FULL TEXT

We will study:

Basic knowledge for every explorer in the electronics domain

Revision of some notions and knowledge

Terminology, conventions and notations

FUNDAMENTALS

Objective

To be armed with appropriate meansand working instruments to understand:

the operating principle of the electronicdevices and their basic applications

the operation of some fundamental circuits

Electrical signals

Time variation of a:

a) continous voltage (dc); b) sinusoidal voltage (ac)

Amplitude: A=3V; Peak to peak value: 6V; Root-mean-square (rms) value of the signal

Period T=2ms; Average value, or the dc component (zero); Instantaneous value, at t=T/4 the instantaneous

value is +3V.

V12.22

AVrms

Sinusoidal voltage

SourcesNotations

only continuous signal (dc value) VS, IS ; only time-varying signal vs, is;

total instantaneous signal (continuous plus time-varying

component) vS , iS

Relations, laws and theorems of electric circuits

Ohms law

V=RI

V= - RI

V

IR mA5;k2.2

Kirchhoffs lawKirchhoffs first law or Kirchhoffs current law (KCL)

I1+I2-I3=0

Kirchhoffs second law or Kirchhoffs voltage law (KVL):

-V1+VR1+V2-VR2=0 02211 IRVIRV

Resistor connections

Series connection

Parallel connection

RRR 21

parallelech

seriesech

R

R

,

,

;k1;k100 21 RR

parallelech

seriesech

R

R

,

,

Resistive dividers

IO vRR

Rv

21

2

iRR

Ri

21

21

iRR

Ri

21

12

Adjustable divider in the range [0.5;1]

Voltage divider

Current divider

Superposition effect method

V0 = V01+V02

Valid only for linear circuits

Capacitor and inductor

Current - voltage relation

Series and parallel connection

dc behavior

ac behavior

C in the time domain

CiC

vC

Defining relation between current and voltage

dttitCdv CC )()(

Considering finite variations:

tivC CC

time constant of the circuit

)()1()0()(

C

tt

CC veevtv

dttitCdv CC )()(

tvtvtRi ICC )(

tvtv

dt

tdvRC IC

C

dt

tdvCti CC

)()(

RC

vI

RC circuit time domain analysis

RC circuit with voltage source

RC circuit time domain analysis

RC circuit with dc voltage source

)()1()0()(

C

tt

CC veevtv

RCVvv ICC ;)(;0)0(

)0(Cv

)(tvC)(Cv

Example

R=5k, C=100nF.

At the initial time moment the capacitor has 0V voltage drop. The input

voltage is VI1=9V for the first 5ms, then it becomes VI2=-5V for the

next 1ms.

a) How does the time variations (waveforms) of the voltage and

current for the capacitor look like?

b) What are the final values of the voltage and current for the

capacitor?

c) What would be the final values of current and voltage for the

capacitor if the capacitor would have the value of C=22nF?

?)( tvO

)()1()0()(

O

tt

OO veevtv

RC circuit with rectangular voltage source

Results

obtained by

simulation

18 /1925

T

10;

25

TT

19 /19

A

A

B

B

T Computes the average value of the input voltage

Charging up a C with a constant current

dttitCdv cc

)0()(1

)(0

C

t

CC vdttiC

tv )0(1

)( CC vItC

tv

Reactive components in ac regim (frequency domain)

inductancefor ;X

capacitorfor ;1

L L

CXC

Reactance

Impedance CL XXjRZ

LLCC jXRZ;jXRZ

LjZ;Cj

1Zc L

Impedances of ideal reactive elements

Tf

22

What are the equivalent of C and L in dc (after the transient regime ?)