1
11. Microwave amplifier design
전자파 연구실
Microwave amplifiers
2
Low noise amplifier
Broad band amplifier
Power amplifier
DC bias (동작점)에 따라 트랜지스터의 S-parameter가 달라짐.
전자파 연구실
11.1 Two port power gains
3
1. Power gain = G = PL/Pin : ratio of power dissipated in the load ZL to the power
delivered to the input of the two-port network.
2. Available gain = GA=Pavn/Pavs : ratio of the power available from the two port network
to the power available from the source
3. Transducer power gain = GT = PL/Pavs : ratio of the power delivered to the load to the
power available from the source.
If the input and output are both conjugately matched to the two-port, then the gain is
maximized and G= GA= GT .
S 
Z S  Z0
Z  Z0
, L  L
ZS  Z0
Z L  Z0
전자파 연구실
4
Input reflection
V1  S11V1  S12V2  S11V1  S12LV2

2

21 1

22 2

21 1

22 L 2
V S V S V S V S V
V1
V2
V2
 S11  S12   S11  S12L 
V1
V1
V1
V2
(1  S 22L )  S 21
V1
Z  Z0
V1
S S 
in    S11  12 21 L  in
V1
1  S 22L Z in  Z 0
Z in  Z 0
1  in
1  in
(Input impedance)
Output reflection
out
S S 
V2
   S 22  12 21 S
V2
1  S11S
전자파 연구실
V1  VS
Z in
 V1  V1  V1 (1  in )
Z S  Z in
Z in  Z 0
1  in
1  in
1  in
1  in
Z0
V (1  S )
1
V1  VS
 VS
 S
(1  in ) Z  Z 1  in
Z S (1  in )  Z 0 (1  in ) 2 1  S in
S
0
1  in
Z0
전자파 연구실
Power gain
2
2
2
V
1  S
1
2
2
Pin 
V1 (1  in )  S
(1  in )
2Z 0
8 1  S in
2
1
1
2
PL 
V2 (1  L ) 
V1
2Z 0
2Z 0

VS
2
8Z 0
S 21 (1  L ) 1  S
2
1  S in
1  S 22L
2
2
S 21 (1  L )
2
2
1  S 22L
2
2
2
S 21 (1  L )
P
G  L 
Pin 1  S 22L 2 (1  in 2 )
2
2
전자파 연구실
7
Available gain
Pavs  Pin 
*
in  S
Pavn  PL 
*
L  out

VS

1  S
2
8 1  S
2
VS
2
8Z 0
2
2
2
2
2
2
2
2
S 21 (1  out ) 1  S
VS S 21 (1  S ) 1  S

* 2
1  S in
8Z 0 1  S11S 2 1  out 2
1  S 22out
S (1  S ) 1  S
P
G A  avn  21
2
2
Pavs
1  S11S
1  out
2
2
2
Transducer power gain
S (1  S )(1  L )
P
GT  L  21
2
2
Pavs
1  S in 1  S 22L
2
2
2
전자파 연구실
8
Conjugate matched case
GT  S 21
L  S  0
2
Unilateral transducer gain: S12=0
S 21 (1  S )(1  L )
2
GTU 
2
1  S11S 1  S 22L
2
2
2
전자파 연구실
9
11.2 Stability
If the input or output port impedance has a negative real part, oscillation
is possible.
in  1,
1.
2.
out  1
Unconditional stability : |Гin|<1, |Гout|<1 for all passive source and
load impedances. ( |Гs|<1 and |ГL|<1 )
Conditional stability : |Гin|<1, |Гout|<1 for a certain range of passive
source and load impedances.
전자파 연구실
Stability circles
in  S11 
S12 S21L
1
1  S22L
out  S 22 
S12 S 21S
1
1  S11S
Output stability circle
2
in
2
S S 
 S11  12 21 L  1
1  S 22L
S11 (1  S 22L )  S12 S 21L  1  S 22L
2
S11  ( S12 S 21  S11S 22 )L  1  S 22L
2
2
2
L  S11  S 22L  1 ,   S11S 22  S12 S 21
2


2
 S 22
2
2
  S  S    (S
  S  SS   1  S
2
L
*
11
22
*
22
L
 S11* )L*  1  S11
2
2
 S 22
2
*
22
2
L
*
11
11
2
2

*
S 22
 S11*
  S 22
2
22

   S 22
2
2
  
*
S 22
 S11*
L
2
 S 22
2
2

S12 S 21

  S11S 22
  S 22
2
2
2

S12 S 21
2
  S 22
2
2
2
  S 22
2
2
2
2
2
전자파 연구실
Case 1)
  S22
L 
*
S 22
 S11*
  S 22
2
 L  CL  RL
Case 2)
2

