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MatLab can be a useful tool in many
applications. |
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We will learn how to analyze a simple electrical
circuit, set the problem up as N equations in N unknowns, and transform the
equations into a matrix formulation that MatLab can solve. |
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Electrical Devices. |
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Kirchhoff’s Laws. |
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Analyzing a Resistor Network. |
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Inverting Matrices. |
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A MatLab Solution. |
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Voltage and Current. |
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Sources. |
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Resistors: Ohms Law. |
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Capacitors: Charge Storage. |
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Inductors: Current Storage. |
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Voltage - the force that pushes electrical
current around a circuit.
(Sometimes called “potential” as in potential energy.) |
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Current - the flow of electrical charge through
a conductor. (Electrons flow
backwards) |
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Conductor - the “pipe” through which an
electrical current flows. |
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Voltage Source: Fixed Voltage waveform |
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Direct Current: A battery |
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Alternating Current: A generator (sine waves) |
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Current Source: Fixed current waveform (AC or
DC) |
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A constriction in the flow of current |
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Analogous to a small orifice in a water pipe, it
takes a high pressure (voltage) to force a flow of water (current) through
the resistance. |
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Ohm’s Law
V=I*R |
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0 - Black |
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1 - Brown |
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2 - Red |
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3 - Orange |
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4 - Yellow |
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A charge storage device |
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Analogous to a water tank that is filled from
the bottom. As the water level
rises (charge divided by the cross sectional area – capacitance), the
pressure (voltage) rises. |
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Capacitor Law
V=Q/C |
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A current storage device |
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Analogous to the inertial effect of the flow of
a fluid. The inductance is the mass
that is moving. |
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Inductor Law
V=L*dI/dt (dI/dt is the “rate of
change”
in the current.
This is analogous
to velocity.) |
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Conservation of Current:
The sum of all currents into a “node” equals zero. |
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Loop Law:
The sum of all voltages around a loop equals zero. |
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Multimeter (Analog and Digital) |
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Voltage - measured relative to a reference,
usually electrical ground. |
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Resistance - meter puts a small current through
the resistor and uses Ohm’s law. |
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Current - careful, the meter can be destroyed by
an over-current. |
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Establish Independent Loop Currents |
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Write Equation for Each Loop |
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Determine voltages in terms of the loop
currents. |
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Sum to zero |
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(note: Alternative, use a set of “Node”
equations) |
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9v = 15k*(I1-I2) + 1k*(I1-I3) |
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0 = 10k*I2 + 15k*(I2-I1)
+ 15k*(I2-I3) |
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0 = 1k*(I3-I1) + 15k*(I3-I2)
+ 3.3k*I3 |
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9v = 16k*I1 - 15k*I2 -
1k*I3 |
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0 =
-15k*I1 + 40k*I2 - 15k*I3 |
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0 = -1k*I1 - 15k*I2 + 19.3k*I3 |
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Rewrite, ordering variables |
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Formulate equivalent as an input column vector
equals a coefficient matrix times an “unknowns” vector |
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Solution: pre-multiply both sides by the inverse
of the coefficient matrix. |
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9v
16k -15k -1k I1 |
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0 =
-15k 40k -15k * I2 |
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0
-1k -15k 19.3k I3 |
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The inverse of a square matrix is that matrix
which, when multiplied by the original matrix yields the Identity matrix |
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In MatLab use “inv()”. |
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I1
0.1396 0.0777
0.0676 9 |
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I2
= 0.0777
0.0785 0.0651 *
0 *10-3 |
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I3 0.0676
0.0651 0.1059 0 |
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I1
1.256 |
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I2
= 0.6992 * 10-3 amps |
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I3 0.6085 |
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Originally from Microsim, now part of OrCad. |
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Demo/student CDROM is free at www.orcad.com,
current version is 9.2, Limited to small circuits and part library. |
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Graphical simulation of circuits and automated
Printed Circuit board layout. |
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Notes