E.E. Essential Knowledge Sereies My Online Courses: https://www.byparams.com/courses Microwave Transistor Amplifier

1. Chapter 4-1
Microwave Transistor Amplifier Design
Chien-Jung Li
Department of Electronics Engineering
National Taipei University of Technology

2. Department of Electronic Engineering, NTUT
Power Gain Equations
2 2
2
212 2
22
1 1
1 1
s LL
T
AVS in s L
P
G S
P S
   
 
    
2 2
2
212 2
11
1 1
1 1
s LL
T
AVS s out L
P
G S
P S
   
 
    
2
2
212 2
22
11
1 1
LL
p
in in L
P
G S
P S
 
 
   
2
2
212 2
11
1 1
1 1
sAVN
A
AVS s out
P
G S
P S
 
 
   
• Transducer Power Gain
• Operating Power Gain
• Available Power Gain
Transistor
[S]


sE
sZ
LZ
PAVNPAVS PLPin
Ms
interface interface
ML
2/45

3. Department of Electronic Engineering, NTUT
Example (I)
• Calculate the PAVS, Pin, PAVN, and PL
1 50Z  
Input
Matching
Network
Output
Matching
Network
1 10 0E  
2 50Z  
0.5 120s   in
out 0.4 90L  
sZ inZ outZ LZ
 S
  11 12
21 22
0.6 160 0.045 16
2.5 30 0.5 90
S S
S
S S
     
    
     
Transistor S parameters:
12 21
11
22
0.627 164.6
1
L
in
L
S S
S
S

     
 
12 21
22
11
0.471 97.63
1
s
out
s
S S
S
S

     
 
2 2
2
212 2
22
1 1
9.43
1 1
s LL
T
AVS in s L
P
G S
P S
   
  
    
 or 9.75 dB
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4. Department of Electronic Engineering, NTUT
Example (II)
2
2
212 2
22
11
13.51
1 1
LL
p
in in L
P
G S
P S
 
  
   
 or 11.31 dB
2
2
212 2
11
1 1
9.55
1 1
sAVN
A
AVS s out
P
G S
P S
 
  
   
 or 9.8 dB
in AVS sP P M T p sG G Mand      
9.43
0.698 1.56 dB
13.51
T
s
p
G
M
G
    
   
   
  
2 2
2
1 1
0.6983 1.56 dB
1
s in
s
s in
M
L AVN LP P M T A LG G Mand      
9.43
0.9874 0.055 dB
9.55
T
L
A
G
M
G
    
   
   
  
2 2
2
1 1
0.9874 0.055 dB
1
L out
L
out L
M  

2 2
1
1
10
0.25 W
8 8 50
AVS
E
P
R
   0.25 W 0.1745 Win sP M
   0.25 W 2.358 WL TP G
  2.358 WL AVN LP P M  2.39 WAVNP
4/45

5. Department of Electronic Engineering, NTUT
Stability
12 21
11
221
L
in
L
S S
S
S

  
 
12 21
22
111
s
out
s
S S
S
S

  
 
• The stability of an amplifier, or its resistance to oscillate, is a very
important consideration in a design and can be determined from the
S parameters, the matching networks, and the terminations.
• Oscillations are possible when either the input or output port presents
a negative resistance, i.e., or ( or for a
unilateral device).
  1in   1out 22 1S11 1S
Transistor
[S]

sE
sZ
out
LZ
in
s L
• The two-port network is said to be unconditionally stable at a given
frequency if the real parts of Zin and Zout are greater then zero for a
passive load and source impedances. For potentially unstable, that is,
some passive load and source terminations can produce input and
output impedances having a negative real part.
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6. Department of Electronic Engineering, NTUT
Stability Considerations
1s 
12 21
22
11
1
1
s
out
s
S S
S
S

   
 
1L 
12 21
11
22
1
1
L
in
L
S S
S
S

   
 
 22 11 12 21
2 2 2 2
22 22
L
S S S S
S S

 
  
   
 11 22 12 21
2 2 2 2
11 11
s
S S S S
S S

 
  
   
11 22 12 21S S S S  
• In terms of reflection coefficients, the conditions for unconditionally
stability at a given frequency are
• The region where produces is determined.L 1in 
• Stability Circles include
and
Transistor
[S]

sE
sZ
out
LZ
in
s L
• The region where produces is determined.s 1out 
and
where
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7. Department of Electronic Engineering, NTUT
The Stability Circles
12 21
2 2
22
L
S S
r
S

