{{{id=26|
# Copyright 2009, P. Lutus
# Released under the GPL (http://www.gnu.org/copyleft/gpl.html)
///
}}}
{{{id=0|
%auto
# reset() # commented out for now -- ticket 7255
# special equation rendering
def render(x,name = "temp.png",size = "normal"):
# if(type(x) != type("")): x = latex(x)
latex.eval("\\" + size + "$" + x + "$",{},"",name)
var('r_l r_c X_l X_c f a b c x y z zl zc r l c L C omega')
radians = pi/180.0
degrees = 180.0/pi
# define arg(x) in degrees
def argd(x):
return N(arg(x) * degrees)
# complex plot function
def plt(q,a,b,typ = abs,col = 'blue'):
return plot(lambda x: typ(q(x)),(x,a,b),rgbcolor=col)
omega = 2*pi*f
# series rlc circuit definition
zs(r,l,c,f) = r + (i*omega*l) - i/(omega*c)
# parallel rlc circuit definition
# from http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/rlcpar.html#c2
zp(r_l,r_c,l,c,f) = ((r_l + i*omega*l)*(r_c - i/(omega*c))) / ((r_l+r_c)+i*(omega*l-1/(omega*c)))
///
}}}
{{{id=60|
# series rlc circuit plot
# plotting range: a = start, b = end (Hertz)
a = 500
b = 2500
# r = .1 ohms, l = 100 microhenries, c = 100 microfarads
r = .1
l = 1e-4
c = 1e-4
q(f) = zs(r,l,c,f)
p1 = plt(1/q,a,b,abs,'#800000')
p2 = plt(q,a,b,arg,'#008000')
show(p1+p2,figsize=(4,3),axes_labels=('freq Hz','admittance $\mho$'))
///
}}}
{{{id=79|
N(1/(2*pi*sqrt(l*c)))
///
1591.54943091895
}}}
{{{id=82|
find_root(lambda f: float(arg(zs(r,l,c,f))),500,2500)
///
1591.5494309189535
}}}
{{{id=61|
for n in range(500,2510,100):
f = float(n)
z = N(zp(0.1,0.1,1e-4,1e-4,f))
print "%6.1f %.1f (%.1f,%+4.1f i) %+5.1f" % (f,z.abs(),z.real(),z.imag(),argd(z))
///
500.0 0.4 (0.1,+0.3 i) +70.2
600.0 0.5 (0.1,+0.4 i) +72.3
700.0 0.6 (0.2,+0.5 i) +73.5
800.0 0.7 (0.2,+0.7 i) +74.0
900.0 0.8 (0.2,+0.8 i) +73.8
1000.0 1.0 (0.3,+1.0 i) +72.8
1100.0 1.3 (0.4,+1.2 i) +70.9
1200.0 1.7 (0.6,+1.5 i) +67.5
1300.0 2.2 (1.1,+2.0 i) +61.5
1400.0 3.1 (2.0,+2.4 i) +50.7
1500.0 4.3 (3.8,+2.2 i) +30.0
1600.0 5.0 (5.0,-0.3 i) -3.0
1700.0 4.2 (3.5,-2.3 i) -32.7
1800.0 3.2 (2.1,-2.4 i) -49.6
1900.0 2.5 (1.3,-2.1 i) -58.7
2000.0 2.0 (0.9,-1.8 i) -63.9
2100.0 1.7 (0.7,-1.6 i) -67.2
2200.0 1.5 (0.5,-1.4 i) -69.4
2300.0 1.3 (0.4,-1.2 i) -70.9
2400.0 1.2 (0.4,-1.1 i) -71.9
2500.0 1.1 (0.3,-1.0 i) -72.6
}}}
{{{id=62|
# parallel rlc circuit plot
# plotting range: a = start, b = end (Hertz)
a = 500
b = 2500
# r_l = .1 ohms, r_c = .1 ohms
# l = 100 microhenries, c = 100 microfarads
r_l = .1
r_c = .1
l = 1e-4
c = 1e-4
q(f) = zp(r_l,r_c,l,c,f)
p1 = plt(q,a,b,abs,'#800000')
p2 = plt(q,a,b,arg,'#008000')
show(p1+p2,figsize=(4,3),axes_labels=('freq Hz','impedance $\Omega$'))
///
}}}
{{{id=86|
# parallel rlc circuit log/linear plot
# plotting range: a = start, b = end, units f*10^n
a = 0
b = 7
r_l = .25
r_c = .75
l = 1e-4
c = 1e-4
q(n) = zp(r_l,r_c,l,c,10^n)
p1 = plt(q,a,b,abs,'#800000')
show(p1,figsize=(4,3),axes_labels=('$f = 10^n Hz$','impedance $\Omega$'),ymin=0)
///
}}}
{{{id=83|
render("z = \\frac{(r_l+i\\omega l)(r_c - \\frac{i}{\\omega_c})}{(r_l + r_c)+i(\\omega_l-\\frac{1}{\\omega_c})}","equ_impedance_parallel.png","huge")
///
}}}
{{{id=68|
render("X_l = \omega_L","equ_inductive_reactance.png","Large")
///
}}}
{{{id=72|
render("$X_c = -\\frac {1}{\omega_C}$","equ_capacitive_reactance.png","Large")
///
}}}
{{{id=73|
render("$\omega = 2 \pi f$","equ_omega.png","Large")
///
}}}
{{{id=74|
render("$z = r + i \omega_L - \\frac {i}{\omega_C}$","equ_rlc_impedance.png","Large")
///
}}}
{{{id=75|
show(abs(z))
///
{\left| z \right|}
}}}
{{{id=78|
render("$f\_0 = \\frac {1}{2 \pi \sqrt {L C}}$","equ_rlc_resonance.png","Large")
///
}}}
{{{id=81|
N(abs(zp(7,13,1e-4,1e-4,1e12)))
///
13.0000000000000
}}}
{{{id=84|
for n in range(0,7):
print "f = 10^%d, z = %5.2f" % (n,N(abs(zp(.25,.75,1e-4,1e-4,10^n))))
///
f = 10^0, z = 0.25
f = 10^1, z = 0.25
f = 10^2, z = 0.26
f = 10^3, z = 0.86
f = 10^4, z = 0.78
f = 10^5, z = 0.75
f = 10^6, z = 0.75
}}}
{{{id=85|
render("$\mho$","mho_symbol.png","Large")
///
}}}
{{{id=87|
render("$\Omega$","ohm_symbol.png","Large")
///
}}}
{{{id=88|
render("$\mho = \Omega i^2$","ohm_times_i_squared.png","Large")
///
}}}
{{{id=89|
render("$\infty$ = 8i","8_times_i.png","Large")
///
}}}
{{{id=91|
j=i
i=0
j^2
///
-1
}}}
{{{id=92|
x*i^2
///
-4*I - 3
}}}
{{{id=93|
x=a+b*i
///
}}}
{{{id=94|
x
///
a + I*b
}}}
{{{id=95|
var('a b')
///
(a, b)
}}}
{{{id=96|
x*i^2
///
-a - I*b
}}}
{{{id=97|
///
}}}