OscillatorsFixed Frequency, Controlled Power•Transmitters•Receivers/Tuners•Clock Circuits

Av

B(j)

+

+ VoutVin 1out v

in v

V A

V A B s

System poles @ AvB(s) = 1

Barkhausen Criteria

System poles @ AvB(s) = 1

Pole in RHP: Oscillation amplitude grows until amplifier starts to clip, then Av’ < Av .

0

Root locus for Av’ < Av

'0( ) 1 (Stable Oscillation)vA B j

0( ) 1 0vA B j

Oscillator Design

Av

B(j)

+

+ VoutVin

Common Base:rin = re

Av = Rc’/re

Common Emitter:rin = (+1)re

Av = -Rc’/re

Frequency Selective Feedback Network

LC NetworkQuartz Crystal

Amplifier GainAv = + Rc’/re

re = 26 mV/IE (from DC Analysis)

Rc’ : Parallel Combination of 1. Transformed Load: RL’ = RL/v

2

2. Parasitic Loading (finite Q): Rcoil = QuXT 3. Feedback Network: Re’ = . . . . .4. Collector Dynamic (AC) Resistance: rc ~ 20 k5. Any other resistances in Collector Circuit

Hartley Oscillator(common base, autotransformer feedback)

E

C1 2

'2

ov

LL

v

n

n n

RR

21

2 1

2

1 2

||

||e E

e E F

nB

n n

r RB

r R R

B B B

'2

1

||e E Fe

r R RR

B

R1

R2

R3R4

RL

n1

n2 n3

CT

LT , Qu

BPBP

VCC

, rc

+ -

R2R3

IB

VCC

R1IC IB

R3 re

IE IB

ie

1 ei

rc

R4

n2

n1

+ ve

-

B

C

E

B

CE

re

2

1 2

3L L

n nR R

n

P T uR X Q

Hartley Oscillator

0.026e

E

vr

I

DC Equivalent

AC Equivalent

R3 re

ie

1 ei

rc RP 'LR

R4

n2

n1

+ ve

- B

CE

32

4 3

e

e

R rB

R R r

11

1 2

nB

n n

+ vc

-

B1vcve = B1B2vc

4 3F eR R R r

R3 re

ie

1 ei

rc RP LR+ ve

- B

CE + vc

-

B=B1B2

21

FF

RR

B

ve = Bvc

Ideal

re

ie

1 ei

rc RP 'LR

+ ve

- B

CE + vc

-

B

FR

ve = Bvc

re

ie

1 ei

+ ve

- B

CE+ vc

-

Bve = Bvc

' 'c c P L FR r R R R

1 1e

c c e ce

vv R i R

r

1 1c c c

v c ee e e

v R RA R i

v r r

Note: any additional resistance placed across the tank circuit must be included as an additional parallel contribution.

B

AV

Barkhausen: is AVB > 1 ? Book Example :f = 1 MhzIC ~ IE = 1 man1 = 10, n2 = 100, n3 = 5 (subscripts changed)

LT = 53 uH, Qu = 50, XT = 333 RL = 50 R3 = 1 kR4 = 0 therefore, B2 = 1rc = 50 k

R1

R2

R3R4

RL

n1

n2 n3

CT

LT , Qu

BPBP

VCC

, rc

re

2626

1e

mVr

mA

11

1 2

2

2

1

10.091

110

5024.2

5 110

0 1 263

50 333 16.7

2.2

L

F

P u T

C c L F P

nB

n n

R k

kR k

B

R Q X k

R r R R R k

220084.6 38.5

26VA dB 84.6 0.091 7.7 1VA B

Maximum Power Considerations

The maximum 0-pk collector AC voltage is:

0 .001 2200 2.2pk C CV I R A V

220 2.21 1

0.12 2 24.2

pkMAX

L

V VP mW

R k

The maximum power to the load is:

VCC was not given for this problem, but we can determine a minimum value required to prevent saturation at max power by recalling that . . .

, ,

, ,

2.2 1 2.2

1 2.2 3.2

CEc opt CE MIN c C

C

CC MIN E CE MIN

VR V R I k mA V

I

V V V V V V

Colpitts Oscillator(common base, capacitive feedback)

E

C3 2

12 3 2 3

2

1 2

'2

1

||

||

||

e E

e E F

e E Fe

X CB

X X C C

r RB

r R R

B B B

r R RR

B