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.