786 Electronic Devices and Circuits

RL

Ii
Ii
−
Light
A1
+
Vo
+
Photo diode

Figure 15.50 I–V converts I i to Vo

15.3 NONLINEAR APPLICATIONS

In nonlinear applications, the op-amp is used in the open-loop configuration. Some of the impor-
tant nonlinear applications of op-amp are considered.

15.3.1 Monostable Multivibrator Using Op-Amp

On the application of a trigger, a monostable multivibrator generates a pulse of duration T, which
is essentially decided by the time constant used in the circuit. A monostable multivibrator using
an op-amp is shown in Figure 15.51.
R

+ D +
VD = 0.7V VC +
− C − + R1
Vo
+
CC
βVsat R2
−
Tigger −
0
V

Figure 15.51 Monostable multivibrator using an op-amp

R R

ic id
+ +
VC = VD Vo = Vsat VC = −βVsat Vo = Vsat
C − C −

Figure 15.52 Charging of C Figure 15.53 Discharge of C

 Applications of Op-Amp 787

The output of the op-amp abruptly jumps between ±Vsat , depending on the input. In the stable
state, let Vo = Vsat . Then C tries to charge to +Vsat through R (Figure 15.52). However, since D
is connected across C, the instant VC = VD = 0.7 V, the diode conducts, preventing any further
increase in VC . Thus, VC is clamped to 0.7 V. The voltage at the non-inverting terminal now is
R2 R2
Vf = Vsat = bVsat, where b = . Therefore, in the stable state, Vo = Vsat and VC = VD .
R1 + R2 R1 + R2
Now in order to drive the multi into the quasistable state, a negative trigger whose magnitude
is more than +bVsat is to be applied so that the net voltage at the non-inverting input terminal
is negative. Consequently, Vo jumps to −Vsat . The result is that D is OFF. The voltage at the
non-inverting terminal is −bVsat . The capacitor C now tries to discharge to −Vsat through R
(Figure 15.53). However, the instant VC is slightly more negative than −bVsat the net voltage
at the non-inverting terminal is positive and Vo jumps to +Vsat . Vf = bVsat . Once again, C tries
to charges to +Vsat , but VC is clamped to VD . The quasistable ends and the multi returns to its
initial stable state. Only when a trigger is applied, once again the multi will be driven into
the quasistable state to generate another pulse of duration T. The waveforms are shown in
Figure 15.54.

0
t
Trigger V
Vsat

VD VD
0
t
VC

-bVsat

-Vsat
+Vsat

Vo
0
t

-Vsat

Figure 15.54 Waveforms of the monostable multivibrator

 788 Electronic Devices and Circuits

The expression for the voltage across C at any given instant of time in an RC circuit is
−t
VC (t ) = Vf − (Vf − Vi ) e r (15.70)
t = RC
From Figure 15.54,
Vf = −Vsat and Vi = VD
−t
∴ VC (t ) = −Vsat − ( −Vsat − VD ) e r

At t = T , VC (t ) = − bVsat
−T
∴ − bVsat = −Vsat + (Vsat + VD ) e r

−T
Vsat (1 − b ) = (Vsat + VD ) e t

 V 
Vsat 1 + D 
T = t log n
(Vsat + VD )
= t log n
 Vsat 
= t log n
1
(15.71)
Vsat (1 − b ) Vsat (1 − b ) ( b)
1 −
since VD << Vsat.
R2 R1
1− b = 1− =
R1 + R2 R1 + R2
If R1 = R2, then 1 − b = 0.5. Therefore,
1 1
T = t log n = t log n = t log n 2 = 0.69t
(1 − b ) 0.5

15.3.2 Astable Multivibrator

An astable multivibrator is a square wave oscillator. A symmetric astable multivibrator using an
Op-amp is shown in Figure 15.55. The only difference that can be seen in this circuit when com-
pared to the circuit of the monostable multivibrator in Figure 15.51 is that the diode is removed,
and there is no need for an external trigger as this circuit is an oscillator.

+
VC +
C − + R1 V
o

VR +
βVsat R2
−
−

Figure 15.55 Symmetric astable multivibrator using an op-amp

 Applications of Op-Amp 789

Let us arbitrarily assume that initiallyVo = Vsat . Then the reference voltageVR = bVsat . Since Vo = Vsat,
C tries to charge to Vsat . However, when VC is slightly more positive than VR ( = bVsat ), Vo switches to
−Vsat . Now, VR = − bVsat . C tries to charge to −Vsat . However, when VC is slightly more negative than
−bVsat , Vo once again switches to Vsat . The process is thus repeated automatically. The result is that
a square wave of peak-to-peak amplitude of 2Vsat and referenced to 0 is generated (Figure 15.56).

