planar wave guide
TRANSCRIPT
Planar waveguides
Planar waveguides are an important subclass of
waveguides (transmission lines)
Planar waveguides can be used in integrated
circuits to connect the various microwave circuit
elements
Examples are shown in the next three slides
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Applications of planar
waveguidesAlso planar transmission lines can be used to
feed microwave energy from a microwave
generator to an antenna as shown
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Applications of planar
waveguidesPlanar waveguides can be used to
interconnect the various parts of a
microwave amplifiers
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Applications of planar
waveguidesPlanar wave guides also can be used to
design filters and phase shifters
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Filter Phase shifter
Types of planar wave guides
There are many types of planar waveguides
available. Examples are
Strip line
Microstrip line
Coplanar waveguide
Slotted lines
These waveguides support TEM, TE and TM
wave propagations
However only TEM will be considered
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Planar waveguide design
parametersWhen designning a given microwave circuit, it is
desired to know the characteristic impedance,
dispersion curves, phase velocity, phase delay,
capacitance, inductance and the attenuation per unit
length of the waveguide
Computing these parameters can be performed by
solving the Helmholtz equation
However, the computation can be greatly simplified
by the use of commercial microwave design tools
such as CST, AWR microwave office, Agilent ADS,
and HFSS
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Strip-line
The strip line is composed from a thin conducting
strip of width π centered between two conducting
ground planes of separation π
The region between the conducting planes is filled
with a dielectric material whose relative permitivity
is ππ as shown
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Strip line
The strip line can be considered as a planar
coaxial cable
Exact solution for the electric field can be
obtained by a method known as conformal
mapping
However this avoided in practice and an
empirical formulas can be used to design the
strip line for specific characteristic impedance
π0, phase velocity π£π, propagation constant π½
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Formulas for Propagation Constant,
Characteristic Impedance
The phase velocity can be given by
π£π =1
ππ=
π
ππ
The propagation constant is given by
π½ =π
π£π= π π0π0ππ = πππ0
The characteristic impedance can be approximated by
π0 =30π
ππ
π
ππ + 0.441π
Where ππ is the effective width of the center conductor
which is approximated by
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Strip line width for specific π0
The strip line width that can be used to design a
strip line with a specific characteristic impedance
can be determined from the following equation
π₯ =30π
πππ0β 0.441
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Attenuation due to conductor
loss
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Example
Find the width for a 50 Ξ© copper stripline
conductor with π = 0.32 ππ and ππ = 2.2. If the
dielectric loss tangent is π‘πππΏ = 0.001 and the
operating frequency is 10 GHz, calculate the
attenuation in ππ΅/π . Assume a conductor
thickness of π‘ = 0.01 mm
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Solution
To find the strip line width we can rely on the
equations in slide 10
πππ0 = 2.2 50 = 74.2 < 120
Therefore
π₯ =30π
ππβ 0.441 = 0.83
We can use the equationπ
π= π₯ β π = ππ₯ = 0.32 Γ 0.83 = 0.266 ππ
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Solution
The total attenuation is the attenuation due to
the conductor loss plus the attenuation due to
dielectric material, therefore
πΌ = πΌπ + πΌπ
πΌπ =ππ‘πππΏ
2But
π = π ππ =2ππ ππ
π= 310.6
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Solution
Now πΌπ =310.6Γ0.001
2= 0.155 ππ/π
The conductor loss can be determined from
The surface resistance for the copper is
π π ππ
2π= 0.026 Ξ© ππ‘ 10 πΊπ»π§
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Solution
πΌπ = 2.6 Γ10β3π π πππ0π΄
30π(π β π‘)= 0.122 ππ/π
The total attenuation is
πΌ = πΌπ + πΌπ = 0.277ππ
ππΌ ππ΅ = 20 log10 ππΌ = 2.41 ππ΅/π
The wavelength at 10 πΊπ»π§ is
π =π
πππ= 2.02 ππ
The attenuation in terms of wavelength is
πΌ ππ΅ = 2.41 Γ 0.0202 = 0.049 ππ΅/π
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Microstrip line
The microstrip line is one of the most popular
type of transmission lines
The microstrip line is composed from a signal
conductor of width π and ground plane
separated by a dielectric material as shown
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Phase velocity, propagation
constant The phase velocity on microstrip line is given by
π£π =π
ππ
The propagation constant is given by
π½ = π π0π0 ππ = π0 ππ
Where ππ is the effective dielectric constant 1 <ππ < ππ
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Effective dielectric constant ππ
The effective dielectric constant can be
approximated by
ππ =ππ + 1
2+ππ β 1
2
1
1 + 12π/π
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Characteristic impedance
analysis formulaIf the dimensions of the microstrip are known, then
the characteristic impedance can be determined
from
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Characteristic impedance
Synthesis formulaIf the microstrip is designed to have a specific
characteristic impedance, then the ratio of its width
π to the dielectric thickness π can be determined
form
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Microstrip attenuation
The attenuations for quasi TEM microstrip are
determined from the following two equations
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Example microstrip design
Design a microstrip line on a 0.5 mm alumina
substrate ( ππ = 9.9, π‘ππ πΏ = 0.001 ) for a 50 Ξ©characteristic impedance.
