# Given the microstrip width, calculate the line impedance and something else.
# This procedure must be called from gnuplot with   
# call "w2z.gp" <width> <thickness> <relative permittivity>    for example  
# call "w2z.gp" 58 31 4.5  where microstrip width is 58mils, heigth is 31mils,
# and relative epsilon is 4.5
# AUTHORS: Paolo Subiaco  <psubiaco@virgilio.it>  http://gw.ir3ip.ampr.org/iw3grx

# microstrip width
w=$0*1.0
h=$1*1.0
er=$2*1.0

y=1-1/er
x=log(w/h+.125)
# Calculate the effective filling fraction (value between 0.5 and 1)
q=(6.51309e-1        - 2.2516e-2*y         - 3.32199e-3*y*y        - 3.85162e-3*y*y*y)        + \
  (6.65212e-2*x      - 1.26976e-3*x*y	   - 6.80530e-5*x*y*y      - 1.03524e-3*x*y*y*y)      + \
  (1.64039e-2*x*x    + 2.59784e-3*x*x*y    + 2.74253e-4*x*x*y*y    + 6.52501e-4*x*x*y*y*y)    + \
  (3.95737e-4*(x**3) + 6.69075e-4*(x**3)*y + 6.84457e-5*(x**3)*y*y + 3.34213e-4*(x**3)*y*y*y) + \
  (1.84365e-3*(x**4) - 2.11987e-4*(x**4)*y + 2.1372e-5*(x**4)*y*y  - 9.56514e-5*(x**4)*y*y*y) - \
  (1.54945e-5*(x**5) - 9.69139e-5*(x**5)*y - 2.71033e-5*(x**5)*y*y - 3.65429e-5*(x**5)*y*y*y) - \
  (6.53285e-5*(x**6) + 2.47067e-5*(x**6)*y + 4.06141e-6*(x**6)*y*y + 1.01064e-5*(x**6)*y*y*y)
print "q=" , q, "   (effective filling fraction)"

# Given q, calculate the effective relative permittivity
eeff=1+q*(er-1)
print "Eeff=" , eeff , " (effective relative permittivity)" 

# Ok, with eeff i can calculate the phase velocity factor
Vph=1.0/sqrt(eeff)
print "Vph=" , Vph, " (phase velocity factor)"
 
# Now calculate Zfs (free space) and then Zo :
x=log(w/h)
Zfs=exp( 4.8394 - 0.45016*x - 0.077456*x*x - 0.0065863*x*x*x + \
    0.0016510*(x**4) + 2.3165e-4*(x**5) - 3.7508e-5*(x**6) )
Zo=Vph*Zfs
print "Zo=" , Zo, "   (line impedance)"