Maximum Gain Amplifiers
For the two-port network shown below, It is well known that maximum
power transfer from the source to the transistor occurs when:
Also, the condition for maximum power transfer from the transistor to
the load
In order to satisfy the maximum power transfer conditions for any
combination of source, transistor, and load, two matching networks
should be connected as show below:
laminate Specifications
Laminate consists of substrate and conductance.
Substrate:
dielectric constant of εr = 3.38±0.05
Thickness = t = 0.406 mm
Conductance:
conductivity = 5.8*106 S/m
thickness of 17mm
Patch Antenna
As a first step in our project we will design the passive patch antenna to
operate at 15GHz frequency. From the equations the length and width of the
patch are calculated to be L= 5.320 mm and W=6.757 mm.
0
-5
dB(S_Z0(1,1))
dB(S(1,1))
-10
-15
-20
-25
-30
-35
14.0
14.2
14.4
14.6
14.8
15.0
freq, GHz
15.2
15.4
15.6
15.8
16.0
The input impedance of antenna at 15GHz is found by plotting the real and
imaginary values of Zin
80
m3
freq= 15.00GHz
real(Zin)=51.709
m3
60
m4
freq= 15.00GHz
imag(Zin)=2.267
imag(Zin)
real(Zin)
40
20
m4
0
-20
-40
-60
14.0
14.2
14.4
14.6
14.8
15.0
freq, GHz
15.2
15.4
15.6
15.8
16.0
The imaginary part of gamma (γ) called (β) is plotted versus frequency in
order to find the exact wavelength in the circuit
560
m2
freq= 15.00GHz
imag(GAMMA(1))=519.016
550
imag(GAMMA(1))
540
530
m2
520
510
500
490
480
14.0
14.2
14.4
14.6
14.8
15.0
15.2
15.4
15.6
15.8
16.0
freq, GHz
It was found that at 15GHz the value of (β) = 519.016 and thus
λ= (2π)/ β = 12 mm.
The effect of changing the width on the performance of the antenna is
simulated and the response is shown in the next figure.
0
dB(antennawidth4_mom_a..S(1,1))
dB(antennawidth3_mom_a..S(1,1))
dB(antenna20width_mom_a..S(1,1))
dB(antenna10width_mom_a..S(1,1))
dB(antennawidth_mom_a..S(1,1))
-5
-10
-15
-20
-25
-30
-35
14.0
14.2
14.4
14.6
14.8
15.0
15.2
15.4
15.6
15.8
16.0
freq, GHz
(1.2W (left), 1.1W, 1.0W, 0.9W, and 0.8W (right))
Transistor:
0.605
3.32
0.6
3.315
0.595
3.31
0.59
3.305
S11
0.585
3.3
0.58
3.295
0.575
3.29
0.57
16
15.5
15
14.5
14
0.565
13.5
16.5
16
15.5
16
15.5
15
Frq
14.5
14
3.285
13.5
14
0.355
0.35
0.345
0.34
0.335
0.33
0.325
0.32
0.315
0.31
0.305
13.5
Frq
14.5
14
0.0915
0.091
0.0905
0.09
0.0895
0.089
0.0885
0.088
0.0875
0.087
0.0865
13.5
S12
Frq
16.5
15
16.5
16
15.5
15
Frq
14.5
S22
16.5
S21
It is rated to work in the 2-18GHz frequency range. The response of the SParameter for the transistor within the range 14 – 16 GHz are shown below
the S-parameters matrix of the transistor is different for different
frequencies. At 15GHz it is specified to be as follows.

o
0
.
58
147


S

o
3
.
296

24



0.089  39 


o 
0.33  171 

o
The s-parameters values will be used in the schematics design
simulations to represent the transistor.
Transistor stability
The transistor needs to be checked for stability at the specific frequency of
operation we are intending to use it at (15GHz).

o
 0.58 147

S

o
3.296  24

K = 1.0058
lΔl= 0.18819

0.089  39 o 



0.33  171o 

Maximum Gain
For unconditionally stable amplifier, the maximum gain can be found
using the following equation.
Gmax 
S 21
S12
K 
Gmax=15.21dB
K 2 1

Design of Matching Network
The two matching networks we are designing in this section will
match the transistor to the antenna and the other will match the
transistor to the source. Each matching network consists of a series
transmission line and a stub. We need to find the lengths of each of
them for each network.
L
s
reflection coefficient
between transistor and
the source
B1  B12  4 C1
S 
2C1
reflection coefficient
between transistor
and the antenna
2
L 
B2  B22  4 C2
2C2
Where
Where
B1  1  S11  S 22  
2
2
2
B2  1  S 22  S11  
2

