Download LECTURE 4

Function Generators
FUNCTION GENERATORS
 Function generators, which are very important and versatile
instruments. provide a variety of output waveforms over a
wide frequency range.
 The most common output waveforms are sine, square,
triangular, ramp. and pulse. The frequency range generally
extends from a fraction of a hertz to at least several hundred
kilohertz.
 Since a function generator provides sine, square, and
triangular wave outputs, any of these may be the primary
waveform generated by the instrument. This primary
waveform can then be applied to the proper circuitry to
generate the remaining waveforms.
 For example, the primary waveform may be a sine wave
generated with the RC or LC oscillator circuit.
However, because of difficulties with amplitude and
frequency stability, particularly at very low frequencies,
oscillators with a sine wave as the primary output are
generally not used.
 Figure 1-9 shows a schematic diagram of one of several
alternative approaches that can be used in a basic function
generator. The primary waveform in the circuit shown is a
square wave.
Fig. 1-9 Circuit for a basic function generator.
 This waveform is chosen because some circuits generating
square waves are simpler and offer significantly better
amplitude and frequency stability than do circuits generating
sine waves.
 The first stage, A1, which is a voltage comparator, generates a
square wave output. The output of A1 is driven to saturation;
therefore, the square wave is either at +Vcc or -Vcc.
 The second stage, A2 is an integrator which generates a
triangular output. The square wave is applied to a square-tosine wave converter that filters out the odd harmonics
making u the square wave while passing on only the
fundamental sine wave.
 The operation of the circuit can be analyzed by starting at the
output of the comparator, which la at either +Vcc or -Vcc.
ConsiderV01 to be at –Vcc.
 The voltage V01 will remain at -Vcc until the voltage at the
inverting input of A, exceeds the voltage at the noninverting
input, which in this case is at zero volts. The noninverting
input voltage. Vx, is due, in par, to the voltage V01 and, in
part, to the voltage V02, according to the expression
V x   Vcc
R1
R2
(1-24)
 V02
R1  R2
R1  R2
 The output V01 changes states when Vx = 0; therefore. we can
say
R1
R2
0   Vcc
 V02
R1  R2
R1  R2
(1-25)
which simplifies to
V02 R2 Vcc R1
(1-26)
 From Eq. 1-26 we can determine the maximum amplitude of
the triangular output. V02, which is expressed as
(1-27)
V02  Vcc
R1
R2
 When the output voltage V02 reaches the amplitude given by
Eq. 1-27. the output of the comparator changes stars and the
triangular wave begins to decrease linearly. Since the output
is symmetrical about by Eq.1-27 also expresses the minimum
value ofV02 at which switching occurs.
 The waveforms at Vx, V01 and V02 are shown in Fig. 1-10 for the
situation in which R1 = R2.
Fig. 1-10 Waveforms for the function generator of Fig. 1-9.
 The frequency of the circuit is controlled by the RC time
constant of the integrator. To obtain an expression for the
frequency. we begin with the expression relating capacitor
current. charge, and time of change:
q  ic t
(1-28)
The rate of charge of the capacitor is
dq  ic dt
(1-29)
 which can be written as
dq
ic 
dt
(1-30)
As the capacitor charges. the relationship between charge,
capacitance, and voltage across the capacitor plates is
q  CV02
(1-31)
 Substituting Eq. 1-31 into Eq. 1-30 yields
ic  C
d (V02 )
dt
(1-32)
Since the input resistance of the operational amplifier is
very high. the current through resistor R is approximately
equal to the charging current of the capacitor. Therefore, we
can write
iR  C
d (V02 )
dt
(1-33)
 In addition, since the voltage gain of the operational
amplifier is very high. the voltage at the input to the
amplifier is very nearly zero. Therefore
iR
V 0
 01
R
(1-34)
 Substituting Eq. 1-34 into Eq. 1-33. we obtain
1
d (V02 ) 
V01 dt
RC
(1-35)
 Integrating both sides of Eq. 1-35, we obtain
V02 
V01
1
V
dt

01
RC 
RC (t )
(1-36)
Substituting Eq. 1-27 into Eq. 1-36 yields
Vcc
R1 V01

t
R2 RC
(1-37)
 Since V01 =Vcc. Eq. 1-37 simplifies to
t  RC
R1
R2
(1-38)
The development of Eq. 1-38 began with Eq. 1-28. which
allows us to compute the charge on a capacitor after a period
of time t. Equation 1-28 is valid only if the initial charge and,
therefore. the initial voltages on the capacitor are zero.
Therefore, the time t in Eq. 1-38 is the time for the capacitor to
charge from 0 V until switching occurs. which is at one-fourth
cycle as shown in Fig. 1-10.
 Therefore, the time t in Eq. 1-38 is the time for the
capacitor to charge from 0 V until switching occurs. which
is at one-fourth cycle as shown in Fig. 1-10. Since Eq. 1-38
becomes
 R1
T  4 RC 
 R2



(1-39)
 The frequency which is the reciprocal of the period, is now
expressed as
f 
1
4 RC
 R2

 R1



(1-40)
EXAMPLE 1-5
 Compute the frequency and the peak amplitude of the
triangular output of the circuit shown in
Fig. 1-11.
Fig. 1-11 Function generator for Example 1-5.
 The amplitude of the triangular waveform can be computed
from Eq. 1-27 a
V02  Vcc
R1
R2
 60 k 
  9V
 (15V ) 
 100 k 
 Figure 10-12 shows an Exact Electronic Model 528 function
generator.
Fig.1-12 Laboratory quality function generator. (Courtesy Exact Electronics.)
 This laboratory – quality instrument generates sine, square,
triangle, ramp, and pulse waveforms over the frequency
range from 03.001 Hz to 20 MHz. The output voltage is 30V
peak to peak in an open circuit and 15V peak to peak across a
50- load.