skripta za mikrotrakasto linijo in pasovno sito
Andrej
commit
220fa85dfa
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#!/usr/bin/python3
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import numpy as np
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import scipy.optimize as opt
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import microstrip as ms
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def Butterworth(n):
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'''
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Return koefficents of Butterworth n-th order filter
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g0 and gn+1 are assumed to be 1
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[g0, g1, ... gn, gn+1] = Buttherworth(n)
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'''
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gi = 2*np.sin((2*np.arange(1,n+1)-1)*np.pi/2/n)
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return np.hstack([1,gi,1])
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def Tchebysheff(n, ripple):
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'''
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Return coefficents of Tchebysheff n-th order filter
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with specified ripple in passband.
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[g0, g1, ... gn, gn+1] = Tchebysheff(n, ripple)
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n <- order of filter
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ripple <- ripple in passband (dB)
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'''
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b = np.log(1/np.tanh(ripple/17.37))
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k = np.sinh(b/2/n)
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g = np.ones(n+2)
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g[1] = 2/k*np.sin(np.pi/2/n)
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for i in range(2,n+1):
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g[i] = 1/g[i-1]*4*np.sin((2*i-1)*np.pi/2/n)*np.sin((2*i-3)*np.pi/2/n)/\
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(k**2+np.sin((i-1)*np.pi/n)**2)
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if n % 2 == 0:
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g[-1] = 1/np.tanh(b/4)**2
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return g
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def mclBPF(h, e_r, fbw, gk, f0):
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'''
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Calculate dimensions of microstrip coupled lines bandpass
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filter.
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h <- height of substrate (mm)
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e_r <- dielectric constant of substrate
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fbw <- fractional bandwidth of bpf
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gk <- filter coefficents
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f0 <- central frequency (GHz)
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'''
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n = len(gk)-2
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J = np.ones(n+1)
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J[0] = np.sqrt(np.pi*fbw/2/gk[0]/gk[1])
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J[-1] = np.sqrt(np.pi*fbw/2/gk[-2]/gk[-1])
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for j in range(1,n):
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J[j] = np.pi*fbw/2/np.sqrt(gk[j]*gk[j+1])
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Zo = np.zeros(n+1)
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Ze = np.zeros(n+1)
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for j in range(n+1):
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Ze[j] = 50*(1+J[j]+J[j]**2)
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Zo[j] = 50*(1-J[j]+J[j]**2)
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lambda4 = 3e8/f0/1e9/4 *1e3
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W = np.zeros(n+1)
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s = np.zeros(n+1)
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l = np.zeros(n+1)
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for j in range(n+1):
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x = ms.get_mcl(Ze[j],Zo[j],h,e_r,f0)
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W[j] = x[0]
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s[j] = x[1]
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dl = ms.open_end(W[j],h,e_r,f0)
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eps = ms.mcl_eps(W[j],h,s[j],e_r,f0)
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# popravek z upostevanjem disperzije
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l[j] = lambda4/np.sqrt(np.sqrt(eps[0]*eps[1]))-dl
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#print(l[j])
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# popravek s staticnim eps
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l[j] = lambda4/np.sqrt(np.sqrt(eps[2]*eps[3]))-dl
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#print(l[j])
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return {'W':W, 's':s, 'l':l, 'f':f0, 'fbw':fbw}
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def prtmclBFP(bfp):
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'''
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Print filter in readable format
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'''
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n = len(bfp['W'])
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print("Microstrip coupled line bandpass filter:\nAll dimensions in mm.")
