Transcript Işık university microwave group

WPR3
Prof. Dr. B. Sıddık YARMAN
Işık University
İstanbul, Turkey
Işık University
Microwave Techniques Group
Newcom WPR3 Contribution Areas
 Design of Front-End Building Blocks
•Filters,
•Matching Networks,
•Amplifiers,
•Phase Shifters.
 Integration of Microwave Front-Ends.
 Power Amplifier Linearization.
Işık University
Microwave Techniques Group
Prof. Dr. B. Sıddık Yarman ([email protected])
Prof. Dr. Ahmet Aksen
([email protected])
Dr. Ali Kılınç
Dr. Ebru Gürsu Çimen
Hacı Pınarbaşı
Metin Şengül
http://www.isikun.edu.tr/~microwave/
Microwave Circuits
Education at Işık
University
•Courses
•Microwave Laboratory
•Research Areas
Microwave Courses
EE 475 Microwave Communications (3 hrs/week + Lab.):
Transmission line theory, transmission lines and waveguides,
impedance transformation and matching techniques, microwave
network analysis and matrix representations, generalized
scattering parameters, signal flow graphs, modal analysis, power
dividers, introduction to microwave communication systems and
microwave propagation.
EE 476 Wireless Communications (3 hrs/week ):
Design and analysis of wireless communication systems, with an
emphasis on understanding the unique characteristics of these
systems. Topics include: cellular planning, mobile radio propagation
and path loss, characterization of multipath fading channels,
modulation and equalization techniques for mobile radio systems,
multiple access alternatives, common air protocols and standards.
EE 536 Microwave Circuit Design for Wireless
Communication(3hrs/week)
Radio Transceiver Technology Requirements, RF Component Requirements
for Transceivers; Filter, Amplifier, Mixer, Frequency Synthesizer and
Dublexer Requirements. RF/Microwave Circuit Implementation Options;
Semiconductor Devices and Passive Devices. Design of microwave filters and
impedance matching networks; Analytic and semi-analytic approaches; LowPower Radio Frequency ICs for Broadcast Radio Receivers and Wireless
Celular Telephone Trancievers
EE 620 Advanced Microwave Circuit Design (3 hrs/week )
Characterization of linear circuits at microwave frequencies: Brune
functions, Piloty functions, realizability conditions for lossless networks,
scattering description of lossless two-ports. Design of microwave filters,
distributed Richards frequency transformation and theorem, Kroda’s
identities, microwave filter design, broadband matching: Analytic and
semianalytic approaches, mixed lumped-distributed network design.
EE 625 Microwave Amplifier Desing (3 hrs/week )
Active circuits at microwave frequencies: Noise parameters, SNR, noise
figure, noise temperature measurements, microwave transistor amplifier
design gain stability, microwave transistor oscillator design, numerical
methods for multistage amplifier design.
Microwave Laboratory
This laboratory provides facilities in undergraduate and graduate training and
research in the field of microwave engineering and antenna systems and
applications. Various passive and active microwave components, basic antenna
types and measurement setups operating at microwave frequencies of up to 10
GHz are among the basic facilities offered in this laboratory.
Hardware Facilities
Lab-Volt Microwave Training Set (10.5 GHz)
HP-Agilent Spectrum Analyzer (9 KHz-1.8 GHz)
Lab-Volt Gunn Oscillator (10.5 GHz)
RF Cable Assemblies and Connectors (10 MHz to 10 GHz)
Waveguide Hardware (2 GHz to 10 GHz)
RF Components : (800 MHz to 10 GHz) Amplifiers, Mixers, Detectors,
Couplers, Power Dividers,Terminations,Attenuators,
Horn Antennas
Software Facilities
AutoCad, PCB Design Software, MATLAB,
Microwave Office, SONNET(EM simulation),
RFT: Microwave Circuit Design and Optimization,
FILPRO(Filter Design)
APLAC RF Design Tool
Research Areas
 Design of Broadband Matching Networks
 Design of Microwave Amplifiers
 Multivariable Network Characterization



