Version 4 SHEET 1 3960 2816 WIRE -192 1200 -224 1200 WIRE -80 1200 -112 1200 WIRE 32 1200 -16 1200 WIRE -224 1296 -224 1200 WIRE -208 1296 -224 1296 WIRE -96 1296 -128 1296 WIRE -64 1296 -96 1296 WIRE 32 1296 32 1200 WIRE 32 1296 16 1296 WIRE -96 1312 -96 1296 WIRE -480 1344 -512 1344 WIRE -352 1344 -400 1344 WIRE -240 1344 -288 1344 WIRE -96 1392 -96 1376 WIRE -512 1440 -512 1344 WIRE -512 1440 -592 1440 WIRE -496 1440 -512 1440 WIRE -384 1440 -416 1440 WIRE -336 1440 -384 1440 WIRE -240 1440 -240 1344 WIRE -240 1440 -256 1440 WIRE -224 1440 -224 1296 WIRE -224 1440 -240 1440 WIRE -128 1440 -224 1440 WIRE -592 1456 -592 1440 WIRE -384 1456 -384 1440 WIRE 32 1456 32 1296 WIRE 32 1456 -64 1456 WIRE 64 1456 32 1456 WIRE -128 1472 -144 1472 WIRE -592 1552 -592 1536 WIRE -384 1552 -384 1520 WIRE 224 1584 208 1584 WIRE 320 1584 304 1584 WIRE -880 1648 -896 1648 WIRE -784 1648 -800 1648 WIRE -560 1648 -576 1648 WIRE -464 1648 -480 1648 WIRE 400 1744 272 1744 WIRE 560 1744 464 1744 WIRE 272 1760 272 1744 WIRE 560 1760 560 1744 WIRE -880 1776 -896 1776 WIRE -784 1776 -800 1776 WIRE -560 1776 -576 1776 WIRE -464 1776 -480 1776 WIRE 64 1776 64 1456 WIRE 224 1776 64 1776 WIRE 272 1856 272 1840 WIRE 560 1856 560 1840 WIRE -880 1904 -896 1904 WIRE -784 1904 -800 1904 FLAG 224 1824 0 FLAG 272 1856 0 FLAG 560 1744 OUT FLAG 560 1856 0 FLAG -592 1552 0 FLAG -96 1392 0 FLAG -384 1552 0 FLAG -144 1472 0 FLAG -896 1648 0 FLAG -896 1776 0 FLAG -896 1904 0 FLAG -576 1648 0 FLAG -576 1776 0 FLAG 64 1456 EQ FLAG 208 1584 0 FLAG -592 1440 IN DATAFLAG -784 1648 "" DATAFLAG -784 1776 "" DATAFLAG -784 1904 "" DATAFLAG -464 1648 "" DATAFLAG -464 1776 "" DATAFLAG 320 1584 "" SYMBOL e 272 1744 R0 SYMATTR InstName E1 SYMATTR Value 1 SYMBOL cap 464 1728 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 WINDOW 123 53 32 VTop 2 SYMATTR InstName C1 SYMATTR Value {Cspk} SYMATTR Value2 Rser={Rspk} SYMBOL ind 544 1744 R0 SYMATTR InstName L1 SYMATTR Value {Lspk} SYMATTR SpiceLine Rser=0 SYMBOL voltage -592 1440 R0 SYMATTR InstName V1 SYMATTR Value ac 1 SYMBOL res -400 1424 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R1 SYMATTR Value {R1} SYMBOL res -240 1424 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value {R1} SYMBOL res -384 1328 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R3 SYMATTR Value {R2} SYMBOL res -96 1184 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R4 SYMATTR Value {R2} SYMBOL res -112 1280 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R5 SYMATTR Value {R3} SYMBOL res 32 1280 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R6 SYMATTR Value {R3} SYMBOL cap -16 1184 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C2 SYMATTR Value {C2} SYMBOL cap -288 1328 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C3 SYMATTR Value {C2} SYMBOL cap -400 1456 R0 SYMATTR InstName C4 SYMATTR Value {C1} SYMBOL cap -112 1312 R0 SYMATTR InstName C5 SYMATTR Value {C3} SYMBOL voltage -784 1648 R90 WINDOW 0 -32 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName V2 SYMATTR