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128 WIRE -464 176 -752 176 WIRE -1328 192 -1360 192 WIRE -1232 192 -1232 96 WIRE -1232 192 -1248 192 WIRE -1008 224 -1040 224 WIRE -896 224 -928 224 WIRE -576 224 -608 224 WIRE -464 224 -464 176 WIRE -464 224 -512 224 WIRE -416 224 -464 224 WIRE -752 240 -752 176 WIRE -640 240 -672 240 WIRE -608 240 -608 224 WIRE -608 240 -640 240 WIRE -1328 304 -1360 304 WIRE -1232 304 -1232 192 WIRE -1232 304 -1248 304 WIRE -640 320 -640 240 WIRE -608 320 -640 320 WIRE -1168 336 -1168 128 WIRE -1152 336 -1168 336 WIRE -1136 336 -1152 336 WIRE -1040 336 -1040 224 WIRE -1040 336 -1072 336 WIRE -1008 336 -1040 336 WIRE -464 336 -464 224 WIRE -464 336 -544 336 WIRE -416 336 -464 336 WIRE -896 352 -896 224 WIRE -896 352 -944 352 WIRE -784 352 -896 352 WIRE -672 352 -704 352 WIRE -608 352 -672 352 WIRE -1008 368 -1024 368 WIRE -672 384 -672 352 WIRE -1152 400 -1168 400 WIRE -1040 400 -1040 336 WIRE -1040 400 -1072 400 WIRE -1024 448 -1024 368 WIRE -672 448 -672 432 WIRE -1136 464 -1168 464 WIRE -672 480 -672 448 WIRE -672 480 -704 480 WIRE -512 480 -528 480 WIRE -480 480 -512 480 WIRE -384 480 -400 480 WIRE -176 480 -192 480 WIRE -384 496 -384 480 WIRE -176 496 -176 480 WIRE -512 576 -512 560 WIRE -464 576 -512 576 WIRE -512 592 -512 576 FLAG -384 496 0 FLAG -176 496 0 FLAG -976 320 V+ IOPIN -976 320 BiDir FLAG -528 480 V+ IOPIN -528 480 BiDir FLAG -976 384 V- IOPIN -976 384 BiDir FLAG -272 480 V- IOPIN -272 480 BiDir FLAG -576 304 V+ IOPIN -576 304 BiDir FLAG -576 368 V- IOPIN -576 368 BiDir FLAG -416 336 Dout IOPIN -416 336 Out FLAG -1072 -48 V+ IOPIN -1072 -48 BiDir FLAG -1072 16 V- IOPIN -1072 16 BiDir FLAG -640 -80 V+ IOPIN -640 -80 BiDir FLAG -640 -16 V- IOPIN -640 -16 BiDir FLAG -1360 0 Din1 IOPIN -1360 0 In FLAG -1360 96 Din2 IOPIN -1360 96 In FLAG -1360 192 Din3 IOPIN -1360 192 In FLAG -1360 304 Din4 IOPIN -1360 304 In FLAG -480 -48 test IOPIN -480 -48 Out FLAG -1264 -96 V- IOPIN -1264 -96 BiDir FLAG -1136 464 V- IOPIN -1136 464 BiDir FLAG -416 224 D_node FLAG -512 -144 N_node FLAG -784 80 Vref IOPIN -784 80 In FLAG -704 480 Vref IOPIN -704 480 In FLAG -1232 -176 Vref IOPIN -1232 -176 In FLAG -1024 448 Vref IOPIN -1024 448 In FLAG -464 576 Vref IOPIN -464 576 Out FLAG -512 672 0 SYMBOL Misc\\battery -496 480 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 -32 56 VBottom 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value 3 SYMBOL Misc\\battery -176 480 R90 WINDOW 0 -32 56 VBottom 2 WINDOW 3 32 56 VTop 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V2 SYMATTR Value 0 SYMBOL res -1056 320 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 -58 60 VTop 2 SYMATTR InstName R1 SYMATTR Value 10k SYMBOL res -912 208 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 -54 55 VTop 2 SYMATTR InstName Hill_D SYMATTR Value 65k SYMBOL Opamps\\UniversalOpamp2 -976 352 R0 SYMATTR InstName U2 SYMBOL res -688 336 R90 WINDOW 0 64 37 VBottom 2 