 
 22 11
2 2
22
L
S S
C
S

 

 
12 21
2 2
11
s
S S
r
S

 
 11 22
2 2
11
s
S S
C
S

 

 
• Output Stability Circle ( values for )L 1in 
 Center
 Radius
• Input Stability Circle ( values for )
 Center
 Radius
s 1out 
1in 
1out 
LC
Lr
LC
sC
sr
sC
-planeL
-planes
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8. Department of Electronic Engineering, NTUT
Determine the Stable Region
LC
LC
Lr 1in 
sr
sC
sC
1out 
• How do we determine the stable region? Inside or outside the
stability circle? The and can help! (see next two slides)11S
-planeL -planes
Output Stability Circle Input Stability Circle
22S
8/45

9. Department of Electronic Engineering, NTUT
Determine the Stable Region of Plane
LC
LC
Lr
1in 
11 1S 
12 21
11
221
L
in
L
S S
S
S

  
 
0L 
LC
LC
0L 
Lr
1in 
• Criteria: virtually make , then and0L  11in S L oZ Z
-planeL -planeL
L
Case (1): 11 1S Case (2):
stable region stable region
9/45

10. Department of Electronic Engineering, NTUT
Determine the Stable Region of Plane
12 21
22
111
s
out
s
S S
S
S

  
 
22 1S  22 1S 
s
Case (1): Case (2):
• Criteria: virtually make , then and0s  22out S s oZ Z
stable region stable region
-planes -planes
0s 0s 
sC sC
sC
srsr
sC
1out  1out 
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11. Department of Electronic Engineering, NTUT
Unconditionally Stable (I)
-planeL -planes
0s 0L 
LC
sC
sC
sr
Lr
LC
1in 
1out 
• For the cases of and11 1S  22 1S 
Make the stability circles completely outside the Smith Chart!
11/45

12. Department of Electronic Engineering, NTUT
Unconditionally Stable (II)
• For the cases of and11 1S  22 1S 
Make the stability circles completely enclose the Smith Chart!
-planeL -planes
0s 
0L 
LC sCsC
sr
Lr
LC
1in 
1out 
12/45

13. Department of Electronic Engineering, NTUT
Stability Tests
   
 
2 2 2
11 22
12 21
1
1
2
S S
K
S S
• Rollet’s Condition (K-∆ test):
For unconditional stability
   11 22 12 21 1S S S Sand
 The K-∆ test is a mathematically rigorous condition for unconditional stability.
However, it cannot be used to compare the relative stability of two or more
devices (or bias conditions) since it involves constraints on two parameters.
K>1 and |∆|<1 must
simultaneously hold for
unconditionally stable
• In 1992, Edwards, et. al. derived a new criterion that involves only a
single parameter μ for unconditional stability. Thus, if μ > 1, the device
is unconditionally stable. In addition, it can be said that larger values of
μ imply greater stability.
2
11
22 11 12 21
1
1
S
S S S S
 

 
  
13/45

14. Department of Electronic Engineering, NTUT
Example (I)
Determined the stability. If the transistor is potentially unstable at a
given frequency, draw the input and output stability circles.
2 2 2
11 22
12 21
1
1
2
S S
K
S S
   
 
   11 22 12 21 1S S S S
K 
0.482 0.221 123 
0.857 0.173 162.9 
1.31 0.174 160
1.535 0.226 121
(GHz)f
0.5
1
2
4
• The S-parameter of a BJT at VCE = 15 V and IC = 15 mA at f=500 MHz,
1 GHz, and 4 GHz are as follows:
2
11
22 11 12 21
1
1
S
S S S S
 

 
  

0.49



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15. Department of Electronic Engineering, NTUT
Example (II)
 22 11
2 2
22
L
S S
C
S

 

 
12 21
2 2
22
L
S S
r
S

 
 11 22
2 2
11
s
S S
C
S

 

