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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 16: Frequency Response"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.10: Bode_diagrams.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.10\n",
+"s=poly(0,'s')\n",
+"h=syslin('c',(10*s)/((1+s)*(s^2+20*s+10000)))\n",
+"disp(h)\n",
+"fmin=0.01\n",
+"fmax=10^4\n",
+"scf(1);clf;\n",
+"//Calculate Bode plot\n",
+"bode(h,fmin,fmax)\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.11: Filters.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.11\n",
+"disp('Given')\n",
+"disp('A high pass filter with cutoff frequency of 3k Hz')\n",
+"//Cutoff frequency(wc)=1/(R*C)\n",
+"//Let us select some standard value of resistor\n",
+"disp('Let R=4.7k ohm')\n",
+"fc=3*10^3;R=4.7*10^3;\n",
+"wc=2*%pi*fc\n",
+"C=1/(R*wc)\n",
+"printf('\n C=%3.2f nF ',C*10^9);\n",
+"s=poly(0,'s')\n",
+"h=syslin('c',(R*C*s)/((1+s*R*C)))\n",
+"disp(h)\n",
+"HW = frmag(h,512);\n",
+"w=0: %pi /511: %pi ;\n",
+"plot(w,HW)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.12: Filters.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.12\n",
+"disp('Given')\n",
+"disp('Bandwidth = 1M Hz and high frequency cutoff = 1.1M Hz')\n",
+"B=10^6;fH=1.1*10^6\n",
+"//B=fH-fL\n",
+"fL=fH-B\n",
+"printf('Low frequency cutoff fL= %d kHz \n',fL*10^-3);\n",
+"wL=2*%pi*fL\n",
+"printf('wL= %3.2f krad/s \n',wL*10^-3);\n",
+"wH=2*%pi*fH\n",
+"printf('wH= %3.3f Mrad/s \n',wH*10^-6);\n",
+"//Now we need to find values for R,L and C\n",
+"//Let X=1/LC\n",
+"B=2*%pi*(fH-fL)\n",
+"X=(wH-B/2)^2-(B^2/4)\n",
+"disp(X)\n",
+"disp('Let L=1H')\n",
+"L=1;\n",
+"C=1/(L*X)\n",
+"disp(C,'C=')\n",
+"//B=R/L\n",
+"R=L*B\n",
+"printf('R= %3.3f Mohm \n',R*10^-6);\n",
+"\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.13: Filters.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.13\n",
+"disp('Given')\n",
+"disp('Voltage gain = 40dB and cutoff frequency = 10k Hz')\n",
+"Av_dB=40\n",
+"Av=10^(Av_dB/20)\n",
+"f=10*10^3\n",
+"B=2*%pi*f\n",
+"//From figure 16.41(a)\n",
+"disp('1+Rf/R1=100(Gain)')\n",
+"//From figure 16.41(b)\n",
+"//The transfer function is \n",
+"disp('V+= Vi*(1/sC)/(1+1/sC)')\n",
+"//Combining two transfer functions\n",
+"disp('V0 = Vi*(1/sC)/(1+1/sC)*(1+Rf/R1)')\n",
+"//The maximum value of the combined transfer function is\n",
+"disp('Maximum value is V0 = Vi*(1+Rf/R1)')\n",
+"disp('Let R1=1k ohm')\n",
+"R1=10^3\n",
+"Rf=(Av-1)*R1\n",
+"printf('Rf= %d kohm \n',Rf*10^-3);\n",
+"disp('C=1 uF')\n",
+"C=10^-6\n",
+"//B=1/(R2*C)\n",
+"R2=1/(C*B)\n",
+"printf('R2= %3.2f ohm \n',R2);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.1: Parallel_Resonance.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.1\n",
+"disp('Given')\n",
+"disp('L=2.5mH Q0=5 C=0.01uF')\n",
+"L=2.5*10^-3; Q0=5; C=0.01*10^-6;\n",
+"w0=1/sqrt(L*C)\n",
+"printf('w0= %3.1f krad/s \n',w0*10^-3);\n",
+"f0=w0/(2*%pi)\n",
+"alpha=w0/(2*Q0)\n",
+"printf('alpha= %3.1f Np/s \n',alpha);\n",
+"wd=sqrt(w0^2-alpha^2)\n",
+"printf('wd= %3.1f krad/s \n',wd*10^-3);\n",
+"R=Q0/(w0*C)\n",
+"printf('R= %3.2f ohm \n',R*10^-3);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.2: Bandwidth_and_high_Q_circuits.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.2\n",
+"disp('Given')\n",
+"disp('R=40Kohm L=1H C=1/64 uF w=8.2krad/s')\n",
+"R=40*10^3; L=1; C=1/64 *10^-6; w=8.2*10^3;\n",
+"//The value of Q0 must be at least 5 \n",
+"Q0=5;\n",
+"w0=1/sqrt(L*C)\n",
+"printf('w0= %3.1f krad/s \n',w0*10^-3);\n",
+"f0=w0/(2*%pi)\n",
+"B=w0/Q0\n",
+"printf('Bandwidth= %3.1f krad/s \n',B*10^-3);\n",
+"//Number of half bandwidths be N\n",
+"N=2*(w-w0)/B\n",
+"disp(N)\n",
