{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ch-10 : Striplines & Microstrip lines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 554 Example 10.1"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import exp, log10, pi, sqrt, log\n",
"#Given,\n",
"\n",
"z0=50 #ohm\n",
"t=0.001 #mm\n",
"b=0.32 #cm\n",
"er=2.20 \n",
"tandel= 0.0005 \n",
"rs=0.026 #ohm\n",
"f=10e9 #Hz\n",
"c=3e8 #m/sec\n",
"\n",
"p=sqrt(er)*z0 \n",
"#As p<120\n",
"w=b*(((30*pi)/p)-0.441)\n",
"print 'Width %0.3f'%w,'cm'\n",
"\n",
"#Attenuation\n",
"k=((2*pi*f*sqrt(er))/c) \n",
"ad=(k*tandel)/2 \n",
"\n",
"#and\n",
"A=1+((2*w)/(b-t))+(((b+t)/((b-t)*pi))*log(((2*b)-t)/t)) \n",
"#Hence \n",
"ac=(2.7e-3*rs*er*z0*A)/(30*pi*(b-t)*1e-2)\n",
"#Total attenution\n",
"a=ad+ac \n",
"\n",
"#Total attenution in db\n",
"x=exp(a) \n",
"alp=20*log10(x) #db/m\n",
"\n",
"#Total attenution in db/lambda:\n",
"lam=c/(sqrt(er)*f) \n",
"lamm=lam*1e2 \n",
"alph=alp/lamm \n",
"print 'Total attenution in db/lambda: %0.3f'%alph, 'db/lambda'\n",
"\n",
"\n",
"#Answer in book for alph is given as 0.856 but it should be 0.0856 as value of f is taken as 10e10 but it should be 10e9"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Width 0.266 cm\n",
"Total attenution in db/lambda: 0.856 db/lambda\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 555 Example 10.2"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given,\n",
"er=9.7 \n",
"h=0.25 #mm\n",
"w=0.25 #mm\n",
"f=5e9 #Hz\n",
"c=3e8 #m/s\n",
"\n",
"#(i) Dielectric constant\n",
"dc=((er+1)/2)+(((er-1)/2)*(1/sqrt(1+12*h/w))) \n",
"print 'Dielectric constant: %0.3f'%dc\n",
"\n",
"#(ii) Phase constant\n",
"lam0=c/f \n",
"pc=sqrt(dc)*(2*pi/lam0) \n",
"print 'Phase constant: %0.3f'%(pc/100),'rad/m'\n",
"\n",
"#(iii) Microstrip wavelength\n",
"lams=lam0/sqrt(dc) \n",
"print 'Microstrip wavelength: %0.3f'%(lams*100),'cm'\n",
"\n",
"#(iv) Capacitance per unit length\n",
"e0=8.854e-12 \n",
"cap=(2*pi*e0)/log((8*h/w)-(w/(4*h))) \n",
"print 'Capacitance per unit length: %0.3e'%cap, 'F/cm'\n",
"\n",
"#(v) Characterstic Impedance\n",
"ci=(60/sqrt(dc))*log((8*h/w)+(w/(4*h))) \n",
"print 'Characterstic impedance: %0.3f'%ci, 'ohm'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dielectric constant: 6.556\n",
"Phase constant: 2.681 rad/m\n",
"Microstrip wavelength: 2.343 cm\n",
"Capacitance per unit length: 2.717e-11 F/cm\n",
"Characterstic impedance: 49.447 ohm\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 556 Example 10.3"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given,\n",
"er=5.23 \n",
"w=10 #mils\n",
"t=2.8 #mils\n",
"h=7 #mils\n",
"\n",
"dc=((er+1)/2)+(((er-1)/2)*(1/sqrt(1+12*h/w))) \n",
"print 'Dielectric constant: %0.3f'%dc\n",
"\n",
"#As w/h>1\n",
"ci=(120*pi)/(sqrt(dc)*((w/h)+1.393+0.667*log((w/h)+1.444))) \n",
"print 'Characterstic impedance: %0.3f'%ci, 'ohm'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dielectric constant: 3.805\n",
"Characterstic impedance: 54.822 ohm\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 556 Example 10.4"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given,\n",
"\n",
"q=2.5 \n",
"dh=1.58 \n",
"er=9 \n",
"f=10 \n",
"c=3e8 \n",
"\n",
"erff=((er+1)/2)+(((er-1)/2)*((1+(12/q))**(-1/2))) \n",
"vp=(c/sqrt(erff))*erff \n",
"fe1=c/(sqrt(vp)*2*dh*q) \n",
"if f<fe1:\n",
" print 'Strip supports TEM mode only' \n",
"else:\n",
" print 'Strip does not support TEM mode only' \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Strip supports TEM mode only\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 557 Example 10.5"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given,\n",
