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(ELEC101)tutorial03.pdf
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Fall 2006
ELEC101 BASIC ELECTRONICS



Outline

.Basic in Signal

CSignal Waveform Example

CPeriodic Waveforms

CExponential Waveforms

CSinusoidal Waveforms

CAverage Value

CEffect Value




Outline

.DC Circuits

CPrinciple of Superposition

CTheveninsTheorem

CNortons Theorem




Signal Waveform Example



Periodic Waveforms

The last four waveforms seen above are special cases of periodic waveforms. A waveform v(t) is periodic with period T if

Text Box: v(t) = v(t + nT) for all values of t, n: integer.

Exponential Waveforms

A is amplitude, is time constant



Example:
transient voltage and current in C and L circuit
=RC
vR(t) = vR(0) exp(-t/CR), e = 2.718



Exponential Waveforms

t =




Sinusoidal Waveforms

Vmis amplitude(maximum value)
Peak to peakvoltage (Vp-p) = 2Vm
is angular frequencyin radians per second (= 2f)
fis frequencyin Hertz (Hz = 1/second),
is phase anglein radians (2radians= 360o)



Sinusoidal Waveforms



Average Value

The average value of a periodic waveform v(t) with period T

For example,
(a) for v(t) = Vmcos t, Vav = 0


Text Box: (b) for
Text Box: = total area under v-t curve/time

Text Box: Vav


Effective Value

The effective value (Veff) or root mean square value (Vrms) of the periodic voltage is equal to the value of the DC voltage that will dissipate the same average power when applied across the same resistor. Some ammeters and voltmeters also give readings in rms



Effective Value

For example:
AC mains in HK = 220V means that
Vrms= 220V, VM = 2202 V,
and v(t) = 2202 sin (2 50t) V (or in cosform)



Useful Formulae



Principle of Superposition

Kill sources: replace independent V source by short circuit(as if V = 0V, V source is equal to a short circuit) , independent I source by open circuit(as if I = 0A, I source is equal to an open circuit).

The network can contain linear dependent V and I sourcesbut they can NOTbe killed.

Text Box: Network containing resistors, voltage and current sources ( resistive network) is a linear network

Linear Network and Superposition

A linear network possess superposition properties

Text Box: if y1(t) is the response (output) of the network to an input x1(t) and y2(t) is the response (output) to an input x2(t), then(1) response to input x1(t) + x2(t) is y1(t) + y2(t) (2) response to input ax1(t) is

Linear Network and Superposition

Example

6V

12V







Concept of Superposition



TheveninsTheorem

A linear (resistive) network, exclusive of the load, can be replaced by an equivalent network containing only an independent voltagein serieswith a resistor,in such a way that the I-Vcurve of the loadis unchanged.



TheveninsTheorem

To find RT


Text Box: where ISC = short circuit current,


Step 1 : Find the Theven