Designing a Conjugate Match for a Microwave Amplifier

Dulce Castro University of Florida, Gainesville FL

Electrical and Computer Engineering Department

Abstract The basic concept of this document is to show how to match the input and output circuits of an amplifier using conjugate matching.

Introduction : An amplifier contains a source, input circuit, transistor, output circuit an and a load. To achieve the maximum gain possible for the amplifier Input/output matching circuit is essential to reduce the unwanted reflection of signal and to improve efficiency of the transmission from source to load [1][2]. In order to increase maximum power obtained from the amplifier conjugate matching of both the input and output circuit is required

I. S-PARAMETERS AND REFLECTION COEFFICIENTS A microwave amplifiers transistor can be seen as a two

port system. A linear two-port network is connected to a voltage source which creates incident and reflective waves shown in Fig 1. A port is defined as any place where voltage and current can be delivered or received. S21 represents reflected power with port 1 as an input and port 2 as an output.

Figure 1: Two port network

The scattering matrix as shown in Fig 2 relates the outgoing waves b1, b2 to the incoming waves a1, a2. The matrix elements S11, S12, S21 and S22 are referred to as the (S-Parameters)

Figure 2: Matrix Elements

The traveling waves can be expressed in as voltages and currents in terms of the wave variables. In order to get some power out of this circuit we need to add a generator (voltage source VG) and a load as seen in Fig 3.

Figure 3: Two port Generator and Load

When the two-port is connected to a generator and load as in Fig. 3, the s-parameter matrix simplify to:

Zin is the input impedance at port 1, ZL is the load impedance. L and in are the reflection coefficients at port 1 and at the load.

II. TIME AVERAGED POWER In order to computer the operating, available and

transducer power gain four different time averaged power quantities must be calculated. The power gains of the two-port can be inferred by analyzing the power into and out of the ports. Pin is the power going into the two-port network from the generator. PL is the power coming out of the two-port network into the load.

A. Time averaged power from the source are all reflection coefficients seen in Figure 4.

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B. Time averaged power delivered to the load C. Maximum available power from the source to the

amplifier circuit

Occurs when input impedance is conjugated matched with source impedance Zin = Zs* and

D. Maximum available power from the amplifier circuit to the source

Occurs when output impedance is conjugated matched with load impedance ZL = Zout* and

III. OPERATING POWER GAIN The power gains of 2-port circuit network with defined as Pin power impedance or PL at an represented with scattering coefficient are classified into Operating Power Gain, Transducer Power Gain and Available Power Gain.

A. Operating Power gain Is the ratio of power (PL) delivered to the load (Z L ) to power (P in ) supplied to 2-port network. Therefore, Operating Power Gain is represented by

GP is the maximum linear output power in an amplifier indicates reflection coefficient of load at the input port of 2-port network and is reflection coefficient of power supplied to the input port

B. Transducer Power Gain Transducer Power Gain is the ratio of, maximum power available from source to , power delivered to the load .

Conjugate Matching: As maximum power is obtained when of circuit network is equal to conjugate complex number of power impedance, if in = , transducer power gain is represented by

GT is simultaneously conjugate matched input and output ports which leads to the maximum linear gain. is the load reflection coefficient.

C. Available Power Gain

The available power gain is the ratio of the power dissipated in the load to the maximum available average power from the source [ ]

IV. EXAMPLE

The input and output networks s parameters are shown below . They are designed to produce and Find Gp, Ga and GT given the following S-parameters

Step 1: Find the input and output reflection coefficients

Step 2: Find Gp, Ga and Gt = 9.44 [ ]

Figure 4: Input and Output Reflection Coefficients

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REFERENCES [1] G. Eason, B. Noble, and I. N. Sneddon, On certain integrals

of Lipschitz-Hankel type involving products of Bessel functions, Phil. Trans. Roy. Soc. London, vol. A247, pp. 529551, April 1955.

[2] K. Whites Lecture 33 Active Microwave circuits : Two port power gains EE481

[3] Edwin C, Becerra Alvarez, Jose M.de la Rose and Federico Sandoval. Design of a 1V 90-nm CMOS Folded Cascode LNA for Multi-Standerd Application. IEEE Proceeding 2010.

[4] Ruey-Lue Wang, Shih-Chih Chen, Cheng-Lin Huang, Chien- Hsuan Lie,Yi-Shu Lin. "2-6GHz Current-Reused LNA With Transformer-type Inductors." IEEE Proceeding 2008.

[5] Leon, Michael Angelo G.Lorenzo and Maria Theresa G.De. "Comparison of LNA Topology for Wimax Application in a Standard 90-nm CMOS Process." 12th International Conference