 
12 21
2 2
11
s
S S
r
S

 
sC sr
1.36 157.6 0.558 2.8 57.86 2.18
1.28 169 0.315 2.62 51.3
(GHz)f
0.5
1
LC Lr
1.71
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16. Department of Electronic Engineering, NTUT
Stabilization Methods
• Stabilization methods described below are used to stabilize the
transistor unconditionally.
1R
2R
6R
5R
3R
4R
 Stabilization of input port through series or shunt resistance, eg., R1, R2.
 Stabilization of output port through series or shunt resistance, eg., R3, R4.
 Stabilization using series or shunt negative feedback, eg., R5, R6. Inductances
and capacitances are also commonly used as feedback elements.
 Stabilization results in a loss of gain and an increase in noise figure.
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17. Department of Electronic Engineering, NTUT
Example (I)
• The S-parameter of a transistor at f=800 MHz are :
11 0.65 95S    12 0.035 40S   21 5 115S   22 0.8 35S   
Determine the stability circle and show how resistive loading can stabilize the
transistor.
2 2 2
11 22
12 21
1
0.547
2
S S
K
S S
   
 
11 22 12 21 0.504 249.6S S S S    
Since K<1, the transistor is potentially unstable at f=800MHz.
1.79 122sC   1.04sr 
1.3 48LC    0.45Lr
 Input Stability Circle:
 Output Stability Circle:
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18. Department of Electronic Engineering, NTUT
Input and Output Stability Circle
1.79 122sC  
1.3 48LC  
18/45

19. Department of Electronic Engineering, NTUT
Stabilization – Input Series Resistance
1.79 122sC  
1.3 48LC  
9 
s
9s sZ Z  
s

sZ
19/45

20. Department of Electronic Engineering, NTUT
Stabilization – Input Shunt Resistance
1.79 122sC  
1.3 48LC  
71.5 
20/45

21. Department of Electronic Engineering, NTUT
Stabilization – Output Series Resistance
1.79 122sC  
1.3 48LC  
29 
21/45

22. Department of Electronic Engineering, NTUT
Stabilization – Output Shunt Resistance
1.79 122sC  
1.3 48LC  
500 
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23. Department of Electronic Engineering, NTUT
Stability Considerations (I)
• For a unilateral transistor, S12=0 (or it is so small that can be set to
zero). In unilateral case, and (the transistor
output signal would not go through back to the input). If , the
transistor presents a negative resistance at the input, and if the
transistor presents a negative resistance at the output.
11in S  22out S 
11 0S 
22 0S 
• For unconditionally stability any passive load and or source in the
network must produce a stable condition. For and ,
we want the stability circles to fall completely outside the Smith Chart.
(Or completely enclosed for and )
11 0S  22 0S 
11 0S  22 0S 
• It is convenient to use the μ parameter to check the stability, the
transistor will be more stable for a larger μ.
• For the unilateral case, we have unconditionally stability if
and for all passive source and load terminations.11 0S  22 0S 
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24. Department of Electronic Engineering, NTUT
Stability Considerations (II)
• A potentially unstable transistor can be made unconditionally stable
by either resistively loading the transistor or by adding negative
feedback. These techniques are nor recommended in narrowband
amplifiers because of the resulting degradation in power gain, noise
figure, and VSWRs.
• Usually, stabilizing one port of a transistor results in an
unconditionally stable device.
• All four choices of resistive loading affects the gain performance of
the amplifier. In practice, resistive loading at the input is not used
because it produces a significant deterioration in the noise
performance of the amplifier.
• Negative feedback can be used to stabilize a transistor by neutralizing
S12 (making S12=0). However, this is not commonly done. In a
broadband design, a common procedure is to use resistive loading to
stabilize the transistor and negative feedback to provide the proper ac
performance (constant gain and low input and output VSWR).
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25. Department of Electronic Engineering, NTUT
Unilateral Transducer Power Gain
11S
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s L22S
   
 
   
2 2
2
212 2
11 22
1 1
1 1
s L
TU s o L
s L
G S G G G
S S
2
2
11
1
1
s
s
s
G
S
 

 
2
21oG S
2
2
22
1
1
L
L
L
G
S
 

 
(dB) (dB) (dB) (dB)TU s o LG G G G  
• Unilateral Transducer Power Gain GTU
• The term Gs and GL represent the gain or loss produced by the
matching or mismatching of the input or output circuits.
12 0S
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26. Department of Electronic Engineering, NTUT
Maximum Unilateral Transducer Power Gain
11S
1E
oZ
oZ
Transistor
oG
Output
matching
,maxLG
Input
matching
,maxsG
11s S
  22L S
 22S
11s S
  22L S
 
