Transcript Creativity Session

topics
 Basic
Transmission Line Equations
 Nine Power Gains of Amplifiers
 Linear and Nonlinear Synthesis/Analysis
 Full-Wave Analysis for Microstrip
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basic transmission line equations
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basic transmission line equations
Z L  ZO
1  L
1  L
L 
Z L  ZO
Z L  ZO
Z in  Z O
Z L  jZO tan d
Z O  jZ L tan d
Important Conclusions from the above equations :

When ZL =ZO, ΓL = 0 and Zin = ZO

For an open transmission line ΓL = 1, Zin = -jZocotθ. Under the condition θ < π/2, the
behavior of the input impedance is like that of a capacitance. Hence a short open-circuit
transmission line can be used as a capacitance element.

For a shorted transmission line ΓL = -1, Zin = -jZotanθ. Under the condition θ < π/2,
the behavior of the input impedance is like that of an inductance. Hence a short shortcircuit transmission line can be used as an inductive element.

When an electrical length θ = π/2 (of physical length l = λ/4), the transmission line is
called a quarter-wave transformer.The quarter-wave transformer has the following important
property:
2
Z
Z in  O
ZL
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basic transmission line equations
For a Matched Lossless two-port Transmission Line with electrical length θ :
S matrix
ABCD matrix
 b1   0
b     j
 2  e
e  j   a1 
 
0   a2 
v1   cos
 i    j sin  / Z
O
 1 
jZ O sin    v2 
cos   i2 
VSWR is the ratio ofVmax to Vmin.The relationship between VSWR and
reflection coefficient is as follows:
Vmax ( x) 1  L
VSWR 

Vmin ( x) 1  L
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VSWR  1
L 
VSWR  1
basic transmission line equations
Shift in Reference Planes
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basic transmission line equations
Shift in Reference Planes
The S-matrices of the 50Ω transmission lines are represented by S1 and S2 :
 0
S1    j
1
e
e  j 1 

0 
 0
S 2    j
2
e
e  j 2 

0 
The S-matrix of the device can be represented by S1 and S2 and the
measured matrix S’ as follows :
 S11
S
 21
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S12   S11 e j 21


S 22  S 21
 e j 2( 2 1 )
S11 e j 2(1  2 ) 

 e j 2 2 
S 22
nine power gains of amplifiers
Power Gains of different amplifiers are determined using Sparameters to get the following results :
Transducer power gain in 50-Ω system
GT  S 21
2
(1  G ) S 21 (1  L )
2
Transducer power gain for arbitrary ΓG and ΓL
GT 
GTU 
(1  G ) S 21 (1  L )
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G
2
2
1  S11G 1  S 22 L
2
S 21 (1  L )
2
Power gain with input conjugate matched
2
(1  S11G )(1  S 22 L )  S12 S 21G L
2
Unilateral transducer power gain
2
2
(1  S11 ) 1  S 22 L
2
2

2
S 21
2
1  S11
2
2
nine power gains of amplifiers
S 21 (1  G )
2
Available power gain with output conjugate
matched
GA 
Maximum available power gain
Gma 
 ) 1  S11G
(1  S 22
2
GTU max 
Maximum stable power gain
Gms 
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U
2

S 21
S 21
2
(1  S11 )(1  S 22 )
2
2
S 21
S12
1 2 S 21 S12  1
2
1  S 22
S 21
( k  k 2  1)
S12
Maximum unilateral transducer power gain
Unilateral power gain
2
2
k S 21 S12  Re(S 21 S12 )
2
full wave analysis for microstrip
METHOD
Spectral Domain
Method
FEATURES
DISADVANTAGES
 One of the most popular
methods for infinitesimally thin
conductors on multilayer
structures
 Cannot handle thick conductor
structures
 Closed-form expressions for
Fourier-transformed Green’s
functions
 For tight coupling the number of
basic functions becomes large; would
involve convergent problems
 Numerical efficiency
Finite Difference
Method
 Mathematical preprocessing is
minimal
 Numerically inefficient
 Precautions must be taken when the
 Can be applied to a wide range of method is applied to an open-region
structures
problem
 Need layer computer storage for
accurate solution
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full wave analysis for microstrip
METHOD
Finite Element
Method
Mode- Matching
Method
FEATURES
 Similar to the finite difference
method
 Developed to solve very large matrix
equations
 Has variational features in the
algorithm and is more flexible in
the application
 Numerically inefficient
 Typically applied to the problem
of scattering at the waveguide
discontinuity
 Several different formulations
possible, all theoretically equivalent;
however, they may be different
numerically
 Often used to solve enclosed
planar structures, including metal
thickness effects
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DISADVANTAGES
 Existence of so-called spurious
(unphysical) zeros
 Precautions must be taken on relative
convergence for some problems
full wave analysis for microstrip
METHOD
Equivalent
Waveguide Model
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FEATURES
 Very useful method for analysis of
microstrip discontinuity problem
DISADVANTAGES
linear and nonlinear synthesis
1.
2.
3.
4.
5.
Matching networks for single-frequency and wide-frequency bands (e.g., a
4:1 for complex loads and termination).
Narrowband/wideband lumped and distributed filter synthesis.
Oscillator synthesis from small- and large-signal S parameters. Parallelseries design, determination of all components, determination of efficiency,
output power, phase noise, and other relevant data.
Open and closed loop, PLL design, phase nosie determination, nonlinear
switching, frequency lock phase lock.
System analysis and optimization for noise figure IMD performance.
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linear and nonlinear analysis
1. When load impedance ZL equals ZO, the characteristic impedance of
the transmission line, the load reflection coefficient ΓL = 0, and the
input impedance equals the characteristic impedance of the
transmission line, namely Zin = ZO.
2. For an open transmission line ΓL = 1, Zin = -jZOcotθ. Under the
condition θ < π/2, the behavior of the input impedance is like that of
a capacitance. Hence a short open-circuit transmission line can be
used as a capacitance element.
3. For a shorted transmission line ΓL = -1, Zin = -jZOtanθ. Under the
condition θ < π/2, the behavior of the input impedance is like that of
an inductance. Hence a short short-circuit transmission line can be
used as an inductive element.
4. When an electrical length θ = π/2 (of physical length l = λ/4), the
transmission line is called a quarter-wave transformer. The quarterwave transformer has the following important property: Zin = ZO2
/ZL.
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