Nonsinusoidal
Oscillators
• rectangle, triangle, saw tooth, pulse, etc.
Multivibrator circuits:
- astable – no stable states (two quasi-stable states; it
remains in each state for predetermined times)
- monostable – one stable state, one non-stable state
- bistable – two stable states
1/15
Astable multivibrators
(Relaxation oscillators)
Operating principle
• using current sources, the time
variation of the voltage across the
capacitor is linear
• using resistances, the time
variation of the voltage across
the capacitor is linear
• if the voltage across the
capacitor is fed to a PF
comparator, a rectangular wave
is obtained
2/15
Astable multivibrator– rectangular
signal generator
t

− 
vC (t ) = vC (0)e τ + 1 − e τ vC (∞)




R1
+
−
vD ( t ) = v − v =
vO (t ) − vC (t )
R1 + R2
−
t
VThL
R1
=
VOL = rVOL
R1 + R2
VThH
R1
=
VOH = rVOH
R1 + R2
3/15
t ∈ (t1, t2 )
t ∈ (t 2, t3 )
VThH = VThL e
−
VThL = VThH e
Tc
τ
T
− c

+ 1 − e τ


VOH ; Tc = τ ln VOH − rVOL

(1 − r )VOH

Td
τ
T
− d

+ 1 − e τ

rVOH − VOL

VOL ; Td = τ ln

(
r − 1)VOL

−
Generally VOH = −VOL
T
1+ r
Tc = Td = = τ ln
2
1− r
T = 2 RC ln
1+ r
1− r
If R1=R2
T = Tc + T d
T = 2 RC ln 3 ≈ 2,2 RC
4/15
Example
±VPS = ±12V, R1=10kΩ, R2=20kΩ,
R=7.5kΩ and C=10nF. The op
amp is a rail-to-rail type.
a) What are the minimum and
maximum values for the voltage
across the capacitor?
b) What is the frequency of te
rectangular signal?
c) Modify the circuit for an adjustable
frequency between fmin=0.8kHz
and fmax=8kHz?
a)
VThL
R1
10
(− 12) = −4V
=
VOL =
R1 + R2
10 + 20
VThH
R1
10
=
VOH =
⋅ 12 = 4V
R1 + R2
10 + 20
5/15
b)
R1
10
1
r=
=
=
R1 + R2 10 + 20 3
1+ r
1+1 3
T = 2 RC ln
= 2 ⋅ 7,5kΩ ⋅ 10nF ⋅ ln
= 166µs
1− r
1−1 3
1
1
= 6kHz
f = =
T 166
c) T = 2 RC ln 1 + r = 2 RCln2 = 1.386RC
1− r
Tmin =
1
f max
= 1.386 R 'C
1
1
R =
=
= 9kΩ R’=8.87kΩ (1%).
1.386 f maxC 1.386 ⋅ 8kHz ⋅10nF
'
Tmax =
1
f min
(
)
= 1.386 R + P C
'
P = 9 R ' = 9 ⋅ 8.87 = 79.8kΩ
P=100kΩ
6/15
Astable multivibrator with an
integrator and a comparator
Rectangular and triangular signal generator
vo1 (t ) = vC (t )
VThH
R1
VThL = − VOH
R2
R1
= − VOL
R2
7/15
C∆vC = iC ∆t
discharge
VOH
0 − VOH
iC =
=−
R
R
∆vC = VThL − VThH ;
∆t = t 2 − t1 = Td
T = Td + Tc
In general VOH = −VOL
VThH − VThL
Td = RC
VOH
VThH − VThL
Tc = RC
− VOL
VThH − VThL
R1
T = 2 RC
= 4 RC
VOH
R2
If R1 = R2
T = 4 RC
1
f =
4 RC
8/15
Example
At saturation the output voltage of AO2 is within 1V of the supply
a) What is the amplitude of the triangular voltage?
b) What is the oscillation frequency?
c) What is the maximum value of the current to the output of each op
amp?
9/15
The independence of the supply voltage
VOH = VZ + 0,7 V;
VOL = −VZ − 0,7 V
The reverse-biased base to emitter junction behaves as a Zener
diode, regulating the voltage at a voltage dependent on the
transistor type and on the emitter current (5V … 8V ) .
10/15
Frequency
adjustment
f max
1 R2
=
;
4 RC R1
1 R2
f =
4 RC R1
f min
1 R2 R4
=
4 RC R1 R4 + Pf
11/15
Offset
adjustment
of the
triangular
voltage
VThL

R1 
R1


= 1 +
Va − VOH

R2
 R2 
Va max
VThH

R1 
R1
Va − VOL
= 1 +
R2
 R2 
Pa + R6
R5
(− VPS ) = 3.75V
=
VPS +
R5 + Pa + R6
R5 + Pa + R6
12/15
Offset
adjustment
of the
triangular
voltage
Va min
R6
P + R5
(− VPS ) = −3,75V
=
VPS +
R5 + Pa + R6
R5 + Pa + R6
The offset can be adjusted between
Vo1max
 11 
= 1 +  ⋅ 3,75 = 5V;
 33 
Vo1min
 11 
= 1 +  ⋅ (−3,75) = −5V
 33 
13/15
14/15
Clock generators
• Quartz-crystal oscillator
f0=1, 2, 4, 5, … , 20MHz
f0=14,31818MHz - video adapter in
personal computers
f0=32,768KHz - digital wrist watch,
divide by 215 to get 1Hz
• NOT gates oscillator
15/15