0195136047.pdf

(Joyce) #1

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.
Free download pdf