Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015 EE 1106 : Introduction to EE Freshman Practicum Lecture-Lab: Introduction to signals and systems,

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


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)


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


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


White Box Systems: Electrical

• Defined by Electro-Magnetic Laws of Physics: Ohm’s Law, Kirchoff’s Laws, Maxwell’s Equations

• Example: Resistor, Capacitor, Inductor


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


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


Energy in an Inductor

Stored Energy

Li

+ v -+ -

dip vi Li

dt pdt dw Li di

21

2W Lidi Li


Physics of a Capacitor

Plate separationdistance, g

Plate area, ACurrent, i, and

Charge, q.

Dielectric material ofpermittivity, .

Voltageacross

platesA

g

+v-

i, q


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


Energy in a Capacitor

Stored Energy:

C

i +v-

dvp vi Cv

dt pdt dw Cvdv

21

2W Cvdv Cv


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


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


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


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


RLC Circuit as a System

Kirchoff’s Voltage Law (KVL):


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


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


SYSTEM

INPUT

OUTPUT

INPUT


OUTPUT


SYSTEM

INPUT

OUTPUT

INPUT


OUTPUT


Integrator and Low Pass Filter from http://www.electronics-tutorials.ws/rc/rc_3.html


Differentiator and High Pass Filter from http://www.electronics-tutorials.ws/rc/rc_3.html


Lab 9 Circuits


Next Time: MSP 430, Bring Computer and Install Code Composer

24

Documents

Dan O. Popa, Intro to EE, Freshman Practicum, Spring 2015 EE 1106 : Introduction to EE Freshman Practicum Lecture-Lab: Introduction to signals and systems,