Analysis of CIRCULAR WAVEGUIDEusing Finite Difference Time Domain Method

JORGE L. LOPEZ CABRERA

TE (Transverse Electric) Mode

The lower cutoff frequency (or wavelength) for a particular TE mode in circular waveguide is determined by the following equation:

(m),

where P'mn is:

m p'm1 p'm2 p'm3

0 3.832 7.016 10.174

1 1.841 5.331 8.536

2 3.054 6.706 9.970

TE (Transverse magnetic) Mode

The lower cutoff frequency (or wavelength) for a particular TE mode in circular waveguide is determined by the following equation:

(m),

where P'mn is:

m p'm1 p'm2 p'm3

0 2.405 5.520 8.654

1 3.832 7.016 10.174

2 5.135 8.417 11.620

CIRCULAR WAVEGUIDE; Location of Source and Observation Points

CIRCULAR WAVEGUIDE

Z (cells)

RH

O (

cells

)

50 100 150 200 250 300 350 400

10

20

30

40

50

60

70

80

90

100

1 2 653 4

SOURCE POINTS

Radio Of 3.75cm

1cm

PLOT OF Zo IN THE POINT 1

0 5 10 15 20 250

200

400

600

800

1000

1200

(Ohm

)

Frequency (GHz)

Impedance Real part

PLOT OF Zo IN THE POINT 6

0 5 10 15 20 250

200

400

600

800

1000

1200

(O

hm)

Frequency (GHz)

Impedance Real part

WAVEGUIDE Step-discontinuity

TIME PLOT OF THE POINT 1

TIME PLOT OF THE POINT 6

Magnitude of GAMMA

2.34 CUTOFF FRECUENCY

2.34 GHzutoff freq.

11

TM21

TE 22

TM22

|Gamma|

CODE OF THE PROGRAMS AND THE

INPUTFILE OF THE WAVEGUIDE

160 100 0.05 0.05 10000 0.7 1 1 4.0 4.0 1 0 20 75 20 0 0 0 0 0 180 1 0 90 90 0 0 0 0 40 50 40 55 40 58 40 62 40 65 40 70 3 1 75 0 77 50 0 0 1.0 1.e21 1 75 50 152 52 0 0 1.0 1.e21 1 150 52 152 100 0 0 1.0 1.e21

clear all; close all; load sig_dist.dat; pennx=sig_dist; col=3;

[x,y]=meshgrid(1:max(pennx(:,1)),1:max(pennx(:,2))); [r,c]=size(pennx); for jj=1:r penn1x(pennx(jj,2)+1,pennx(jj,1)+1)=pennx(jj,col); end

figure; contour(penn1x,50); title 'WAVEGUIDE PLOT' xlabel 'Waveguide long (Z axis) in cells ' ylabel 'Radio of the waveguide in cells' legend ('20 cells = 1cm') grid;

GAMMA CODE FOR THEPROGRAM MAT LAB %Computes gamma of a Circular Waveguide clear all; %ONLY CHANGE THE NUMBERS OR THE TIME_POINTS_? %AND YOU ARE GOING TO HAVE THE PLOTS OF Impedance Real part %FOR BOR AND ANALYTICAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Zin bor load Time_Point_6.dat;%CHANGE TO NUMBER erho=Time_Point_6(:,1);%CHANGE TO NUMBER hphi=Time_Point_6(:,5);%CHANGE TO NUMBER

load timestep.dat; dt=timestep; %Nfft=size(erho,1);; Nfft=60000; df=1/(dt*Nfft); f1=1.5e9; f2=20e9;

erho_f=(fft(erho,Nfft)); hphi_f=(fft(hphi,Nfft)); Zin=real(erho_f./hphi_f); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Zo bor load Time_Point_6_inf.dat;%CHANGE TO NUMBER erho_1=Time_Point_6_inf(:,1);%CHANGE TO NUMBER hphi_1=Time_Point_6_inf(:,5);%CHANGE TO NUMBER

%%%%%%%%%%%%%%%%%%%% erho_f_1=(fft(erho_1,Nfft));% NO CHANGE TO NUMBER hphi_f_1=(fft(hphi_1,Nfft));% NO CHANGE TO NUMBER Zo=real(erho_f_1./hphi_f_1);% NO CHANGE TO NUMBER

df=1/(dt*Nfft); N1=floor(f1*Nfft*dt); N2=ceil(f2*Nfft*dt); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% GAMMA_BOR=((Zin-Zo)./(Zin+Zo)); GAMMA_mag_BOR=(abs(GAMMA_BOR)); GAMMA_dB_BOR= 20*log10(GAMMA_mag_BOR);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Zo ANALYTICAL F=[1.e9:1.e6:25.e9]; %hz LAMDA=3.e8./F; k =2*pi./LAMDA; Pnm=1.841; a=0.0375; %m BETA=((k.^2)-(Pnm/a).^2).^(1/2); eta=377; %ohm Zo_AN=(eta.*k)./BETA; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Zin ANALYTICAL F=[1.e9:1.e6:25.e9]; %hz LAMDA=3.e8./F; k =2*pi./LAMDA; Pnm=1.841; a=.075; %m BETA=((k.^2)-(Pnm/a).^2).^(1/2); eta=377; %ohm Zin_AN=(eta.*k)./BETA; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% GAMMA_AN=((Zin_AN-Zo_AN)./(Zin_AN+Zo_AN)); GAMMA_mag_AN=(abs(GAMMA_AN)); GAMMA_dB_AN= 20*log10(GAMMA_mag_AN); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%figure; plot((N1:N2)/(dt*Nfft)/1.e9,GAMMA_BOR(N1:N2),'b');

hold on; plot(F/1.e9,real(GAMMA_AN),'r'); grid; ylabel(' (Ohm)'); xlabel('Frequency (GHz)'); title('GAMMA OF THE POINT 6') axis([0 14 -6 3.5]) legend('BOR','ANALYTICAL')