C1  S11  S 22
C2  S 22  S11
2
2
2
Design of Matching Network
The equations were programmed in Matlab and produced the following values
S  1.0548  141.1253o
Rejected since
s
>1 means active source
S  0.94806  141.1253o
accepted since
s
<1 means passive source
Rejected since
L >1 means active load
L  1.0902  172.0453o
L  0.91723  172.0453o
accepted since
L >1 means active source
Design of Matching Network
S  0.94806  141.1253o
L(series)=0.472λ
L(stub)=0.223λ
Design of Matching Network
L  0.91723  172.0453o
L(series)=0.521λ
L(stub)=0.216λ
Maximum Gain Amplifier
The maximum gain amplifier circuit is drawn in ADS. The design is shown in
the next figure.
Maximum Gain Amplifier
20
m2
m2
freq=15.00GHz
dB(S(2,1))=15.046
10
dB(S(2,1))
dB(S(1,1))
0
-10
-20
-30
m1
freq= 15.00GHz
dB(S(1,1))=-40.470
-40
m1
-50
14.0
14.2
14.4
14.6
14.8
15.0
15.2
15.4
15.6
15.8
16.0
freq, GHz
We can see from the curves shown above that at 15GHz the maximum
gain is 15.046db and the reflection is below -40 db.
Maximum Gain Amplifier Layout
A layout of the circuit with the antenna is shown in the next figure.
Design of Specified Gain Amplifier Antenna
In this chapter we will design specified gain amplifiers of various
specified gains (12db, 10db and 8db). The design process of specified
gain amplifier circuit is similar to that of the maximum gain amplifier
design. The difference however lies in the matching networks only.
laminate Specifications
The same substrate that was used for the maximum gain amplifier antenna is
used for the design of the specified gain active antenna. The substrate has a
dielectric constant of er = 3.38±0.05. The substrate is 0.406 mm thick and
the metal used is copper with specified conductivity of 5.8*106 S/m and a
thickness of 17mm.
Patch Antenna
The patch antenna that was designed in the previous chapter is used for the design
of the specified gain active antenna. The impedance of the antenna at 15GHz was
found to be Zin = 51.709+j2.267 ohm.
Design of Specified Gain Amplifier Antenna
Transistor:
The same transistor that was used in the maximum design antenna is used
for the design of the specified gain active antenna.

