q5.e; 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 +0.734" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.739" ljust at B.w; "+694.96u" ljust at B.ne+(-1.1,-0.1); "-698.45u" ljust at B.se+(-1.1,0.05); " +3.49u\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 Q9.s; Q6:[B:box ht 1.4 wid 1.4; "\f(CWQ6\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 +0.739" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.739" ljust at B.w; "+694.96u" ljust at B.ne+(-1.1,-0.1); "-698.45u" ljust at B.se+(-1.1,0.05); " +3.49u\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 Q8.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 +0.729" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.729" ljust at B.w; "+459.29u" ljust at B.ne+(-1.1,-0.1); "-461.60u" ljust at B.se+(-1.1,0.05); " +2.31u\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 +1.880" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.724" ljust at B.w; "+382.60u" ljust at B.ne+(-1.1,-0.1); "-384.52u" ljust at B.se+(-1.1,0.05); " +1.92u\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 Q1.e; Q7:[B:box ht 1.4 wid 1.4; "\f(CWQ7\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 +1.473" ljust at B.ne+(-0.5,-0.03); " +0.000" ljust at B.se+(-0.5,0.05); " +0.728" ljust at B.w; "+439.85u" ljust at B.ne+(-1.1,-0.1); "-442.06u" ljust at B.se+(-1.1,0.05); " +2.21u\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 Q1.s; 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 +0.724" ljust at B.ne+(-0.5,-0.03); " +0.056" ljust at B.se+(-0.5,0.05); " +0.728" ljust at B.w; "+154.54u" ljust at B.ne+(-1.1,-0.1); "-155.32u" ljust at B.se+(-1.1,0.05); "+776.58n\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 Q7.e; .PE .nf \f(CW[1]: 0.72889 [2]: 0.72432 [3]: 0.05622 [4]: 1.88045 [5]: 0.73924 [6]: 1.16932 [7]: 1.47330 [8]: 0.72781 [9]: 0.73418 \fP .fi .ce \fBHybrid: Solution 3; signature: 24.23484; ||rho(x*,1)|| 2.798e-17 (Stable)\fP \&-------- PostScript ------------ %!PS-Adobe-1.0 %%Creator: HPF version 3.4 SUN4-P2 28 Feb 1990 %%CreationDate: Sun Nov 4 20:22:43 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 358.000000 -2176.000000 translate %%EndProlog %%Page: x0y0 1 gsave n 2174 1334 m [] 0 setdash 2 w 2174 1304 l s n 2156 1289 m 4 w 2192 1289 l s n 2165 1274 m 2183 1274 l s n 2144 1304 m 2204 1304 l s n 1424 704 m 2 w 1424 674 l s n 1406 659 m 4 w 1442 659 l s n 1415 644 m 1433 644 l s n 1394 674 m 1454 674 l s n 2024 629 m 2 w 2024 599 l s n 2006 584 m 4 w 2042 584 l s n 2015 569 m 2033 569 l s n 1994 599 m 2054 599 l s n 1799 284 m 2 w 1799 254 l s n 1781 239 m 4 w 1817 239 l s n 1790 224 m 