(Mixed Lumped-distributed Networks)
Data Modelling
Design of Broadband Phase Shifters
CAD Tools for Broadband Microwave Circuit Design



Real Frequency Technique (RFT) Toolboxes
Modelling Toolbox
Wideband Microwave Circuit Designer (WMCD) Integrated
Toolbox
Design of Broadband
Matching Networks
•Broadband Matching Problem
•Analytic vs Real Frequency Techniques
•Real Frequency Broadband Matching Techniques
Broadband Matching Problem
ZG
+
EG
PA
PL
Lossless
N
ZL
Power transmission problem between a complex
generator and load
T ( ) 
PL
PA
Gain-Bandwith Optimization
Analytic versus Real Frequency
Techniques in Broadband Matching
Analytic Theory


An analytic form of transfer function is chosen,
which should include load network
Applicable to simple problems
Real frequency techniques




No need to choose circuit topology
No need to choose transfer function
Well behaved numeric
Experimental load data is directly processed
Real Frequency Broadband
Matching Techniques






Line Segment Technique (Carlin, 1977)
Parametric Approach (Fettweis, 1979)
Simplified Real Frequency Technique
(Yarman, 1982)
Direct Computational Technique
(Yarman & Carlin 1983)
RFT for Mixed Lumped-Distributed Circuits
(Aksen & Yarman, 1994)
....
Line Segment Technique
Design Parmeters:{Ri}
N
R
n
R( )  R0   ai ( ) Ri
i 1
Z  R  jX
Unknown real part R() is represented
as a number of straight-line segments
Rk-1
Rk

k
n
i
i
  i ,
 i 1     i ,
   i 1 ,
i
1
y 
bi ( ) 
ln
dy

 ( i   i 1 ) i 1 y  
Rn=0
k-1
 b ( ) R
i 1

1
   
i 1
ai (  )  
  i   i 1

0
R()
R
X ( )  H R( ) X ( ) 
n
Optimize TPG
T ( ) 
4 R( ) R ( )
( R( )  R ( ))  ( X ( )  X ( ))
L
2
L
L
2
Parametric Approach
N
R
Z ( p)
Z is minimum reactive
•Based on parametric representation of Brune functions,
analytic form of the impedance function is directly generated,
•The direct control of transmission zeros is ensured,
•Computational complexity is reduced,
•The gain function is explicit in terms of free parameters.
Design Parameters:{p0,p1,...pn} singularities of the
network; Roots of the driving point impedance
n
Bi
n( p )
Z ( p) 
 B0  
i 1 p  p
d ( p)
i
B 
i
0,.......deg f  n

B  1
 D ,....deg f  n

 f ( p ) f ( p )
p D ( p  p )
i
i
0
n
2
i
n
k 1
k i
2
2
k
i
2
n
f(p) denotes transmission zeros of N
d(p) is strictly Hurwitz
Optimize TPG
n
d ( p)  Dn  ( p  pi )
i1
T ( ) 
4 R( ) R ( )
( R( )  R ( ))  ( X ( )  X ( ))
L
2
L
L
2
Simplified Real Frequency Technique
ZG
1
2
+
E
N
ZL
R1=1
R2=1
S1
SG
S2
SL
Belevitch Representation of Scattering Parameters:
S  h( p ) / g ( p )
S   f ( p) / g ( p)
S  f ( p) / g ( p)
S  h( p) / g ( p)
11
21
12
22
Losslessness Equation:
g(p)g(-p) = h(p)h(-p) + f(p)f(-p)
Design Parameters:{h0,h1,...hn} coefficients of the h(p) polynomial
Initialize f and h
Optimize TPG
contruct
T   
g
contruct
S(p) parameters
2
2
2
(1  SG )(1  S L ) f ( j )
g ( j )  h( j ) SG  σS L h(-j )  SG g ( j )
2
Direct Computational Technique
ZG
E
1
2
Design Parameters:{A0,D0,D1,...Dn}
coefficients of the R2(w)=Re[in(jw)]
+
N
ZL
Zin
1
R ( w) 
2
2
A
D  D w  ...  D w
o
2
0
N
1
2n
n
Initialize Di,A0
ZL
Generate Z2(p) via Gewertz Procedure
Z2=R2+jX 2
S1
1
N ( p) a  a p  ....  a p
Z ( p) 