Find the length of this line required to produce a
phase delay of 270Β° at 10 GHz, and compute the
total loss on this line, assuming copper
conductors.
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Solution If we assume that
π
π< 2, the width π can be
determined from
π
π=
8ππ΄
π2π΄ β 2
π΄ =π060
ππ + 1
2+ππ β 1
ππ β 10.23 +
0.11
ππ= 2.142
π/π = 0.9654 which is less than 2
The required width of microstrip line is π =0.9654π = 0.483 ππ
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Solution
The length of the line that can produce a phase
shift of π = 270Β° can be determined from the
electrical length
ππ = 6.665π = π½π = πππ0π = 270
π0 =2ππ
π= 209.4 πβ1
π =270
π180
πππ0= 8.72 ππ
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Solution
By solving for πΌπ and πΌπ , we have a total
attenuation of πΌ = πΌπ + πΌπ = 0.022 + 0.094 =0.116 ππ΅π/ππ
The attenuation within the length of the phase
shifter is given by
ππ‘π‘πππ’ππ‘πππ = πΌππ΅ππ Γ πππππ‘β ππ π‘βπ ππππππ‘π‘πππ’ππ‘πππ = 0.116 Γ 0.872 = 0.101 ππ΅
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Coplanar waveguide
The coplanar waveguide is composed
from a central conductor with two ground
planes as shown below
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Coplanar waveguide
The impedance of the coplanar waveguide can
be determined the width of the central conductor
π and the spacing from the ground planes π
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Commercial software
The dimensions of planar wave guide can
be adjusted for specific π0, π£π, π½, πππ π by
using CAD tool such on line tools or
Linecalc in ADS
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Linecalc
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You can find the line calculator program
under tools, then LineCalc
Starting the line calculatorIf you press the start LineCalc item, you may obtain a
window as shown below
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Entering the dielectric parameters
You can enter the
dielectric (substrate)
parameters in the
following section of
the LineCalc window
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Computing
π0, πβππ π π βπππ‘ π , ππ (Analysis)Enter the width and length of the transmission line and
click on the analyze window, the LineCalc program will
compute π0, π, ππ as illustrated by
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Computing the π and πΏ for a
specific π0 and π (Synthesis)Enter the value of the desired π0 and the phase shift in
the section provided, press synthesize, the program will
compute the width and length of the transmission line
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Comparison of Common Transmission
Lines and Waveguides
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Microwave Frequency Bands (taken from wikipedia)
Letter Designation Frequency range
L band 1 to 2 GHz
S band 2 to 4 GHz
C band 4 to 8 GHz
X band 8 to 12 GHz
Ku band 12 to 18 GHz
K band 18 to 26.5 GHz
Ka band 26.5 to 40 GHz
Q band 33 to 50 GHz
U band 40 to 60 GHz
V band 50 to 75 GHz
E band 60 to 90 GHz
W band 75 to 110 GHz
F band 90 to 140 GHz
D band 110 to 170 GHz