Chapter 32 Oscillators. 2 Basics of Feedback Block diagram of feedback amplifier Forward gain, A Feedback, B Summing junction, ∑ Useful for oscillators.

Chapter 32

Oscillators

2

Basics of Feedback

• Block diagram of feedback amplifier

• Forward gain, A

• Feedback, B

• Summing junction, ∑

• Useful for oscillators

∑ A

B

vin

vF

vout

+

-

3

Basics of Feedback• Op-amps

– Inverting & non-inverting– Negative feedback 180°out of phase w/input– High input impedance– Low output impedance– Wide bandwidth– Stable operation

4

Basics of Feedback

• Oscillators– Positive feedback– In-phase with input– Unstable

5

Basics of Feedback• Block diagram analysis

∑ A

B

vin vout

( )

1

e in f

out in f

f out

out

in

v v v

v A v v

v Bv

v A

v AB

= −

= −

=

=+

ve

vf

+

-

6

Basics of Feedback

• Inverting amplifier

∑ A

B

vin vout

ve

vf

+

-

( )

F

1

in

out

in

out

outf

finout

fine

11

1

1

R

RB

BBA

v

v

AB

A

v

v

Bvv

vvAv

vvv

=

≈+

−=

+−=

=

−−=

−−=

7

Relaxation Oscillator• Square wave generator

• Composed of– Schmitt trigger comparator– Positive feedback– RC circuit to determine period

8

Relaxation Oscillator

• Schmitt Trigger– R1 and R2 form a voltage divider

– Portion of output applied at + input– Hysteresis: output dependent on input and

previous value of input

9

Relaxation Oscillator

• Schmitt Trigger– Hysteresis: upper and lower trip points– Can use a voltage follower for adjustable trip

points

10

Relaxation Oscillator• Schmitt trigger

11

Relaxation Oscillator• Schmitt Trigger

Relaxation Oscillator

12

Relaxation Oscillator• R1 and R2 voltage divider

• Capacitor charges through RF

• VC < +VSAT then C charges toward +VSAT

• VC > –VSAT then C charges toward –VSAT

( )2

1 2REF SAT

RV V

R R= ±

+

13

Relaxation Oscillator• Schmitt Trigger Relaxation Oscillator

Equations

( )( )2

1

( ) 1

22 ln 1

tRC

F

C F O

F

R C

v t V V e

RT R C

R

τ−

=

= − −

⎛ ⎞= +⎜ ⎟

⎝ ⎠

14

Wien Bridge Oscillator• For a sinusoidal oscillator output

– Closed loop gain ≥ 1– Phase shift between input and output = 0° at

frequency of oscillation

• With these conditions a circuit– Oscillates with no external input

• Positive feedback = regenerative feedback

15

Wien Bridge Oscillator• Regenerative oscillator

– Initial input is small noise voltage– Builds to steady state oscillation

• Wien Bridge oscillator– Positive feedback, RC network branch– Resistor branch establish amplifier gain

16

Wien Bridge Oscillator• Circuit

17

Wien Bridge Oscillator• Equations

0

1 2 1 2

2 1

1 1 2 2 2 1

1 2 1 2

0

1Output frequency

2

if and then

1 1and

2 3

fR R C C

R CB

RC R C R C

R R C C

f BRC

π

π

= =

=+ +

= =

= =

18

Wien Bridge Oscillator

• Another form of Wien Bridge

19

Wien Bridge Oscillator• For a closed-loop gain, AB = 1

– Op-amp gain ≥ 3

• Improved circuit– Separate RF into 1 variable and 1 fixed

resistor– Variable: minimize distortion– Zener Diodes: limit range of output voltage

20

Phase-Shift Oscillator• Three-section R-C network

– ≈ 60° per section– Negative FB = 180°– 180° + (60° + 60° + 60°) = 360° = Positive FB

0

1Output frequency

2 629 Required voltage ain

fRC

A gπ

=

=

21

Phase-Shift Oscillator• Circuit

22

LC Oscillators• LC circuits can produce oscillations

• Used for– Test and measurement circuits– RF circuits

23

LC Oscillators• Named after pioneer engineers

– Colpitts– Hartley– Clapp– Armstrong

24

LC Oscillators• Colpitts oscillator

– fs = series resonance

– fp = parallel resonance

– L-C network → 180° phase shift at fp

25

LC Oscillators

______

-

+

______

RF

Rin

+V

–V

vout

C2 C1

L

26

LC Oscillators• Equations

222

1 21 2

1 2

0

1 2

1 2

1Impedance: ( )

( ) 1

1Oscillator frequency:

2

s LCZ s

s LC Cs C C

C C

fC C

LC C

π

+=

⎛ ⎞+ +⎜ ⎟+⎝ ⎠

=

+

27

LC Oscillators

• Hartley oscillator– Similar to Colpitts– L and C’s interchanged

– Also have fs and fp

28

LC Oscillators

______

-

+

______

RF

Rin

+V

–V

vout

L1

C1

L2

( )( )

( )

21 2

21 2

0

1 2

1( )

1

1

2

sL s L CZ s

s L L C

fL L Cπ

+=

+ +

=+

29

Crystal Oscillators• Quartz crystals• Mechanical device• Higher frequencies (>1 MHz)• Stability• Accuracy• Reliability • Piezoelectric effect

30

Crystal Oscillators• Electrical model

– Both have parallel and series resonance

• Symbol– Quartz crystal– metal plates

C1 L1RF

C0

31

Crystal Oscillators• Impedance varies with

frequency• Square wave crystal

oscillator circuit• Choose C1 and C2

– Oscillation frequency between fs and fp

______

R2

R1

vout

C1

XTAL

C2

CMOS Inverter

R2

32

555 Timer• IC

– Internal circuit

33

555 Timer• Usage

– Monostable timing– Astable mode = relaxation oscillator– Trigger voltage– Control voltage– Threshold voltage– R-S flip-flop

34

555 Timer• Relaxation oscillator

NE555

______

1 5

vout3

4

VCC = +15 V

8

7

26

RA

RB

C 0.01 μF

( )( )( )

1

2

ln(2)

ln(2)

ln(2) 2

1

B

A B

A B

T R C

T R R C

T R R C

fT

= ∗

= ∗ +

= ∗ +

=

35

555 Timer• Monostable Circuit (one-shot)

• Trigger high → vout = low

• Trigger low → vout = highNE555

______

1 5

vout3

4

VCC = +15 V

8

7

26

RA

C

0.01 μF______

Trigger

36

Voltage Controlled Oscillator-VCO

• ∆fout ∆vin

LM566C

______

5

vout

14

VCC

6

7

81 nF

C1______

Voltage Input3

R1

Square wave

Triangle wave

Outputs

( )1 1

2.4 CC CO

CC

V Vf

RCV

−=

∝

∝