D( p) b  b p  ....  b p
0
1
0
1
2
2
Optimize TPG
2
1
2
G
S 
G
Z 1
Z 1
G
G
n
(1 | S | )(1 | S | )
T ( ) 
|1 S S |
G
S 
L
Z 1
Z 1
L
L
S1 
1
H Z L  Z 2*
H* Z L  Z 2
n
n
H
f*
D
n
Design of Distributed Structures



Design of broadband microwave networks; Filters, Matching
Networks and Amplifiers with Transmission Line structures.
Available Real Frequency Design techniques can directly be
employed for distributed designs by making use of Richards’
transformation   tanh  p 
Planar implementation techniques; Microstrip, Stripline,
coplanar line, suspended substrate in MIC and MMIC
Network Synthesis
• Darlington Synthesis for Lumped Networks
• Richards Synthesis for Distributed Networks
or
• Generalized Network Synthesis via Transfer Matrix
Factorization
Decomposing the lossless reciprocal two-port N into two
cascade connected lossless two-port Na and Nb.
T=TaTb
Na
1
Ta 
fa
Nb
N
 a g a*

  a ha*
ha 
 ,
ga 
1
Tb 
fb
 b g b*

  b hb*
hb 

gb 
Mixed Lumped-Distributed Circuits
( Multivariable Network Characterization )
Z  Z  p,  
S  S  p,  
p    j
  tanh  p   :Delay length of unit
elements
Multivariable description and insertion loss synthesis of mixed
element structures


Parasitics, discontinuities and device to medium interface
modelling
Computer aided design and simulation of MIC layouts
Scattering Description in Two Variables



f ( p,  ) , g ( p, ) , h( p, ) are real polynomials
g ( p,  ) is a Scattering Hurwitz polynomial
h( p,  ) is monic, is a unimodular constant
g ( p,  )  p T  g  and
where
h( p,  )  p T  h 
n
p T  1 p p 2  p p ,  T  1 2 n




and
Boundary Conditions
2 n /2
 Transmission Zeros : f ( p,  )  f 0 ( p)(1   ) 
S p   f ( p,0), g ( p,0), h( p,0)
 Lumped Prototype :
 Distributed Prototype : S   f (0,  ), g (0,  ), h(0,  )
 Connectivity Information
 h00 h01
h
10 h11
h  
 


h
h
 n p 0 n p 1
 g 00
g
10
g  
 

 g n p 0
g 01
g 11

g np1





 hn p n 

 h0n
 h1n
 
g 0 n 
 g 1n 

 

 g n p n 

Losslessness Condition
g ( p,  ) g ( p, )  h( p,  )h( p, )  f ( p,  ) f ( p, )
Fundamental Equation Set (FES)
k 1
g
2
0,k
 2 ( 1)
l0
i
k
  (1)
i j  l
j 0 l  0
i

j 0
(1)
i j
k l
k 1

( g j ,k g i  j ,k  2
(1)
k l
2
0,k
g0,l g0, 2 k  l h
f
i
k
k 1
 2 ( 1)k  l (h0,l h0, 2 k  l  f 0,l f 0, 2 k  l )
l0

( k  0,1,....., n )
2
0,k

g j ,l gi j , 2 k 1 l    ( 1)i j l h j ,l hi j , 2 k 1 l
j 0 l 0
i
g j ,l g i  j , 2 k  l ) 
l 0

