POZAR chapter : Notes Examples and Exercises 07/04/2018 15:37:03.
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John Bofarull Guix jgb2012@sky.com attached: -- 1 / 2
2.- Circular waveguide:
Find cut-off frequencies of cylindrical waveguide with internal radius a=.5cm f0=14GHz. Find attenuation [dB] along 30cm, inside Au plated
Firstly, one has to find the lower cut-off
frequencies and compare them to f0, to make
sure that the chosen waveguide diameter
matches the carrier frequency.
TE
TM
pozar_03_example_02_1.m
These are the 5 lowest order Bessel functions of 1st kind x[0 15]
x=[0:.001:15];
M=5;N=5;
y=zeros(M(end),numel(x));
for k=0:1:M-1
y(k+1,:)=besselj(k,x);
end
figure(1);hold on;
for k=1:1:M
plot(x,y(k,:));
end
grid on;grid minor;
title('Bessel functions 1st kind with order 0 to 4')
J0(x) zeros for TM cut-offs
p={};
for k=1:1:M
[nx0,ny0]=intersections(x,y(k,:),x,zeros(1,numel(x)));
p{k}=nx0;
end
p{:}
And these are the 1st derivative of the 5 lowest order Bessel
functions of 1st kind x[0 15]
yd=diff(y')';x(1)=[];
figure(2);hold on;
for k=1:1:M
plot(x,yd(k,:));
end
grid on;grid minor;
title('1st derivative Bessel functions 1st kind with order 0 to 4')
dJ0(x)/dx zeros for TE cut-offs
p1={} % roots of 1st derivative
p = 2.404825587623834
5.520078116818740
8.653727924339442
11.791534449561969
14.930917711006265
= 0
3.831705997281383
7.015586687090941
10.173468147302287
13.323691944300002
= 0
5.135622324716259
8.417244151376378
11.619841177883227
14.795951783895344
= 0
6.380161906569109
9.761023131142311
13.015200727876815
= 0
7.588342449349021
11.064709497802784
14.372536680265153
p1 =
3.832206002438044
7.016086681407118
10.173968140669018
13.324191945277430
= 1.841683794603466
5.331942785453609
8.536816379612693
11.706504916618902
14.864088639390504
= 3.054736905459390
6.706633213085026
9.969967828343043
13.170870863085048
= 4.201688902908669
8.015736610027316
11.346424323015373
14.586348295875927
= 5.318053105903168
9.282896290396334
12.682408452626339
