Waveguides Short notes | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


Short Notes on W a v eguides
1. In tro duction
• W a v eguides are structures that guide electromagnetic (EM) w a v es, t ypically at micro w a v e frequen-
cies, with minimal loss.
• Common t yp es: Rectangular, circular, and dielectric w a v eguides.
• Used in high-frequency applications where free-space propagation or transmission lines are ine?i-
cien t.
2. Basic Principles
• W a v eguides confine EM w a v es through total in ternal reflection or metallic b oundaries.
• Supp ort sp ecific mo des of propagation (TE, TM, TEM) determined b y b oundary conditions.
• No TEM mo de in hollo w metallic w a v eguides due to lac k of a cen ter conductor.
• Propagation o ccurs ab o v e a cutoff frequency f
c
, b elo w whic h w a v es are atten uated.
3. T yp es of W a v eguides
• Rectangular W a v eguide : Hollo w metal structure with dimensions a×b .
– Common mo des: TE
mn
(transv erse electric), TM
mn
(transv erse magnetic).
– Cutoff frequency for TE
mn
or TM
mn
:
f
c
=
c
2
v
(
m
a
)
2
+
(
n
b
)
2
where c is the sp eed of ligh t, m,n are mo de indices.
• Circular W a v eguide : Cylindrical metal tub e, radius a .
– Mo des: TE
mn
, TM
mn
, defined b y Bessel functions.
– Cutoff frequency dep ends on Bessel function ro ots.
• Dielectric W a v eguide : Non-conductiv e (e.g., optical fib er), guides w a v es via refractiv e index
con trast.
4. Propagation Mo des
• TE Mo des : Electric field transv erse to propagation direction ( E
z
= 0 ).
• TM Mo des : Magnetic field transv erse to propagation direction ( H
z
= 0 ).
• Dominan t Mo de : Lo w est cutoff frequency (e.g., TE
10
in rectangular w a v eguides).
• Phase V elo cit y : v
p
=
c
v
1-(fc/f)
2
, greater than c .
• Group V elo cit y : v
g
=c
v
1-(f
c
/f)
2
, less than c .
5. W a v eguide P arameters
• Cutoff W a v elength : ?
c
=
c
fc
.
1
Page 2


Short Notes on W a v eguides
1. In tro duction
• W a v eguides are structures that guide electromagnetic (EM) w a v es, t ypically at micro w a v e frequen-
cies, with minimal loss.
• Common t yp es: Rectangular, circular, and dielectric w a v eguides.
• Used in high-frequency applications where free-space propagation or transmission lines are ine?i-
cien t.
2. Basic Principles
• W a v eguides confine EM w a v es through total in ternal reflection or metallic b oundaries.
• Supp ort sp ecific mo des of propagation (TE, TM, TEM) determined b y b oundary conditions.
• No TEM mo de in hollo w metallic w a v eguides due to lac k of a cen ter conductor.
• Propagation o ccurs ab o v e a cutoff frequency f
c
, b elo w whic h w a v es are atten uated.
3. T yp es of W a v eguides
• Rectangular W a v eguide : Hollo w metal structure with dimensions a×b .
– Common mo des: TE
mn
(transv erse electric), TM
mn
(transv erse magnetic).
– Cutoff frequency for TE
mn
or TM
mn
:
f
c
=
c
2
v
(
m
a
)
2
+
(
n
b
)
2
where c is the sp eed of ligh t, m,n are mo de indices.
• Circular W a v eguide : Cylindrical metal tub e, radius a .
– Mo des: TE
mn
, TM
mn
, defined b y Bessel functions.
– Cutoff frequency dep ends on Bessel function ro ots.
• Dielectric W a v eguide : Non-conductiv e (e.g., optical fib er), guides w a v es via refractiv e index
con trast.
4. Propagation Mo des
• TE Mo des : Electric field transv erse to propagation direction ( E
z
= 0 ).
• TM Mo des : Magnetic field transv erse to propagation direction ( H
z
= 0 ).
• Dominan t Mo de : Lo w est cutoff frequency (e.g., TE
10
in rectangular w a v eguides).
• Phase V elo cit y : v
p
=
c
v
1-(fc/f)
2
, greater than c .
• Group V elo cit y : v
g
=c
v
1-(f
c
/f)
2
, less than c .
5. W a v eguide P arameters
• Cutoff W a v elength : ?
c
=
c
fc
.
1
• A tten uation: Due to conductor losses (in w alls) or dielectric losses (in media).
• Characteristic Imp edance : V aries with mo de; for T E mo des:
Z
TE
=
?
v
1-(f
c
/f)
2
, ? =
v
µ
0
?
0
6. Applications
• Micro w a v e comm unication (satellite, radar).
• An tenna feed systems (e.g., horn an tennas).
• High-p o w er RF systems (e.g., particle accelerators).
• Optical comm unication (dielectric w a v eguides in fib er optics).
7. Practical Considerations
• F requency Range : W a v eguides op erate effectiv ely b et w een f
c
and higher-order mo de cutoff.
• Losses : Increase with surface roughness or p o or m aterial conductivit y .
• Mo de Excitation : Requires prop er coupling (e.g., prob es, lo ops) to excite desired mo de.
• Size : W a v eguides are bulky at lo w er frequencies, limiting use b elo w micro w a v e range.
8. Conclusion
• W a v eguides e?icien tly guide EM w a v es at high freque ncies, supp orting sp ecific propagation mo des.
• Their design and mo de selection are critical for minimizing losses and ensuring reliable p erformance
in micro w a v e and optical systems.
2