This document provides information about circular waveguides. It begins by defining a circular waveguide as a tubular circular conductor that supports TE or TM wave propagation modes. Cutoff wavelengths depend on the internal radius of the waveguide. Common modes for circular waveguides are labeled similarly to rectangular waveguides. The document also provides examples of calculating cutoff wavelengths and wavelengths in a guide for a given signal frequency and waveguide dimensions. It concludes by discussing microstrip and stripline transmission lines used at higher microwave frequencies when waveguides become impractical.

1. Waveguide
Circular waveguide
By S. Naiman
TE (Assistant Lecturer)
Lecture 8

2. Circular waveguide
A circular waveguide is a tubular circular conductor.
A wave propagating through this type of guide can be a TE or TM
mode.
When the guide is a dielectric cylinder with no metal wall, we have the
what is equivalent to a simple optical fibre. The analysis is parallel
except for the fact that field can (generally) exist outside the fibre and
the boundary conditions are modified to take into account the air-
dielectric interface.
We need a cylindrical coordinate system
any point is
(ρ,φ,z)

3. Circular waveguide cont….
• In general terms the behavior is the same as in RG.
• However different geometry means diff application
hence a separate investigation
• Fro m the analysis o f be havio r :
• The law governing the propagation of waves in
waveguides are independent of the cross sectional
shape and dimensions of the guide.
• All the parameters and definitions evolved for RG
apply to circular with minor modification

4. Mo de s are labe le d so m e what diffe re ntly
The cutoff wavelength must be different due to
different geometry
• Where r= internal radius of waveguide
• kr= solution of a bessel function equation
kr
r
o
π
λ 2
=
The interger m now denote the number of full wave intensity variations around
circumference and n represent half wave intensity changes radially out from
the center to the wall

5. TE TM
Mode (kr) Mode (kr) Mode (kr) Mode (kr)
TE0,1 3.83 TE0,2 7.02 TM0,1 2.40 TM0,2 5.52
TE1,1 1.84 TE1,2 5.33 TM1,1 3.83 TM1,2 7.02
TE2,1 3.05 TE2,2 6.71 TM2,1 5.14 TM2,2 8.42
Values of (kr) forprincipalmodes incircularwaveguides
Example:
Calculate the cutoff wavelength, the guide wavelength and
characteristic wave impedance of a circular waveguide whose
internal diameter is 4cm, for a 10-GHz signal propagated in it
in the TE1,1 mode
TE11- dominant mode

6. Recall Lossless propagation
This reduces to ( );g g kγ β γ→ →
2 2
g ckβ ω µε= ± −
We now look for TE & TM solutions (modes)

7. Cutoff
The permissible values of kc then can be written
Example: Suppose the TE11 mode is propagating in the guide
of radius 5cm at a frequency of 3GHz
We have a cutoff wavenumber of 2
1.841 1.841/5 10
36.82
ck a −
= = ×
=The cutoff frequency is
8
0 0
36.82 3 10
1.75
22
c
c
k
f GHz
ππ µ ε
× ×
= = =
a
kr
ck =

8. Example (ctd)
Similarly the phase propagation factor is:
2 2 1
0 0 50.9g ck rads mβ ω µ ε −
= − =
The wavelength in the guide is
2
12.3g
g
cm
π
λ
β
= =
And the wave impedance is 0
465TE
g
g
Z
ωµ
β
= = Ω

9. mode pictures

10. Dominant mode example
The dominant mode is the TE11,
Design an airfilled circular guide such that only the dominant
mode will propagate over a bandwidth of 10GHz.
From slide above we have
11
1.841
2
cTE
c
f
aπ
=
The cutoff of the next higher mode TM01 is the upper bound of
the bandwidth given by.
01
2.405
2
cTM
c
f
aπ
=

11. Example continue..
The bandwidth is the difference between these two frequencies.
[ ]01 11
2.405 1.842 10
2
cTM cTE
c
bandwidth f f Ghz
aπ
= − = − =
from which we find: a = 0.269 cm.
substituting this back into the expressions for the cutoff
frequencies we find:
11
01
32.7
42.7
cTE
cTM
f GHz
f GHz
=
=
Note that the recommended frequency
range for TE11 mode propagation for
WC-25 (0.635cm diam) is 31.8 - 43.6GHz