1808 224 l s n 1769 254 m 1829 254 l s n 449 389 m 2 w 449 359 l s n 431 344 m 4 w 467 344 l s n 440 329 m 458 329 l s n 419 359 m 479 359 l s n 1049 809 m 2 w 1049 779 l s n 1031 764 m 4 w 1067 764 l s n 1040 749 m 1058 749 l s n 1019 779 m 1079 779 l s n 599 809 m 2 w 599 779 l s n 581 764 m 4 w 617 764 l s n 590 749 m 608 749 l s n 569 779 m 629 779 l s n 1124 1124 m 2 w 1109 1124 l s n 1187 1124 m 1199 1124 l s n 1133 1142 m 4 w 1124 1124 l s n 1163 1142 m 1178 1106 l 1187 1124 l s n 1133 1142 m 1148 1106 l 1163 1142 l s n 1424 944 m 2 w 1424 929 l s n 1424 1007 m 1424 1019 l s n 1406 953 m 4 w 1424 944 l s n 1406 983 m 1442 998 l 1424 1007 l s n 1406 953 m 1442 968 l 1406 983 l s n 1514 659 m 2 w 1514 644 l s n 1514 722 m 1514 734 l s n 1496 668 m 4 w 1514 659 l s n 1496 698 m 1532 713 l 1514 722 l s n 1496 668 m 1532 683 l 1496 698 l s n 1799 359 m 2 w 1799 344 l s n 1799 422 m 1799 434 l s n 1781 368 m 4 w 1799 359 l s n 1781 398 m 1817 413 l 1799 422 l s n 1781 368 m 1817 383 l 1781 398 l s n 1799 1019 m 2 w 1799 1004 l s n 1799 1082 m 1799 1094 l s n 1781 1028 m 4 w 1799 1019 l s n 1781 1058 m 1817 1073 l 1799 1082 l s n 1781 1028 m 1817 1043 l 1781 1058 l s n 1049 1424 m 2 w 1049 1409 l s n 1049 1487 m 1049 1499 l s n 1031 1433 m 4 w 1049 1424 l s n 1031 1463 m 1067 1478 l 1049 1487 l s n 1031 1433 m 1067 1448 l 1031 1463 l s n 449 1424 m 2 w 449 1409 l s n 449 1487 m 449 1499 l s n 431 1433 m 4 w 449 1424 l s n 431 1463 m 467 1478 l 449 1487 l s n 431 1433 m 467 1448 l 431 1463 l s n 2204 1404 m 2 w 2218 1404 l s n 2204 1476 m 2218 1476 l s n 2211 1469 m 2211 1483 l s n 2165 1448 m 2165 1436 l 2174 1427 l 2183 1436 l 2183 1448 l s n 2174 1409 m 2174 1379 l s n 2174 1469 m 2174 1499 l s n 2174 1439 29 360.000000 719.912109 a s n 1978 793 m 4 w 1978 706 l s n 1980 793 m 1980 706 l s n 1979 749 m 2 w 1934 749 l s n 1979 719 m 2024 704 l 2006 698 l s n 2024 704 m 2011 721 l s n 2024 704 m 2024 689 l s n 1979 779 m 2024 794 l 2024 809 l s n 1753 583 m 4 w 1753 496 l s n 1755 583 m 1755 496 l s n 1754 539 m 2 w 1709 539 l s n 1754 509 m 1799 494 l 1781 488 l s n 1799 494 m 1786 511 l s n 1799 494 m 1799 479 l s n 1754 569 m 1799 584 l 1799 599 l s n 1753 1393 m 4 w 1753 1306 l s n 1755 1393 m 1755 1306 l s n 1754 1349 m 2 w 1709 1349 l s n 1754 1319 m 1799 1304 l 1781 1298 l s n 1799 1304 m 1786 1321 l s n 1799 1304 m 1799 1289 l s n 1754 1379 m 1799 1394 l 1799 1409 l s n 1003 1003 m 4 w 1003 916 l s n 1005 1003 m 1005 916 l s n 1004 959 m 2 w 959 959 l s n 1004 929 m 1049 914 l 1031 908 l s n 1049 914 m 1036 931 l s n 1049 914 m 1049 899 l s n 1004 989 m 1049 1004 l 1049 1019 