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print("\tW\ts\tl")
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for i in range(n):
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print("{}:\t{:.2f}\t{:.2f}\t{:.2f}".format(i+1,bfp['W'][i],\
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bfp['s'][i],bfp['l'][i]))
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print("Length of filter: {} mm".format(sum(bfp['l'])))
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print("Width of filter: {} mm".format(sum(bfp['W'])+sum(bfp['s'])))
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if __name__ == '__main__':
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gk = Tchebysheff(7,0.05)
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#bfp = mclBPF(1.54, 3.66, 0.1, gk, 10.2)
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bfp = mclBPF(0.76, 3.66, 0.1, gk, 10.2)
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#prtmclBFP(bfp)
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print(ms.getWf(50, 0.76, 3.66, 10.2))
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print("=== interstage filter za bfp840 ===")
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gk = Butterworth(7)
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bfp = mclBPF(0.8, 3.66, 0.3, gk, 10.5)
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prtmclBFP(bfp)
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print("=== interstage filter za bfp840 ===")
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gk = Butterworth(5)
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bfp = mclBPF(0.8, 3.66, 0.3, gk, 10.5)
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prtmclBFP(bfp)
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print("=== interstage filter za bfp840 ===")
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gk = Butterworth(5)
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bfp = mclBPF(0.8, 3.66, 0.05, gk, 10.5)
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prtmclBFP(bfp)
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print("=== interstage filter za bfp840 ===")
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gk = Butterworth(3)
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bfp = mclBPF(0.8, 3.66, 0.05, gk, 10.5)
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prtmclBFP(bfp)
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@ -0,0 +1,333 @@
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#!/usr/bin/python3
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import numpy as np
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import scipy.optimize as opt
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np.seterr(under='ignore')
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### STATIC approx
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def eps_re(u, e_r):
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'''
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Calculate effective dielectric constant
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using the expressions given in
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E. Hammerstad and O. Jensen, "Accurate Models for
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Microstrip Computer-Aided Design," 1980 IEEE MTT-S
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International Microwave symposium Digest, Washington,
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DC, USA, 1980, pp. 407-409.
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doi: 10.1109/MWSYM.1980.1124303
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e_re = eps_re(u, e_r):
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u <- ratio W/h
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e_r <- substrate relative dielectric constant
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e_re -> effective relative dielectric constant
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of microstrip line
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'''
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a = 1 + np.log((u**4 + (u/52)**2)/(u**4+0.432))/49 +\
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np.log(1+(u/18.1)**3)/18.7
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b = 0.564*( (e_r-0.9)/(e_r+3) )**(0.053)
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e_re = 0.5*(e_r+1)+0.5*(e_r-1)*(1+10/u)**(-a*b)
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return e_re
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def getZc(u, e_r):
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'''
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Calculate characteristic impedance Zc
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using the expressions given in
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E. Hammerstad and O. Jensen, "Accurate Models for
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Microstrip Computer-Aided Design," 1980 IEEE MTT-S
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International Microwave symposium Digest, Washington,
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DC, USA, 1980, pp. 407-409.
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doi: 10.1109/MWSYM.1980.1124303
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(neglected thickness of copper)
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Zc = getZc(u, e_r)
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u <- ratio W/h
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e_r <- substrate relative dielectric constant
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Zc -> characteristic impedance of microstrip line
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'''
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F = 6 + (2*np.pi-6)*np.exp(-(30.666/u)**0.7528)
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e_re = eps_re(u, e_r)
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Zc = (120*np.pi)/(2*np.pi*np.sqrt(e_re))*np.log(\
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F/u + np.sqrt(1 + (2/u)**2))
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return Zc
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### Dispersion correction
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def eps_f(W,h,e_r,f):
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'''
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Calculate effective dieletric constant using formulas given by:
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M. Kirschning and R. H. Jansen, "Accurate Model for Effective
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Dielectric Constant of Microstrip with Validity up to Millimeter-Wave
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Frequencies," Electronics Letters, vol. 8, no. 6, pp. 272-273,
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Mar. 1982.
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R. H. Jansen and M. Kirschning, "Arguments and an accurate Model
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for the Power-Current Formulation of Microstrip Characteristic
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Impedance," Archiv für Elektronik und Übertragungstechnik (AEÜ),
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vol. 37, pp. 108-112, 1983.
