maximum gain amplifiers for the two-port network shown below, it is well known that maximum power...

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.

14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.814.0 16.0

-30

-25

-20

-15

-10

-5

-35

0

freq, GHz

dB(S

(1,1

))dB

(S_Z

0(1,

1))

The input impedance of antenna at 15GHz is found by plotting the real and imaginary values of Zin

m3freq=real(Zin)=51.709

15.00GHz

m4freq=imag(Zin)=2.267

15.00GHz

14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.814.0 16.0

-40

-20

0

20

40

60

-60

80

freq, GHz

real

(Zin

)

Readout

m3

imag

(Zin

)

Readout

m4

The imaginary part of gamma (γ) called (β) is plotted versus frequency in order to find the exact wavelength in the circuit

m2freq=imag(GAMMA(1))=519.016

15.00GHz

14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.814.0 16.0

490

500

510

520

530

540

550

480

560

freq, GHz

imag

(GA

MM

A(1

))

Readout

m2

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.

14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.814.0 16.0

-30

-25

-20

-15

-10

-5

-35

0

freq, GHz

dB(a

nten

naw

idth

_mom

_a..S

(1,1

))dB

(ant

enna

10w

idth

_mom

_a..S

(1,1

))dB

(ant

enna

20w

idth

_mom

_a..S

(1,1

))dB

(ant

enna

wid

th3_

mom

_a..S

(1,1

))dB

(ant

enna

wid

th4_

mom

_a..S

(1,1

))

(1.2W (left), 1.1W, 1.0W, 0.9W, and 0.8W (right))

It is rated to work in the 2-18GHz frequency range. The response of the S-Parameter for the transistor within the range 14 – 16 GHz are shown below

Transistor:

3.285

3.29

3.295

3.3

3.305

3.31

3.315

3.32

13.51414.51515.51616.5

Frq

S21

0.565

0.57

0.575

0.58

0.585

0.59

0.595

0.6

0.605

13.51414.51515.51616.5

Frq

S11

0.08650.0870.08750.0880.08850.0890.08950.090.09050.0910.0915

13.51414.51515.51616.5

Frq

S12

0.3050.310.3150.320.3250.330.3350.340.3450.350.355

13.51414.51515.51616.5

Frq

S22

the S-parameters matrix of the transistor is different for different frequencies. At 15GHz it is specified to be as follows.

oo

oo

S

17133.024296.3

39089.014758.0

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).

oo

oo

S

17133.024296.3

39089.014758.0

K = 1.0058

lΔl= 0.18819

Maximum Gain

For unconditionally stable amplifier, the maximum gain can be found using the following equation.

12

12

21max KK

S

SG

Gmax=15.21dB

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.

sreflection coefficient between transistor and the source

Lreflection coefficient between transistor and the antenna

1

2

12

11

2

4

C

CBBS

Where

22

22

2

111 1 SSB

22111 SSC

2

2

2222

2

4

C

CBBL

Where

22

11

2

222 1 SSB

11222 SSC

The equations were programmed in Matlab and produced the following values

oS 1253.1410548.1


oS 1253.14194806.0

oL 0453.1720902.1

oL 0453.17291723.0

Rejected since >1 means active sources

accepted since <1 means passive source

Rejected since >1 means active load

accepted since >1 means active source

s

L

L


oS 1253.14194806.0

L(series)=0.472λ

L(stub)=0.223λ

oL 0453.17291723.0

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.

DA_MLine1_Max_Gain#2DA_MLine1

Lelec=0.472Lphys=0 mmZo=50 OhmF=15 GHzSubst="MSub1"







S2P_EqnS2P1

Z[2]=50Z[1]=50S[2,2]=-0.325-j*0.051S[2,1]=3.011-j*1.34S[1,2]=0.069-j*0.056S[1,1]=-0.486+j*0.315

S_ParamSP1

Step=10 MHzStop=16 GHzStart=14 GHz

S-PARAMETERS MSUBMSub1

Rough=0 mmTanD=0T=0 mmHu=1.0e+033 mmCond=1E+50Mur=1Er=3.38H=0.406 mm

MSub

TermTerm2

Z=51.7+j*2.26 OhmNum=2

TermTerm1

Z=50 OhmNum=1

m1freq=dB(S(1,1))=-40.470

15.00GHz

m2freq=dB(S(2,1))=15.046

15.00GHz

m1freq=dB(S(1,1))=-40.470

15.00GHz

m2freq=dB(S(2,1))=15.046

15.00GHz

14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.814.0 16.0

-40

-30

-20

-10

0

10

-50

20

freq, GHz

dB(S

(1,1

))

Readout

m1

dB(S

(2,1

))

Readout

m2

Maximum Gain Amplifier

We can see from the curves shown above that at 15GHz the maximum gain is 15.046db and the reflection is below -40 db.