l s n 1003 1303 m 4 w 1003 1216 l s n 1005 1303 m 1005 1216 l s n 1004 1259 m 2 w 959 1259 l s n 1004 1229 m 1049 1214 l 1031 1208 l s n 1049 1214 m 1036 1231 l s n 1049 1214 m 1049 1199 l s n 1004 1289 m 1049 1304 l 1049 1319 l s n 1213 1303 m 4 w 1213 1216 l s n 1215 1303 m 1215 1216 l s n 1214 1259 m 2 w 1169 1259 l s n 1214 1229 m 1259 1214 l 1241 1208 l s n 1259 1214 m 1246 1231 l s n 1259 1214 m 1259 1199 l s n 1214 1289 m 1259 1304 l 1259 1319 l s n 1471 853 m 4 w 1471 766 l s n 1469 853 m 1469 766 l s n 1469 809 m 2 w 1514 809 l s n 1469 779 m 1424 764 l 1443 758 l s n 1424 764 m 1438 781 l s n 1424 764 m 1424 749 l s n 1469 839 m 1424 854 l 1424 869 l s n 496 583 m 4 w 496 496 l s n 494 583 m 494 496 l s n 494 539 m 2 w 539 539 l s n 494 509 m 449 494 l 468 488 l s n 449 494 m 463 511 l s n 449 494 m 449 479 l s n 494 569 m 449 584 l 449 599 l s n 646 1003 m 4 w 646 916 l s n 644 1003 m 644 916 l s n 644 959 m 2 w 689 959 l s n 644 929 m 599 914 l 618 908 l s n 599 914 m 613 931 l s n 599 914 m 599 899 l s n 644 989 m 599 1004 l 599 1019 l s n 646 1303 m 4 w 646 1216 l s n 644 1303 m 644 1216 l s n 644 1259 m 2 w 689 1259 l s n 644 1229 m 599 1214 l 618 1208 l s n 599 1214 m 613 1231 l s n 599 1214 m 599 1199 l s n 644 1289 m 599 1304 l 599 1319 l s n 1124 1082 m 1127 1085 l 1139 1085 l 1142 1082 l 1142 1079 l 1139 1076 l 1130 1076 l s n 1124 1067 m 1127 1064 l 1139 1064 l 1142 1067 l 1142 1073 l 1139 1076 l s n 1154 1064 m 1151 1064 l 1151 1067 l 1154 1067 l 1154 1064 l s n 1190 1064 m 1172 1064 l 1172 1067 l 1178 1073 l 1187 1073 l 1190 1076 l 1190 1082 l 1187 1085 l 1175 1085 l 1172 1082 l s n 1196 1076 m 1205 1076 l 1205 1073 l 1214 1064 l s n 1196 1064 m 1196 1085 l s n 1205 1076 m 1214 1085 l s n 1139 1169 m 1139 1190 l 1154 1190 l 1157 1187 l 1157 1181 l 1154 1178 l 1139 1178 l s n 1157 1169 m 1148 1178 l s n 1163 1187 m 1163 1190 l 1181 1190 l 1181 1187 l 1172 1178 l 1172 1169 l s n 1274 914 m 1289 914 l 1292 917 l 1292 932 l 1289 935 l 1277 935 l 1274 932 l 1274 926 l 1277 923 l 1289 923 l 1292 926 l s n 1316 920 m 1298 920 l 1313 935 l 1313 914 l s n 1322 923 m 1322 917 l 1325 914 l 1337 914 l 1340 917 l 1340 923 l 1337 926 l 1325 926 l 1322 923 l s n 1325 926 m 1322 929 l 1322 932 l 1325 935 l 1337 935 l 1340 932 l 1340 929 l 1337 926 l s n 1352 914 m 1349 914 l 1349 917 l 1352 917 l 1352 914 l s n 1385 932 m 1370 917 l 1370 932 l 1373 935 l 1385 935 l 1388 932 l 1385 932 l s n 1370 917 m 1373 914 l 1385 914 l 1388 917 l 1388 932 l s n 1349 1004 m 1349 1025 l 1364 1025 l 1367 1022 l 1367 1016 l 1364 1013 l 1349 1013 l s n 1367 1004 m 1358 1013 l s n 1379 1022 m 