,max 2
11
1
1
sG
S


,max 2
22
1
1
LG
S


2
,max ,max ,max 212 2
11 22
1 1
1 1
TU s o LG G G G S
S S
 
 
• Maximum Unilateral Transducer Power Gain GTU,max
Optimize and to provide maximum gain in Gs and GL.s L
and
2
2
11
1
1
s
s
s
G
S
 

 
2
2
22
1
1
L
L
L
G
S
 

 
and
and
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27. Department of Electronic Engineering, NTUT
General Form of the Matching Gain
2
2
1
1
i
i
ii i
G
S
 

 
• General form of the matching gains Gs and GL :
 with 11, and with 22i s ii i L ii   
(1) Unconditionally stable case: 1iiS 
,max 2
1
1
i
ii
G
S


,max0 i iG G 
i iiS
 For optimum terminations:
Other values of (mismatched) produce Gi between zero and Gi,max:i
• The values of that produce a constant gain Gi will be shown to lie in a
circle in the Smith Chart. These circles are called constant Gi circles.
i
Constant Gs circles: i = s
Constant GL circles: i = L
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28. Department of Electronic Engineering, NTUT
Constant Gi Circle – Unconditionally Stable
• Normalized Gain Factor:
   
2
2 2
,max
1
1 1
1
ii
i i ii ii
i ii i
G
g G S S
G S
 
    
 
such that 0 1ig 
• Constant Gi circle in the Smith Chart
The values of that produce a constant values
of gi lie in a circle.
i
i ii g gC r  
 
2
1 1i
i ii
g
ii i
g S
C
S g


 
 
 
2
2
1 1
1 1i
i ii
g
ii i
g S
r
S g
 

 
Each gi generates a constant Gi circle.
When gi =1 gives
0igr  ig iiC S
and
Maximum gain is
represented by a
point located at iiS
giC
gir
iiS
i iiS 
 
iU
iV
-planei
Maximum gain Gi,max occurs
 Locate iiS
 Determine Gi and gi
 Use gi to find igr,igC
 Center:
 Radius:
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29. Department of Electronic Engineering, NTUT
Example (I)
• The S parameters of a BJT measured at VCE = 10 V, IC = 30 mA, and
the operating frequency f = 1 GHz, in a 50-Ohm system, are:
11 0.73 175 ,S   12 0,S  21 4.45 65 , andS   22 0.21 80S   
(a) Calculate the optimum terminations.
(b) Calculate Gs,max, GL,max, and GTU,max in dB.
(c) Draw several Gs constant-gain circles.
(d) Design the input network for Gs = 2 dB.
(a)
11 0.73 175s S
    
12 0S  unilateral
Optimum terminations: 22 0.21 80L S
   and
7.6 2.35sZ j   and 48.5 21.5LZ j  
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30. Department of Electronic Engineering, NTUT
Example (II)
(b)
 ,max 2
11
1
2.141 3.31 dB
1
sG
S
  

 ,max 2
22
1
1.046 0.195 dB
1
LG
S
  

 
2
21 19.8 12.97 dBoG S  
The transistor inherently provides 12.97 dB gain
   ,max dB 3.31 12.97 0.195 16.47 dBTUG    
Input and output matching networks provide
excess gain for transducer power
(c) ,max 3.31 dBsG 
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31. Department of Electronic Engineering, NTUT
Example (III)
(d) Matching to Gs = 2dB
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32. Department of Electronic Engineering, NTUT
Constant Gi Circle – Potentially Unstable
(2) Potentially unstable case: 1iiS 
2
2
1
1
i
i
ii i
G
S
 

 
Critical value of
,
1
, andi c i
ii
G
S
   
i
   
2
2 21
1 1
1
i
i i ii ii
ii i
g G S S
S
 
   
 
Since , thus 0ig 1iiS 
 
2
1 1i
i ii
g
ii i
g S
C
S g


 
 
 
2
2
1 1
1 1i
i ii
g
ii i
g S
r
S g
 

 
Maximum gain Gi,max (infinite) occurs
 Center
 Radius
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33. Department of Electronic Engineering, NTUT
 When and , has a maximum value, and the ratio is bounded
by
Unilateral Figure of Merit (I)
• When S12 can be set to zero, the design procedure is much simpler. In
order to determine the error involved in assuming S12 = 0, we form
the magnitude ratio of GT and GTU, namely,
2
1
1
T
TU
G
G X