WINDOW 3 66 49 VTop 2 SYMATTR InstName beta_D SYMATTR Value 100k SYMBOL Opamps\\UniversalOpamp2 -576 336 R0 SYMATTR InstName U1 SYMBOL cap -688 384 R0 SYMATTR InstName C1 SYMATTR Value 10µf SYMBOL res -1232 288 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R4 SYMATTR Value 1k SYMBOL res -1008 -160 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 -54 55 VTop 2 SYMATTR InstName Hill_N SYMATTR Value 55k SYMBOL Opamps\\UniversalOpamp2 -1072 -16 R0 SYMATTR InstName U3 SYMBOL res -752 -48 R90 WINDOW 0 62 44 VBottom 2 WINDOW 3 65 52 VTop 2 SYMATTR InstName beta_N SYMATTR Value 100k SYMBOL Opamps\\UniversalOpamp2 -640 -48 R0 SYMATTR InstName U4 SYMBOL cap -752 0 R0 SYMATTR InstName C2 SYMATTR Value 10µf SYMBOL res -1232 176 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R7 SYMATTR Value 1k SYMBOL res -1232 80 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R10 SYMATTR Value 1k SYMBOL res -1232 -16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R11 SYMATTR Value 1k SYMBOL res -1120 -160 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 -54 55 VTop 2 SYMATTR InstName R12 SYMATTR Value 10k SYMBOL cap -592 -160 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 -26 79 VTop 2 SYMATTR InstName C3 SYMATTR Value 10µf SYMBOL res -736 -144 R90 WINDOW 0 62 44 VBottom 2 WINDOW 3 65 52 VTop 2 SYMATTR InstName alpha_N SYMATTR Value 100k SYMBOL cap -512 208 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 -26 79 VTop 2 SYMATTR InstName C4 SYMATTR Value 10µf SYMBOL res -656 224 R90 WINDOW 0 62 44 VBottom 2 WINDOW 3 65 52 VTop 2 SYMATTR InstName alpha_D SYMATTR Value 100k SYMBOL res -1056 384 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value 10k SYMBOL res -1120 -96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R3 SYMATTR Value 10k SYMBOL res -528 464 R0 SYMATTR InstName R5 SYMATTR Value 10k SYMBOL res -528 576 R0 SYMATTR InstName R6 SYMATTR Value 700 TEXT -888 240 Left 2 ;1/(1+N) TEXT -976 -144 Left 2 ;D/(1+D) TEXT -568 -72 Left 2 ;N TEXT -336 -312 Left 2 ;Hill slope is set by kD=kN=K\nFor n=2:\nK slope Hill_N Hill_D\n.001 20.5 195k 205k\n0.01 6.5 55k 65k\n0.1 2.1 11k 21k\n0.42 1.0 1 10k TEXT -336 -104 Left 2 ;slope = 0.65/sqrt(K) TEXT -336 -48 Left 2 ;Matlab syb toolbox code to\nsolve for slope\nX = sym('X');\nK = sym('K');\n%n = sym('n') ;\nH = X^2/(K+X^2) ;\nDH = diff(H);\nMAXPOS = solve(diff(DH))\nsubs(DH,MAXPOS) TEXT -1032 16 Left 2 ;D^n/(kN+D^n) TEXT -936 384 Left 2 ;kD/(kD+N^n) TEXT -1368 360 Left 2 ;\n average TEXT -1216 496 Left 2 ;Small offset to \nshift symmetry TEXT -496 312 Left 2 ;D TEXT -776 -232 Left 2 ;Differential integrator TEXT -712 160 Left 2 ;Differential integrator TEXT -448 256 Left 2 !.ic V(D_node)=-0.0 TEXT -536 -120 Left 2 !.ic V(D_node)=-0.0 TEXT -1440 -136 Left 2 ;Small offset to \nshift symmetry TEXT -896 672 Left 2 ;700 to 1500 works well\n700 gives good match at k=0.01\nAt k=0.1, transient is good, steady state is too binary