1382 1025 l 1382 1004 l s n 1376 1004 m 1388 1004 l s n 1559 677 m 1562 680 l 1574 680 l 1577 677 l 1577 674 l 1574 671 l 1565 671 l s n 1559 662 m 1562 659 l 1574 659 l 1577 662 l 1577 668 l 1574 671 l s n 1601 680 m 1586 680 l 1583 677 l 1583 662 l 1586 659 l 1598 659 l 1601 662 l 1601 668 l 1598 671 l 1586 671 l 1583 668 l s n 1625 659 m 1607 659 l 1607 662 l 1613 668 l 1622 668 l 1625 671 l 1625 677 l 1622 680 l 1610 680 l 1607 677 l s n 1637 659 m 1634 659 l 1634 662 l 1637 662 l 1637 659 l s n 1670 677 m 1655 662 l 1655 677 l 1658 680 l 1670 680 l 1673 677 l 1670 677 l s n 1655 662 m 1658 659 l 1670 659 l 1673 662 l 1673 677 l s n 1559 719 m 1559 740 l 1574 740 l 1577 737 l 1577 731 l 1574 728 l 1559 728 l s n 1577 719 m 1568 728 l s n 1583 728 m 1583 722 l 1586 719 l 1598 719 l 1601 722 l 1601 728 l 1598 731 l 1586 731 l 1583 728 l s n 1586 731 m 1583 734 l 1583 737 l 1586 740 l 1598 740 l 1601 737 l 1601 734 l 1598 731 l s n 1649 362 m 1652 365 l 1664 365 l 1667 362 l 1667 359 l 1664 356 l 1655 356 l s n 1649 347 m 1652 344 l 1664 344 l 1667 347 l 1667 353 l 1664 356 l s n 1691 365 m 1676 365 l 1673 362 l 1673 347 l 1676 344 l 1688 344 l 1691 347 l 1691 353 l 1688 356 l 1676 356 l 1673 353 l s n 1715 344 m 1697 344 l 1697 347 l 1703 353 l 1712 353 l 1715 356 l 1715 362 l 1712 365 l 1700 365 l 1697 362 l s n 1727 344 m 1724 344 l 1724 347 l 1727 347 l 1727 344 l s n 1760 362 m 1745 347 l 1745 362 l 1748 365 l 1760 365 l 1763 362 l 1760 362 l s n 1745 347 m 1748 344 l 1760 344 l 1763 347 l 1763 362 l s n 1724 404 m 1724 425 l 1739 425 l 1742 422 l 1742 416 l 1739 413 l 1724 413 l s n 1742 404 m 1733 413 l s n 1748 422 m 1751 425 l 1763 425 l 1766 422 l 1766 419 l 1763 416 l 1754 416 l s n 1748 407 m 1751 404 l 1763 404 l 1766 407 l 1766 413 l 1763 416 l s n 1862 1019 m 1844 1019 l 1844 1022 l 1850 1028 l 1859 1028 l 1862 1031 l 1862 1037 l 1859 1040 l 1847 1040 l 1844 1037 l s n 1874 1019 m 1871 1019 l 1871 1022 l 1874 1022 l 1874 1019 l s n 1892 1028 m 1892 1022 l 1895 1019 l 1907 1019 l 1910 1022 l 1910 1028 l 1907 1031 l 1895 1031 l 1892 1028 l s n 1895 1031 m 1892 1034 l 1892 1037 l 1895 1040 l 1907 1040 l 1910 1037 l 1910 1034 l 1907 1031 l s n 1934 1025 m 1916 1025 l 1931 1040 l 1931 1019 l s n 1958 1025 m 1940 1025 l 1955 1040 l 1955 1019 l s n 1964 1031 m 1973 1031 l 1973 1028 l 1982 1019 l s n 1964 1019 m 1964 1040 l s n 1973 1031 m 1982 1040 l s n 1844 1079 m 1844 1100 l 1859 1100 l 1862 1097 l 1862 1091 l 1859 1088 l 1844 1088 l s n 1862 1079 m 1853 1088 l s n 1886 1079 m 1868 1079 l 1868 1082 l 1874 1088 l 1883 1088 l 1886 1091 l 1886 1097 l 1883 1100 l 1871 1100 l 