0195136047.pdf

14 CIRCUIT CONCEPTS

vs

is

+

+

−

−

0

i

vs vs v is

is

(a)

i

+

−

0

i

v

(b)

v

Figure 1.1.6Circuit symbols andi–vcurves.(a)Ideal voltage source.(b)Ideal current source.

voltage or current does depend on the value of some other voltage or current. As an example, a

voltage amplifierproducing an output voltagevout=Avin, wherevinis the input voltage andAis

the constant-voltage amplification factor, is shown in Figure 1.1.7, along with its controlled-source

model using the diamond-shaped symbol. Current sources controlled by a current or voltage will

also be considered eventually.

Waveforms

We are often interested inwaveforms, which may not be constant in time. Of particular interest

is aperiodic waveform, which is atime-varying waveformrepeating itself over intervals of time

T>0.

f(t)=f(t±nT ) n= 1 , 2 , 3 ,··· (1.1.19)

The repetition timeTof the waveform is called theperiodof the waveform. For a waveform

to be periodic, it must continue indefinitely in time. The dc waveform of Figure 1.1.5(a) can be

considered to be periodic with an infinite period. Thefrequencyof a periodic waveform is the

reciprocal of its period,

f=

1

T

Hertz (Hz) (1.1.20)

A sinusoidal or cosinusoidal waveform is typically described by

f(t)=Asin(ωt+φ) (1.1.21)

whereAis the amplitude,φis the phase offset, andω= 2 πf = 2 π/Tis the radian frequency

of the wave. Whenφ=0, a sinusoidal wave results, and whenφ=90°, a cosinusoidal wave

results. Theaverage valueof a periodic waveform is the net positive area under the curve for one

period, divided by the period,

Fav=

1

T

∫T

0

f(t)dt (1.1.22)

+ +

− −

vin vout

(a)

Voltage

amplifier

+

+

−

−

Avin vout

(b)

Figure 1.1.7Voltage amplifier and its

controlled-source model.