334 lines
12 KiB
Python
334 lines
12 KiB
Python
#!/usr/bin/python3
|
||
|
||
import numpy as np
|
||
import scipy.optimize as opt
|
||
|
||
np.seterr(under='ignore')
|
||
### STATIC approx
|
||
def eps_re(u, e_r):
|
||
'''
|
||
Calculate effective dielectric constant
|
||
using the expressions given in
|
||
E. Hammerstad and O. Jensen, "Accurate Models for
|
||
Microstrip Computer-Aided Design," 1980 IEEE MTT-S
|
||
International Microwave symposium Digest, Washington,
|
||
DC, USA, 1980, pp. 407-409.
|
||
doi: 10.1109/MWSYM.1980.1124303
|
||
|
||
e_re = eps_re(u, e_r):
|
||
u <- ratio W/h
|
||
e_r <- substrate relative dielectric constant
|
||
e_re -> effective relative dielectric constant
|
||
of microstrip line
|
||
'''
|
||
a = 1 + np.log((u**4 + (u/52)**2)/(u**4+0.432))/49 +\
|
||
np.log(1+(u/18.1)**3)/18.7
|
||
b = 0.564*( (e_r-0.9)/(e_r+3) )**(0.053)
|
||
|
||
e_re = 0.5*(e_r+1)+0.5*(e_r-1)*(1+10/u)**(-a*b)
|
||
return e_re
|
||
|
||
def getZc(u, e_r):
|
||
'''
|
||
Calculate characteristic impedance Zc
|
||
using the expressions given in
|
||
E. Hammerstad and O. Jensen, "Accurate Models for
|
||
Microstrip Computer-Aided Design," 1980 IEEE MTT-S
|
||
International Microwave symposium Digest, Washington,
|
||
DC, USA, 1980, pp. 407-409.
|
||
doi: 10.1109/MWSYM.1980.1124303
|
||
(neglected thickness of copper)
|
||
|
||
Zc = getZc(u, e_r)
|
||
u <- ratio W/h
|
||
e_r <- substrate relative dielectric constant
|
||
Zc -> characteristic impedance of microstrip line
|
||
'''
|
||
F = 6 + (2*np.pi-6)*np.exp(-(30.666/u)**0.7528)
|
||
e_re = eps_re(u, e_r)
|
||
Zc = (120*np.pi)/(2*np.pi*np.sqrt(e_re))*np.log(\
|
||
F/u + np.sqrt(1 + (2/u)**2))
|
||
return Zc
|
||
|
||
### Dispersion correction
|
||
def eps_f(W,h,e_r,f):
|
||
'''
|
||
Calculate effective dieletric constant using formulas given by:
|
||
M. Kirschning and R. H. Jansen, "Accurate Model for Effective
|
||
Dielectric Constant of Microstrip with Validity up to Millimeter-Wave
|
||
Frequencies," Electronics Letters, vol. 8, no. 6, pp. 272-273,
|
||
Mar. 1982.
|
||
R. H. Jansen and M. Kirschning, "Arguments and an accurate Model
|
||
for the Power-Current Formulation of Microstrip Characteristic
|
||
Impedance," Archiv für Elektronik und Übertragungstechnik (AEÜ),
|
||
vol. 37, pp. 108-112, 1983.
|
||
http://qucs.sourceforge.net/tech/node75.html
|
||
|
||
e_re = eps_f(W,h,e_r,f)
|
||
W <- width of microstrip (mm)
|
||
h <- height of substrate (mm)
|
||
e_r <- substrate relative dielectric cosntatn
|
||
f <- frequency (GHz)
|
||
e_re -> effective dielectric constant of microstrip line
|
||
'''
|
||
fn = f*h
|
||
u = W/h
|
||
P1 = 0.27488 + (0.6315+0.525/(1+0.0157*fn)**20)*u - 0.065683*np.exp(\
|
||
-8.7513*u)
|
||
P2 = 0.33622*(1-np.exp(-0.03442*e_r))
|
||
P3 = 0.0363*np.exp(-4.6*u)*(1-np.exp(-(fn/38.7)**4.97))
|
||
P4 = 1+2.751*(1-np.exp(-(e_r/15.916)**8))
|
||
Pf = P1*P2*((0.1844+P3*P4)*fn)**1.5763
|
||
eps0 = eps_re(u,e_r)
|
||
return e_r - (e_r - eps0)/(1+Pf)
|
||
|
||
def getZcf(W,h,e_r,f,R=False):
|
||
'''
|
||
Calculate characteristic impedance using formulas given by:
|
||
M. Kirschning and R. H. Jansen, "Accurate Model for Effective
|
||
Dielectric Constant of Microstrip with Validity up to Millimeter-Wave
|
||
Frequencies," Electronics Letters, vol. 8, no. 6, pp. 272-273,
|
||
Mar. 1982.
