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1.
11Sep06
What Circuit Analysis means.
The circuit world is wonderful.
What you will visit and what you will learn.
Get introduced to concepts of circuit, graph, state, and dynamics.
Get introduced to two corresponding domains: time and frequency.
2.
12Sep06
Quantities involved in circuits.
Introduce current, charge, voltage, power.
Voltage is a potential difference.
Letters you should use to designate circuit quantities: i, q, u or v,
p
Review SI units: names and symbols.
Do not capitalize names, may look offensive
Why do you need pico and nano.
Why do you need giga and tera.
Notice the difference between k and K.
Symbols are not commutative.
Dots and parentheses are useful when you need exponents.
3.
14Sep06
Elements you use to make up simple resistive circuits.
Independent sources: voltage source and current source.
Dependent or controlled sources: four combinations.
A passive element: the resistor, resistance and conductance.
A law for resistance and conductance: Ohm’s law.
How you should choose directions for voltage and currents.
Choose the passive sign convention.
Power delivered by active devices and by passive devices.
Names you should learn: graph, direct graph, planar graph, node,
branch, loop, fundamental loop, mesh, tree, twig, cotree, link, cut
set, fundamental cut set.
There are some simple relationships between graph quantities.
All-important circuit laws: KVL and KCL (basic form).
Spell Kirchhoff right.
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Why are engineers always looking for nodes and for loops.
KCL and KVL also applies to other kinds of networks (hydro, goods,
transportation, power, forces).
The rationale of “when you add them up together the result is null”.
These simple equations have practical importance too.
4.
18Sep06
Nodal analysis: principles.
Recall KVL and Ohm’s law.
You need a reference node or datum.
A simple example: 4 nodes, 5 resistances, 2 independent current
sources.
Write down the equations.
Put them in matrix form like this G v  i
G v = i.
This matrix equation can be written just by inspection.
G is symmetric, diagonal dominant.
i is the rhs, thus is known as data.
v is the unknown, ie 3 voltages are unknown until you solve the
linear system.
Use v = G\i in Matlab
Note that v is a sufficient result, when you know v you also know
everything else.
Introduce now a voltage controlled current source.
The matrix G is no longer symmetric, is a sum of a symmetric matrix
with another one (asymmetric) due to the dependent source.
The rhs is still made up of independent sources.
Try now for a current controlled current source (instead of voltage
controlled).
5.
19Sep06
Nodal analysis: review.
Nodal analysis can also be used for circuits with voltage sources.
Both independent and dependent voltage sources can be used.
The dimension of the problem changes:
sometimes for less, by
inspection; or for more, in a general procedure.
A simple example: 4 nodes, 3 resistances, one independent voltage
source, one current controlled voltage source.
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The dimension is five by a general linear procedure, or one by a
shrewd inspection and an informal analysis.
Create another example with additional complexity by introducing an
extra branch.
Notice the independent source voltages on the rhs.
6.
21Sep06
Loop analysis: principles.
Guess a parallelism with nodal analysis -- duality.
Notice that KVL vs KCL, node voltages vs loop currents.
What are loop currents?
How can loop currents add up?
Is there another current law?
Do you need a reference node?
A simple example: 4 nodes, 5 resistances, 2 independent voltage
sources.
Now you have voltage sources where before you had current sources.
Recall loop, fundamental loop, mesh.
Write down the equations.
Put them in matrix form like this R i  v
G v = i.
This matrix equation can be written just by inspection.
R is symmetric, diagonal dominant.
v is the rhs, thus is known as data.
i is the unknown, ie the two loop currents are unknown until you
solve the linear system.
Use i = R\v in Matlab
Note that i is a sufficient result, when you know the loop currents
you also know everything else.
Introduce now dependent voltage sources: change the example.
What happens to matrix R?
Create now a complex example:
one independent voltage source, one
dependent voltage source, one independent current source, one
dependent current source.
Add four resistances in a four mesh
network.
Try to work this example out.
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7.
25Sep06
Loop analysis: review.
Consider again example from past class.
There are many ways to solve it.
One way is a general, systematic approach involving 4 eqs for the 4
KVLs, 4 eqs for the 4 resistances, and 4 eqs for the 4 sources.
This 12 eqs system can easily be written in an Ax=b format.
A and b are sparse.
Other ways to solve the problem consist of using some symbolic
manipulation or a smart inspection of the loops to choose.
A popular smart inspection is to run away from loops which include
current sources (whether independent or not).
This way you can solve the circuit with only 2 eqs on loop currents.
Consider now the all-important Superposition Principle.
A system is linear iff the Superposition Principle applies.
The name Superposition Principle is well picked.
See what it means.
Extend the concept and see that if the system is linear there is no
added value to team work -- the total result is just the sum of
individual results.
Often it is convenient to deal with all the sources together, but
sometimes you are better off dealing with a few of them separately.
Examples.
8.
26Sep06
Tricks for analyzing circuits by hand: use superposition principle
for handling sources and use special arrangements for passive
elements.
Series of resistances add up.
Parallel of conductances add up and write the corresponding formulas
for resistances.
Wye-delta (or star-triangle) configurations: where they appear and
when should you convert one into another.
Derive the conversion formulas.
Choose notation to make it easy to remember.
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9.
28Sep06
Join together all the tricks: superposition, series and parallel
associations, and wye-delta transformations, and couple them with the
supernode and superloop techniques.
Examples: three examples of nodal analysis based circuit with a
single equation, two examples of loop analysis with a single
equation, and one example of loop analysis with delta-wye transform.
10.
2Oct06
What is the concept of port or pair of terminals?
Why do you need ports?
Can you think of an equivalent circuit?
How would you proceed to
develop one?
Develop Thevenin’s and Norton’s equivalents.
Work some simple examples for Thevenin’s and for Norton’s theorems.
Work an example with dependent sources and apply Thevenin’s.
Use the definition of resistance for non-trivial problems.
Work a complex example: vT is sometimes difficult to compute and RT
is even more difficult.
11.
3Oct06
Review of Thevenin’s and Norton’s theorems.
Convert Thevenin’s into Norton’s and vice-versa.
What is reciprocity?
What is the mystery in exchanging the role of a voltage source and an
ammeter?
When does the reciprocity theorem hold?
What is the law of conservation of power?
Is current orthogonal to voltage?
What does that orthogonality mean?
Does orthogonality still hold for two different circuits, of for a
circuit at different instants of time?
What is Tellegen’s theorem?
Is Tellegen’s theorem valid for any kind of network, even for
nonlinear circuits?
What are adjoint circuits?
Do an example for Tellegen’s theorem.
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12.
9Oct06
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