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mstrip.cc

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// mstrip.cc
// SuperMix version 1.0  C++ source file
//
// Copyright (c) 1999 California Institute of Technology.
// All rights reserved.
//
// Redistribution and use in source and binary forms for noncommercial
// purposes are permitted provided that the above copyright notice and
// this paragraph are duplicated in all such forms and that any
// documentation and other materials related to such distribution and
// use acknowledge that the software was developed by California
// Institute of Technology. Redistribution and/or use in source or
// binary forms is not permitted for any commercial purpose. Use of
// this software does not include a permitted use of the Institute's
// name or trademark for any purpose.
//
// DISCLAIMER:
// THIS SOFTWARE AND/OR RELATED MATERIALS ARE PROVIDED "AS-IS" WITHOUT
// WARRANTY OF ANY KIND INCLUDING ANY WARRANTIES OF PERFORMANCE OR
// MERCHANTABILITY OR FITNESS FOR A PARTICULAR USE OR PURPOSE (AS SET
// FORTH IN UCC 23212-2313) OR FOR ANY PURPOSE WHATSOEVER, FOR THE
// LICENSED PRODUCT, HOWEVER USED.  IN NO EVENT SHALL CALTECH/JPL BE
// LIABLE FOR ANY DAMAGES AND/OR COSTS, INCLUDING BUT NOT LIMITED TO
// INCIDENTAL OR CONSEQUENTIAL DAMAGES OF ANY KIND, INCLUDING ECONOMIC
// DAMAGE OR INJURY TO PROPERTY AND LOST PROFITS, REGARDLESS OF
// WHETHER CALTECH/JPL SHALL BE ADVISED, HAVE REASON TO KNOW, OR IN
// FACT SHALL KNOW OF THE POSSIBILITY.  THE USER BEARS ALL RISK
// RELATING TO QUALITY AND PERFORMANCE OF THE SOFTWARE AND/OR RELATED
// MATERIALS.
//
// Change history:
// 8/4/99:   Removed calculation of attenuation constant (alpha), and
//           fixed error found by A. Karpov when using dielectrics with
//           nonzero loss tangent. The error was related to improper
//           use of units. (J.Z.)
//           Loss is now handled by using effective loss tangent (tandel)
//           
// 3/22/99:  changed VERYBIG to MSTRIP_H_VERYBIG

#include <math.h>
#include "units.h"
#include "mstrip.h"

