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What are Microwave Circuits

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Title: What are Microwave Circuits


1
What are Microwave Circuits
  • General Introduction
  • Said Mikki

2
Some Basic Definitions
  • Microwave Circuits Electrical circuits used at
    microwave frequencies for performing signal
    processing tasks like amplification, frequency
    conversion, mixing, detection, phase shifting,
    filtering, and power dividing.
  • Microwave Frequencies The EM spectrum that spans
    the range from 300 MHz to 300 GHz (wavelengths
    ranging from 1 m to 1 mm).
  • Microwave Engineering The main objective of
    microwave engineering is to develop simplified
    Lumped/Distributed-Element circuital models that
    are capable of predicting the performance of
    interest of the physical circuit. The generalized
    multi-port network theory is considered a chapter
    in the circuit theory of microwave systems.

3
Basic Classification
In general, an RF microwave system is a complex
module that contains a combination of passive and
active devices.
4
The Concept of Circuit
  • What is the meaning of circuit ?
  • Does the concept of circuit working in the
    microwave frequencies differ from the traditional
    concept of low-frequency circuits that we are all
    familiar with?
  • Circuits can be defined simply as
    interconnections of devices satisfying Kirchoffs
    Voltage low (KVL) and Kirchoffs Current Low
    (KCL).
  • Circuits are usually classified to Lumped-Element
    circuits and Distributed-Element Circuits. The
    definition above include both types.
  • What is the difference then between
    Lumped-Element Circuit Theory and
    Distributed-Element Circuit Theory? (Hint The
    operation frequency? How?)

5
Various Circuital Worlds
6
Maxwells Theory
  • The exact or the numerical full-wave solution
    leads to a complete description of the Microwave
    Circuits because all the six EM field components
    will be known in principle.
  • In general, a circuit model for an
    electromagnetic problem is a simplification of
    the original, usually complicated, problem. The
    circuit representation is a model that aims to
    describe only a finite number of quantities of
    interest like voltage, current, input impedance.
  • The consideration of other quantities requires
    improving the circuit model. This improvement
    needs knowledge that can be obtained only by
    means outside the scope of the circuit model
    itself, such as full-wave numerical solution or
    measurement.
  • Any circuit model that can convey all the
    information obtained through the full-wave
    solution is called Maxwellian Circuit.
  • The exact and rigorous procedure for obtaining
    such circuits is relatively new.

7
Basic Electromagnetic Solution Plane Waves
  • Propagation of EM waves can be fully described by
    the studying the plane wave
  • Mathematical basis for the above assumption is
    the 4-dimensional Fourier integral theorem.
    Arbitrary well-behaved functions can be written
    as expansion of plane waves summed over all
    possible values of the propagation vector k and
    the radian frequency ?.
  • The wavelength is given by

8
Lumped Elements
The Demarcation Criterion of Lumped/Distributed
Element Circuits
  • The effective size of the device p is very small
    compared to the wavelength

p
EM Wave
Lumped-Element Device
  • Thus, the device can not see the wave because
    the phase variations are negligible.

9
Distributed Elements
  • The maximum dimension of the device p is
    comparable with the wavelength
  • Thus, the device can see the wave because the
    phase variations are affecting now.

10
The Relation Between Circuit Theory and Maxwells
Theory
  • Unless the circuit is Maxwellian, that is,
    derived rigorously from a full-wave solution, the
    circuit model can not model exactly all the
    aspects of the performance of a microwave
    circuit.
  • Maxwells Theory implies or generates the
    distributed/lumped element circuit theory, but
    the opposite is NOT true.
  • Circuit Theory can describe special parameters of
    interest, like voltages, currents, input
    impedance, but they fail to predict the correct
    behavior under more complex conditions, like the
    radiation from discontinuity.
  • The circuit model is mode-dependent If other
    modes are excited in the physical waveguide, then
    the circuit model must be modified to take them
    into account (usually become much more
    complicated).
  • The microwave engineer must keep himself always
    alert to the relation between his circuit and the
    full EM solution. Approximations and
    simplifications can be made only if the
    implications are understood. Development of new
    circuit models nowadays must make reference to
    measurements or full-wave solution, at least in
    the development and validation phase of the model.

11
First Example Lumped-Element Circuit
Here, Kirchoffs Voltage Law fails to describe
the behavior of the circuit. For example, A
positive/negative resistance must be incorporated
with the receiving antenna device to correctly
describe the radiation loss/gain caused by the
antenna. Circuit Theory can not predict these
resistances. In other words, Circuit Theory can
not sense the interaction of a circuit with the
outside world.
12
Second Example Distributed-Element Circuit
  • The transmission line theory predicts that the
    received power for both lines are the same if the
    TL length and filling medium are identical.
  • This might not be correct because by introducing
    a bend (discontinuities), radiation losses occur
    at the discontinuity causing the two powers to
    be different.
  • Transmission line theory fails to predict
    radiation losses or higher order modes at
    discontinuities. These things must be found from
    full wave solution of Maxwells equations and
    then incorporated in the circuit model.

13
General Conclusions
  • Circuit Theory is mainly a topological theory.
    The impact of the geometrical details of the
    circuit which is the real distinguishing
    characteristics of microwave circuits can be
    predicted only if Maxwells equations are solved
    for the problem in hand.
  • However, the use of circuit models can
    considerably make the life of microwave engineers
    easier because we are interested most of the time
    in terminal quantities like voltages and
    currents, not in the total EM field every where
    in space.
  • With the availability of modern fast PC these
    days, the above philosophy is slightly
    challenged. It is relatively easy now to convert
    a circuit model schematics into a full-wave
    solution layout and conduct a full numerical
    solution of the original problem. This means that
    validation of the circuit models can be achieved
    almost online by synchronizing the schematics
    with the layout.
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