Pangantar Oscillator dan jenis-jenis osilator

dasar telekomunikasi

2. Objectives
konsep dasar osilator
prinsip dasar pengoperasian osilator
Analisis pengoperasian osilator RC dan LC
pengoperasian rangkaian osilator relaksasi
dasar

3. Pendahuluan
 Osilator merupakan rangkaian elektronik yang
menghasilkan bentuk gelombang periodik pada
keluarannya tanpa sumber sinyal eksternal. Ini
digunakan untuk mengubah dc ke ac.
 Osilator adalah rangkaian yang menghasilkan
sinyal kontinu dari beberapa jenis tanpa
memerlukan input.
 Sinyal-sinyal ini memiliki berbagai tujuan.
Sistem komunikasi, sistem digital (termasuk
komputer), dan peralatan uji menggunakan
osilator

4. Ref:06103104HKN EE3110 Oscillator4
Oscillators
Osilasi: efek yang berulang kali dan teratur
berfluktuasi terhadap nilai rata-rata
Osilator: rangkaian yang menghasilkan osilasi
Karakteristik: bentuk gelombang, frekuensi,
amplitudo, distorsi, stabilitas

5. Ref:06103104HKN EE3110 Oscillator5
Application of Oscillators
Oscillators are used to generate signals,
e.g.

Used as a local oscillator to transform the RF
signals to IF signals in a receiver;

Used to generate RF carrier in a transmitter

Used to generate clocks in digital systems;

Used as sweep circuits in TV sets and CRO.

6. Figure 9.67 Repetitive ramp waveform.
Oscillators
Osilator adalah rangkaian yang
menghasilkan sinyal periodik
Osilator mengubah daya DC dari catu
daya menjadi daya sinyal AC secara
spontan - tanpa memerlukan sumber
masukan AC

7. Introduction
 Osilator adalah rangkaian yang menghasilkan sinyal berulang
dari tegangan DC.
 Osilator umpan balik bergantung pada umpan balik positif dari
output untuk mempertahankan osilasi.
 Osilator relaksasi menggunakan rangkaian pengaturan waktu
RC untuk menghasilkan sinyal non-speckles seperti gelombang
persegi
Sine wave
Square
wave
Sawtooth
wave

8. Types of oscillators
1.RC oscillators

Wien Bridge

Phase-Shift
2.LC oscillators

Hartley

Colpitts

Crystal
3.Unijunction / relaxation oscillators

9. Figure 9.68 A linear oscillator is formed by connecting an amplifier and
a feedback network in a loop.
Linear Oscillators

10. Ref:06103104HKN EE3110 Oscillator10
Integrant of Linear
Oscillators
Untuk input sinusoidal terhubung
“Linear” karena keluarannya mendekati sinusoidal
Osilator linier berisi:
-jaringan umpan balik pemilihan frekuensi
- penguat untuk mempertahankan penguatan loop pada kesatuan

+
+
Amplifier (A)
Frequency-Selective
Feedback Network (

)
Vf
Vs Vo
V

Positive
Feedback

11. Ref:06103104HKN EE3110 Oscillator11
Basic Linear Oscillator

+
+
SelectiveNetwork

(f)
Vf
Vs Vo
V

A(f)
)(
fso VVAAVV 

and
of
VV
A
A
V
V
s
o


1
If V
s
= 0, the only way that V
o
can be nonzero
is that loop gain A=1 which implies that
0
1||




A
A
(Barkhausen Criterion)

12. Basic principles for oscillation
 An oscillator is an amplifier with positive
feedback.
A
b
V
e
V
f
V
s
V
o
+
(1)
fse VVV 
(2)
ofβVV
  (3)
osfseo βVVAVVAAVV 