(1)
 (i  1,3,...,2n p  1,


k 1
g n2p ,k
 (1)
2
l 0
k l
k 1
g n p ,l g n p ,2k l  hn2p ,k
f j ,l f i j , 2 k 1 l

k  0,1,....., n  1)
k 1

h j ,k hi  j ,k  f j ,k f i  j ,k  2 (1) k l h j ,l hi  j , 2k l  f j ,l f i  j , 2k l

l 0

i j 
j 0


f n2p ,k

( i  2,4,...,2n p  2,
 (1)
2
l 0
k l

k  0,1,....., n )
(hn p ,l hn p ,2k l  f n p ,l f n p ,2k l )
( k  0,1,....., n )



Example : Low-Pass Ladder with Unit Elements
Boundary Conditions
Connectivity Information
g ( p,0) g ( p,0)  h( p,0)h( p,0)  1
gij  0, i  0n ,
g(0, )g(0,)  h(0, )h(0,)  (1   )
g ( p,0), g (0,  ) : Strictly Hurwitz
2 n
j  0n
g11  g 01g10  h01h10
g kl  hkl  0 for
hkl  g kl for
  hn p 0 / g n p 0
k  l  n  1 k , l  0,1,....n
k  l  n  1 k , l  0,1,....n   1
n p  n  1
 1 if
Multivariable Characterization of Regular Mixed
Element Two-Ports
Explicit design equations
Low-Pass,
Symmetrical,
High-Pass,
Band-Pass
Impedance Description in Two Variables
L
Z1
C1
Z1
Z ( p , λ)
n( p,  )
Z ( p,  ) 
d ( p,  )
n
n
n( p,  )   Ni ( p) , d ( p,  )   Di ( p) i
i
i 0
np
i 0
np
Di ( p)   D ji p , N i ( p)   N ji p j
j 0
j
j 0
C2
1Ω
Boundary Conditions
Transmission Zeros:
f ( p,  )  f0 ( p)(1   2 )n / 2
n
Bi
n( p,0)
Lumped Prototype: Z1 ( p,0) 
 B0  
i 1 p  p
d ( p,0)
i
p
Bi 
 f 0 ( pi ) f 0 ( pi )
np
pi Dn  ( pk2  pi2 )
2
 0 , deg f  n p
, B0  
2
1/
D
n ,deg f  n p

( k 1)
( k i )
f ( p,0)  f0 ( p)
n
Ci
n
(0,

)
Distributed Prototype: Z (0,  ) 
 C0  
1
i 1   
d (0,  )
i

f (0,  )  (1   2 ) n / 2

Even Part Condition
Z ( p ,  )  Z (  p ,  ) f ( p ,  ) f (  p ,   )
Ev Z ( p,  ) 

2
d ( p,  )d ( p,  )
1
1
1
Transmission Zeros:
n
f ( p,  )   Fi ( p) i
i 0
np
Fi ( p)   Fji p j
j 0
Even Part constraint: n( p,  ) d (  p,  )  n(  p,  ) d ( p,  )
 2 f ( p,  ) f (  p,  )
Design Example:Single Stage Amplifier
PORT
P= 1
Z= 50 Ohm
IND
ID= L1
L= 1.814 nH
TLIN
ID= TL1
Z0=
42.36 Ohm
EL=
90 Deg
F0=
15.78 GHz
TLIN
ID= TL2
Z0=
49.21 Ohm
EL=
90 Deg
F0=
15.78 GHz
IND
ID= L2
L= 3.777 nH
SUBCKT
ID= AM012MXQF
NET=
"S_Parameters"
1
CAP
ID= C1
C= 2.3 pF
Front – End Equalizer
TLIN
ID= TL3
Z0=
58.28 Ohm
EL=
90 Deg
F0=
15.78 GHz
IND
ID= L3
L= 4.32 nH
TLIN
ID= TL4
Z0=
52.56 Ohm
EL=
90 Deg
F0=
15.78 GHz
IND
ID= L4
L= 3.246 nH
2
P=
Z=
CAP
ID= C2
C= 1.3 pF
PORT
2
50 Ohm
Back – End Equalizer
Z 2 ( p,  ) 
n2 ( p,  )
d 2 ( p,  )
n1 ( p,  )  (0.7156 p3  0.8858 p 2  1.8967 p  1) 
n ( p,  )
Z 2 ( p,  )  2
d 2 ( p,  )
 (3.2864 p 2  2.9152 p  2.2168)   2 (1.482 p  1.1087)
n2 ( p,  )  (0.6148 p 3  1.3484 p 2  1.4053 p  1) 
 2 0.9019
d1 ( p,  )  (0.6592 p 2  0.816 p  1)   (2.319 p  1.809)
d 2 ( p,  )  (0.6474 p 2  1.105 p  1)   (2.2035 p  2.196)
 2 0.8608
Transducer Power Gain (dB)
 (2.7302 p 2  3.4821 p  1.8313)   2 (1.765 p  1.161)
2
1
2
0
1
9
1
8
1
7
1
6
1
5
MATLAB
AWR
1
1.2
1.4
1.
Frequency (GHz) 6
1.
8
2
Symmetrical Mixed
Element Structures




