Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015 EE Freshman Practicum Lecture-Lab: Introduction to signals and systems, RLC dynamical circuit
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
EE 1106: Introduction to EEFreshman Practicum
Lecture-Lab: Introduction to signals and systems, RLC dynamical circuit
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Signals and Systems
– Signal: • Any time dependent physical quantity• Constant – DC, Variable - AC• Electrical, Optical, Mechanical
– System:• Object in which input signals interact to
produce output signals.• Linear System has some have fundamental
properties that make it predictable: – Sinusoid in, sinusoid out of same frequency
(when transients settle)– Double the amplitude in, double the amplitude
out (when initial state conditions are zero)?
x(t)
u(t) y(t)
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
System Modeling
• Building mathematical models based on observed data, or other insight for the system.– Parametric models (analytical): ODE, PDE– Non-parametric models: graphical models -
plots, look-up cause-effect tables– Mental models – Driving a car and using the
cause-effect knowledge– Simulation models – Many interconnect
subroutines, objects in video game
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Types of Models
• White Box – derived from first principles laws: physical,
chemical, biological, economical, etc.– Examples: RLC circuits, MSD mechanical
models (electromechanical system models).
• Black Box – model is entirely derived from measured data– Example: regression (data fit)
• Gray Box – combination of the two
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
White Box Systems: Electrical
• Defined by Electro-Magnetic Laws of Physics: Ohm’s Law, Kirchoff’s Laws, Maxwell’s Equations
• Example: Resistor, Capacitor, Inductor
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Physics of an Inductor
Truncated hollow cylinder of permeability, area, A, andlength lm.
Coil ofN turns
Flux linkage,
Core flux,
Coil current, i
i+-
A
lmN
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Voltage Drop Across Inductor
Note Passive SignConvention
Li
+ v -+ -
2 2
m m
d d N Ai N A div
dt dt l l dt
2
m
N AL
l
di
v Ldt
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Energy in an Inductor
Stored Energy
Li
+ v -+ -
dip vi Li
dt pdt dw Li di
21
2W Lidi Li
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Physics of a Capacitor
Plate separationdistance, g
Plate area, ACurrent, i, and
Charge, q.
Dielectric material ofpermittivity, .
Voltageacross
platesA
g
+v-
i, q
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Physics of a Capacitor
Current:
Capacitance:
Note PassiveSign Convention:
C
i, q +v-
dq d Av A dvidt dt g g dt
A
Cg
dvi C
dt
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Energy in a Capacitor
Stored Energy:
C
i +v-
dvp vi Cv
dt pdt dw Cvdv
21
2W Cvdv Cv
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Inductors in SeriesL1 L2
+ v1 - + v2 -+ v -
i
1 2 1 2
di div v v L L
dt dt
1 2 eq
di div L L L
dt dt
1 2eqL L L
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Capacitors in Parallel
C1 C2
i1 i2
i
+v-
1 2 1 2
dv dvi i i C C
dt dt
1 2 eq
dv dvi C C C
dt dt 1 2eqC C C
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Inductors in Parallel
L1 L2
i
i1 i2+-
1 21 2 eq
i i iL L L
1 2
1 1 1
eqL L L
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Capacitors in Series
C1 C2
+ v1 - + v2 -
q q q
+ v -
1 21 2 eq
q q qv v v
C C C
1 2
1 1 1
eqC C C
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
RLC Circuit as a System
Kirchoff’s Voltage Law (KVL):
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
INPUT
SYSTEM
OUTPUT
RC Circuit as an Example of First order Linear Time Invariant System
from http://www.electronics-tutorials.ws/rc/rc_1.html with modifications
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
SYSTEM
INPUT
OUTPUT
INPUT
RC Circuit as an Example of First order Linear Time Invariant System from http://www.electronics-tutorials.ws/rc/rc_3.html with modifications
OUTPUT
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
SYSTEM
INPUT
OUTPUT
INPUT
RC Circuit as an Example of First order Linear Time Invariant System from http://www.electronics-tutorials.ws/rc/rc_3.html with modifications
OUTPUT
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
SYSTEM
INPUT
OUTPUT
INPUT
RC Circuit as an Example of First order Linear Time Invariant System from http://www.electronics-tutorials.ws/rc/rc_3.html with modifications
OUTPUT
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Integrator and Low Pass Filter from http://www.electronics-tutorials.ws/rc/rc_3.html
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Differentiator and High Pass Filter from http://www.electronics-tutorials.ws/rc/rc_3.html
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Lab 9 Circuits
Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015
Next Time: MSP 430, Bring Computer and Install Code Composer
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