|
||
R. H. Jansen and M. Kirschning, "Arguments and an accurate Model
|
||
for the Power-Current Formulation of Microstrip Characteristic
|
||
Impedance," Archiv für Elektronik und Übertragungstechnik (AEÜ),
|
||
vol. 37, pp. 108-112, 1983.
|
||
http://qucs.sourceforge.net/tech/node75.html
|
||
|
||
Zc = Zcf(W,h,e_r,f,R=False)
|
||
W <- width of microstrip (mm)
|
||
h <- height of substrate (mm)
|
||
e_r <- substrate relative dielectric cosntatn
|
||
f <- frequency (GHz)
|
||
R=False <- flag telling whether to return R17 or not
|
||
Zc -> characteristic impedance of microstrip line
|
||
R17 -> parameter used to calculate impedance and coupled line
|
||
return only if R=True
|
||
'''
|
||
fn = f*h
|
||
u = W/h
|
||
ef = eps_f(W,h,e_r,f)
|
||
e0 = eps_re(u,e_r)
|
||
|
||
R1 = 0.03891*e_r**1.4
|
||
R2 = 0.267*u**7
|
||
R3 = 4.766*np.exp(-3.228*u**0.641)
|
||
R4 = 0.016 + (0.0514*e_r)**4.524
|
||
R5 = (fn/28.843)**12.0
|
||
R6 = 22.20*u**1.92
|
||
|
||
R7 = 1.206-0.3144*np.exp(-R1)*(1-np.exp(-R2))
|
||
R8 = 1+1.275*(1-np.exp(-0.004625*R3*e_r**1.674)*(fn/18.365)**2.745)
|
||
R9 = 5.086*R4*R5*np.exp(-R6)*(e_r-1)**6/\
|
||
((0.3838+0.386*R4)*(1+1.2992*R5)*(1+10*(e_r-1)**6))
|
||
|
||
R10 = 0.00044*e_r**2.136+0.0184
|
||
R11 = (fn/19.47)**6/(1+0.0962*(fn/19.47)**6)
|
||
R12 = 1/(1+0.00245*u**2)
|
||
R13 = 0.9408*ef**R8-0.9603
|
||
R14 = (0.9408-R9)*e0**R8-0.9603
|
||
R15 = 0.707*R10*(fn/12.3)**1.097
|
||
R16 = 1+0.0503*e_r**2*R11*(1-np.exp(-(u/15)**6))
|
||
R17 = R7*(1-1.1241*R12*np.exp(-0.026*fn**1.15656-R15)/R16)
|
||
|
||
Z0 = getZc(u,e_r)
|
||
Zc = Z0*(R13/R14)**R17
|
||
if R:
|
||
return (Zc, R17)
|
||
else:
|
||
return Zc
|
||
|
||
def getWf(Zk,h,e_r,f):
|
||
'''
|
||
Calculate width of microstrip line when also
|
||
taking in to account dispersion.
|
||
|
||
W = getWf(Zk,h,e_r,f)
|
||
Zk <- characteristic impedance (ohms)
|
||
h <- substrate height
|
||
e_r <- substrate relative di. costant
|
||
f <- frequency (GHz)
|
||
W -> widht of microstrip line (mm)
|
||
'''
|
||
u = opt.root_scalar(lambda X: Zk-getZcf(X,h,e_r,f),x0=h,\
|
||
method='brentq', bracket=[0.01,100])
|
||
return u.root
|
||
|
||
### coupled lines
|
||
def mcl_eps(W,h,s,e_r,f):
|
||
'''
|
||
Calculate effective odd and even permittivity of parallel
|
||
coupled microstrip lines.