2 2
2
212 2
11
1 1
1 1
s L
T
s out L
G S
S
   

    
2 2
2
212 2
11 22
1 1
1 1
s L
TU
s L
G S
S S
   

   
  
12 21
11 221 1
s L
s L
S S
X
S S
 

   
2 2
1 1
1 1
T
TU
G
GX X
 
 
11s S
  22L S
  TUG
   
2 2
1 1
1 1
T
TU
G
GU U
 
 
is known as the
Unilateral Figure of Merit
and
where
  

 
12 21 11 22
2 2
11 221 1
S S S S
U
S S
where
33/45

34. Department of Electronic Engineering, NTUT
Unilateral Figure of Merit (II)
f
 dBU
5
10
15
• The value of U varies with frequency because of its dependence on
the S parameter.
100 MHz 1 GHz
   @100 MHz, and 1 GHz 15 dB 0.03U   
   
2 2
1 1
1 0.03 1 0.03
T
TU
G
G
 
 
0.9426 1.031T
TU
G
G
  0.26 dB 0.26 dBT
TU
G
G
  
• The maximum error is ±0.26 dB at 100 MHz and 1 GHz. In some
designs this error is small enough to justify the unilateral assumption.
34/45

35. Department of Electronic Engineering, NTUT
Simultaneous Conjugate Match: Bilateral Case
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s Lout
s in

   L out

  
• Maximum Simultaneous Conjugate Matched Transducer Power Gain GT,max
and
 
 
22
1 1 1
1
4
2
Ms
B B C
C
and
12 21
11
221
L
in s
L
S S
S
S
 
    
 
12 21
22
111
s
out L
s
S S
S
S
 
    
 
and
 
 
22
2 2 2
2
4
2
ML
B B C
C
    
2 2 2
1 11 221B S S     
2 2 2
2 22 111B S S

  1 11 22C S S 
  2 22 11C S S
where
35/45

36. Department of Electronic Engineering, NTUT
Stability and Simultaneous Conjugate Match
 
 
22
1 1 1
1
4
2
Ms
B B C
C
 
 
22
2 2 2
2
4
2
ML
B B C
C
 1K  1K
 1K  1K
Simultaneous conjugate
match can be achieved
Simultaneous conjugate
match doesn’t exist
Potentially unstable or
Unstable
  1   1
Unconditionally
stable
Potentially
unstable
Any reference to a simultaneous conjugate match assumes
that the two port network is unconditionally stable.
36/45

37. Department of Electronic Engineering, NTUT
Maximum Stable and Available Gain
   

    
2 2
2
212 2
22
1 1
1 1
s L
T
in s L
G S
S
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s Lout

    s in Ms

    L out ML
  
   
   
2
2 21 2
,max 212 2
1222
11
1
1 1
ML
T
Ms ML
S
G S K K
SS
• Maximum Simultaneous Conjugate Matched Transducer Power Gain GT,max
and
• Maximum Stable Gain (MSG) is defined when K =1:
 21
12
MSG
S
G
S
(potentially unstable)
(unconditionally stable)
37/45

38. Department of Electronic Engineering, NTUT
Operating Power-Gain Circle
  
  
  
   
  
 
2 2
21 2
212
211
22
22
1
1 1
1
L
p p
L
L
L
S
G S g
S
S
S
• Unconditionally stable bilateral case:
   
   
 
           
2 2
2 2 2 2 2 2
22 11 11 22 2
1 1
1 1 2Re
L L
p
L L L L
g
S S S S C

  2 22 11C S S
Gp and gp are the functions of the device
S parameters and ΓL. The values of ΓL
that produce a constant gp are shown to
lie on a circle, known as an operating
power-gain circle.
  L p pC r
 


  
2
2 2
221
p
p
p
g C
C
g S  
 

  
2 2
12 21 12 21
2 2
22
1 2
1
p p
p
p
K S S g S S g
r
g S
 Center  Radius
where
• Operating Power-Gain Circle:
38/45

39. Department of Electronic Engineering, NTUT
Maximum Operating Power-Gain
 
 

  
2 2
12 21 12 21
2 2
22
1 2
1
p p
p
p
K S S g S S g
r
g S
• The maximum operating power gain occurs when rp = 0.
  