12. Disadvantages
• Circular waveguide cross section area is much bigger
than that of corresponding rectangular waveguide used
to carry the same signal.
• Easier to manufacture than rectangular
• Easier to join together
• At frequency in excess of 10 GHz, TE0,1 has the
lowest attenuation than any other guide.
Advantages

13. Other waveguides
• Ridged or flexible waveguides
• Ridged waveguides- RG sometime made of single or
double ridges . Hence lower the value of cutoff wavelength. This allow
a guide with smaller dimensions to be used for any given frequency.
• Flexible waveguides: sometime we require WG with
movement, this may be bending, twisting, stretching or
vibration

14. Waveguide coupling , matching and
attenuation
• Practical aspect of their use
• Various junctions, accessories, methods of impedance
matching and also attenuation
Methods of exciting waveguide
In order to launch a particular mode , arrangement/combination of one or
more antenna is generally used
Couple a coaxial line directly to waveguide
couple waveguide to each other by means of slot in common wall
Antenna should be placed to setup mode and yet matching is
essential

15. When microwave transmission system consist
of partly coaxial and partly waveguide
Coupling taper
slot
TEM mode in coaxial is transformed into dominant mode in the waveguide

16. Slot coupling
• If hole or slot is made in the wall of waveguide ,
energy will escape from the waveguide through the
slot or possible enter into the waveguide from
outside.
• Coupling by means of one or more slot can be
method of feeding energy into a waveguide from
another waveguide or cavity resonator
• Coupling: E field line that would have been terminated by wall
enter the second waveguide
• placement of slot interrupts the flow of wall current , magnetic
field is setup extending into the second guide

17. Waveguide joins
• Coupling is by means of flange to ensure good
mechanical and electrical, hence low radiation and
internal reflection
• Rotating join used in radar

18. Multiple junction
• To combine two or more signals( or to spilt a
signal into two or more parts) in a waveguide
system multiple junction is used
– For simple interconnection –T-shaped
– Complex- Hybrid T or Hybrid Ring

21. Impedance matching and turning
• Same as in TL has to be achieved in WG
• Obstacle : Reflection in a WG system cause
impedance mismatches hence as in TL find lumped
impedance and place in pre-calculated point to
overcome the mismatch
• Eg
• Irises- introduce capacitive or inductive to the guide
hence mismatch

22. The screws shown are used as waveguide
matcher as for double stub tuner in TL
Screws

23. Attenuation in waveguide
Waveguide below the cutoff have the following
attenuation
– Reflection from obstacles, discontinuities, misaligned
waveguide section
– Losses due to currents flowing in the waveguide walls
– Losses in the dielectric filling the waveguide
– 2&3 depends on wall material ,its roughness and frequency
used

24. l
eA α
= where 0
2
λ
π
α =
=l Length of waveguide
dBeeA lll
dB 00
5.5440
loglog20 λλ
πα
===
A waveguide below cutoff is often used as an adjustable,
calibrated attenuator for UHF and microwave applications
Adjusting the length of the waveguide hence its attenuation

25. Calculate the voltage attenuation provided by a 25-cm
length of waveguide having a= 1cm and b= 0.5cm, in
which a 1-GHz signal is propagated in the dominant mode
Example

26. • A piece of WG closed at both ends with metallic plane
• Form a standing wave partten and oscillation takes
place if it is suitably exicited
• Used as turned circuit at given f
• Type : sphere, cylinder , rectangular prism
• Drawback: Resonant freq are harmonically related
Cavities resonant

28. Application
• The same purpose as turned LC circuits but at
higher frequencies
• i.e. input/ output turned circuit of amplifier,
• Turned circuit of oscillator
• Resonant circuit used for filtering/ mixer
• Cavity meter -microwave frequency measuring
device

29. Microwave components and
devices
Auxiliary Components
directional couplers,
baluns,
slotted line
stiple lines,
microstrips

30. Directional couplers
• Sometime known as nonreflecting termination.
• It is necessary to measure power being delivered
to a load or an antenna
• Method : sampling techniques which measure
fraction of power is used. and total can be
calculated
• It is imperative that , only the forward wave in the
main line is measured and not reflected one.