"\n",
"er=9.7 \n",
"h=0.5 #mm\n",
"w=0.5 #mm\n",
"lt=2e-4 \n",
"t=0.02 #mm\n",
"f=5e9 #Hz\n",
"fg=5 #HZ\n",
"c=3e8 \n",
"rs=8.22e-3*sqrt(fg) \n",
"\n",
"#(i) Dielectric constant\n",
"dc=((er+1)/2)+(((er-1)/2)*(1/sqrt(1+12*h/w))) \n",
"print 'Dielectric constant: %0.3f'%dc\n",
"\n",
"#(ii) Characterstic Impedance\n",
"ci=(60/sqrt(dc))*log((8*h/w)+(w/(4*h))) \n",
"print 'Characterstic impedance: %0.3f'%ci,'ohm'\n",
"\n",
"#(iii) Dielectric attenuation\n",
"lam0=c/f \n",
"alphd=(pi/lam0)*(er/sqrt(dc))*((dc-1)/(er-1))*lt \n",
"print 'Dielectric attenuation: %0.3f'%alphd,'Np/m'\n",
"\n",
"#Conductor attenuation\n",
"r1=(0.94+(0.132*(w/h))-(0.0062*((w/h)**2)))*((1/pi)+(1/(pi**2))*log((4*pi*w)/t))*(rs/(w*1e-3))\n",
"r1m=r1*1e-2 \n",
"r2=(w/h)/(((w/h)+5.8+(0.03*(h/w))))*(rs/(w*1e-3)) \n",
"r2m=r2*1e-2 \n",
"alphc=(r1+r2)/(2*ci) \n",
"print 'Conductor attenuation: %0.3f'%alphc,'Np/m'\n",
"\n",
"#(iv) Total attenuation\n",
"A=alphc+alphd \n",
"Adb=A*8.686*1e-2 \n",
"print 'Total attenuation: %0.3f'%Adb,'db/cm'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dielectric constant: 6.556\n",
"Characterstic impedance: 49.447 ohm\n",
"Dielectric attenuation: 0.025 Np/m\n",
"Conductor attenuation: 0.411 Np/m\n",
"Total attenuation: 0.038 db/cm\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 558 Example 10.6"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"\n",
"sig=5.8e7 \n",
"f=10 #GHz\n",
"h=0.12e-2 #m\n",
"\n",
"q=62.8*h*sqrt(f*sig) \n",
"print 'conductor Q of the stripline:' ,round(q)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"conductor Q of the stripline: 1815.0\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 558 Example 10.7"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"Er=6 \n",
"h=4e-3 #m\n",
"\n",
"#(i) W for Z0=50W\n",
"Z0=50 #W\n",
"W=(120*pi*h)/(sqrt(Er)*Z0) \n",
"print 'Required Width: %0.3f'%(W*1000), 'mm'\n",
"\n",
"#(ii)Stripline capacitance\n",
"E0=8.854e-12 \n",
"C=(E0*Er*W)/h \n",
"print 'Stripline capacitance: %0.3f'%(C*10**12),'pF/m'\n",
"\n",
"#(iii)Stripline inductance\n",
"Mu0=4*pi*10e-7 \n",
"L=(Mu0*h)/W \n",
"print 'Stripline inductance: %0.3f'%(L*10**5),' muH/m'\n",
"\n",
"#(iv)Phase velocity\n",
"c=3e8 \n",
"vp=c/sqrt(Er) \n",
"print 'Phase velocity',vp, 'm/s'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Required Width: 12.312 mm\n",
"Stripline capacitance: 163.522 pF/m\n",
"Stripline inductance: 0.408 muH/m\n",
"Phase velocity 122474487.139 m/s\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 559 Example 10.8"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"cl=3e8 #m/s\n",
"f=5e9 #Hz\n",
"Er=9 \n",
"C=-10 #db\n",
"Z0=50 #ohm\n",
"#Length\n",
"L=(cl/f)/(4*sqrt(Er)) \n",
"print 'Length:' ,L*100,'cm'\n",
"\n",
"#Coupling coefficient\n",
"C0=10**(C/20) \n",
"print 'Coupling coefficient: %0.3f'%C0\n",
"\n",
"#Even and odd mode impedance\n",
"Z0e=(Z0*sqrt(1+C0))/sqrt(1-C0) \n",
"print 'Even mode impedance: %0.3f'%Z0e,'ohm'\n",
"\n",
"\n",
"Z0o=(Z0*sqrt(1-C0))/sqrt(1+C0) \n",
"print 'Odd mode impedance: %0.3f'%Z0o,'ohm'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Length: 0.5 cm\n",
"Coupling coefficient: 0.316\n",
"Even mode impedance: 69.371 ohm\n",
"Odd mode impedance: 36.038 ohm\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 560 Example 10.9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"Z0=50 #ohm\n",
"C=3 #db\n",
"\n",
"#Line impedance\n",
"Z01sqr=(1-(10**(C/-10))) \n",
"Z01=sqrt(Z0*Z0*Z01sqr) \n",