A layout of the circuit with the antenna is shown in the next figure.

Maximum Gain Amplifier Layout

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.

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.

laminate Specifications

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.

Patch Antenna


Transistor:

The same transistor that was used in the maximum design antenna is used for the design of the specified gain active antenna.

oo

oo

S

17133.024296.3

39089.014758.0

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.


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:


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


Similar decomposition can be performed for the expression of the maximum unilateral transducer gain:

where:

maximum source gain

maximum load gain


Now, the normalized gain factors can be defined as follows:

normalized source gain factor =

where

normalized load gain factor

where

Matching Network


After the derivation of equations 26 and 27 we get

equation of the constant circle in the plane ,(

where: center of the constant circle

radius of the constant circle

Similar treatment of equation (27), yields the equation of the constant gL circle in the ΓL plane:


Matching Network

)equation of the constant circle in the plane,(

where

c center of the circle

constant radius of the circle


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 .

22.183.0 TU

T

G

G

SUsing the Matlab program we found the values of Cs , Rs , CL , and RL and marked them on smith chart to find the values of For the gains 12, 10 and 8 db

and L


Matching Network Gain of 12db

L(series)=0.05λ

L(stub)=0.103λ

0.18143

0.55-~147’



L(series)=0.146λ

L(stub)=0.024λ

0.23965

0.3089~171’


The 12db specified gain amplifier circuit is drawn in ADS. The design is shown in the next figure.

DA_MLine1_EE499G12DA_MLine1








MSUBMSub1

Rough=0 mmTanD=0T=0 mmHu=1.0e+033 mmCond=1.0E+50Mur=1Er=3.38H=0.406 mm

MSub

S_ParamSP1


S-PARAMETERS

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=51.7+j*2.26 OhmNum=2

S2P_EqnS2P1

Z[2]=50Z[1]=50S[2,2]=-0.325-j*0.051S[2,1]=3.011-j*1.34S[1,2]=0S[1,1]=-0.486+j*0.315

The simulation of the circuit shown above produces the following response that is shown in the following figure.

m2freq=dB(S(1,1))=-10.955

15.00GHz

m1freq=dB(S(2,1))=11.926

15.00GHz

14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.814.0 16.0

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

-12

14

freq, GHz

dB(S

(1,1

))

Readout

m2

dB(S

(2,1

))

Readout

m1


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


A layout of the circuit with the antenna is shown in the next figure .



L(series)=0.07λ

L(stub)=0.027λ

0.3727

0.4693-~147’



L(series)=0.382λ

L(stub)=0.065λ

0.46974

0.25062~171’











S2P_EqnS2P1

Z[2]=50Z[1]=50S[2,2]=-0.325-j*0.051S[2,1]=3.011-j*1.34S[1,2]=0S[1,1]=-0.486+j*0.315

MSUBMSub1


MSub

S_ParamSP1


S-PARAMETERS

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=51.7+j*2.26 OhmNum=2

The simulation of the circuit shown above produces the following response that is shown in the following figure


m2freq=dB(S(1,1))=-5.705

15.00GHz

m1freq=dB(S(2,1))=10.057

15.00GHz

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 15.914.0 16.0

-6

-4

-2

0

2

4

6

8

10

-8

12

freq, GHz

dB

(S(1

,1))

Readout

m2

dB

(S(2

,1))

Readout

m1

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.



L(series)=0.325λ

L(stub)=0.032λ

0.49605

0.3948-~147’



L(series)=0.356λ

L(stub)=0.11λ

0.60041

0.2025~171’











S2P_EqnS2P1

Z[2]=50Z[1]=50S[2,2]=-0.325-j*0.051S[2,1]=3.011-j*1.34S[1,2]=0S[1,1]=-0.486+j*0.315

MSUBMSub1


MSub

S_ParamSP1


S-PARAMETERS

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=51.7+j*2.26 OhmNum=2


The simulation of the circuit shown above produces the following response that is shown in the following figure

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.

m2freq=dB(S(1,1))=-3.831

15.00GHz

m1freq=dB(S(2,1))=8.167

15.00GHz

14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.814.0 16.0

-4

-2

0

2

4

6

8

-6

10

freq, GHz

dB(S

(1,1

))

Readout

m2

dB(S

(2,1

))

Readout

m1

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

There have three type of power divider.

Wilkinson Power divider Lossless T-Junction Resistive T-Junction


Type Power Loss Matching Isolation

Lossless T-Junction

lossless matched at input port only

no isolation between output

ports

Resistive T-Junction

lossy matched at all ports

no isolation between output

ports


lossless when the output ports are matched

matched at all ports

Perfect isolation between output

ports



λ /4

λ /4

maximum gain amplifiers for the two-port network shown below, it is well known that maximum power...

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