void mstrip(double h, double w, double t1, double t2, 
            double esub, double eup, double Qsub, double Qup, double freq,
            double &Z0, double &epeff, double &tandel, double &g2)
{
//
//    J. Zmuidzinas 11/18/87
//    Translated to C/C++  9/15/97
//
//    Based on equations given by Hammerstad and Jensen, IEEE Microwave
//    Symposium proceedings, pp.407-409, 1980.
//
//    Lengths are converted to be in microns and frequencies in GHz.
//
//    Input parameters:
//
//    h - substrate thickness
//    w - width of microstrip
//    t1 - conductor thickness (strip)
//    t2 - conductor thickness (ground)
//    esub - dielectric constant of substrate
//    eup - dielectric constant superstrate (usually = 1)
//    freq - frequency
//    Qsub - dielectric quality factor of substrate (1/tan(delta))
//    delta is defined as the phase angle of the complex
//    dielectric constant of the substrate
//    Qup - dielectric quality factor of superstrate
//
//
//    Output parameters:
//
//    Z0 - characteristic impedance
//    epeff - effective dielectric constant
//         (wavelength = free space wavelength / sqrt(epeff)
//    tandel - effective loss tangent of line. Defined so that
//         beta = (2*Pi/wavelength)*(1 + i*tandel)
//         where beta is the complex propagation factor; i = sqrt(-1).
//    g2 - geometrical factor for loss calculations; = 2/w for wide lines
//
//
      double u, Z01, fu, a, b, tnorm, delu1, delur,
             u1, ur, fp, G, eta0 ;
      double ex, coth, cosh, Z02, ee0, ee1, Kfact,
             Qc, Qd, Q0, q ;
      double x1, x2 ;
//
      h /= Micron;       /* easier to scale now              */
      w /= Micron;       /* to units that subroutine expects */
      t1 /= Micron;      /* and to restore units later       */
      t2 /= Micron;
      freq /= GHz;
//
// Convert substrate dielectric constant to be relative to superstrate
//
      esub /= eup ;
//
      eta0 = ZVacuum/Ohm ;
      eta0 /= sqrt(eup) ;
      u = w/h ;
//
//     Calculate thickness corrections
//
      tnorm = t1/h ;                         /* ?? need more thinking */
      ex = exp(sqrt(6.517*u)) ;
      coth = (ex+1./ex)/(ex-1./ex) ;
      delu1 = (tnorm/Pi)*log(1. + 4*exp(1.)/(tnorm*coth*coth)) ;
      ex = exp(sqrt(esub-1.)) ;
      cosh = 0.5*(ex+1./ex) ;
      delur = 0.5*(1. + 1./cosh)*delu1 ;
      u1 = u + delu1 ;
      ur = u + delur ;
//
//     Calculate characteristic impedance
//
      u = ur ;
      fu = 6. + (2.*Pi-6.)*exp( -(pow((30.666/u), 0.7528)) ) ;
      Z01 = eta0*log(fu/u + sqrt(1.+((2./u)*(2./u))))/(2.*Pi) ;
      x1 = u*u*u*u + (u/52.)*(u/52.) ;
      x2 = u*u*u*u + 0.432 ;
      a = 1.+ (1./49.)*log(x1/x2) ;
      a += (1./18.7)*log(1.+(u/18.1)*(u/18.1)*(u/18.1)) ;
      b = 0.564*( pow((esub-0.9)/(esub+3.), 0.053) ) ;
      ee0 = (esub+1.)/2. + ((esub-1.)/2.)*pow( (1.+10./u), (-a*b) ) ;
//
      Z0 = Z01/sqrt(ee0) ;
//
//     calculate finite thickness corrections to effective diel. const.
//
      u = u1 ;
      fu = 6. + (2.*Pi-6.)*exp( -pow((30.666/u), 0.7528) ) ;
      Z02 = eta0*log(fu/u + sqrt(1.+((2./u)*(2./u))))/(2.*Pi) ;
      ee1 = ee0*((Z02/Z01)*(Z02/Z01)) ;
//
//     corrections for dispersion
//
      G = (Pi*Pi/12.)*((esub-1.)/ee1)*sqrt(2.*Pi*Z0/eta0) ;
//
//     Cutoff frequency in GHz of first TE mode ; here h in microns.
//
      fp = 397.887*Z0/h ;
//
//     dispersion-corrected dielectric constant
//
      epeff = esub - (esub-ee1)/(1.+G*((freq/fp)*(freq/fp))) ;
//
//     dispersion-corrected characteristic impedance
//
      Z0 = Z0*sqrt(ee1/epeff)*(epeff-1.)/(ee1-1.) ;
//
//     Attenuation - dielectric Losses
//
      q = (epeff - 1.)/(esub - 1.) ;
      Qd = ((1.-q) + q*esub)/((1.-q)/Qup + q*esub/Qsub) ;
//
      u = w/h ;
      Kfact = exp(-1.2*pow((Z01/eta0), 0.7)) ;     /* ?? need more thinking */
      g2 = 2.*Kfact/w ;
//
//     Assume no resistive losses - these will be taken into
//     account later
//
      Qc = MSTRIP_H_VERYBIG ;   /* just big ! */
//
//     Total attenuation
//
      Q0 = 1/(1/Qd + 1/Qc) ;
      tandel = 0.5/Q0 ;
//
// Now fix up units
//
      Z0 *= Ohm ;        /* we calculated the impedance in Ohms */
      g2 /= Micron ;     /* g2 has units of  1/length */
      epeff *= eup ;     /* we calculated relative to superstrate */
}

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