o
 0.58 147

S

o
3.296  24


0.089  39 o 



0.33  171o 

The s-parameters values will be used in the schematics design simulations to represent
the transistor. The transistor was determined to be unconditionally stable at 15 GHz.
Design of Specified Gain Amplifier Antenna
in some cases, it is required to design the amplifier for a specific value of
the gain rather than the maximum value.
This specific value of the gain can be achieved by designing the input and
output matching circuits to provide values for
and
different from
those required for maximum gain
and
To simplify the analysis, a unilateral transistor is considered. For most
practical cases
transistor is very small, such that it behaves effectively
as unilateral, The error caused by unilateral approximation is given by:
where: U = unilateral figure of merit
The expression of the unilateral transducer gain, which has been proved
before, can be decomposed into three gain factors as follows:
Design of Specified Gain Amplifier Antenna
The expression of the unilateral transducer gain, which has been proved
before, can be decomposed into three gain factors as follows:
where:
,
source gain factor
constant gain factor
,
load gain factor
Design of Specified Gain Amplifier Antenna
Similar decomposition can be performed for the expression
of the maximum unilateral transducer gain:
where:
maximum source gain
maximum load gain
Design of Specified Gain Amplifier Antenna
Now, the normalized gain factors can be defined as follows:
normalized source gain factor
where
normalized load gain factor
where
=
Design of Specified Gain Amplifier Antenna
Matching Network
After the derivation of equations 26 and 27
we get
equation of the constant
where:
center of the constant
radius of the constant
circle in the
circle
circle
plane),
Design of Specified Gain Amplifier Antenna
Matching Network
Similar treatment of equation (27), yields the equation of the constant
gL circle in the ΓL plane:
(equation of the constant
where
center of the
circle in the
plane),
circle
c
constant radius of the
circle
Design of Specified Gain Amplifier Antenna
Matching Network
We then developed a Matlab program to the values of the
error and Cs , Rs , CL , and RL for the source and load
respectively.
The error was found to be the following.
GT
0.83 
 1.22
GTU
Using the Matlab program we found the values of Cs , Rs , CL , and RL and
marked them on smith chart to find the values of L and S
For the
gains 12, 10 and 8 db
Design of Specified
Gain Amplifier Antenna
Matching Network Gain of 12db
0.55~-147’
0.18143
L(series)=0.05λ
L(stub)=0.103λ
Design of Specified
Gain Amplifier Antenna
Matching Network Gain of 12db
0.3089~171’
0.23965
L(series)=0.146λ
L(stub)=0.024λ
Design of Specified Gain Amplifier Antenna
The 12db specified gain amplifier circuit is drawn in ADS. The design is shown
in the next figure.
Design of Specified Gain Amplifier Antenna
The simulation of the circuit shown above produces the following response that is shown
in the following figure.
14
m1
12
m1
freq= 15.00GHz
dB(S(2,1))=11.926
10
8
6
dB(S(2,1))
dB(S(1,1))
4
2
0
-2
-4
m2
freq=15.00GHz
dB(S(1,1))=-10.955
-6
-8
m2
-10
-12
14.0
14.2
14.4
14.6
14.8
15.0
15.2
15.4
15.6
15.8
16.0
freq, GHz
We can see from the curves shown above that at 15GHz the maximum gain is
11.926db and the reflection is below -10.955 db
Design of Specified Gain Amplifier Antenna
A layout of the circuit with the antenna is shown in the next figure.
Design of Specified
Gain Amplifier Antenna
Matching Network Gain of 10db
0.4693~-147’
0.3727
L(series)=0.07λ
L(stub)=0.027λ
Design of Specified
Gain Amplifier Antenna
Matching Network Gain of 10db
0.25062~171’
0.46974
L(series)=0.382λ
L(stub)=0.065λ
Design of Specified Gain Amplifier Antenna
The 10db specified gain amplifier circuit is drawn in ADS. The
design is shown in the next figure.
Design of Specified Gain Amplifier Antenna
The simulation of the circuit shown above produces the following response
that is shown in the following figure
12
m1
10
m1
freq=15.00GHz
dB(S(2,1))=10.057
8
6
dB(S(2,1))
dB(S(1,1))
4
2
0
-2
-4
m2
freq=15.00GHz
dB(S(1,1))=-5.705
m2
-6
-8
14.0
14.1
14.2
14.3 14.4
14.5
14.6
14.7
14.8 14.9
15.0
15.1
15.2
15.3 15.4
15.5
15.6
15.7
15.8
15.9 16.0
freq, GHz
We can see from the curves shown above that at 15GHz the maximum gain is
10.057db and the reflection is below -5.705 db.
Design of Specified Gain Amplifier Antenna
A layout of the circuit with the antenna is shown in the next figure.
Design of Specified
Gain Amplifier Antenna
Matching Network Gain of 8db
0.3948~-147’
0.49605
L(series)=0.325λ
L(stub)=0.032λ
Design of Specified
Gain Amplifier Antenna
Matching Network Gain of 8db
0.2025~171’
0.60041
L(series)=0.356λ
L(stub)=0.11λ
Design of Specified Gain Amplifier Antenna
The 8db specified gain amplifier circuit is drawn in ADS. The design is
shown in the next figure.
Design of Specified Gain Amplifier Antenna
The simulation of the circuit shown above produces the following response
that is shown in the following figure
10
m1
8
m1
freq=15.00GHz
dB(S(2,1))=8.167
6
dB(S(2,1))
dB(S(1,1))
4
2
0
m2
freq=15.00GHz
dB(S(1,1))=-3.831
-2
m2
-4
-6
14.0
14.2
14.4
14.6
14.8
15.0
15.2
15.4
15.6
15.8
16.0
freq, GHz
We can see from the curves shown above that at 15GHz the maximum
gain is 8.167db and the reflection is below -3.831 db.
Design of Specified Gain Amplifier Antenna
A layout of the circuit with the antenna is shown in the next figure.
Wilkinson Power divider
It has been demonstrated before that one way of increasing the bandwidth of
the amplifier is to design for less than the maximum gain. However, the return
loss of the reduced gain amplifier becomes relatively large even at the design
frequency. To overcomes the return loss problem, while maintaining the gain
flatness, a power divider circuit such as that shown below is used:
RS
ZL
Wilkinson Power divider
There have three type of power divider.
Wilkinson Power divider
Lossless T-Junction
Resistive T-Junction
Wilkinson Power divider
Type
Power Loss
Matching
Isolation
Lossless TJunction
lossless
matched at
input port only
no isolation
between output
ports
Resistive TJunction
lossy
matched at all
ports
no isolation
between output
ports
Wilkinson
Power
divider
lossless when
the output
ports are
matched
matched at all
ports
Perfect isolation
between output
ports
Wilkinson Power divider
λ /4
λ /4