2 2
12 21 ,max 12 21 ,max1 2 0p pK S S g S S g
   2
,max
12 21
1
1pg K K
S S
    21 2
,max ,max
12
1p T
S
G K K G
S
• The value of ΓL that produces Gp,max follows by substituting gp =
gp,max for Cp. This value of ΓL = Cp,max must be equal to ΓML.
 

  
  
,max 2
,max 2 2
,max 221
p
ML p
p
g C
C
g S
39/45

40. Department of Electronic Engineering, NTUT
Maximum Operating Power Gain
• For a given Gp,ΓL is selected from the constant operating power-gain
circles. Gp,max, results when ΓL is selected at the distance where
gp,max = Gp,max /|S21|2 . The maximum output power results when a
conjugate match is selected at the input (i.e., ), and it follows
that the input power is equal to the maximum available input power.
Therefore, in this circumstances GT,max = Gp,max . The values of Γs and
ΓL that result in Gp,max are identical to ΓMs and ΓML , respectively.

  s in
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s L

• Design Procedure:
40/45

41. Department of Electronic Engineering, NTUT
Example (I)
• Design a microwave amplifier using a GaAs FET to operate f = 6 GHz
with maximum transducer power gain. The transistor S parameters
at the linear bias point, VDS = 4 V and IDS = 0.5 IDDS, are
  11 0.641 171.3S  12 0.057 16.3S  21 2.058 28.5S   22 0.572 95.7S
Use (1) Transducer power gain method (2) Operating power gain
method to find the matching networks (3) Gp=9 dB amplifier design
(1) Transducer power gain method
 1.504K   0.3014 109.88 Unconditionally stable
 0.1085UCheck unilateral:   0.89 dB 1 dBT
TU
G
G
S12 cannot be neglected
(bilateral case)
       1 2 1 20.9928, 0.8255, 0.4786 177.3 , 0.3911 103.9B B C C
  0.762 177.3Ms
  0.718 103.9ML
        
 
2
,max
2.058
1.504 1.504 1 13.74 or 11.38 dB
0.057
TG
41/45

42. Department of Electronic Engineering, NTUT
Example (II)
(2) Operating power gain method:
 

    
  
,max 2
,max 2 2
,max 22
0.718 103.9
1
p
ML p
p
g C
C
g S
 
  ,max
,max 2 2
21
13.74
3.24
2.058
p
p
G
g
S
,max 0pr

  
       
  
12 21
11
22
0.762 177.3
1
ML
Ms in
ML
S S
S
S
(3) Operating power gain method: Gp = 9 dB
 ,max ,max 13.74T pG G
    
2 2
21 2.058 4.235 or 6.27 dBS
  2
21
7.94
1.875
4.235
p
p
G
g
S
1.504K   0.3014 109.88   2 0.3911 103.9C  0.431pr  0.508 103.9pC
42/45

43. Department of Electronic Engineering, NTUT
Example (III)
 Select point A for matching:   0.36 47.5L

  
       
  
12 21
11
22
0.629 175.51
1
L
s in
L
S S
S
S
 Since , it follows that
GT = Gp = 9 dB

  s in
 

 

1 0.622
4.3
1 0.622out
VSWR
43/45

44. Department of Electronic Engineering, NTUT
Available Power-Gain Circle
  
  
  
   
  
 
2 2
21 2
212
222
11
11
1
1 1
1
s
A a
s
s
s
S
G S g
S
S
S
• Unconditionally stable bilateral case:
   
 
 
      
2
2 2 2 2 2
21 22 11 1
1
1 2Re
sA
a
s s
G
g
S S S C

  1 11 22C S S
Ga and ga are the functions of the device
S parameters and Γs. The values of Γs
that produce a constant ga are shown to
lie on a circle, known as an available
power-gain circle.
  s a aC r
 


  
1
2 2
111
a
a
a
g C
C
g S  
 

  
2 2
12 21 12 21
2 2
11
1 2
1
a a
a
a
K S S g S S g
r
g S
 Center  Radius
• Available Power-Gain Circle:
where
44/45

45. Department of Electronic Engineering, NTUT
Design Procedures
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s Lout
• Design using operating power gain:
• Design using available power gain:
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s L

  
45/45