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Lecture-3
Microwave Engineering
Instructor: Athar Hanif
Quiz-1 Time Allowed: 30 minutes
Total Marks: 20
Q.1:A plane wave traveling in z- direction in a
dielectric medium with єr =2.55 has an electric
field given by Ey = E0 cos(ωt-βz). The
frequency is 2.4 GHz, and E0 = 30 V/m.
a) Find the amplitude and direction of the
magnetic field.
(2 Marks)
b) Find the phase velocity and wavelength.
(3 Marks)
a) Find the phase shift between the positions Z1 =
0.5 m and Z2 = 1.7 m. (5 Marks)
Quiz-1 Time Allowed: 30 minutes
Total Marks: 20
Q.2: A RFC is constructed by winding four
turns of AWG 38 copper wire(σcu
=64.516х106S/m) on a 2 mm ceramic
core diameter(μr = 1) of 0.1 mm length.
Estimate
a)
b)
c)
d)
The inductance
Stray capacitance
Resistance
Resonance frequency
(3 Marks)
(2 Marks)
(2 Marks)
(3 Marks)
Microstrip Transmission Line
 Most popular type of planer transmission
line
 Geometry of microstrip line
Microstrip Transmission Line
 Dielectric were not present(єr =1)
 Simple TEM waves
 Dielectric were present(єr ≠1)
 Does not support TEM waves
Microstrip Transmission Line
 In practical application, h<<λ
 Fields are quasi-TEM
vp 
c
e
  k0  e
 Єe is the effective dielectric constant
1< єe< єr
Microstrip Design
 Step-1: find W/h ratio
єr and Z0 = known
 Step-2: For W/h ≤ 2
Microstrip Design
 For W/h ≥ 2
 Step-3: Effective dielectric constant
Microstrip Design
 Step-4: Find Z0
 For W/h ≤ 1
 For W/h ≥ 1
Microstrip Design
 Step-5: (1) Attenuation due to dielectric loss
0 r  e  1 tan 
d 
Np / m
2  e  r  1
Where tanδ is the loss tangent of the dielectric
Microstrip Design
 Attenuation due to conductor loss
c
Rs

Np / m
Z 0W
Rs 
 0
2
Rs is the surface resistivity of the conductor
Microstrip Design
Microstrip Design
Design Problems
 Problem-1: calculate the width and the length of
a microstrip line for a 50Ω characteristic
impedance and a 900 phase shift at 2.5 GHz.
The substrate thickness is h = 0.127cm, with єr =
2.20
 Problem-2: Design a microstrip transmission line
for a 100Ω characteristic impedance. The
substrate thickness is 0.158cm, with єr = 2.20.
What is the guide wavelength on this
transmission line if the frequency is 4.0 GHz.
Assignment
 Problem: A 100Ω microstrip line is printed
on a substrate of thickness 0.0762 cm,
with a dielectric constant of 2.2. Ignoring
losses and fringing fields, find the shortest
length of this line that appears at its input
as a capacitor of 2.5 pF at 2.5 GHz.
Repeat for an inductance of 5 nH.
Stripline
 Most popular type of planer transmission
line
 Geometry of microstrip line
Stripline
 Phase velocity and the propagation constant of
the stripline is given by
c
vp 
r
Stripline
  k0  r
Stripline Design
 Step-1: Find√ єr Z0
 Step-2: Find the strip width
W  x; for  r Z 0  120

b 0.85  0.6  x; for  r Z 0  120

where
30
x
 0.441
 r Z0
Stripline Design
• Step-3: Dielectric attenuation
k tan 
d 
2
where
2 f  r
k 
c
Stripline Design
 Attenuation due to conductor loss
 2.7  103 Rs r Z 0
for  r Z 0  120

30 (b  t )

c  
Np / m
 0.16 Rs Bfor  Z  120
r
0

Z
b
0

with
2W
1 bt
2b  t
A  1

ln(
)
bt  bt
t
b
0.414t
1
4 W
B  1
(0.5 

ln
(0.5W  0.7t )
W
2
t
Stripline Design
Where ‘t’ is the thickness of the strip
 Rs is the surface resistivity of the conductor
and given by

0
Rs 

2
Stripline Design
 Step-4: Total attenuation constant is given by
   d   c ( Np / m)

dB   20 log e (dB / m)

 Step-5: The wavelength on the stripline is


c
r f
 Attenuation in term of wavelength
Design Problems
 Problem-1: Find the width for a 50Ω copper
stripline conductor, with b = 0.32cm and єr = 2.20.
If the dielectric loss tangent is 0.001 and the
operating frequency is 10 GHz, calculate the
attenuation in dB/λ. Assume a conductor
thickness of t = 0.01mm.
 Problem-2: Design a stripline transmission line for
a 70Ω characteristic impedance. The ground
plane separation is 0.316 cm, and the dielectric
constant of the filling material is 2.20. What is the
guide wavelength on this transmission line if the
frequency is 3.0 GHz.
Assignment (due on 22-06-2009)
 Problem: A microwave antenna feed network
operating at 5 GHz a 50 Ω printed
transmission line that is 16λ long. Possible
choices are (1) copper microstrip, with d =
0.16 cm, єr = 2.20, and tanδ = 0.001, or (2)
copper stripline, with b = 0.32 cm, єr = 2.20,
and tanδ = 0.001. Which line should be used,
if attenuation is to be minimized?
Project-1(due on 06-07-2009)
 Design a microstrip line (characteristic
impedance = 50 Ω, phase shift = 900,substrate
FR-4 thickness = 31mil, 61mil, dielectric
constant = 4.47, and tangent loss = 0.019)




Hand calculations
Verify your design using SERENADE
HARDWARE implementation
Results (hardware )
Instructions




Each group has two students.
Do your own work.
Write project report.
No late submission.
Instructions
The format for design report should be as follows
1. Title page (including your name, the course number
and the date)
Your signature after the statement
I certify that this design is the result of my own
efforts.
(Signature)
Date:
2. Design objectives and specifications
3. Design steps (including all, mentioned in problem
statement)
4. Design modifications, if any
5. Computer design verifications
6. Results (hardware)
7. Conclusions