|
||
M. Kirschning, R. H. Jansen, and N. H. L. Koster,
|
||
"Coupled microstrip parallel-gap model for improved filter and coupler design,"
|
||
Electronics Letters, vol. 19, no. 10, pp. 377–379, May 1983,
|
||
doi: 10.1049/el:19830261.
|
||
|
||
even, odd = mcl_eps(W,h,s,e_r,f):
|
||
W <- width of microstrip (mm)
|
||
h <- height of substrate (mm)
|
||
s <- spacing between lines (mm)
|
||
e_r <- substrate relative dielectric cosntatn
|
||
f <- frequency (GHz)
|
||
even -> even mode dielectric constant
|
||
odd -> odd mode dielectric constant
|
||
'''
|
||
u = W/h
|
||
g = s/h
|
||
fn = f*h
|
||
|
||
eps0 = eps_re(u,e_r)
|
||
|
||
v = u * (20+g**2)/(10+g**2)+ g*np.exp(-g)
|
||
ae = 1+np.log((v**4+(v/52)**2)/(v**4+0.432))/49+np.log(1+(v/18.1)**3)/18.7
|
||
be = 0.564*((e_r-0.9)/(e_r+3))**0.053
|
||
even0 = 0.5*(e_r+1)+0.5*(e_r-1)*(1+10/v)**(-ae*be)
|
||
|
||
ao = 0.7287*(eps0-0.5*(e_r+1))*(1-np.exp(-0.179*u))
|
||
bo = 0.747*e_r/(0.15+e_r)
|
||
co = bo - (bo-0.207)*np.exp(-0.414*u)
|
||
do = 0.593+0.694*np.exp(-0.562*u)
|
||
odd0 = (0.5*(e_r+1)+ao-eps0)*np.exp(-co*g**do)+eps0
|
||
|
||
P1 = 0.27488+(0.6315+0.525/(1+0.0157*fn)**20)*u-0.065683*np.exp(-8.7513*u)
|
||
P2 = 0.33622*(1-np.exp(-0.03442*e_r))
|
||
P3 = 0.0363*np.exp(-4.6*u)*(1-np.exp(-(fn/38.7)**4.97))
|
||
P4 = 1+2.751*(1-np.exp(-(e_r/15.916)**8))
|
||
P5 = 0.334*np.exp(-3.3*(e_r/15)**3)+0.746
|
||
P6 = P5*np.exp(-(fn/18)**0.368)
|
||
P7 = 1+4.069*P6*g**0.479*np.exp(-1.347*g**0.595-0.17*g**2.5)
|
||
Fe = P1*P2*((P3*P4+0.1844*P7)*fn)**1.5763
|
||
even = e_r - (e_r - even0)/(1+Fe)
|
||
|
||
P8 = 0.7168*(1+1.076/(1+0.0576*(e_r-1)))
|
||
P9 = P8-0.7913*(1-np.exp(-(fn/20)**1.424))*np.arctan(2.481*(e_r/8)**0.946)
|
||
P10 = 0.242*(e_r - 1)**0.55
|
||
P11 = 0.6366*(np.exp(-0.3401*fn)-1)*np.arctan(1.263*(u/3)**1.629)
|
||
P12 = P9 + (1-P9)/(1+1.183*u**1.376)
|
||
P13 = 1.695 * P10/(0.414+1.605*P10)
|
||
P14 = 0.8928+0.1072*(1-np.exp(-0.42*(fn/20)**3.215))
|
||
P15 = np.abs(1-0.8928*(1+P11)*np.exp(-P13*g**1.092)*P12/P14)
|
||
Fo = P1*P2*((P3*P4+1.844)*fn*P15)**1.5763
|
||
odd = e_r - (e_r - odd0)/(1+Fo)
|
||
|
||
return even,odd,even0,odd0
|
||
|
||
def mclZcf(W,h,s,e_r,f):
|
||
'''
|
||
Calculate odd and even characteristic impedance of parallel
|
||
coupled microstrip lines.
