Title: What are Microwave Circuits
1What are Microwave Circuits
- General Introduction
- Said Mikki
2Some 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.
3Basic Classification
In general, an RF microwave system is a complex
module that contains a combination of passive and
active devices.
4The 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?)
5Various Circuital Worlds
6Maxwells 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.
7Basic 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
8Lumped 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.
9Distributed 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.
10The 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.
11First 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.
12Second 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.
13General 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.