EE 41139Microwave Technique*Transistor Amplifier Design

Transducer Gain and Stability

Design for Maximum Gain

Mixers

Microwave Technique

EE 41139Microwave Technique*Transducer Gain and Stability a single stage transistor amplifier with matching networks at the input and output terminals of the transistor is shown below:

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EE 41139Microwave Technique*Transducer Gain and Stability the reflection coefficient on the input side of the transistor is given by

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EE 41139Microwave Technique*Transducer Gain and Stability

similarly, the reflection coefficient on the output side of the transitor is given by

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EE 41139Microwave Technique*Transducer Gain and Stability we can define a transducer gain as the ratio of the power delivered to the load to the power available from the source

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EE 41139Microwave Technique*Transducer Gain and Stability

Microwave Technique

EE 41139Microwave Technique*Transducer Gain and Stability

the power available from the source is the maximum power that can be delivered to the network, i.e.,

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EE 41139Microwave Technique*Transducer Gain and Stability therefore, the transducer gain is given by

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EE 41139Microwave Technique*Transducer Gain and Stability

is the gain of the input matching network, is the gain of the amplifier and is the gain of the output matching network

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EE 41139Microwave Technique*Transducer Gain and Stability the transistor is said to be unilateral when = 0 or is very small, the unilateral transducer gain reduces to

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EE 41139Microwave Technique*Transducer Gain and Stability note that the overall gain is dictated by the gain due to the matching networks as well as the gain of the transistorthe network is said to be unconditionally stable if and for all passive source and load impedance

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EE 41139Microwave Technique*Transducer Gain and Stability Note that both and depends on and , respectivelywe need to find the range that these conditions are satisfied

and

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EE 41139Microwave Technique*Transducer Gain and Stability for a unilateral device, these conditions reduces to andlet us consider the first condition that

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EE 41139Microwave Technique*Transducer Gain and Stability

here D is the determinant of the scattering matrix

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EE 41139Microwave Technique*Transducer Gain and Stability if we square both sides of the above equation

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EE 41139Microwave Technique*Transducer Gain and Stability our goal here is to derive an expression for

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EE 41139Microwave Technique*Transducer Gain and Stability to simplify our discussion, let us consider the expression that

|a|2

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EE 41139Microwave Technique*Transducer Gain and Stability If we set , the above equation for can be written as

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EE 41139Microwave Technique*Transducer Gain and Stability

in deriving the above result, we make use of and

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EE 41139Microwave Technique*Transducer Gain and Stability the above equation written in the form represents a circle on a complex plane with the center at and a radius with similar result can be obtained for with the roles of and interchanged

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EE 41139Microwave Technique*Transducer Gain and Stability to check the stable region, let us consider the diagram below:

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EE 41139Microwave Technique*Transducer Gain and Stability

since we obtained the above circle at , the possible stable region is either outside or inside this circle with the additional constraint that

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EE 41139Microwave Technique*Transducer Gain and Stability

consider a matched load so that is zero which leads to If ,therefore , is in the stable condition

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EE 41139Microwave Technique*Transducer Gain and Stability therefore, the stable region is defined as the shaded region below:

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EE 41139Microwave Technique*Transducer Gain and Stability

on the other hand, if , it implies that and the point =0 is in the unstable region

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EE 41139Microwave Technique*Transducer Gain and Stability the stable region is therefore given by the shaded region below for

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EE 41139Microwave Technique*Transducer Gain and Stability similar discussions can be applied to the input stability circlemathematically, the amplifier will be unconditionally stable if the following necessary and sufficient conditions are met

and

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EE 41139Microwave Technique*Design for Maximum Gain (Conjugate Matching)

maximum power transfer from the input matching network to the transistor occurs when while the maximum power transfer from the transistor to the output matching network occurs at

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EE 41139Microwave Technique*Design for Maximum Gain (Conjugate Matching)

for a lossless matching sections, the maximum overall gain will be given by

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EE 41139Microwave Technique*Design for Maximum Gain (Conjugate Matching) we need to determine and ; for maximum power transfer, they are given by

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EE 41139Microwave Technique*Design for Maximum Gain (Conjugate Matching)

with the above expression, we can determine either or by first eliminating one of them

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EE 41139Microwave Technique*Design for Maximum Gain (Conjugate Matching) taking the complex conjugate of the second equation and substituting the result into the first equation, we obtain

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EE 41139Microwave Technique*Design for Maximum Gain (Conjugate Matching) The solution is

Where

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EE 41139Microwave Technique*Design for Maximum Gain (Conjugate Matching) For , the solutions are identical to those of except that the roles of and are interchanged for the unilateral case = * and = *

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EE 41139Microwave Technique*MixersA mixer uses the nonlinearity of a diode to generate an output spectrum consisting of the sum and difference frequencies of two input signals.In a receiver application, a low-level RF signal and an RF local oscillator (LO) signal are mixed together to produce an intermediate frequency (IF)

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EE 41139Microwave Technique*Mixers and a much higher frequency

the signal will pass through a low-pass filter to get rid of the higher frequency

down-conversion in a heterodyne receiver

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EE 41139Microwave Technique*Mixers

up-conversion in a transmitterthe IF signal usually has a frequency between 10 and 100 MHz, and can be amplified with a low-noise amplifer

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EE 41139Microwave Technique*Mixersthis is called a heterodyne receiver, and is useful because it has much better sensitivity and noise characteristics than the direct detection scheme

it also has the advantage of being able to tune over a band by simply changing the LO frequency, without the need for a high-gain, wideband RF amplifier

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EE 41139Microwave Technique*Balanced Mixer

a balanced mixer combines two or more identical single-ended mixers with a 3dB hybrid junction (90o or 180o) to give either better input SWR or better RF/LO isolation

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EE 41139Microwave Technique*Balanced Mixer the mixer circuit consists of two single-ended mixers with matched characteristics, driven with a 3dB coupler

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EE 41139Microwave Technique*Balanced Mixer consider that a small random noise voltage , vn(t), is superimposed on the local oscillator signal, the first order term of this noise voltage will be cancelled in this balanced mixer , ,

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EE 41139Microwave Technique*Balanced Mixer we have a 90o hybrid so that the voltages across the two diodes are

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EE 41139Microwave Technique*Balanced Mixer the V-I characteristic of the diode is given bynote that the quadratic term of the will give rise to the desire mixer product and the directions of Diode 1 and Diode 2 are reversed, we have

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EE 41139Microwave Technique*Balanced Mixer the diode currents, after passing through a low-pass filter, consist of a DC term, the noise term and the IF term:

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EE 41139Microwave Technique*Balanced Mixer

summing the two currents, we have

therefore, the first order term of the noise is eliminated

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EE 41139Microwave Technique*Tutorial 5Design a stop-band filter by incorporating a photonic bandgap structure on the microstrip line. The stop-band frequency is dictated by the periodicity of the PBG unit-cell. Be creative in generating the shape of the PBG. First check your design by simulations using Ensemble. Fabricate your design and compare your results with simulations.

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