Zo PLOT CODE FOR THE PROGRAM MAT LAB %Computes Input Impedance of a Circular Waveguide clear all; %ONLY CHANGE THE NUMBERS OR THE TIME_POINTS_? %AND YOU ARE GOING TO HAVE THE PLOTS OF Impedance

Real part %FOR BOR AND ANALYTICAL load Time_Point_5.dat; erho=Time_Point_5(:,1); hphi=Time_Point_5(:,5);

load timestep.dat; dt=timestep; %Nfft=size(erho,1);; Nfft=60000; df=1/(dt*Nfft); f1=1.5e9; f2=20e9;

erho_f=(fft(erho,Nfft)); hphi_f=(fft(hphi,Nfft)); z=real(erho_f./hphi_f); %figure; df=1/(dt*Nfft); N1=floor(f1*Nfft*dt); N2=ceil(f2*Nfft*dt); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%% da=[1.e9:1.e6:25.e9]; %hz lambda=3.e8./da; k =2*pi./lambda; Pnm=1.841; a=.0375; %cm beta=((k.^2)-(Pnm/a).^2).^(1/2); eta=377; %ohm l=(eta.*k)./beta;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure; plot((N1:N2)/(dt*Nfft)/1.e9,z(N1:N2),'b'); grid; ylabel(' (Ohm)'); xlabel('Frequency (GHz)'); title('Impedance Real part') axis([0 25 0 1200])

hold on plot(da/1.e9,real(l),'--r'); legend('BOR','ANALYTICAL')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%plot((N1:N2)/(dt*Nfft)/1.e9,imag(z(N1:N2)),'b'); %grid; %ylabel(' (Ohm)'); %xlabel('Frequency (GHz)'); %title('Impedance Imaginary part ')

TIME PLOT CODE FOR THEPROGRAM MAT LAB clear all; close all; col=1; %erho %load Time_Point_1.dat; %field(:,1)=Time_Point_1(:,col); %load Time_Point_2.dat; %field(:,2)=Time_Point_2(:,col); %load Time_Point_3.dat; %field(:,3)=Time_Point_3(:,col); %load Time_Point_4.dat; %field(:,4)=Time_Point_4(:,col); %load Time_Point_5.dat; %field(:,5)=Time_Point_5(:,col); load Time_Point_6.dat; field(:,6)=Time_Point_6(:,col); figure; plot(field) title 'TIME PLOT OF THE POINT 6' grid;

SIGNAL PLOT CODE FOR THEPROGRAM MAT LAB clear all; close all; load sig_dist.dat; pennx=sig_dist; col=3;

[x,y]=meshgrid(1:max(pennx(:,1)),1:max(pennx(:,2))); [r,c]=size(pennx); for jj=1:r penn1x(pennx(jj,2)+1,pennx(jj,1)+1)=pennx(jj,col); end

figure; contour(penn1x,50); title 'WAVEGUIDE PLOT' xlabel 'Waveguide long (Z axis) in cells ' ylabel 'Radio of the waveguide in cells' legend ('20 cells = 1cm') grid;

INPUTFILE CODE FOR THEPROGRAM BOR 160 100 0.05 0.05 10000 0.7 1 1 4.0 4.0 1 0 20 75 20 0 0 0 0 0 180 1 0 90 90 0 0 0 0 40 50 40 55 40 58 40 62 40 65 40 70 3 1 75 0 77 50 0 0 1.0 1.e21 1 75 50 152 52 0 0 1.0 1.e21 1 150 52 152 100 0 0 1.0 1.e21

Cutoff Frequency Program %CUTOFF FRECUENCIES OF A CIRCULAR WAVEGUIDE TEmn PROGRAM

%PUT IN (a) THE RADIO OF THE WAVE GUIDE a=.0375; %IS THE INTERNAL RADIO OF THE WAVEGUIDE

%PUT IN n THE NUMBER OF 0 or 1 or 2 %n=1;

%PUT IN m THE NUMBER OF 1 or 2 or 3 %m=1; if n==0 % begin of the switch 1 if m == 1 Pnm = 3.832 elseif m == 2 Pnm = 7.016 elseif m == 3 Pnm = 10.174 elseif (m<0 | m>2) disp('pick other number for m') break end

Cutoff Frequency Program Cont. elseif n==1 %begin of the n ==2 if m == 1; Pnm = 1.841 elseif m == 2; Pnm = 5.331 elseif m == 3; Pnm = 8.536 elseif (m<0 | m>2) disp('pick other number for m') break end elseif n==2 %begin of the switch 3 if m == 1; Pnm = 3.054 elseif m == 2; Pnm = 6.706 elseif m == 3; Pnm = 9.970 elseif (m<0 | m>2) disp('pick other number for m') break end end if ( n >= 0 & n <=2 ) kc=(Pnm/a); Eo=(8.854*10^-12); Uo=(4*pi*10^-7); den=(2*pi*sqrt(Eo*Uo)); fc=(kc/den); n m Pnm fc else disp('pick other number for n') break end clear;

BibliographyTHEORICAL INFORMATION

MICROWAVE ENGINEERING / DAVID M. POZAR. -3RD ED.

CLIP ART

http://www.fnrf.science.cmu.ac.th/theory/waveguide/Waveguide%20theory%208.html

http://www.rfcafe.com/references/electrical/waveguide.htm