S12 S 21
  S 22
2
CL 
2
*
S 22
 S11*
S 22  
2
, RL 
2
S12 S 21
  S 22
2
2
  S22
 L  CL  RL
Case 1)
CL 
*
S 22
 S11*
S 22  
2
, RL 
2
S12 S 21
  S 22
2
2
Case 2)
전자파 연구실
Input stability circle
Case 1)
  S11
S 
S11*  S 22*
  S11
2
 S  CS  RS
Case 2)
2

S12 S 21
  S11
2
CS 
2
S11*  S 22*
S12 S 21
S11  
  S11
2
, RS 
2
2
2
  S11
 S  CS  RS
CS 
S11*  S 22*
S11  
2
2
, RS 
Case 1)
S12 S 21
  S11
2
2
Case 2)
CS
RS
CS
RS
S  1
S  1
전자파 연구실
Test for unconditional stability : K-Δ test
(1) K-Δ test
CL  RL  1
CS  RS  1
원 내부 영역이 |Γin|=1
인 원과 겹치지 않으면
됨.
  S11
CL 
1  S11  S 22  
2
K
2
2 S12 S 21
*
S 22
 S11*
S 22  
2
2
, RL 
S12 S 21
  S 22
2
2
2
 1,
  1   S11S22  S12S21
(2) μ test

1  S11
* 2
11
S 22  S
2
 S12 S 21
1
전자파 연구실
Example 11.2 Transistor stability
전자파 연구실
전자파 연구실
11.3 Single-stage transistor amplifier
Design for maximum gain (Conjugate matching)
(1) Maximum power transfer from the source to the transistor
in  S*
(2) Maximum power transfer from the transistor to the load
out  L*
GT ,max 
1
1  S
2
S 21
1  L
2
2
1  S 22L
2
아래 식에 대해 연립 방정식 풀어야 함
S*  in  S11 
S12 S 21L
1  S 22L
L*  out  S 22 
S12 S 21S
1  S11S
전자파 연구실
전자파 연구실
Example 11.3 Conjugately matched amplifier design
전자파 연구실
전자파 연구실
1
전자파 연구실
전자파 연구실
Unilateral figure of merit
Transducer power gain
S (1  S )(1  L )
P
GT  L  21
2
2
Pavs
1  S in 1  S 22L
2
2
2
Unilateral transducer gain: S12=0
S 21 (1  S )(1  L )
2
GTU 
2
2
1  S11S 1  S 22L
2
2
1
GTU
1


(1  U ) 2 GU
(1  U ) 2
Unilateral figure of merit :
U
S12 S21 S11 S22
(1  S11 )(1  S22 )
2
2
전자파 연구실
Impedance matching
전자파 연구실
Constant resistance, reactance circles
imag
x
r=0
r=0.5
r=1
r=2
0
0.5
1
real
R
2
imag
x
2
x=0.5
x=1
1
x=2
0.5
R
real
0.5
1
x=-2
x=-1
2
x=-0.5
전자파 연구실
25
Impedance-admittance chart
ZL= 200-j 100 
Z0= 100 
f = 500MHz
0.0
1
0.2
Add series L
X
 1.2  X   L  1.2 Z 0
Z0
L 
1 .2 Z 0

Add shunt C
B  0.3Y0 
 38.2 [nH]
0.5
C 
1.2
0.3
 C
Z0
0.3
 0.95 [pF]
 Z0
전자파 연구실
26
Basic Smith chart operation
1. Translation
  2 l
( z   l )
 ( z  0)
( z  l )  ( z  0) e j 2  l
2. Add series element
L
C
전자파 연구실
27
3. Add shunt element
L
C
전자파 연구실
28
Example 5.1
Figure 5.3a (p. 226)
Solution to Example 5.1.
(a) Smith chart for the L-section
matching networks.
3
ZL= 200-j 100 
Z0= 100 
f = 500MHz
2
5
1
4
전자파 연구실
5.2 Single stub tuning
ZL= 60-j 80 
Z0= 50 
f = 2GHz
Translate by ‘d’
y1  1  j1.4
zL  1.2  j1.6
d2  0.266 
1
1
zL  1.2  j1.6
d1  0.11
0.314
0.314
0.422
D를 변화시켜 1+jb 원의 원주 상에 yL이
오도록 한다.
29
전자파 연구실
30
Add shunt stub (shorted)
l1  0.096 
l2  0.405 
y1  1  j1.4
y1  1  j1.4
1+jb 원의 원주 상의 지점을 shunt stub(병
렬 stub)을 달아서 Γ원의 원점으로 옮기
면 impedance matching이 완료됨.
전자파 연구실
31
0.422
Impedance matching 순서
zL이 1+jb 원의 원주 상에 올 수
있도록 d1을 조절한다.
(점선 원) 상에zL이 옮겨 올 수 있
도록 L1을 조절한다.
d2  0.266 
y1  1  j1.4
d1  0.11
zL  1.2  j1.6
1
0.314
전자파 연구실
Unilateral case
Without feedback,
S*  in  S11 
S12  0
  out
*
L
S12 S 21L
1  S 22L
S S 
 S 22  12 21 S
1  S11S
The impedance matching
becomes very simple job.
S*  in  S11
L*  out  S 22
Without rb’c and Cc, this transistor
become unilateral.
전자파 연구실
Stabilization method
Input stability
in 
Z in  Z 0
 1 and
Z in  Z 0
Re{ Z in }  0
out 
Z out  Z 0
1
Z out  Z 0
Re{Z out }  0
and
트랜지스터가 unstable한 경우 직렬 또는 병렬로 저항을 연결하면 안정도가 바뀐다.
Re{Z in  Rin  Z S }  0
or
Re{Yin  Gin  YS }  0
전자파 연구실
Output stability
The corresponding condition is
  Z L}  0
Re{Z out  Rout
or
  YL }  0
Re{Yout  Gout
전자파 연구실
Neutralization or unilateralization
전자파 연구실
Constant gain circle and design for specified gain
S (1  S )(1  L )
P
GT  L  21
2
2
Pavs
1  S in 1  S 22L
2
2
2
Without feedback, an amplifier becomes unilateral.
S12  0
(1  S )
2
GTU  GS G0GL 
1  S11S
2
(1  L )
2
S 21
2
1  S 22L
2