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http://qucs.sourceforge.net/tech/node75.html
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e_re = eps_f(W,h,e_r,f)
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W <- width of microstrip (mm)
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h <- height of substrate (mm)
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e_r <- substrate relative dielectric cosntatn
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f <- frequency (GHz)
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e_re -> effective dielectric constant of microstrip line
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'''
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fn = f*h
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u = W/h
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P1 = 0.27488 + (0.6315+0.525/(1+0.0157*fn)**20)*u - 0.065683*np.exp(\
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-8.7513*u)
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P2 = 0.33622*(1-np.exp(-0.03442*e_r))
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P3 = 0.0363*np.exp(-4.6*u)*(1-np.exp(-(fn/38.7)**4.97))
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P4 = 1+2.751*(1-np.exp(-(e_r/15.916)**8))
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Pf = P1*P2*((0.1844+P3*P4)*fn)**1.5763
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eps0 = eps_re(u,e_r)
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return e_r - (e_r - eps0)/(1+Pf)
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def getZcf(W,h,e_r,f,R=False):
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'''
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Calculate characteristic impedance using formulas given by:
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M. Kirschning and R. H. Jansen, "Accurate Model for Effective
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Dielectric Constant of Microstrip with Validity up to Millimeter-Wave
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Frequencies," Electronics Letters, vol. 8, no. 6, pp. 272-273,
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Mar. 1982.
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R. H. Jansen and M. Kirschning, "Arguments and an accurate Model
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for the Power-Current Formulation of Microstrip Characteristic
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Impedance," Archiv für Elektronik und Übertragungstechnik (AEÜ),
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vol. 37, pp. 108-112, 1983.
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http://qucs.sourceforge.net/tech/node75.html
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Zc = Zcf(W,h,e_r,f,R=False)
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W <- width of microstrip (mm)
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h <- height of substrate (mm)
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e_r <- substrate relative dielectric cosntatn
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f <- frequency (GHz)
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R=False <- flag telling whether to return R17 or not
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Zc -> characteristic impedance of microstrip line
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R17 -> parameter used to calculate impedance and coupled line
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return only if R=True
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'''
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fn = f*h
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u = W/h
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ef = eps_f(W,h,e_r,f)
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e0 = eps_re(u,e_r)
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R1 = 0.03891*e_r**1.4
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R2 = 0.267*u**7
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R3 = 4.766*np.exp(-3.228*u**0.641)
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R4 = 0.016 + (0.0514*e_r)**4.524
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R5 = (fn/28.843)**12.0
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R6 = 22.20*u**1.92
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R7 = 1.206-0.3144*np.exp(-R1)*(1-np.exp(-R2))
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R8 = 1+1.275*(1-np.exp(-0.004625*R3*e_r**1.674)*(fn/18.365)**2.745)
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R9 = 5.086*R4*R5*np.exp(-R6)*(e_r-1)**6/\
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((0.3838+0.386*R4)*(1+1.2992*R5)*(1+10*(e_r-1)**6))
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R10 = 0.00044*e_r**2.136+0.0184
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R11 = (fn/19.47)**6/(1+0.0962*(fn/19.47)**6)
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R12 = 1/(1+0.00245*u**2)
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R13 = 0.9408*ef**R8-0.9603
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R14 = (0.9408-R9)*e0**R8-0.9603
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R15 = 0.707*R10*(fn/12.3)**1.097
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R16 = 1+0.0503*e_r**2*R11*(1-np.exp(-(u/15)**6))
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R17 = R7*(1-1.1241*R12*np.exp(-0.026*fn**1.15656-R15)/R16)
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Z0 = getZc(u,e_r)
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Zc = Z0*(R13/R14)**R17
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if R:
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return (Zc, R17)
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else:
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return Zc
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def getWf(Zk,h,e_r,f):
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'''
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Calculate width of microstrip line when also
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taking in to account dispersion.
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W = getWf(Zk,h,e_r,f)
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Zk <- characteristic impedance (ohms)
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h <- substrate height
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e_r <- substrate relative di. costant
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f <- frequency (GHz)
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W -> widht of microstrip line (mm)
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'''
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u = opt.root_scalar(lambda X: Zk-getZcf(X,h,e_r,f),x0=h,\
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method='brentq', bracket=[0.01,100])
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return u.root
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### coupled lines
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def mcl_eps(W,h,s,e_r,f):
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'''
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Calculate effective odd and even permittivity of parallel
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coupled microstrip lines.
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M. Kirschning, R. H. Jansen, and N. H. L. Koster,
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"Coupled microstrip parallel-gap model for improved filter and coupler design,"
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Electronics Letters, vol. 19, no. 10, pp. 377–379, May 1983,
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doi: 10.1049/el:19830261.
