Circuits Review

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Circuits Review
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Analog Circuit Review
DC Circuits constant currents and
voltages AC Circuits time-varying currents
and voltages whose time-average values are zero
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DC Circuits Principles
Current Free electrons moving along field lines
in a material due to an external macroscopic
electric field.
dq quantity of positive charge crossing a
specified surface in a time dt. Unit of q is the
coulomb, unit of t is seconds Unit of I is the
ampere (1 coulomb per second)
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DC Circuits Principles
Electrostatic Potential the amount of energy
available to move charge. The change in potential
across a distance dr in an electric field E is
given by
E is the field strength, dr is the distance
The change in potential energy U of a charge q is
related directly to the change in its electric
potential V by
Therefor, units of potential must be in energy
per unit of charge. Unit of V is the Volt, V.
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DC Circuits Principles
The change in potential across some macroscopic
object always represents the difference between
two potentials (generally, one of these
potentials is ground, 0V by convention)
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DC Circuits Principles
Ohms Law
This linear relation holds for most materials
(not semiconductors).
R is the resistance of a circuit element unit is
the ohm, ?. It is a function of both the
material and the shape of the device.
?, resistivity of the material, ohm-meters L,
length of the material, meters A,
cross-sectional area of the material, meter2
? changes with temperature (? with T in most
metals, ? with T in carbon, silicon), as well as
with the applied voltage and current
(semiconductors).
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DC Circuits Principles
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DC Circuits Principles
Circuit Terminology Element a resistance (more
generally, an impedance) or an EMF Point
anywhere along the ideal conductors connecting
elements is the same point Node a point where
three or more current-carrying elements are
connected Branch one element or several in
series connecting two adjacent nodes Interior
loop a circuit loop that is not subdivided by a
branch
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DC Circuits Principles
EMFs put energy into the electronic system, and
resistors remove it by conversion to heat (random
motion of electrons in the material). All
circuit elements have a non-zero resistance (with
the exception of superconductors). The inverse
of resistance is conductance, C 1/R, with units
of mhos or siemens. Variable resistors are
devices which allow the amount of resistive
material between the device terminals to be
varied by rotating or sliding a contact.
Types of variable resistors sliders potentiomet
ers trimmers
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DC Circuits Principles
Power in DC Circuits
Unit watts, W
(Power dissipated by a resistor)
(Resistors are rated according to their power
dissipation)
Series Resistance
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DC Circuits Principles
Parallel Resistance
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DC Circuits Principles
Circuit simplification using series and parallel
equivalent circuits
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DC Circuits Principles
The Voltage / Current Divider
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DC Circuits Principles
Circuit Simplification Using Equivalent Circuits
A two-terminal, linear, DC circuit composed of
any combination of voltage sources, current
sources, and resistors can be replaced with an
equivalent circuit composed of an ideal voltage
source and a series resistor (Thevenin equivalent
circuit) or an ideal current source and a
parallel resistor (Norton equivalent circuit)
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DC Circuits Principles
Determination of the Thevenin and Norton Circuit
Elements Step 1 Thevenin Calculate the
open-circuit voltage, VAB. This voltage is
VTh. Norton Calculate the short-circuit
current through an imagined shorting wire
between A and B. This current is IN. Step
2 Both Determine both VTh and IN from step 1
and divide the first by the second to get the
equivalent resistance.
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DC Circuits Principles
Measurement considerations
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AC Circuit Principles
With time varying currents, we must consider
variations in the energy stored in the electric
field associated with every potential difference,
and the magnetic field generated by every
current.
Capacitance ability to store energy in an
electric field, unit farad (resists fast
changes in voltage) Inductance ability to
store energy in a magnetic field, unit
henry (resists fast changes in current)
These field energies are present in all circuit
elements, but can often be ignored, except, of
course, in elements designed to exploit them.
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AC Circuit Principles
Capacitor a device designed to exhibit
capacitance, generally modeled as two parallel
plates separated by a dielectric
material. Regardless of the configuration,
Q magnitude of charge distributed on either
surface V potential difference between the
surfaces C capacitance, in farads, F (commonly
?F or pF)
An ideal capacitance is constant, dependent only
on the physical configuration of the materials,
and not a function of V or Q.
? is the dielectric constant of the
dielectric material ?0 is the permittivity of
free space A is the area of a plate d is the
plate separation
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AC Circuit Principles
Capacitors serve four principle functions in
electronic circuits 1) Because it can store
charge and energy, a capacitor can be used as a
non-ideal source of current or voltage. 2)
Since it will pass AC but not DC current, a
capacitor can be used to connect parts of a
circuit that must operate at different DC
voltages. 3) When used in combination with a
resistor that limits the current, a capacitor
will smooth the sharp edges from a voltage
signal. 4) When charged or discharged by a
constant current, a capacitor will develop a
voltage signal with a constant slope.
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AC Circuit Principles
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AC Circuit Principles
The RC circuit
1) Initially, capacitor charged with Q0 on top
plate, and -Q0 on bottom plate. At t 0, the
voltage across the charged capacitor is
2) For t gt 0, charge flows off the capacitor,
causing the voltage across the capacitor and the
loop current to decrease with time.
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AC Circuit Principles
The product RC is called the time constant of the
system, and will have units of seconds if R is in
ohms and C is in farads. It defines the time
required for V(t) to fall to 1/e of its initial
value.
Physical analogs (e.g. flow in a
vein) potential difference - pressure
difference between two points along
vein current - rate of flow of
blood resistance - friction along the walls of
the vein, viscosity of blood capacitance -
energy stored as the walls of the vein stretch or
the blood is compressed
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AC Circuit Principles
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AC Circuit Principles
Inductor a device designed to exhibit
inductance, generally modeled as a coil of wire
(solenoid). By Faradays law of self-inductance,
a changing current in a circuit induces a back
EMF in the circuit that opposes the change. The
multiple loops of the solenoidal inductor
concentrate the effect so that most of the back
EMF appears across its terminals.
L inductance ?m magnetic flux I current ?0
permeability of free space 4? x 10-7 H/m n
N/l A area of a single loop l the total
length of the inductor N total number of turns
Sensor Application LVDT
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AC Circuit Principles
Ideally, the inductance is determined by the
physical configuration of materials, and is not a
function of either V or I. Unit the henry, H.
In many ways, the inductor is the electronic
opposite of the capacitor No voltage drop
appears across its terminals when a DC signal is
applied For a given applied voltage, it acts
to limit the rate of change of the current (a
larger inductor produces a smaller dI/dt)
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AC Circuit Principles
The inductance defines the relationship between
the back EMF and the change in current through
the inductor.
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AC Circuit Principles
Actual inductors are far from ideal - the coil is
formed from a long length of wire with adjacent
loops separated by a thin layer of insulating
varnish the resulting inductor will generally
have a significant series resistance and a
troublesome parallel capacitance
The physical geometry of a circuit should
minimize stray inductance.
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AC Circuit Principles
The LCR circuit
(Physical analogs to resistance, capacitance
inductance allow second-order physical systems to
be modeled with electrical components.)
(From Kirchoffs Laws)
Solution to the differential equation takes three
forms, dependant on the relationship between the
relative values of R, L and C.
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AC Circuit Principles
R2 lt 4L/C, underdamped R2 gt 4L/C,
overdamped R2 4L/C, critically damped
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