13. Basic principles for oscillation
 The closed loop gain is:
  
osfs
eo
βVVAVVA
AVV



oso
VAAVV 
 
soAVVA 1
 Aβ
A
V
V
A
s
o
f


1

14. Basic principles for oscillation
 In general A and  are functions of frequency
and thus may be written as;
is known as loop gain


sβsA1
sA
s
V
V
sA
s
o
f


sβsA

15. Basic principles for oscillation
 Writing the loop gain becomes;
 Replacing s with j
 and
ssβAsT


sT1
sA
sA
f




jωT1
jωA
jωA
f


jωβjωAjωT 

16. Basic principles for oscillation
 At a specific frequency f
0


At this frequency, the closed loop gain;
will be infinite, i.e. the circuit will have finite
output for zero input signal - oscillation
1
000
 jωβjωAjωT



00
0
0
jωβjωA1
jωA
jωA
f



17. Basic principles for oscillation
 Thus, the condition for sinusoidal oscillation
of frequency f
0
is;
 This is known as Barkhausen criterion.
 The frequency of oscillation is solely
determined by the phase characteristic of the
feedback loop – the loop oscillates at the
frequency for which the phase is zero.
1
00
jωβjωA

18. Figure 9.69 Linear oscillator with external signal X
in injected.
Barkhausen Criterion – another way

19. Barkhausen Criterion

20. How does the oscillation get
started?
Noise signals and the transients associated with the
circuit turning on provide the initial source signal that
initiate the oscillation

21. Practical Design Considerations
Usually, oscillators are designed so that the loop gain
magnitude is slightly higher than unity at the desired
frequency of oscillation
This is done because if we designed for unity loop gain
magnitude a slight reduction in gain would result in
oscillations that die to zero
The drawback is that the oscillation will be slightly
distorted (the higher gain results in oscillation that grows
up to the point that will be clipped)

22. Basic principles for oscillation
 The feedback oscillator is widely used for
generation of sine wave signals.
The positive (in phase) feedback arrangement
maintains the oscillations.
The feedback gain must be kept to unity to
keep the output from distorting.

23. Basic principles for oscillation
In phase
Noninverting
amplifier
V
f V
o
A
v
Feedback
circuit

24. Design Criteria for Oscillators
1.The magnitude of the loop gain must be
unity or slightly larger
– Barkhaussen criterion
2.Total phase shift, of the loop gain mus t be
Nx360° where N=0, 1, 2, …
1Aβ

25. RC Oscillators
 RC feedback oscillators are generally limited
to frequencies of 1 MHz or less.
 The types of RC oscillators that we will
discuss are the Wien-bridge and the phase-
shift

27. Wien-bridge Oscillator
 It is a low frequency oscillator which ranges
from a few kHz to 1 MHz.

28. Figure 9.70 Typical linear oscillator.
Another way

29. Wien-bridge Oscillator
 The loop gain for the oscillator is;
 where;
 and;



















sp
p
ZZ
Z
R
R
sβsAsT
1
2
1
sRC
R
Z
p


1
sC
sRC
Z
s


1

30. Wien-bridge Oscillator
 Hence;
 Substituting for s;
 For oscillation frequency f
0


 
















RC/jRCjR
R
jT
001
2
0
13
1
1



 
















/sRCsRCR
R
sT
13
1
1
1
2

 
















RC/jRCjR
R
jT


13
1
1
1
2
][
0

31. Wien-bridge Oscillator
 Since at the frequency of oscillation, T(j)
must be real (for zero phase condition), the
imaginary component must be zero;
 which gives us – [how?! – do it now]
0
1
0
0 
RCj
RCj


RC
1
0

32.  
 
 
RC
RC
RC
RC
RCj
RCj
RCj
RCj
RCj
RCj
1
1
1
1.1
1
1)(
1
0
1
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0



















33. Wien-bridge Oscillator
 From the previous eq. (for oscillation
frequency f
0),
 the magnitude condition is;































3
1
1
03
1
11
1
2
1
2
R
R
R
R

 
















RC/jRCjR
R
jT
001
2
0
13
1
1


213
1
2

R
R
To ensure oscillation, the ratio R
2/R
1
must be slightly greater than 2.

