Maximum Gain Amplifiers For the twoport network shown

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 17 mm

Patch Antenna As a first step in our project we will design the passive patch antenna to operate at 15 GHz frequency. From the equations the length and width of the patch are calculated to be L= 5. 320 mm and W=6. 757 mm.

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

The imaginary part of gamma (γ) called (β) is plotted versus frequency in order to find the exact wavelength in the circuit It was found that at 15 GHz 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. (1. 2 W (left), 1. 1 W, 1. 0 W, 0. 9 W, and 0. 8 W (right))

Transistor: It is rated to work in the 2 -18 GHz 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 15 GHz it is specified to be as follows. 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 (15 GHz). K = 1. 0058 lΔl= 0. 18819

Maximum Gain For unconditionally stable amplifier, the maximum gain can be found using the following equation. Gmax=15. 21 d. B

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. reflection coefficient between transistor and the source Where reflection coefficient between transistor and the antenna Where

Design of Matching Network The equations were programmed in Matlab and produced the following values Rejected since >1 means active source accepted since <1 means passive source Rejected since >1 means active load accepted since >1 means active source

Design of Matching Network L(series)=0. 472λ L(stub)=0. 223λ

Design of Matching Network 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 We can see from the curves shown above that at 15 GHz the maximum gain is 15. 046 db 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 (12 db, 10 db and 8 db). 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 17 mm. 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 15 GHz was found to be Zin = 51. 709+j 2. 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. 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 , (plane

Design of Specified Gain Amplifier Antenna Matching Network Similar treatment of equation (27), yields the equation of the constant g. L 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. 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 For the and gains 12, 10 and 8 db

Design of Specified Gain Amplifier Antenna Matching Network Gain of 12 db 0. 55~-147’ 0. 18143 L(series)=0. 05λ L(stub)=0. 103λ

Design of Specified Gain Amplifier Antenna Matching Network Gain of 12 db 0. 3089~171’ 0. 23965 L(series)=0. 146λ L(stub)=0. 024λ

Design of Specified Gain Amplifier Antenna The 12 db 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. We can see from the curves shown above that at 15 GHz the maximum gain is 11. 926 db 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 10 db 0. 4693~-147’ 0. 3727 L(series)=0. 07λ L(stub)=0. 027λ

Design of Specified Gain Amplifier Antenna Matching Network Gain of 10 db 0. 25062~171’ 0. 46974 L(series)=0. 382λ L(stub)=0. 065λ

Design of Specified Gain Amplifier Antenna The 10 db 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 We can see from the curves shown above that at 15 GHz the maximum gain is 10. 057 db 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 8 db 0. 3948~-147’ 0. 49605 L(series)=0. 325λ L(stub)=0. 032λ

Design of Specified Gain Amplifier Antenna Matching Network Gain of 8 db 0. 2025~171’ 0. 60041 L(series)=0. 356λ L(stub)=0. 11λ

Design of Specified Gain Amplifier Antenna The 8 db 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 We can see from the curves shown above that at 15 GHz the maximum gain is 8. 167 db 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 at all ports Perfect isolation between output ports

Wilkinson Power divider λ /4