Value {R1/1K} SYMBOL voltage -784 1776 R90 WINDOW 0 -32 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName V3 SYMATTR Value {R2/1K} SYMBOL voltage -784 1904 R90 WINDOW 0 -32 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName V4 SYMATTR Value {R3/1K} SYMBOL voltage -464 1648 R90 WINDOW 0 -32 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName V5 SYMATTR Value {C1/1u} SYMBOL voltage -464 1776 R90 WINDOW 0 -32 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName V6 SYMATTR Value {C3/1u} SYMBOL voltage 320 1584 R90 WINDOW 0 -32 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName V7 SYMATTR Value {Vb} SYMBOL opamps\\UniversalOpamp2 -96 1456 R0 SYMATTR InstName U1 SYMATTR SpiceModel level.1 TEXT 136 1376 Left 2 !.param Vb = Vas / ((Qtc/Qts) * (Qtc/Qts) - 1.)\n.param Fc = Fs * sqrt(( Vas/Vb) + 1.) \n.param Lspk = 1\n.param Cspk = 1. / (39.47842 * Fc * Fc * Lspk)\n.param Rspk = 6.2831853 * Fc / Qtc TEXT 136 1152 Left 2 !.param Fs =95\n.param Qts=0.472\n.param Vas=0.04481 TEXT 440 2008 Left 2 !.ac oct 10 10 10K TEXT -1248 1368 Left 2 !.param k = (Fc0/Fcx-Qt0/Qtx)/(Qt0/Qtx-Fcx/Fc0)\n.param R1 = (1/(2*pi*Fc0*C2*(2*Qt0*(1+k))))\n.param R2 = 2*k*R1\n.param R3 = R1*(Fc0/Fcx)**2\n.param C1 = C2*(2*Qt0*(1+k))**2\n.param C3 = C1*(Fcx/Fc0)**2\n;.param gain=40*Log10(Fc0/Fcx) ; FYI TEXT -576 1096 Top 2 ;Linkwitz-Riley Transform: equalize a driver in a sealed box to a different Q and cutoff frequency TEXT 416 1096 Top 2 ;Driver Characteristics TEXT 408 1264 Top 2 ;Sealed Box TEXT 440 1912 Center 2 ;Plot V(eq) to see Linkwitz transfer function\nPlot V(out)/V(eq) to see speaker transfer function\nPlot V(out) for net transfer function TEXT 432 1672 Top 2 ;Voltage to Sound Pressure Level Equiv. Circuit TEXT -184 1992 Top 2 ;This example schematic is supplied for informational/educational purposes only. TEXT -224 1080 Bottom 2 ;This is the theory of the PA system used in the 2015 World Circuit Seminar\nTour except (i) the electronics I traveled with include baffle step\ncompensation (ii) the microphone aperture was adjusted to add\n4dB @ 16kHz to enhance sibilance and (iii) the drivers were a vertical array. TEXT -472 1880 Center 2 ;These voltage sources read\nout the component values to\nimplement the equalizer TEXT 560 1552 Center 2 ;Sealed box\nvolume in same\nunits as Vas TEXT -592 1168 Center 2 ;Input Parameters TEXT 168 1320 Left 2 !.param Qtc = 0.7071 TEXT 536 1320 Center 2 ;Input parameter TEXT 544 1152 Center 2 ;Input parameters appropriate\nfor the Fountek FR88EX\n 3" Full Range Al cone TEXT -1256 1152 Left 2 !.param C2=.047u\n.param Fc0 = Fc ; Fc untransformed\n.param Qt0 = Qtc ; Qtc untransformed\n.param Fcx = 80 ; Fc transformed(chosen on spectral analysis of my voice)\n.param Qtx = 0.7071 ; Qtc transformed RECTANGLE Normal 96 1984 -1280 1088 2 RECTANGLE Normal -288 1968 -960 1584 2 RECTANGLE Normal 672 1648 176 1520 2 RECTANGLE Normal 672 1344 144 1296 2 RECTANGLE Normal 736 1248 128 1088 2 RECTANGLE Normal 752 1888 128 1264 2 RECTANGLE Normal -336 1288 -1264 1128 2