34. Wien-bridge Oscillator
 With the ratio;
 then;
K = 3 ensures the loop gain of unity –
oscillation

K > 3 : growing oscillations

K < 3 : decreasing oscillations
2
1
2

R
R
31
1
2

R
R
K

35. Wien-bridge oscillator.
Wien-Bridge Oscillator – another way
12
1
2
2
2
RR
R
R


3211
,
1
2


R
R
Again
invertingnon

36. Figure 9.75 Example of output voltage of the oscillator.
Wien-Bridge oscillator output

37. Ref:06103104HKN EE3110 Oscillator37
Wien Bridge Oscillator
Frequency Selection Network
Let
1
1
1
C
X
C

 and
111 C
jXRZ 
2
2
1
C
X
C


22
22
1
22
2
11
C
C
C jXR
XjR
jXR
Z












Therefore, the feedback factor,
)/()(
)/(
222211
2222
21
2
CCC
CC
i
o
jXRXjRjXR
jXRXjR
ZZ
Z
V
V





222211
22
))((
CCC
C
XjRjXRjXR
XjR



Vi Vo
R1C1
R2C2
Z1
Z2

38. Ref:06103104HKN EE3110 Oscillator38
 can be rewritten as:
)(
2121221221
22
CCCCC
C
XXRRjXRXRXR
XR


For Barkhausen Criterion, imaginary part = 0, i.e.,
0
2121

CC
XXRR
Supposing,
R
1
=R
2
=R and X
C1
= X
C2
=X
C
,
2121
21
21
/1
11
or
CCRR
CC
RR




)(3
22
CC
C
XRjRX
RX


0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
F
e
e
d
b
a
c
k
f
a
c
t
o
r


-1
-0.5
0
0.5
1
P
h
a
s
e
Frequency

=1/3
Phase=0
f(R=Xc)

39. Ref:06103104HKN EE3110 Oscillator39
Example
Rf
+

R
R
C
C
Z1
Z2
R1
Vo
By setting , we get
Imaginary part = 0 and
RC
1

3
1

Due to Barkhausen Criterion,
Loop gain A
v
=1
where
A
v : Gain of the amplifier
1
131
R
R
AA
f
vv 
2
1

R
R
f
Therefore,
Wien Bridge Oscillator

40. Phase-Shift Oscillator
 The phase shift oscillator utilizes three RC
circuits to provide 180º phase shift that
when coupled with the 180º of the op-amp
itself provides the necessary feedback to
sustain oscillations.
 The gain must be at least 29 to maintain the
oscillations.
 The frequency of resonance for the this type
is similar to any RC circuit oscillator:
RC
f
r
62
1



41. Phase-Shift Oscillator
vi
v1
v1
v2
v2v3
vo
C
C
C
R
R
R
R2
iv
sRC
sRC
v 







1
1
iv
sRC
sRC
v
2
2
1








i
v
sRC
sRC
v
3
3
1








3
3
1
)( 







sRC
sRC
s
v
v
i

R
R
v
v
sA
o 2
3
)( 

42. Phase-Shift Oscillator
 Loop gain, T(s):
 Set s=jw
3
2
1
)()()( 













sRC
sRC
R
R
ssAsT 
   
222222
2
2
3
2
331
))((
)(
1
)(
CRRCjCR
RCRCj
R
R
jT
RCj
RCj
R
R
jT































43. Phase-Shift Oscillator
 To satisfy condition T(jw
o)=1, real component
must be zero since the numerator is purely
imaginary.
 the oscillation frequency:


Apply w
o
in equation:
To satisfy condition T(jw
o)=1
031
222
 CR
RC3
1
0

 





















8
1
)3/1(3)3/(0
)3/1)(3/(
)(
22
R
R
j
j
R
R
jT
o

8
2

R
R
The gain greater than 8, the circuit will
spontaneously begin oscillating &
sustain oscillations

44. Phase-Shift Oscillator
RC
f
o
62
1

 29
2

R
R
The gain must be at
least 29 to maintain
the oscillations

45. LC Oscillators
 Use transistors and LC tuned circuits or
crystals in their feedback network.
 For hundreds of kHz to hundreds of MHz
frequency range.
 Examine Colpitts, Hartley and crystal
oscillator.