+"//Admittance Y(s)=(1+i*N)/R\n",
+"//Finding the magnitude and angle\n",
+"magY=sqrt(1+N^2)/R\n",
+"angY=atan(N)*(180/%pi)\n",
+"disp(angY,'angY=')\n",
+"printf('admittance value=%3.2f uS',magY*10^6)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.3: Series_Resonance.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.3\n",
+"disp('Given')\n",
+"disp('R=10 ohm L=2mH C=200 nF w=48 krad/s vs=100*cos(wt) mV')\n",
+"R=10; L=2*10^-3; C=200*10^-9; w=48*10^3;\n",
+"vsamp=100;\n",
+"w0=1/sqrt(L*C)\n",
+"printf('w0= %3.1f krad/s \n',w0*10^-3);\n",
+"Q0=w0*L/R\n",
+"printf('Q0=%d \n',Q0)\n",
+"B=w0/Q0\n",
+"printf('Bandwidth= %3.1f krad/s \n',B*10^-3);\n",
+"//Number of half bandwidths be N\n",
+"N=2*(w-w0)/B\n",
+"disp(N)\n",
+"//Impedance Z(s)=(1+i*N)*R\n",
+"//Finding the magnitude and angle\n",
+"magZ=sqrt(1+N^2)*R\n",
+"angZ=atan(N)*(180/%pi)\n",
+"disp(angZ,'angZ=')\n",
+"printf('Equivalent impedance value=%3.2f ohm \n',magZ)\n",
+"//Approx current magnitude is\n",
+"Iamp=vsamp/magZ\n",
+"printf('\n Approx current magnitude= %3.2f mA \n',Iamp);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.4: Other_resonant_forms.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.4\n",
+"disp('Given')\n",
+"disp('R1=2 ohm R2=3 ohm L=1H C=125mF')\n",
+"R1=2;R2=3 ; L=1;C=125*10^-3;\n",
+"w0=sqrt(1/(L*C)-(R1/L)^2)\n",
+"printf('w0=%d rad/s \n',w0)\n",
+"//Input admittance is 1/R2+i*w*C+1/(R+I*w*L)\n",
+"Y=1/3+%i/4+1/(2+%i*2)\n",
+"printf('Y= %3.4f S \n',Y)\n",
+"//Now input impedance at resonance \n",
+"Z=1/Y\n",
+"printf('Z= %3.4f ohm \n',Z)\n",
+"//Resonant frequency f=1/sqrt(L*C)\n",
+"f=1/sqrt(L*C)\n",
+"printf('f=%3.2f rad/s \n',f);\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.5: Equivalent_Series_and_parallel_combination.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.5\n",
+"disp('Given')\n",
+"disp('R=5 ohm L=100mH w=100 rad/s')\n",
+"Rs=5; Ls=100*10^-3 ;w=100;\n",
+"//Let Xs be the capacitive and inductive reactance \n",
+"Xs=w*Ls\n",
+"Q=Xs/Rs\n",
+"//As Q is greater than 5 we can approximate as\n",
+"Rp=Q^2*Rs\n",
+"Lp=Ls\n",
+"printf('The parallel equivalent is \n');\n",
+"printf('Rp= %d ohm \t Lp=%d mH',Rp,Lp*10^3);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.6: Scaling.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.6\n",
+"disp('Given')\n",
+"disp('Km=20 Kf=50')\n",
+"Km=20; Kf=50;\n",
+"s=poly(0,'s')\n",
+"//From figure 16.20(a)\n",
+"C=0.05; L=0.5;\n",
+"//Performing magnitude as well as frequency scaling simultaneously\n",
+"Cscaled =C/(Km*Kf)\n",
+"Lscaled = L*Km/Kf\n",
+"printf('Scaled values are \n')\n",
+"printf('Cscaled =%d uF \t Lscaled =%d mH \n',Cscaled*10^6,Lscaled*10^3)\n",
+"//Converting the Laplace transform of the circuit\n",
+"//From figure 16.20(c)\n",
+"disp('Vin=V1+0.5s*(1-0.2*V1)')\n",
+"disp('V1=20/s')\n",
+"//On substituting V1 in equation of Vin\n",
+"\n",
+"Zin=(s^2-4*s+40)/(2*s)\n",
+"disp(Zin,'Zin=')\n",
+"//Now we need to scale Zin\n",
+"//We will multiply Zin by Km and replace s by s/Kf\n",
+"Zinscaled=horner(Km*Zin,s/Kf)\n",
+"disp(Zinscaled,'Zinscaled')\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.8: Bode_diagrams.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//Example 16.8\n",
+"//From figure 16.26\n",
+"disp('Writing the expression for voltage gain')\n",
+"disp('Vout/Vin=4000*(-1/200)*(5000*10^8/s)/((5000+10^8/s)*(5000+10^6/20s))')\n",
+"//On simplification\n",
+"s=poly(0,'s')\n",
+"h=syslin('c',(-2*s)/((1+s/10)*(1+s/20000)))\n",
+"disp(h)\n",
+"fmin=0.01\n",
+"fmax=10^7\n",
+"scf(1);clf;\n",
+"bode(h,fmin,fmax)\n",
+""
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2025-07-06 13:30:59 +0000