1868 1097 l s n 884 1442 m 887 1445 l 899 1445 l 902 1442 l 902 1439 l 899 1436 l 890 1436 l s n 884 1427 m 887 1424 l 899 1424 l 902 1427 l 902 1433 l 899 1436 l s n 914 1424 m 911 1424 l 911 1427 l 914 1427 l 914 1424 l s n 950 1424 m 932 1424 l 932 1427 l 938 1433 l 947 1433 l 950 1436 l 950 1442 l 947 1445 l 935 1445 l 932 1442 l s n 956 1433 m 956 1427 l 959 1424 l 971 1424 l 974 1427 l 974 1433 l 971 1436 l 959 1436 l 956 1433 l s n 959 1436 m 956 1439 l 956 1442 l 959 1445 l 971 1445 l 974 1442 l 974 1439 l 971 1436 l s n 980 1436 m 989 1436 l 989 1433 l 998 1424 l s n 980 1424 m 980 1445 l s n 989 1436 m 998 1445 l s n 959 1499 m 959 1520 l 974 1520 l 977 1517 l 977 1511 l 974 1508 l 959 1508 l s n 977 1499 m 968 1508 l s n 1001 1520 m 986 1520 l 983 1517 l 983 1502 l 986 1499 l 998 1499 l 1001 1502 l 1001 1508 l 998 1511 l 986 1511 l 983 1508 l s n 494 1499 m 494 1520 l 509 1520 l 512 1517 l 512 1511 l 509 1508 l 494 1508 l s n 512 1499 m 503 1508 l s n 536 1520 m 518 1520 l 518 1511 l 533 1511 l 536 1508 l 536 1502 l 533 1499 l 521 1499 l 518 1502 l s n 494 1442 m 497 1445 l 509 1445 l 512 1442 l 512 1439 l 509 1436 l 500 1436 l s n 494 1427 m 497 1424 l 509 1424 l 512 1427 l 512 1433 l 509 1436 l s n 524 1424 m 521 1424 l 521 1427 l 524 1427 l 524 1424 l s n 548 1442 m 551 1445 l 551 1424 l s n 545 1424 m 557 1424 l s n 581 1442 m 566 1427 l 566 1442 l 569 1445 l 581 1445 l 584 1442 l 581 1442 l s n 566 1427 m 569 1424 l 581 1424 l 584 1427 l 584 1442 l s n 605 1442 m 590 1427 l 590 1442 l 593 1445 l 605 1445 l 608 1442 l 605 1442 l s n 590 1427 m 593 1424 l 605 1424 l 608 1427 l 608 1442 l s n 614 1436 m 623 1436 l 623 1433 l 632 1424 l s n 614 1424 m 614 1445 l s n 623 1436 m 632 1445 l s n 2057 1460 m 2039 1460 l 2039 1451 l 2054 1451 l 2057 1448 l 2057 1442 l 2054 1439 l 2042 1439 l 2039 1442 l s n 2069 1439 m 2066 1439 l 2066 1442 l 2069 1442 l 2069 1439 l s n 2102 1457 m 2087 1442 l 2087 1457 l 2090 1460 l 2102 1460 l 2105 1457 l 2102 1457 l s n 2087 1442 m 2090 1439 l 2102 1439 l 2105 1442 l 2105 1457 l s n 2069 1520 m 2069 1508 l 2078 1499 l 2087 1508 l 2087 1520 l s n 2111 1502 m 2108 1499 l 2099 1499 l 2093 1505 l 2093 1514 l 2099 1520 l 2108 1520 l 2111 1517 l s n 2135 1502 m 2132 1499 l 2123 1499 l 2117 1505 l 2117 1514 l 2123 1520 l 2132 1520 l 2135 1517 l s n 1967 824 m 1961 830 l s n 1949 839 m 1949 830 l 1955 824 l 1961 824 l 1967 830 l 1967 839 l 1961 845 l 1955 845 l 1949 839 l s n 1973 842 m 1976 845 l 1988 845 l 1991 842 l 1991 839 l 1988 836 l 1979 836 l s n 1973 827 m 1976 824 l 1988 824 l 1991 827 l 1991 833 l 1988 836 l s n 1742 614 m 1736 620 l s