Nonsinusoidal Signal Generators

• 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

• From one stable state the circuit switches in the other state

under the action of an control signal (input signal).

• From one non-stable state the circuit switches in the other

state automatically.

C in the time domain

CiC

vC

Defining relation between current and voltage

dttitCdv CC )()(

Considering finite variations:

tivC CC

time constant of the circuit

)()1()0()(

C

tt

CC veevtv

dttitCdv CC )()(

tvtvtRi ICC )(

tvtv

dt

tdvRC IC

C

dt

tdvCti C

C

)()(

RC

vI

RC circuit with voltage source

RC circuit – time domain analysis

RC circuit with dc voltage source

)()1()0()(

C

tt

CC veevtv

RCVvv ICC ;)(;0)0(

)0(Cv

)(tvC)(Cv

?)( tvO

)()1()0()(

O

tt

OO veevtv

RC circuit with rectangular voltage source

Results

obtained by

simulation

7 / 21

52

T

10;

25

TT

8 /19

A

A

B

B

TComputes (after a certain time – transient regime) the average value of the input voltage

Charging the C with a constant current

dttitCdv cc

)0()(1

)(0

C

t

CC vdttiC

tv )0(

1)( CC vIt

Ctv

)()1()0()(

C

tt

CC veevtv )0(1

)( CC vItC

tv

with a R and a DC voltage source with a constant current source

Charging the capacitor - summary

Astable multivibrators (Relaxation oscillators)

Operating principle

• if the voltage across the

capacitor is fed to a PF

comparator, a rectangular

wave is obtained

• the time variation of the

voltage across the capacitor

is exponential type

)(1)0()(

C

tt

CC veevtv

OHOHThH

OLOLThL

rVVRR

RV

rVVRR

RV

21

1

21

1

1. Astable multivibrator-rectangular signal generator

tvtvRR

Rvvtv COD

21

1)(

vD

OLOH V V Generally

r

rTTT dc

1

1ln

2

r

rRCT

1

1ln2

If R1=R2

RCRCT 2,23ln2

;VeeVV OH

TT

ThLThH

cc

1 OH

OLOHc

Vr

rVVT

1ln

;VeeVV OL

TT

ThHThL

dd

1 OL

OLOHd

Vr

VrVT

1ln

)( 2,1 ttt

)( 3,2 ttt

dc TTT

Problem

±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 the

rectangular signal?

c) Modify the circuit for an adjustable

frequency between fmin=0.8kHz and

fmax=8kHz?

V4122010

10

V4122010

10

21

1

21

1

OHThH

OLThL

VRR

RV

VRR

RV

a)

3

1

2010

10

21

1

RR

Rrb)

μs5.103311

311ln10nFk5.72

1

1ln2

r

rRCT

kHz7.9166

11

Tf

c)

C386.11 '

max

min Rf

T

kΩ910nFkHz8386.1

1

386.1

1

max

'

Cf

R R’=8.87kΩ (1%).

C386.11 '

min

max PRf

T k8.7987.899 'RP

P=100kΩ

RCRCr

rRCT 1.386ln22

1

1ln2

2. Astable multivibrator with an integrator and a comparator

OLThH VR

RV

2

1

OHThL VR

RV

2

1

Rectangular and

triangular signal

generator

tvtv Co 1

tivC CC

R

V

R

Vi OHOHC

0

d

ThHThLC

Tttt

VVv

12

;

OH

ThLThHd

V

VVRCT

OL

ThLThHc

V

VVRCT

cd TTT

OLOH VV generalIn

2

142R

RRC

V

VVRCT

OH

ThLThH

21If RR RC

fRCT4

14

discharge

Problem

At saturation the output voltage of op-amps 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?

The independence of the supply voltage

V7,0V;7,0 ZOLZOH VVVV

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 ) .

OH

ThLThH

V

VVRCT

2

If can be adjusted, than the period (frequency) can be adjusted'

OHV

Frequency adjustment

'

Ov

;2

1OLThH V

R

RV ;

2

1OHThL V

R

RV

'

2

12

1

4

2

2OH

OH

OH

OH

V

V

R

RRC

V

VR

R

RCT

;OLOH VV OHThLThH V

R

RVV

2

12

Ov

'

OvOH

OH

V

V

R

R

RCf

'

1

2

4

1

fPR

R

R

R

RCf

R

R

RCf

4

4

1

2min

1

2max

4

1;

4

1

Frequency adjustment - cont.

;If;If4

4''

o

f

ooo vPR

Rvvv

'

ov

maxf

minf

Problem

Consider rail-to-rail op-amps

a) What is the oscillation frequency?

b) Modify the circuit to obtain an adjustable frequency in the range of

[5; 25] kHz.

OHaThL VR

RV

R

RV

2

1

2

11

OLaThH V

R

RV

R

RV

2

1

2

11

Offset adjustment

of the triangular

voltage

V75.365

5

65

6max

PS

a

PS

a

aa V

RPR

RV

RPR

RPV

From Pa one can move the hysteresis along the horizontal axis, thus

adjusting the offset (dc level) of the triangular voltage.

V75,365

5

65

6min

PS

a

PS

a

a VRPR

RPV

RPR

RV

The offset can be adjusted between

V5)75,3(33

111V;575,3

33

111 min1max1

oo VV

Offset adjustment

of the triangular

voltage

Specialized integrated circuits for signals generation

• 8038 - Precision Waveform Generator/Voltage Controlled Oscillator

(triangular, square, sine, sawtooth, pulse) OBSOLETE PRODUCT

• NE566 - Function generator VCO, square, triangular - 1MHz

• AD9833 - Low power, programmable waveform generator: sine,

triangular, and square wave. No external components. Frequency and phase

are software programmable. 3-wire serial interface. Power-down function

(SLEEP). 0 MHz to 12.5 MHz output frequency range .

• 555 - highly stable device for generating accurate time delays or

oscillation (astable and monostable)

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

Clock generators

• Quartz-crystal oscillator

• NOT gates oscillator