G 
 S

 G0 


 GL 


2
(1  S ) 
2
1  S11S 

2

S 21

2
(1  L ) 

2
1  S 22L 

GS, GL are maximized when S*  S11, L*  S 22
GS ,max 
1
1  S11
, GL ,max 
2
1
1  S 22
2
gS, gL are defined as normalized gain factors
(1  S )
GS
2
gS 

(1  S11 )
2
GS ,max 1  S11S
2
(1  L )
GL
2
gL 

(1  S 22 )
2
GL ,max 1  S 22L
2
전자파 연구실
전자파 연구실
Figure 11-8b (p. 557)
(b) RF circuit. (c) Transducer gain and return loss.
전자파 연구실
Low noise amplifier design
F  Fmin 
2
RN
YS  Yopt
GS
YS  GS  jBS :Source admittance presented to transistor
Yopt
:Optimum source admittance that result in minimum noise figure.
Fmin
RN
GS
: Minimum noise figure of transistor, attained when
:equivalent noise resistance of a transistor
:Real part of source admittance
2
F  Fmin
S  opt
R
 N
Z 0 (1   2 ) 1   2
S
opt
전자파 연구실
Figure 11-9b (p. 561)
(b) RF circuit.
전자파 연구실
11.4 Broadband transistor amplifier design
전자파 연구실
Balanced amplifier
Figure 11-10 (p. 562)
A balanced amplifier using 90° hybrid couplers.
VA1 
1 
j 
V1 , VB1 
V1
2
2
(V1 ) : Incident input voltage
The output voltage can be found as
V2  
j 
1 
j
1
j
VA 2 
VB 2  
GAVA1 
GBVB1   V1 (GA  GB )
2
2
2
2
2
V2
j
 S 21     (GA  GB )
V1
2
전자파 연구실
The total reflected voltage at the input can be written as
V1 
1  j 
1
j
1
VA1 
VB1 
AVA1 
BVB1  V1 (A  B )
2
2
2
2
2
V1 1
 S11    ( A  B )
V1
2
F  ( FA  FB ) / 2
Figure 11-11 (p. 564)
Gain and return loss, before and after optimization,
for the balanced amplifier of Example 11.6.
전자파 연구실
Distributed amplifiers
•
Very wideband width
•
Good input and output matching
•
Not good noise figure
•
Not very high gain
•
Occupies large area
Equivalent circuit for one FET
전자파 연구실
Gate equivalent circuit
Figure 11-13 (p. 566)
(a) Transmission line circuit for the gate line
of the distributed amplifier;
(b) equivalent circuit of a single unit cell of
the gate line.
Drain equivalent circuit
Figure 11-14 (p. 566)
(a) Transmission line circuit for the drain
line of the distributed amplifier;
(b) equivalent circuit of a single unit cell of
the drain line.
전자파 연구실
Gate transmission line equivalent circuit
전자파 연구실
Drain transmission line equivalent circuit
전자파 연구실
Gate source voltage on n-th FET :
Total output current on N-th terminal of of the drain line:
전자파 연구실
전자파 연구실
부품 라이브
러리
전자파 연구실
전자파 연구실
전자파 연구실
전자파 연구실
시물레이션
시작
전자파 연구실
전자파 연구실
Stability
전자파 연구실
Stability
전자파 연구실