n 1724 629 m 1724 620 l 1730 614 l 1736 614 l 1742 620 l 1742 629 l 1736 635 l 1730 635 l 1724 629 l s n 1766 614 m 1748 614 l 1748 617 l 1754 623 l 1763 623 l 1766 626 l 1766 632 l 1763 635 l 1751 635 l 1748 632 l s n 1727 1409 m 1721 1415 l s n 1709 1424 m 1709 1415 l 1715 1409 l 1721 1409 l 1727 1415 l 1727 1424 l 1721 1430 l 1715 1430 l 1709 1424 l s n 1751 1415 m 1733 1415 l 1748 1430 l 1748 1409 l s n 1082 974 m 1076 980 l s n 1064 989 m 1064 980 l 1070 974 l 1076 974 l 1082 980 l 1082 989 l 1076 995 l 1070 995 l 1064 989 l s n 1106 995 m 1091 995 l 1088 992 l 1088 977 l 1091 974 l 1103 974 l 1106 977 l 1106 983 l 1103 986 l 1091 986 l 1088 983 l s n 962 1289 m 956 1295 l s n 944 1304 m 944 1295 l 950 1289 l 956 1289 l 962 1295 l 962 1304 l 956 1310 l 950 1310 l 944 1304 l s n 986 1310 m 968 1310 l 968 1301 l 983 1301 l 986 1298 l 986 1292 l 983 1289 l 971 1289 l 968 1292 l s n 1292 1289 m 1286 1295 l s n 1274 1304 m 1274 1295 l 1280 1289 l 1286 1289 l 1292 1295 l 1292 1304 l 1286 1310 l 1280 1310 l 1274 1304 l s n 1304 1307 m 1307 1310 l 1307 1289 l s n 1301 1289 m 1313 1289 l s n 1337 1307 m 1322 1292 l 1322 1307 l 1325 1310 l 1337 1310 l 1340 1307 l 1337 1307 l s n 1322 1292 m 1325 1289 l 1337 1289 l 1340 1292 l 1340 1307 l s n 1382 824 m 1376 830 l s n 1364 839 m 1364 830 l 1370 824 l 1376 824 l 1382 830 l 1382 839 l 1376 845 l 1370 845 l 1364 839 l s n 1394 842 m 1397 845 l 1397 824 l s n 1391 824 m 1403 824 l s n 542 614 m 536 620 l s n 524 629 m 524 620 l 530 614 l 536 614 l 542 620 l 542 629 l 536 635 l 530 635 l 524 629 l s n 548 632 m 548 635 l 566 635 l 566 632 l 557 623 l 557 614 l s n 692 1004 m 686 1010 l s n 674 1019 m 674 1010 l 680 1004 l 686 1004 l 692 1010 l 692 1019 l 686 1025 l 680 1025 l 674 1019 l s n 698 1013 m 698 1007 l 701 1004 l 713 1004 l 716 1007 l 716 1013 l 713 1016 l 701 1016 l 698 1013 l s n 701 1016 m 698 1019 l 698 1022 l 701 1025 l 713 1025 l 716 1022 l 716 1019 l 713 1016 l s n 647 1169 m 641 1175 l s n 629 1184 m 629 1175 l 635 1169 l 641 1169 l 647 1175 l 647 1184 l 641 1190 l 635 1190 l 629 1184 l s n 653 1169 m 668 1169 l 671 1172 l 671 1187 l 668 1190 l 656 1190 l 653 1187 l 653 1181 l 656 1178 l 668 1178 l 671 1181 l s n 1049 1349 5 0.000000 359.912109 a fill s n 2024 1349 m 2024 809 l s n 1859 449 m 1850 449 l 1850 467 l 1859 467 l s n 1868 467 m 1871 470 l 1883 470 l 1886 467 l 1886 464 l 1883 461 l 1874 461 l s n 1868 452 m 1871 449 l 1883 449 l 1886 452 l 1886 458 l 1883 461 l s n 1895 449 m 1904 449 l 1904 467 l 1895 467 l s n 1139 569 m 1130 569 l 1130 587 l 1139 587 l s n 1148 578 m 1148 572 l 1151 569 l 1163 569 l 1166 572 l 