Symmetrical Mixed-Element Lossless Two-Ports
Symmetrical Interconnect Models
Symmetrical Two-port Characterization
Design Example
Symmetrical Lossless Two-Ports
Constructed with Mixed Elements
C2
Z2
C1
Z1
C1 Z2
C2
Typical Applications
•Microwave amplifiers and antenna matching networks,
•RF front-end interstage interconnect modelling of high speed,
high frequency analog/digital systems
Symmetrical Interconnect Models
•Assures the sharp roll-off on the performance
characteristics,
•Facilitate the production of the same value elements
employing the MMIC or VLSI technology,
•Leads to savings in both design and manufacturing effort,
•Reduce the required execution time and memory.
Symmetrical Two-port Characterization
 S11 p,   S22  p, 
 h(p,) even or odd polynomial
h  p,   h p, 
np n

i j
 p,   
h
h
p
 h(p,) polynomial: 



i0 j0 ij





h
h  ij
ij 0
for i  j  is odd
for i  j  is even
 Generate ΛH, ΛG in terms of properly selected independent
coefficient set {hij}
 Construct h(p, ), g(p, ) and hence S(p, )
Design Example:Two Stage Amplifier
Scattering Parameters of the 0.3m Lownoise Gate GaAs MESFET NE76000 Biased
at VDS = 3 V, IDS = 10 mA
Freq.
GHz
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
s11
m
s21
p
0.99 -27
0.97 -39
0.95 -50
0.92 -61
0.89 -70
0.87 -78
0.86 -87
0.83 -96
0.81 -104
m
s12
p
3.19 158
3.08 148
2.95 138
2.81 129
2.67 120
2.55 113
2.45 104
2.33 97
2.24 90
m
0.04
0.06
0.07
0.09
0.09
0.10
0.11
0.11
0.12
Input matching
network
1
2
Interstage matching
network
1
2
NEC76000
1
2
Output matching
network
1
NEC76000
2
1
2
Z=50 Ohm
s22
p
m
p
74
66
59
51
47
41
36
30
29
0.67
0.66
0.64
0.62
0.60
0.59
0.58
0.57
0.57
-16
-23
-30
-36
-42
-47
-53
-58
-63
Z=50 Ohm
Z0
Z2
Z1
Z0
Z1
50 Ohm 50 Ohm
50 Ohm
Input
Z0= 95.1842Ω
C= 0.33136pF
0
1.3784
0 

1.0000 2.4290 1.000 
H  
G  


0
1.8863
  0.5205
 0.5205 1.9817 1.8863
Interstage matching network:
0
1.8592
0 

 1.0000 2.7307 1.0000 
H  
G  


0
2.6065
  0.4949
 0.4949 2.2715 2.6065
Output matching network:
0
2.6678
0
0.2332