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even, odd = mcl_eps(W,h,s,e_r,f):
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W <- width of microstrip (mm)
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h <- height of substrate (mm)
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s <- spacing between lines (mm)
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e_r <- substrate relative dielectric cosntatn
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f <- frequency (GHz)
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even -> even mode dielectric constant
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odd -> odd mode dielectric constant
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'''
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u = W/h
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g = s/h
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fn = f*h
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eps0 = eps_re(u,e_r)
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v = u * (20+g**2)/(10+g**2)+ g*np.exp(-g)
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ae = 1+np.log((v**4+(v/52)**2)/(v**4+0.432))/49+np.log(1+(v/18.1)**3)/18.7
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be = 0.564*((e_r-0.9)/(e_r+3))**0.053
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even0 = 0.5*(e_r+1)+0.5*(e_r-1)*(1+10/v)**(-ae*be)
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ao = 0.7287*(eps0-0.5*(e_r+1))*(1-np.exp(-0.179*u))
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bo = 0.747*e_r/(0.15+e_r)
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co = bo - (bo-0.207)*np.exp(-0.414*u)
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do = 0.593+0.694*np.exp(-0.562*u)
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odd0 = (0.5*(e_r+1)+ao-eps0)*np.exp(-co*g**do)+eps0
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P1 = 0.27488+(0.6315+0.525/(1+0.0157*fn)**20)*u-0.065683*np.exp(-8.7513*u)
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P2 = 0.33622*(1-np.exp(-0.03442*e_r))
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P3 = 0.0363*np.exp(-4.6*u)*(1-np.exp(-(fn/38.7)**4.97))
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P4 = 1+2.751*(1-np.exp(-(e_r/15.916)**8))
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P5 = 0.334*np.exp(-3.3*(e_r/15)**3)+0.746
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P6 = P5*np.exp(-(fn/18)**0.368)
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P7 = 1+4.069*P6*g**0.479*np.exp(-1.347*g**0.595-0.17*g**2.5)
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Fe = P1*P2*((P3*P4+0.1844*P7)*fn)**1.5763
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even = e_r - (e_r - even0)/(1+Fe)
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|
|
||||||
|
P8 = 0.7168*(1+1.076/(1+0.0576*(e_r-1)))
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|
P9 = P8-0.7913*(1-np.exp(-(fn/20)**1.424))*np.arctan(2.481*(e_r/8)**0.946)
|
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|
P10 = 0.242*(e_r - 1)**0.55
|
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|
P11 = 0.6366*(np.exp(-0.3401*fn)-1)*np.arctan(1.263*(u/3)**1.629)
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|
P12 = P9 + (1-P9)/(1+1.183*u**1.376)
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|
P13 = 1.695 * P10/(0.414+1.605*P10)
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|
P14 = 0.8928+0.1072*(1-np.exp(-0.42*(fn/20)**3.215))
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|
P15 = np.abs(1-0.8928*(1+P11)*np.exp(-P13*g**1.092)*P12/P14)
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|
Fo = P1*P2*((P3*P4+1.844)*fn*P15)**1.5763
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|
odd = e_r - (e_r - odd0)/(1+Fo)
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|
return even,odd,even0,odd0
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|
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|
def mclZcf(W,h,s,e_r,f):
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|
'''
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|
Calculate odd and even characteristic impedance of parallel
|
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|
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,
|
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|
doi: 10.1049/el:19830261.
|
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|
|
||||||
|
even, odd = mcl_eps(W,h,s,e_r,f):
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|
W <- width of microstrip (mm)
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|
h <- height of substrate (mm)
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|
s <- spacing between lines (mm)
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|
e_r <- substrate relative dielectric cosntatn
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|
f <- frequency (GHz)
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|
Ze -> even mode charachterstic impedance
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|
Zo -> odd mode characteristic impedance
|
||||||
|
'''
|
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|
u = W/h
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|
g = s/h
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|
fn = f*h
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|
|
||||||
|
eps0 = eps_re(u,e_r)
|
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|
epsf = eps_f(W,h,e_r,f)
|
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|
even,odd,even0,odd0 = mcl_eps(W,h,s,e_r,f)
|
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|
Z0 = getZc(u,e_r)
|
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|
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
|
||||||
Loading…
Reference in New Issue