1166 578 l 1163 581 l 1151 581 l 1148 578 l s n 1151 581 m 1148 584 l 1148 587 l 1151 590 l 1163 590 l 1166 587 l 1166 584 l 1163 581 l s n 1175 569 m 1184 569 l 1184 587 l 1175 587 l s n 1829 914 m 1820 914 l 1820 932 l 1829 932 l s n 1856 914 m 1838 914 l 1838 917 l 1844 923 l 1853 923 l 1856 926 l 1856 932 l 1853 935 l 1841 935 l 1838 932 l s n 1865 914 m 1874 914 l 1874 932 l 1865 932 l s n 1574 839 m 1565 839 l 1565 857 l 1574 857 l s n 1589 857 m 1592 860 l 1592 839 l s n 1586 839 m 1598 839 l s n 1610 839 m 1619 839 l 1619 857 l 1610 857 l s n 1364 1154 m 1355 1154 l 1355 1172 l 1364 1172 l s n 1391 1175 m 1376 1175 l 1373 1172 l 1373 1157 l 1376 1154 l 1388 1154 l 1391 1157 l 1391 1163 l 1388 1166 l 1376 1166 l 1373 1163 l s n 1400 1154 m 1409 1154 l 1409 1172 l 1400 1172 l s n 974 1079 m 965 1079 l 965 1097 l 974 1097 l s n 1001 1100 m 983 1100 l 983 1091 l 998 1091 l 1001 1088 l 1001 1082 l 998 1079 l 986 1079 l 983 1082 l s n 1010 1079 m 1019 1079 l 1019 1097 l 1010 1097 l s n 659 1109 m 650 1109 l 650 1127 l 659 1127 l s n 668 1109 m 683 1109 l 686 1112 l 686 1127 l 683 1130 l 671 1130 l 668 1127 l 668 1121 l 671 1118 l 683 1118 l 686 1121 l s n 695 1109 m 704 1109 l 704 1127 l 695 1127 l s n 1379 1364 m 1370 1364 l 1370 1382 l 1379 1382 l s n 1406 1370 m 1388 1370 l 1403 1385 l 1403 1364 l s n 1415 1364 m 1424 1364 l 1424 1382 l 1415 1382 l s n 374 1154 m 365 1154 l 365 1172 l 374 1172 l s n 383 1172 m 383 1175 l 401 1175 l 401 1172 l 392 1163 l 392 1154 l s n 410 1154 m 419 1154 l 419 1172 l 410 1172 l s n 1289 1529 m 1280 1529 l 1280 1547 l 1289 1547 l s n 1316 1550 m 1298 1550 l 1298 1541 l 1313 1541 l 1316 1538 l 1316 1532 l 1313 1529 l 1301 1529 l 1298 1532 l s n 1337 1547 m 1322 1532 l 1322 1547 l 1325 1550 l 1337 1550 l 1340 1547 l 1337 1547 l s n 1322 1532 m 1325 1529 l 1337 1529 l 1340 1532 l 1340 1547 l s n 1349 1529 m 1358 1529 l 1358 1547 l 1349 1547 l s n 2174 1334 m 2174 1379 l s n 2174 1574 m 2174 1499 l s n 1799 1574 m 2174 1574 l s n 1049 794 m 1049 809 l 1049 899 l s n 1514 809 5 0.000000 359.912109 a fill s n 1424 899 5 0.000000 359.912109 a fill s n 1424 704 m 1424 749 l s n 1514 899 m 1514 809 l s n 1424 899 m 1514 899 l s n 1049 1349 m 1709 1349 l 2024 1349 l s n 1049 1319 m 1049 1349 l s n 599 809 m 599 899 l s n 959 959 5 0.000000 359.912109 a fill s n 959 1049 m 959 959 l s n 689 1259 5 0.000000 359.912109 a fill s n 1799 1574 5 0.000000 359.912109 a fill s n 1049 1574 5 0.000000 359.912109 a fill s n 599 1349 5 0.000000 359.912109 a fill s n 449 1349 5 0.000000 359.912109 a fill s n 1799 1124 5 0.000000 359.912109 a fill s n 1424 1124 5 0.000000 