 1.0000 4.0584 3.1765 1.0268


 H    0.5094
0
3.9160
0   G   0.5094 3.4263 5.4621 1.4782

 0
0
 0.3765
0
1.3766 
0.3765 1.4398 1.3766
C
Interstage
Output
Z0 = 114.7467 Ω
C = 0.31506pF
Z1= 95.6074 Ω
Z2= 145.0932 Ω
C = 0.16215pF
Transducer Power Gain
Coefficients of Equalizers
Input matching network:
50 Ohm
C
C
Gain dB
25
20
15
10
5
Input Gain
Pe rform ance of am plifie r
0
0.2
0.3
0.4
0.5
0.6
0.7
Frequency GHz
0.8
0.9
1
Design of Broadband
Microwave Amplifiers
•Broadband Amplifier Design
•Design Issues
• Front and back equalizer design
•Multistage Amplifier Design
•Power Amplifier design
Broadband Amplifier Design
Design Issues
 Gain-Bandwidth Constraints
 Performance criteria (Gain, Noise Figure, SWR,
Dynamic Range, Linearity )
 Numerical transistor data utilization and modelling
 Design of front-end, back-end and interstage equalizers
 Power amplifier design
 Hybrid/MIC/MMIC Implementation
Front and Back Equalizer Design
1
+
A
N1
E
1
S221
T1   TG 
TG   S 21 1
1
+
A
N1
E
N2
1
^
A22
T2   T1 
S 21 2
2
1  Aˆ 22 S 21 2
2
A21 A12 S 22 1

A22  A22 
1  S 22 1 A11
2
A21
2
1  S 22 1 A11
2
 1  S11 1
2
Multistage Amplifier Design
1
+
Ak -1
N1
E
Tk   Tk 1 
Tk/   Tk
2
2
1  Aˆ 22 k
2
^
S 21 k 1
S22k
2
1  Sˆ 22 k A11 k 1  Aˆ 22 S11 k 1
1
Ak
^
A
22(k-1)
^
S221
A21 k
N1
2
Nk+1
^
A22k
1
Circuit Data
Modelling
Data Modeling Tasks



Given a numerical data set which measured over a frequency
band as an impedance, admittance or reflectance as realimaginary or magnitude-phase
Match a network function which satisfies Positive-Realness
conditions
Generate network equivalent constructed with passive circuit
elements.
Applications




Antenna modeling
To analyze their electrical behavior such as the gain
bandwidth limitations or power delivering capabilities
Impedance matching
Design of high speed/high frequency analog/digital mobile
communication sub-systems manufactured on VLSI chips
Passive device modeling
Such as components, connectors, power/signal line’s behavior
characterization, simulation
Active device
Input or output port model for impedance matching, noise
figure merits
Approaches

Modeling by Immitance functions
using Non-Linear optimization
using interpolation techniques
• Polynomial interpolation
• Lagrange interpolation
Rm
Xm
Xf
Zin
Real Part
Data
Imaginary
Part Data
ZM : Minimum Reactance
Function
ZF : Foster Function
Approaches

