What Circuit Analysis Means. the Circuit World Is Wonderful. What You Will Visit and What


What Circuit Analysis Means. the Circuit World Is Wonderful. What You Will Visit and What

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.

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.
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.

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 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.

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.


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.

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.

12. 9Oct06