359.912109 a fill s n 1049 1124 5 0.000000 359.912109 a fill s n 1049 1049 5 0.000000 359.912109 a fill s n 1799 749 5 0.000000 359.912109 a fill s n 1514 539 5 0.000000 359.912109 a fill s n 1049 1049 m 959 1049 l s n 689 959 m 959 959 l s n 1049 1124 m 1109 1124 l s n 1049 1019 m 1049 1049 l 1049 1124 l 1049 1199 l s n 1424 1019 m 1424 1124 l s n 1259 1124 m 1424 1124 l s n 1199 1124 m 1259 1124 l s n 1424 1124 m 1799 1124 l s n 1424 869 m 1424 899 l 1424 929 l s n 1424 869 m 1424 854 l s n 1514 734 m 1514 809 l s n 1514 644 m 1514 539 l s n 539 539 m 1514 539 l 1709 539 l s n 1799 284 m 1799 344 l s n 1799 434 m 1799 479 l s n 2024 629 m 2024 689 l s n 1799 749 m 1934 749 l s n 1799 599 m 1799 749 l 1799 1004 l s n 1799 1094 m 1799 1124 l s n 449 389 m 449 479 l s n 599 1019 m 599 1199 l s n 599 1319 m 599 1349 l s n 974 1259 m 959 1259 l s n 689 1259 m 959 1259 l s n 689 1349 m 689 1259 l s n 449 1349 m 599 1349 l 689 1349 l s n 449 599 m 449 1349 l 449 1409 l s n 1049 1349 m 1049 1409 l s n 1049 1499 m 1049 1574 l s n 1799 1409 m 1799 1574 l s n 449 1574 m 1049 1574 l 1799 1574 l s n 449 1499 m 449 1574 l s n 1799 1364 m 1799 1367 l 1817 1385 l s n 1799 1385 m 1817 1367 l 1817 1364 l s n 1823 1382 m 1826 1385 l 1838 1385 l 1841 1382 l 1841 1379 l 1838 1376 l 1829 1376 l s n 1823 1367 m 1826 1364 l 1838 1364 l 1841 1367 l 1841 1373 l 1838 1376 l s n 1853 1364 m 1850 1364 l 1850 1367 l 1853 1367 l 1853 1364 l s n 1871 1382 m 1874 1385 l 1886 1385 l 1889 1382 l 1889 1379 l 1886 1376 l 1877 1376 l s n 1871 1367 m 1874 1364 l 1886 1364 l 1889 1367 l 1889 1373 l 1886 1376 l s n 1895 1382 m 1898 1385 l 1910 1385 l 1913 1382 l 1913 1379 l 1910 1376 l 1901 1376 l s n 1895 1367 m 1898 1364 l 1910 1364 l 1913 1367 l 1913 1373 l 1910 1376 l s n 1799 539 m 1799 542 l 1817 560 l s n 1799 560 m 1817 542 l 1817 539 l s n 1823 557 m 1826 560 l 1838 560 l 1841 557 l 1841 554 l 1838 551 l 1829 551 l s n 1823 542 m 1826 539 l 1838 539 l 1841 542 l 1841 548 l 1838 551 l s n 1853 539 m 1850 539 l 1850 542 l 1853 542 l 1853 539 l s n 1871 557 m 1874 560 l 1886 560 l 1889 557 l 1889 554 l 1886 551 l 1877 551 l s n 1871 542 m 1874 539 l 1886 539 l 1889 542 l 1889 548 l 1886 551 l s n 1895 557 m 1898 560 l 1910 560 l 1913 557 l 1913 554 l 1910 551 l 1901 551 l s n 1895 542 m 1898 539 l 1910 539 l 1913 542 l 1913 548 l 1910 551 l s n 1154 1259 m 1169 1259 l s n 989 1259 m 1154 1259 l s n 1259 1199 m 1259 1124 l s n 1259 1319 m 1154 1319 l 1154 1259 l s n 1154 1259 5 0.000000 359.912109 a fill s n 1259 1124 5 0.000000 359.912109 a fill s n 1799 1124 m 1799 1289 l s showpage grestore %%Trailer restore .