Modeling by Scattering parameters
 using Non-Linear optimization
 using iterative solution
Belevitch Representation
of Scattering Parameters:
Sin
N
Lossless
two-ports
S  h( p ) / g ( p )
11
1Ω
S  f ( p) / g ( p)
21
S   f ( p) / g ( p)
12
S  h( p) / g ( p)
22
An Antenna modeling example
Given measured impedance
data
Freq
(MHz)
Real part
data
()
Imaginary
part data ()
20
0.6
-6.0
30
0.8
-2.2
40
0.8
0
45
1.0
1.4
50
2.0
2.8
55
3.4
4.6
60
7.0
7.6
65
15.0
8.8
70
22.4
-5.4
75
11.0
-13.0
80
5.0
-10.8
90
1.6
-6.8
100
1.0
-4.4
Program screen
An Antenna modeling example
Report of Program
--- Result of Modelling --Real Part Modelling
Result = Successful
Trial number: 60
Error: 3.8979
Function type: Impedance
Interp. method: Lagrange
Zeros:
Chebyshev roots: 3 12
Samples: 2 9
Minimum reactance functions
R_w2_nom =0.000000e+000 0.000000e+000 1.000000e+000
R_w2_den =7.812500e+000 -7.544643e+000 1.865737e+000
Z_s_nom =0.000000e+000 4.964006e+000 5.359813e-001
Z_s_den =2.046303e+000 2.209465e-001 1.000000e+000
Synthesis of Minimum reactance functions
C1= +4.12228e-001
L2= +4.96401e+000
R3= +5.35981e-001
Foster Modelling
Result = Successful
Error: 1.3751
Func. type: FF-1, poles at zero, infinity and finite freq.
Samples: 1 8 10 13
pole freq. =6.745369e-001 7.745967e-001
Residues =2.534267e-002 3.561921e-002 1.870885e+000 1.489978e+000
Synthesis of Foster functions
L1= +5.56982e-002
C2= +3.94591e+001
L3= +5.93654e-002
C4= +2.80747e+001
L5= +1.87088e+000
C6= +6.71151e-001
End of report.
Future Works
A modeling process can be done for
•One-port device
Done
•Multi-port device
Future project
And modeled devices can be
•Passive device
Done
•Active device
Partially done
Design of Broadband
Phase Shifters
0o-360o Wide Range Digital Phase Shifters
Current Projects:
CAD Tools for Broadband
Microwave Circuit Design
RFT Toolboxes:
 Modelling Toolbox
WMCD Integrated Toolbox
RFT Matching Network Design Toolboxes
Toolboxes
•
Line Segment Technique
•
Direct Computational Technique
•
Parametric Technique
•
Simplifed Real Frequency Technique
•
Mixed Lumped-distributed Design
Modelling Toolbox
WIDEBAND
MICROWAVE
CIRCUIT
DESIGNER
WMCD Integrated Toolbox
Broadband matching toolbox:
Design and optimization of broadband matching networks
and amplifiers via real frequency techniques
Lumped Element Design
Distributed Element Design
Mixed Lumped-Distributed Design
Multistage Amplifier Design
Options:
•
•
•
•
Line Segment Approach
Direct Computational Technique
Parametric Approach
Simplifed Real Frequency Technique
v1.0
Design Example: Double Matching Problem
1
Transducer Power Gain
2H
1H
Gain(dB)
+
E
1
N
1F
1
0.9
0.8
0.7
Z(p)
Generator
1
1H
Load
0.6
2H
0.5
1:n
L2
0.4
+
C3 C1
0.3
1F
E
1
- New parametric
0.2
_._ SRFT
0.1
0


Bandwidth: 0  w  1
Complexity of equalizer:
n=3 (Low pass)
0.6821 p 2  0.4435 p  0.2276
Z ( p)  3
p  0.6503 p 2  0.6186 p  0.1852
0
0.2
0.4
0.6
0.8
Frequency
1
1.2
w
Comparision of RFT Results (Normalized values)
Min.Gain
Ripple
n
C1
L2
C3
Scattering
approach
0.922
0.0768
1.188
1.322
2.475
1.113
Parametric
approach
0.923
0.0639
1.119
1
1.3526
2.390
2
1.167
6
Impedance
approach
0.924
0.0629
1.119
8
1.351
2.394
1
1.166
Design Example: Single Stage Amplifier
Scattering Data for HFET 2001
Frequen
cy
S21
S11
m
GHz
6
8
10
12
14
16
m
p
0.88
0.83
0.79
0.76
0.73
0.71
-65
-85
-101
-113
-126
-141
2.00
1.81
1.64
1.48
1.39
1.32
S12
p
125
109
95
84
73
61
HFET 2001
1
1:n1
m
0.05
0.06
0.06
0.06
0.06
0.07
p
60
53
51
52
54
55
m
0.71
0.68
0.66
0.66
0.64
0.63
p
38.4075 p 2  43.5549 p  36.4939
Z1 (p)  3
p  1.1340 p 2  52.0466 p  57.9444
Back- End
-22
-30
-37
-43
-48
-56
2.5812 p 3  1.0295 p 2  2.6049 p  0.5583
Z 2 ( p)  4
p  0.3988 p 3  2.8390 p 2  0.9461 p  0.8543
1:n2
L4
Transducer Power Gain
L6
Gain(dB)
L2
C5
+
C3
Front-End
S22
C1
E
C7
1
8
7.5
back-end
7
6.5
6
Normalized element values
5.5
C1 = 0.0260
C4 = 0.3874
5
L2 = 0.7516
L5 = 1.4105
4.5
C3 = 1.4
C6 = 1.307
n1 = 0..6298
L7 = 1.6386
n2 = 1.53
front-end
4
3.5
3
0.4
0.5
0.6
0.7
0.8
Frequency
0.9
1
w
Design Example:Two Stage Amplifier
Scattering Data for HP 1 μm FET
Coefficients of Mixed Element Equalizer
Front-End
Interstage
0.4481 0.6233
 0