"print 'Z01: %0.3f'%Z01, 'ohm'\n",
"\n",
"Z02=Z01/(sqrt(1-(1/sqrt(2))**2)) \n",
"print 'Z02:' ,round(Z02),'ohm'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Z01: 35.313 ohm\n",
"Z02: 50.0 ohm\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 560 Example 10.10"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"W=6 #m\n",
"s=2.2 #m\n",
"b=4.8 #m\n",
"Er=2.2 \n",
"\n",
"#Even and odd mode impedance\n",
"Z0e=((120*pi)*(b-s))/(2*sqrt(Er)*W) \n",
"print 'Even mode impedance: %0.3f'%Z0e,'ohm'\n",
"\n",
"\n",
"Z0o=(Z0e*s)/b \n",
"print 'Odd mode impedance: %0.3f'%Z0o,'ohm'\n",
"\n",
"#Mid band coupling\n",
"x=(Z0e-Z0o)/(Z0e+Z0o) \n",
"C=-20*log10(x) \n",
"print 'Mid band coupling: %0.3f'%C,'db'\n",
"\n",
"#Answer in book for C is given as 54.2 but it should be 8.60"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Even mode impedance: 55.070 ohm\n",
"Odd mode impedance: 25.240 ohm\n",
"Mid band coupling: 8.602 db\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 562 Example 10.11"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"Er=6 \n",
"d=3e-3 #m\n",
"Z0=50 #ohm\n",
"E0=8.854e-12 #F/m\n",
"Mu0=4*pi*10e-7 #H/m\n",
"\n",
"#(i) W \n",
"W=(377*d)/(sqrt(Er)*Z0) \n",
"print 'Required Width: %0.3f'%(W*1000),'mm'\n",
"\n",
"#(ii)Stripline capacitance\n",
"C=(E0*Er*W)/d \n",
"print 'Stripline capacitance: %0.3f'%(C*10**12),'pF/m'\n",
"\n",
"#(iii)Stripline inductance\n",
"L=(Mu0*d)/W \n",
"print 'Stripline inductance: %0.3f'%(L*10**6), 'muH/m'\n",
"\n",
"#(iv)Phase velocity\n",
"c=3e8 \n",
"vp=c/sqrt(Er) \n",
"print 'Phase velocity' ,vp,'m/s'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Required Width: 9.235 mm\n",
"Stripline capacitance: 163.526 pF/m\n",
"Stripline inductance: 4.082 muH/m\n",
"Phase velocity 122474487.139 m/s\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 562 Example 10.12"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"Er=2.56 \n",
"w=25 #mils\n",
"t=14 #mils\n",
"d=70 #mils\n",
"E0=8.854e-12 #F/m\n",
"\n",
"#(i) K factor\n",
"K=1/(1-(t/d)) \n",
"print 'K factor:' ,K\n",
"\n",
"#(ii) Fringe capacitance\n",
"C=((E0*Er)*(2*K*log(K+1)-(K-1)*log(K**2-1)))/pi \n",
"print 'Fringe capacitance: %0.3f'%(C*10**12), 'pF/m'\n",
"\n",
"#(iii) Charecteristic Impedance\n",
"X=1/(((w*K)/d)+(C/(E0*Er)))\n",
"Z0=(94.15*X)/sqrt(Er) \n",
"print 'Charecteristic Impedance: %0.3f'%Z0,'ohm'\n",
"\n",
"\n",
"#Answer in book for Z0 is given as 50.29 but it should be 51.7"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"K factor: 1.25\n",
"Fringe capacitance: 15.665 pF/m\n",
"Charecteristic Impedance: 51.729 ohm\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Page Number: 563 Example 10.13"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Given\n",
"Z0=50 #ohm\n",
"#Sincr ratio of power is 2:3\n",
"x1=5/2 \n",
"y1=5/3 \n",
"#Output Impedance\n",
"Z1=x1*Z0 \n",
"Z2=y1*Z0 \n",
"print 'Output Impedance 1:',Z1,'ohm'\n",
"print 'Output Impedance 2: %0.3f'%Z2,'ohm'\n",
"\n",
"#Input Impedance\n",
"Zin=[((Z2*2*Z2)/3)/((Z2+(2*Z2)/3))] \n",
"\n",
"#Looking into Z1, Z2 is || to Z0\n",
"A1=(Z2*Z0)/(Z2+Z0) \n",
"\n",
"#Looking into Z, Z2 is || to Z0\n",
"A2=(Z1*Z0)/(Z1+Z0) \n",
"\n",
"#Reflection Coeffcients\n",
"R1=(A1-Z1)/(A1+Z1) \n",
"R2=(A2-Z2)/(A2+Z2) \n",
"\n",
"print 'Reflection Coeffcients:\\n', R1,'\\n',R2, "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Output Impedance 1: 125.0 ohm\n",
"Output Impedance 2: 83.333 ohm\n",
"Reflection Coeffcients:\n",
"-0.6 \n",
"-0.4\n"
]
}
],
"prompt_number": 21
}
],
"metadata": {}
}
]
}