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#!/usr/bin/env perl
use Math::Complex;
use Math::Trig;
# proportion of total resistance for a log taper pot
sub logpot($) {
my $x = shift;
my $ym = 0.2;
my $b = ( ( 1. / $ym ) - 1. );
$b = $b * $b;
my $a = 1. / ( $b - 1. );
return $a * ( $b**$x ) - $a;
}
# proportion of resistance between two points on a log pot
sub logprop($$$) {
my ( $v, $t1, $t2 ) = @_;
$v = logpot($v);
$t1 = logpot($t1);
$t2 = logpot($t2);
return ( $v - $t1 ) / ( $t2 - $t1 );
}
# compute impedance of two elements in parallel
sub par($$) {
my ( $a, $b ) = @_;
return 1. / ( ( 1. / $a ) + ( 1. / $b ) );
}
# impedance of capacitor in nF at frequency f
sub cap($$) {
my ( $c, $f ) = @_;
my $z = $c * 1.e-9 * 2 * pi * $f;
$z = -i / $z;
return $z;
}
@fns = ();
@frqs = ();
# calc gain at frequeny f and knob position k (0-10)
sub calc_gain($$) {
my ( $f, $k ) = @_;
# position of taps on pot.
my $te = 0.4; # terminal e
my $td = 0.6; # terminal d
my $rac = 470000.;
#terminal c is input
#terminal b is output
#terminal a is ground
# loads on terminals d and e
my $ld = 18000. + cap( 47., $f ); #18k+47nF
my $le = 4700. + cap( 250., $f ); #4.7k+250nF
#compute resistances of track
my $rae = $rac * logpot($te);
my $rad = $rac * logpot($td);
my $red = $rad - $rae;
my $rdc = $rac - $rad;
my $tot = $rae + $red + $rdc;
print "Track resistances: $rae + $red + $rdc = $tot\n";
# next compute the efective impedances of each leg
my $erae = par( $rae, $le );
my $erad = par( $erae + $red, $ld );
my $ered = $erad - $erae;
my $erac = $erad + $rdc;
my $erdc = $erac - $erad;
my $etot = $erac;
# input filter
$etot += 150000. + cap( 15., $f ); # 150k +15nF
#balance control
$etot += par( 1100., cap( 120., $f ) );
print "Effective total impedance $erae + $ered + $erdc = $erac\n";
# compute the potentials for a 1V input
my $pe = $erae / $etot;
my $pd = $erad / $etot;
my $pa = $erac / $etot;
my $ped = $pd - $pe;
my $pda = $pa - $pd;
my $v = $k / 10.;
my $hf;
if ( $v < $te ) {
$hf = $pe * logprop( $v, 0, $te );
}
elsif ( $v < $td ) {
$hf = $pe + ( $ped * logprop( $v, $te, $td ) );
}
else {
$hf = $pd + ( $pda * logprop( $v, $td, 1. ) );
}
return abs($hf);
}
open P, "|gnuplot";
print P "set term png size 1280,1024\n";
print P "set output 'volume.png'\n";
print P "set logscale x\n";
print P "set logscale y\n";
print P "set yrange [:1.1]\n";
print P "set xlabel 'frequency/Hz'\n";
print P "set ylabel 'gain'\n";
print P "plot ";
for ( my $k = 1 ; $k < 10.5 ; ++$k ) {
my $gmax = 0;
for ( my $f = 20 ; $f < 20000.1 ; $f *= 1.1 ) {
my $g = calc_gain( $f, $k );
$gmax = $g if $g > $gmax;
}
my $fn = "volume-" . $k . ".dat";
open F, ">", $fn;
for ( my $f = 20 ; $f < 20000.1 ; $f *= 1.1 ) {
my $g = calc_gain( $f, $k );
print F $f, " ", $g, " ", $g / $gmax, "\n";
}
close F;
print P " '" . $fn . "' using 1:2 with lines title '" . $k . "',";
}
print "\n";
close P;
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