 H   0.5099 0.7650 0.5375
 0.2299 0.1384
0 
0.8473 5.0087
 0


 0.4506 1.0495 7.0368 
0.2796 1.1308
0 
2.1348 1.1783
 1


 G  0.8484 1.5828 0.5375
0.2299 0.1384
0 
H
3.5963 5.1076
 1


 G   0.8731 2.7581 7.0368
0.2796 1.1308
0 
Back-End
G
2.6776 1.4065
 1


1
.
6526
2.6279 2.9181

0.6803 2.5887
0 


0
0 
0.4797
1.5352 0.9890 
 0



1
.
1706
0.3663  2.9181
H  
 0.0215  2.5887
0 



0
.
4797
0
0 

Transducer Power Gain
15
2nd stage gain
1st stage gain
14
13
12
L1=42.3pH,
C1=170pF,
Z1=54.23Ω,
Z2=30Ω,
L2=165pH,
C2=52.8pF,
Z3=20Ω,
Z4=200Ω,
τ1= τ2= 0.2,
τ3= τ4=0.2,
C3=182pF,
L3=60.2pH,
C4=170.8pF,
Z5=40Ω,
Z6=16.82Ω
τ5= τ6=0.25
TPG (dB)
11
10
9
8
7
6
5
4
4
4.5
5
5.5
6
6.5
Frequency(GHz)
7
7.5
8
Selected Publications






Yarman B.S., “Broadband Network”, Wiley Encyclopedia of Electrical and
Electronics Engineering John G.Webster, Editor, Vol 2, pp.589-605, 1999,
John Wiley&Sons corp.
A. Aksen, H. Pınarbası,B. S. Yarman ”A Parametric Approach to Construct
Two-Variable Positive Real Impedance Functions for the Real Frequency
Design of Mixed Lumped-Distributed Matching Networks IEEE MTT- 2004,
pp. 1851-1854, 6-11 June 2004
A.Aksen, B.S.Yarman, “A Real Frequency Approach to Describe Lossless TwoPorts Formed with Mixed Lumped and Distributed Elements” ” (Dedicated to
Professor Alfred Fettweis on the occasion of his 75 th birthday),
Int.J.Electron.Commun.(AEÜ) 55 (2001) No.6, pp.389-396
B.S.Yarman, A.Aksen, A.Kılınç, “An Immitance Based Tool for Modelling
Passive One-Port Devices by Means of Darlington Equivalents” (Dedicated to
Professor Alfred Fettweis on the occasion of his 75 th birthday),
Int.J.Electron.Commun.(AEÜ) 55 (2001) No.6, pp.443-451
A.Aksen, B.S.Yarman, “Cascade synthesis of two-wariable lossless two-port
networks with lumped elements and transmission lines”, in Multidimensional
Signals, Circuits and Systems, Editors: K.Galkowski and J.Wood, Chapter 12,
pp.219-232, Taylor and Francis, New York, 2001
B.S.Yarman, E. G. Çimen, A. Aksen, “Description of symmetrical lossless twoports in two-kinds of elements for the design of microwave communication
systems in MMIC realization”, ECCTD2001 (European Conference on Circuit
Theory and Design), Espoo, Finland, 28-31 August, 2001