Vsat

βVsat

0
t
VC

−βVsat

−Vsat
T/2 T/2

Figure 15.56 Waveforms of the astable multivibrator

From Figure 15.56, −t

VC (t ) = Vf − (Vf − Vi ) e t

Vf = Vsat and Vi = −bVsat . Therefore,

−t
VC (t ) = Vsat − (Vsat + bVsat ) e t
T
At t = , VC (t ) = bVsat. Therefore,
2 −T 2

bVsat = Vsat − (Vsat + bVsat ) e t

T 1+ b
= t log n
2 1− b
Therefore,
1+ b
T = 2t log n (15.72)
1− b
R2 R2 1
If R1 = 1.16R2 , b = = = = 0.46
R1 + R2 1.16R2 + R2 2.16
Therefore,
1 + 0.46
T = 2t log n = 2t log n 2.70 = 2t
1 − 0.46
Alternately, it may also be said that if R2 = 0.86R1 ,T = 2t

1 1 1
and f = = = (15.73)
T 2t 2RC
 790 Electronic Devices and Circuits

The peak-to-peak output voltage swing = Vsat − ( −Vsat ) = 2Vsat .

If the output swing is to be limited to a desired value, Zener diodes D1 and D2 with breakdown
voltage of VZ are connected as shown in Figure 15.57.

+ +
VC RS +
C − + R1 VD
− Vo
VR + +
βVsat R2 VZ
−
− −

Figure 15.57 Symmetric astable multivibrator to obtain the desired output

The peak-to-peak output voltage swing =2 (VZ + VD ) , where VD is forward-bias voltage of the
Zener diode and VZ the breakdown voltage. RS may be included to limit current.

Astable Multivibrator with Variable Duty Cycle A symmetric astable multivibrator has the same
charging and discharging time constants and hence has a duty cycle of 50 percent. To have an astable
multivibrator with variable duty cycle, the charging and discharging time constants need to be
different. To enable this to happen, the circuit in Figure 15.55 is modified as shown in Figure 15.58.
D1 R3

R4 D2

+
VC +
C − + R1
Vo
VR +
βVsat R2
− −

Figure 15.58 Astable multivibrator with variable duty cycle

When Vo = +Vsat, D2 is ON and the charging time constant of C is R4C .

When Vo = −Vsat, D1 is ON and the discharging time constant of C is R3C . Therefore,
 Applications of Op-Amp 791

R4
Duty cycle =
R3 + R4
By adjusting R3 and R4 , the duty cycle can be varied.

15.3.3 Triangular Wave Generator

It is already known that the integral of a square wave is a triangular wave. Hence, the circuit
in Figure 15.59 can be used to generate a triangular wave. Here, the output of the square wave
generator (Figure 15.55) is integrated by a practical integrator (Figure 15.33).

R RF

− 0 CF

RA
−

+ 0
C R1 +
+ Vo
VR −
R2

Square wave generator Integrator

Figure 15.59 Triangular wave generator

15.3.4 Comparator
A comparator is a circuit that compares the voltage amplitude of the input signal with a reference
voltage and tells the instant at which the input has reached a reference level. An op-amp in the
open-loop configuration can be used as a comparator. The output Vo under open-loop conditions
can swing between ±Vsat . If the open-loop gain Ad is 100000, then Vi needed to drive Vo to Vsat is
Vsat /Ad , which is typically of the order of few microvolts. A comparator can be (i) non-inverting
comparator and (ii) inverting comparator.
Non-inverting Comparator A non-inverting comparator is one in which the input signal is
applied to the noninverting terminal of the op-amp. The reference voltage VR may be set as zero,
positive voltage, or negative voltage. If the reference voltage is set as 0, then the comparator is also
called a zero-crossing detector.
Non-inverting comparator with VR = 0 or zero-crossing detector The circuit in Figure 15.60
is a non-inverting zero-crossing detector. The waveforms are shown in Figure 15.61.
When Vi ≥ 0, Vo = Vsat (shaded region). When Vi < 0, Vo = −Vsat (non-shaded region). The
transfer characteristic that shows the relation between the input and the output is shown in
Figure 15.62.