rho = lambda z: (z-1)/(z+1) # return the (complex) reflection coefficient
zz = lambda r: (1 + r)/(1 - r) # return the normalized impedance from the reflection coefficient
def cart(z):
return (z.real(), z.imag())
def rhoxy(z):
'''return the real and imaginary part of the reflection coefficient as a tuple'''
r = rho(z)
return (r.real(), r.imag())
def screal(x):
'''generate smith chart coordinates of constant real part; these are complete circles'''
r = rhoxy(x + 0j)
radius = 0.5*(1 - r[0])
return circle((1 - radius, 0), radius)
def scimag(y):
'''generate smith chart coordinates of constant imaginary part; these are circular arcs'''
rx = lambda t: rhoxy(t + 1j*y)[0]
ry = lambda t: rhoxy(t + 1j*y)[1]
return parametric_plot((rx,ry),(0,50))
def polar(z):
'''return the polar form of a cartesian complex number, as a tuple'''
return (abs(z), arg(z))
# draw an unlabeled smith chart
smithchart = screal(0) + screal(1/3) + screal(1) + screal(3) + scimag(0) + scimag(1/3) + scimag(-1/3) + scimag(1) + scimag(-1) + scimag(3) + scimag(-3)
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class SmithChart:
'''a class for drawing and manipulating Smith Charts
by John D Sahr jdsahr@u.washington.edu'''
def __init__(self):
'''initialize a smith chart'''
self.chart = smithchart
self.last_rho = None
self.markradius = 0.015
self.mark_ind = 0
self.fontsize = 15
self.admittance_mode = True
self.annotation = []
def clear(self):
'''reset the smith chart'''
self.chart = smithchart
self.last_rho = None
self.mark_ind = 0
self.admittance_mode = True
self.annotation = []
def mark(self, label = True):
'''make a small circular mark at the last location on the chart'''
self.chart += circle(cart(self.last_rho), self.markradius, rgbcolor = (0,0,0))
center = (self.last_rho.real(), self.last_rho.imag())
polar = self.polar(self.last_rho)
if label == False: # don't label at all.
return
elif label == True: # generate a generic label
tag = chr(self.mark_ind + ord('A'))
self.mark_ind += 1
elif type(label) == type('a string'): # use a custom label
tag = label
else: # error out
raise 'improper label passed to mark'
tagloc = (center[0]+3*self.markradius, center[1]+3*self.markradius)
self.chart += text(tag, tagloc, fontsize=self.fontsize)
msg = '%4s :: rho %5.3f at %6.1f deg; ' % (tag, polar[0], polar[1])
z = zz(self.last_rho)
msg += '%6.3f + %6.3fj' % (z.real(),z.imag())
self.annotation.append(msg)
def markz(self, z, label = True):
'''mark a (normalized) impedance on the Smith Chart'''
center = rho(z)
self.last_rho = center.real() + 1j*center.imag()
self.mark(label)
def marky(self, z, label = True):
'''mark a (normalized) impedance at its admittance position on the Smith Chart'''
self.markz(1/z, label)
def markr(self, r, dolabel = True):
'''mark the smith chart given a (complex) reflection coefficient'''
self.markz(zz(r),dolabel)
def polar(self, r):
'''convert a complex number in cartesian format to mag, phase(degrees) format as a tuple'''
return( r.abs(), 180*r.arg()/math.pi)
def togen(self, wavelengths, rgbcolor=(1,0,1), dolabel = True):
'''start at the current point on the Smith Chart, and rotate <wavelengths> towards the generator'''
if self.last_rho == None:
raise "not anywhere yet!"
radius = sqrt(self.last_rho[0]^2 + self.last_rho[1]^2)
t1 = math.atan2(self.last_rho[1],self.last_rho[0])
t2 = t1 - 4*math.pi*wavelengths
self.last_rho *= exp(1j*(t2-t1))
t = var('t')
self.chart += parametric_plot((radius*cos(t), radius*sin(t)), (t,t1,t2), rgbcolor=rgbcolor)
self.mark(dolabel)
def singlestub(self, z, bottom = True):
'''solve a single stub match using shorted stub.
There are two solutions: inductive (bottom) or capacitive (top)'''
self.markz(z, 'Zl') # mark the location of the load impedance
self.marky(z, 'Yl') # mark the location of the load admittance
magRhoL = self.last_rho.abs()
argRhoL = self.last_rho.arg()
self.chart += circle((0,0), magRhoL, rgbcolor = (1,0,0)) # the circle of const |refcoef|
argMatch = acos(magRhoL) # the intersection of the circle with the 1 + jX circle
if bottom != True: # ... get the capacitive stub instead
argMatch = -argMatch
ym1 = zz(magRhoL*exp(1j*argMatch)) # ... get the intersection point
self.markz(ym1,'Ym1') # ... and mark it
stb1 = 0 - 1j*ym1.imag() # ... the input admittance of the stub
self.markz(stb1,'stb1') # ... and mark it
stubloc = 180*(argRhoL - argMatch)/math.pi - 360 # compute the location of the stub
while stubloc < 0.0:
stubloc += 360
stublength = -180.0*rho(stb1).arg()/math.pi - 360 # compute the length of the stub
while stublength < 0.0:
stublength += 360
print 'stub location: %6.3f :: ' % (stubloc*0.5/360),
print 'stub length: %6.3f' % (stublength*0.5/360)
def show(self):
'''draw the annotated smith chart'''
self.chart.show(aspect_ratio = 1, axes = False)
for x in self.annotation:
print x
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h = SmithChart()
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h.clear()
h.markz(sqrt(4.2),'Z1');
h.show()
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Z1 :: rho 0.344 at 180.0 deg; 0.488 + 0.000jh.chart.save('yaya.pdf',aspect_ratio = 1, axes = False)
h.clear()
h.marky(0.5-0.5j,'1/Z1');
h.togen(0.339-0.25)
h.togen(0.125)
h.show()
r = abs(h.last_rho)
(1 + r)/(1-r)
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1/Z1 :: rho 0.447 at 63.4 deg; 1.000 + 1.000j
A :: rho 0.447 at -0.6 deg; 2.618 + -0.033j
B :: rho 0.447 at -90.6 deg; 0.661 + -0.739j
2.61803398874989h.clear()
h.singlestub(1.25-1.25j, True)
h.show()
stub location: 0.097 :: stub length: 0.115 stub location: 0.097 :: stub length: 0.115 |
Zl :: rho 0.495 at -49.6 deg; 1.250 + -1.250j
Yl :: rho 0.495 at 130.4 deg; 0.400 + 0.400j
Ym1 :: rho 0.495 at 60.3 deg; 1.000 + 1.140j
stb1 :: rho 1.000 at -82.5 deg; 0.000 + -1.140jhelp(SmithChart)
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