|
||
M. Kirschning, R. H. Jansen, and N. H. L. Koster,
|
||
"Coupled microstrip parallel-gap model for improved filter and coupler design,"
|
||
Electronics Letters, vol. 19, no. 10, pp. 377–379, May 1983,
|
||
doi: 10.1049/el:19830261.
|
||
|
||
even, odd = mcl_eps(W,h,s,e_r,f):
|
||
W <- width of microstrip (mm)
|
||
h <- height of substrate (mm)
|
||
s <- spacing between lines (mm)
|
||
e_r <- substrate relative dielectric cosntatn
|
||
f <- frequency (GHz)
|
||
Ze -> even mode charachterstic impedance
|
||
Zo -> odd mode characteristic impedance
|
||
'''
|
||
u = W/h
|
||
g = s/h
|
||
fn = f*h
|
||
|
||
eps0 = eps_re(u,e_r)
|
||
epsf = eps_f(W,h,e_r,f)
|
||
even,odd,even0,odd0 = mcl_eps(W,h,s,e_r,f)
|
||
Z0 = getZc(u,e_r)
|
||
Z0f, Q0 = getZcf(W,h,e_r,f,R=True)
|
||
|
||
Q1 = 0.8695*u**0.194
|
||
Q2 = 1+0.7519*g+0.189*g**2.31
|
||
Q3 = 0.1975+(16.6 + (8.4/g)**6)**-0.387 +np.log(g**10/(1+(g/3.4)**10))/241
|
||
Q4 = 2*Q1/Q2/(np.exp(-g)*u**Q3+(2-np.exp(-g))*u**-Q3)
|
||
|
||
Ze0 = np.sqrt(eps0/even0)*Z0/(1-Z0/377*np.sqrt(eps0)*Q4)
|
||
|
||
Q5 = 1.794 + 1.14*np.log(1+0.638/(g+0.517*g**2.43))
|
||
Q6 = 0.2305+np.log(g**10/(1+(g/5.8)**10))/281.3+np.log(1+0.598*g**1.154)/5.1
|
||
Q7 = (10+190*g**2)/(1+82.3*g**3)
|
||
#print(-6.5-0.95*np.log(g)-(g/0.15)**5)
|
||
Q8 = np.exp(-6.5-0.95*np.log(g)-(g/0.15)**5)
|
||
Q9 = np.log(Q7)*(Q8+1/16.5)
|
||
Q10 = (Q2*Q4-Q5*np.exp(np.log(u)*Q6*u**-Q9))/Q2
|
||
|
||
Zo0 = np.sqrt(eps0/odd0)*Z0/(1-Z0/377*np.sqrt(eps0)*Q10)
|
||
|
||
# dispersion accounted
|
||
Q11 = 0.893*(1-0.3/(1+0.7*(e_r-1)))
|
||
Q12 = 2.121*(fn/20)**4.91*np.exp(-2.87*g)*g**0.902/(1+Q11*(fn/20)**4.91)
|
||
Q13 = 1+0.038*(e_r/8)**5.1
|
||
Q14 = 1+1.203*(e_r/15)**4/(1+(e_r/15)**4)
|
||
Q15 = 1.887*np.exp(-1.5*g**0.84)*g**Q14/(1+0.41*(fn/15)**3*u**(2/Q13)/(0.125+u**(1.625/Q13)))
|
||
Q16 = Q15 * (1+ 9/(1+0.403*(e_r-1)**2))
|
||
Q17 = 0.394*(1-np.exp(-1.47*(u/7)**0.672))*(1-np.exp(-4.25*(fn/20)**1.87))
|
||
Q18 = 0.61*(1-np.exp(-2.13*(u/8)**1.593))/(1+6.544*g**4.17)
|
||
Q19 = 0.21*g**4/(1+0.18*g**4.9)/(1+0.1*u**2)/(1+(fn/24)**3)
|
||
Q20 = Q19 * (0.09+1/(1+0.1*(e_r-1)**2.7))
|
||
Q21 = np.abs(1-42.54*g**0.133*np.exp(-0.812*g)*u**2.5/(1+0.033*u**2.5))
|
||
|
||
re = (fn/28.843)**12
|
||
qe = 0.016+(0.0514*e_r*Q21)**4.524
|
||
pe = 4.766*np.exp(-3.228*u**0.641)