32. Directional couplers
• A Directional coupler is one of the coupling unit used
for the purpose of measuring forward waves of the
main line
• Example:
• The two hole directional coupler consisting of a
piece of TL to be connected in series with the main
line, together with the piece of auxiliary line coupled
to the main line via two probes through slots in the
joined outer walls of the two coaxial

33. Directional couplers
• The Directivity of a directional coupler is a standard
method of measuring the extent of the unwanted
waves
• e.i if the ratio of forward to reverse power measured
by detector is 30dB, then directional coupler is said
to have directivity of 30dB
• Directional coupling define the ratio of the forward
wave in the main line to forward wave in the
auxiliary line

34. Baluns
• A balun, or balance to unbalance transformer, is a
circuit elements used to connect a balanced line to
unbalanced line or antenna
• At LF an ordinary tuned transformer is used with
unbalanced primary and centre tapped secondary
winding to which the balanced antenna is
connected.
• For HF different TL baluns exist for different
purpose i.e narrowband and broadband application

35. Wideband Folded Dipole
Antenna total length approx 90ft
600 Ω Terminating Resistance/Balancing Network
12 : 1 Stepdown Balun to 50 Ω
Example – Barker & Williamson BWD 1.8 – 30 MHz Wideband Folded Dipole
Courtesy of Barker & Williamson Manufacturing Inc.

36. Baluns types
• The most common baluns are narrowband one
– Choke
– Sleeve
– Bazooka baluns

37. The slotted Line
• A piece of TL is constructed in such a way that the
voltage or current along it can be measured continuously
over its length.
• A traveling detector facilitate the easiness of
determine distance of probe from either end of
TL
• Lecher line –LF OR Slotted Line- HF
• The slotted line must have the same
characteristics as the main line connected to it
in series

38. The slotted Line
• Permit convenient and accurate measurement
of the position and size of the first voltage
maximum from load and any subsequent one,
without interfering with the quantities being
measured.
• Measurement of these quantities permits
calculation of
• Load impedance
• Standing wave ratio
• Frequency of generator being used.

39. Microstrip and strip line
• At frequency of about 300MHz, the characteristic
of open and shorted TL, have little relevance.
• At low frequency TL would be too long for practical
use as reactive components or tuned circuits.
• For HF (300MHz to 3000MHz) applications ,
special TL constructed with copper patterns on a
printed circuit PC board have been developed to
interconnect components on PC board

40. When d btn source and load is few inches or less,
coaxial cable TL are impractical to use
Reasons
Connector , terminator and cables themselves are
simply too large.
microstrip and stripline uses traces (tracks) on the PC
board itself.
Traces can be etched using the same process as
other traces on the board
Microstrip and strip line

41. Microstrip and strip line
Microstrip have been developed to interconnect
components on PC board.
Microstrip occurs when the line are etched onto the
surface of the PC board only.
Stripeline occurs when the line are etched in the middle
layer of a multilayer PC board
They can be used to construct TL, Inductors,
capacitors, turned circuit, filters, phase shifters and
impedance matching devices

42. Microstrip

43. Microstrip

44. Microstrip
Microstrip is a flat conductor separated from ground plane
by an insulating dielectric material
The ground plane serves as the circuit common point and
must be at least 10 times wider than top conductor and
must be connected to ground
It is generally 0.5λ or 0.25λ at the frequency of operating
and equivalent to unbalanced TL
Short are preferred comparisons to open line cause open
have a great tendency to radiate

45. It depends on its physical characteristics.
50-200Ω can be archieved by simply changing its
dimension
For unbalanced Microstrip
Characteristic Impedance
)ln( 8.0
98.5
41.1
87
tw
h
oZ ++
= ε
Where:
Ε=dielectric constant( fibreglass=4.5, Teflon=3)
W=width of copper trace
t=thickness of copper trace
H=distance btn copper trace and the ground plane

46. Stripline is a flat conductor sandwitched btn two ground
plane
It is more difficult to manufacture than microstrip, it is less
likely to radiate. Hence losses is less than in microstrip
L=0.5λ or 0.25λ and shorted are prefered
Stripline
)ln( 8.0(67.0
460
h
tw
d
oZ +
= πε