SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
UNIT III IMPEDANCE MATCHING IN HIGH FREQUENCY LINES
Part A
1. What are guided waves? Give examples
The electromagnetic waves that are guided along or over conducting or dielectric surface are called guided waves.
Examples: Parallel wire, transmission lines
2. What is TE wave or H wave?
Transverse electric (TE) wave is a wave in which the electric field strength E is entirely transverse. It has a magnetic
field strength Hz in the direction of propagation and no component of electric field Ez in the same direction
3. What is TH wave or E wave?
Transverse magnetic (TM) wave is a wave in which the magnetic field strength H is entirely transverse. It
has a electric field strength Ez in the direction of propagation and no component of magnetic field Hz in the same
direction
4. What is a TEM wave or principal wave?
TEM wave is a special type of TM wave in which an electric field E along the direction of propagation is also zero. The
TEM waves are waves in which both electric and magnetic fields are transverse entirely but have no components of
Ez and Hz.it is also referred to as the principal wave.
5. What is a dominant mode?
The modes that have the lowest cut off frequency is called the dominant mode.
6. Give the dominant mode for TE and TM waves
Dominant mode: TE10 and TM10
7. What is cut off frequency?
The frequency at which the wave motion ceases is called cut-off frequency of the waveguide.
8. What is cut-off wavelength?
It is the wavelength below which there is wave propagation and above which there is no wave propagation.
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
9. Mention the characteristics of TEM waves.
a) It is a special type of TM wave
b) It doesn’t have either e or H component
c) Its velocity is independent of frequency
d) Its cut-off frequency is zero.
10. Define attenuation factor
Attenuation factor = (Power lost/ unit length)/(2 x power transmitted)
11.Mention the applications of wave guides
The wave guides are employed for transmission of energy at very high frequencies where the attenuation caused by
wave guide is smaller.Waveguides are used in microwave transmission.Circular waveguides are used as attenuators
and phase shifters
12. Distinguish TE and TM waves
TE TM
Electric field strength E is entire Magnetic field strength H is entirely
transverse transverse.
It has z component of magnetic It has z component of electric field Ez
field Hz
It has no z component of electric It has no z component of magnetic field
field (Ez=0) (Hz=0)
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
UNIT-4
PART-B (16 MARKS)
1. Explain the transmission of TM waves between parallel conducting plates. Also derive its relevant field
components.
TM waves also called as E-waves
Magnetic(H) field totally along Y-Axis
H-field exists only in the direction transverse to the direction of propagation(Z)
No component of H field in Z-direction
The equations for field components of TM waves is given by(Non-zero values)
…. (1)
Fields Hx=Ey=Hz=0
1.wave equation for Hy component is given by
….(2)
2.The above equation is a differential equation and its solution is given by
where C3,C4- arbitrary constants
3.Showing the variations with respect to time and Z-direction, the solution can be written as
4.Boundary condition: Etang=Hnorm=0
Htang is not equal to 0 and hence obtain the expression for Ez interms of Hy and equate it to zero to
obtain the arbitrary constants.
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
Then the boundary conditions is given by Ez=0 at X=0
Ez=0 at X=a., for all vales of t & z … (5)
st
5.To satisfy the 1 B.C.,C3=0
To satisfy the 2nd B.C., where m=1,2…
Hence equation( 4) becomes
… (6)
6. To find the other field components Ex and Hy.
and
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
Hence the field components for TM mode in Zero-subscript Notation is given by
2. Explain the transmission of TE waves between parallel conducting plates. Also derive its relevant field
components.
TE waves also called as H-waves
Electric(E) field totally along Y-Axis
E-field exists only in the direction transverse to the direction of propagation(Z)
No component of E field in Z-direction
The equations for field components of TE waves is given by(Non-zero values)
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
… (1)
Fields Ex=Hy=Ez=0
1.wave equation for Hy component is given by
… (2)
2.The above equation is a differential equation and its solution is given by
where C1,C2- arbitrary constants
3.Showing the variations with respect to time and Z-direction, the solution can be written as
4.Boundary condition: Etang=Hnorm=0
Then the boundary conditions is given by Ey=0 at X=0
Ey=0 at X=a., for all vales of t & z ... (4)
st
5.To satisfy the 1 B.C.,C2=0
To satisfy the 2nd B.C., where m=1,2… … (5)
Hence equation( 3) becomes
… (6)
6. To find the other field components Hx and Hz
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
Hence the field components for TM mode in Zero-subscript Notation is given by
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
3. Explain in detail the characteristics(properties) of TE,TM & TEM waves.
i. characteristics of TE & TM Waves
At low frequency (ω),
At High frequency(ω)
which Means only high frequencies are allowed to propagate.hence the system acts as High Pass Filter(HPF).
The characteristics of TE & TM waves are
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
1. Cut-off frequency (fc)
SUB CODE: EC 2305 DEPT OF ECE
2. Phase-constant(β)
3. Cut-off wavelength(λc)
4. Guide-wavelength (λg)
5. Phase velocity(Vp)
6. Group velocity(Vg)
7. Characteristic wave impedance(Zo)
1. Cut-off frequency (fc): It is defined as the frequency at which the propagation constant(γ) changes from
real to imaginary. For m- mode & a-distance between parallel plates
2. Phase-constant(β)
3.Cut-off wavelength(λc)
4.Guide-wavelength (λg): It is defined as the distance travelled for the phase shift through 2π radians.
5.Phase velocity(Vp): It is defined as the rate at which the wave changes its phase as the wave propagates.
m/sec where v- velocity of light=3*10^8 m/sec
6.Group velocity(Vg): It is defined as the actual velocity with which the wave propagates
m/sec
The relationship between phase and group velocity is given by
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
7.Characteristic wave impedance(Zo): It is the ratio of relative amplitudes of electric field to the magnetic
field.
ii.characteristics of TEM Waves
4. A pair of perfectly conducting planes are separated 4cm in air.For a frequency of 5000MHz with TM1
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
mode.,fined following i.cut-off frequency ii.cut-off wavelength iii.phase constant β
SUB CODE: EC 2305 DEPT OF ECE
5. For a frequency of 6000 MHz and plane separation 7 cm,find following for TE1 mode.
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
SUB: Transmission Lines and Wave Guides PPG INSTITUTE OF TECHNOLOGY
SUB CODE: EC 2305 DEPT OF ECE