|
||
de = 5.086*qe*re*np.exp(-22.2*u**1.92)*(e_r-1)**6/(0.3838+0.386*qe)/(1+1.2992*re)/(1+10*(e_r-1)**6)
|
||
|
||
Ce = 1+1.275*(1-np.exp(-0.004625*pe*e_r**1.674*(fn/18.365)**2.745))-Q12+Q16-Q17+Q18+Q20
|
||
Ze = Ze0*( (0.9408*epsf**Ce-0.9603)/( (0.9408-de)*eps0**Ce-0.9603))**Q0
|
||
|
||
Q29 = 15.16/(1+0.196*(e_r-1)**2)
|
||
Q28 = 0.149*(e_r-1)**3/(94.5+0.038*(e_r-1)**3)
|
||
Q27 = 0.4*g**0.84*(1+(2.5*(e_r-1)**1.5)/(5+(e_r-1)**1.5))
|
||
Q26 = 30 - ( 22.2*((e_r-1)/13)**13)/(1+3*((e_r-1)/13)**12) - Q29
|
||
Q25 = (0.3*fn**2)/(10+fn**2)*(1+(2.333*(e_r-1)**2)/(5+(e_r-1)**2))
|
||
Q24 = 2.506*Q28*u**0.894/(3.575+u**0.894)*((1+1.3*u)*fn/99.25)**4.29
|
||
Q23 = 1+0.005*fn*Q27/(1+0.812*(fn/15)**1.9)/(1+0.025*u**2)
|
||
Q22 = 0.925*(fn/Q26)**1.536/(1+0.3*(fn/30)**1.536)
|
||
|
||
Zo = Z0f+(Zo0*(odd/odd0)**Q22 - Z0f*Q23)/(1+Q24+(0.46*g)**2.2*Q25)
|
||
return Ze,Zo
|
||
|
||
def get_mcl(Ze, Zo, h, e_r, f):
|
||
'''
|
||
Find width W and gap s of parallel coupled microstrip lines
|
||
|
||
[W, s] = get_mcl(Ze, Zo, h, e_r, f):
|
||
Ze <- even mode characteristic impedance (ohm)
|
||
Zo <- odd mode ch. impedance (ohm)
|
||
h <- height of substrate (mm)
|
||
e_r <- relative permitivity of substrate
|
||
f <- frequency (GHz)
|
||
W -> strip width (mm)
|
||
s -> gap (mm)
|
||
'''
|
||
Z = np.array([Ze,Zo])
|
||
u = opt.root(lambda X: Z - np.array(mclZcf(X[0],h,X[1],e_r,f)), [h/2,h/5],method='lm')
|
||
return u.x
|
||
|
||
def open_end(W, h, e_r, f):
|
||
'''
|
||
Calculate open end displacment dl of microstrip open end.
|
||
Kirschning, M., R. H. Jansen, and N. H. L. Koster.
|
||
"Accurate model for open end effect of microstrip lines."
|
||
Electronics Letters 17.3 (1981): 123-125.
|
||
|
||
dl = open_end(W,h,e_r,f)
|
||
W <- width of microstrip line (mm)
|
||
h <- height of substrate (mm)
|
||
e_r <- relative dielectric constant of substrate
|
||
f <- frequency (GHz)
|
||
'''
|
||
epsf = eps_f(W,h,e_r,f)
|
||
u = W/h
|
||
|
||
x1 = 0.434907*(epsf**0.81+0.26)/(epsf**0.81-0.189)*(u**0.8544+0.236)/(u**0.8544+0.87)
|
||
x2 = 1 + u**0.371/(2.358*e_r+1)
|
||
x3 = 1 + 0.5274*np.arctan(0.084*u**(1.9413/x2))/epsf**0.9236
|
||
x4 = 1 + 0.0377*np.arctan(0.067*u**1.456)*(6-5*np.exp(0.036*(1-e_r)))
|
||
x5 = 1 - 0.218*np.exp(-7.5*u)
|
||
|
||
return x1*x3*x5/x4 *h
|