46. Colpitts Oscillator
 The Colpitts oscillator is a type
of oscillator that uses an LC
circuit in the feed-back loop.
The feedback network is made
up of a pair of tappedtapped
capacitorscapacitors (C(C
1 1 and Cand C
22)) and an an
inductor Linductor L to produce a
feedback necessary for
oscillations.
The output voltage is
developed across C
1.
The feedback voltage is
developed across C
2.

47. Colpitts Oscillator
 KCL at the output node:
 voltage divider
produces:
 substitute eq(2) into
eq(1):
0
11
21



sC
sL
V
Vg
R
V
sC
V
o
gsm
oo
ogs
V
sL
sC
sC
V 














2
2
1
1
  0
1
1
12
2
2













 sC
R
LCssCgV
mo
- Eq (1)
- Eq (2)

48. Colpitts Oscillator
 Assume that oscillation has started, then
Vo
≠0
 Let s=jω
 both real & imaginary component must be
zero

Imaginary component:
  0
1
21
2
2
21
3







R
gCCs
R
LCs
CLCs
m
  0
1
21
2
21
2
2









 CLCCCj
R
LC
R
g
m












21
21
1
CC
CC
L
o

- Eq (3)

49. Colpitts Oscillator
 both real & imaginary component must be
zero

Imaginary component:
 Combining Eq(3) and Eq(4):
 to initiate oscillations spontaneously:
R
g
R
LC
m
1
2
2


Rg
C
C
m

1
2









1
2
C
C
Rg
m
- Eq (4)

50. Hartley Oscillator
 The Hartley oscillator
is almost identical to
the Colpitts oscillator.
 The primary
difference is that the
feedback network of
the Hartley oscillator
uses tappedtapped inductors inductors
(L(L
11 and L and L
22)) and a single a single
capacitor Ccapacitor C.

51. Hartley Oscillator
 the analysis of Hartley oscillator is identical
to that Colpitts oscillator.
 the frequency of oscillation:
 CLL
o
21
1



52. Crystal Oscillator
 Most communications and digital applications
require the use of oscillators with extremely stable extremely stable
outputoutput. Crystal oscillators are invented to overcome
the output fluctuationoutput fluctuation experienced by conventional
oscillators.
Crystals used in electronic applications consist of a
quartz wafer held between two metal plates and
housed in a a package as shown in Fig. 9 (a) and (b).

53. Crystal Oscillator
 Piezoelectric Effect
The quartz crystal is made of silicon oxide (SiO
2
)
and exhibits a property called the piezoelectricpiezoelectric

When a changing an alternating voltage is applied
across the crystal, it vibrates at the frequency of
the applied voltage. In the other word, the
frequency of the applied ac voltage is equal to the
natural resonant frequency of the crystal.

The thinner the crystal, higher its frequency of
vibration. This phenomenon is called piezoelectric
effect.

54. Crystal Oscillator
 Characteristic of Quartz
Crystal

The crystal can have two resonant
frequencies;

One is the series resonance frequency
f
1
which occurs when X
L
= X
C
. At this
frequency, crystal offers a very low
impedance to the external circuit
where Z = R.

The other is the parallel resonance (or
antiresonance) frequency f
2 which
occurs when reactance of the series
leg equals the reactance of C
M. At this
frequency, crystal offers a very high
impedance to the external circuit
R
L
C
C
M

55. Crystal Oscillator
 The crystal is connected as a series element
in the feedback path from collector to the
base so that it is excited in the series-
resonance mode
BJT
FET

56. Crystal Oscillator
 Since, in series resonance, crystal impedance is the smallest
that causes the crystal provides the largest positive feedback.
Resistors R
1, R
2, and R
E provide a voltage-divider stabilized dc
bias circuit. Capacitor C
E provides ac bypass of the emitter
resistor, R
E to avoid degeneration.
The RFC coil provides dc collector load and also prevents any
ac signal from entering the dc supply.
The coupling capacitor C
C has negligible reactance at circuit
operating frequency but blocks any dc flow between collector
and base.
The oscillation frequency equals the series-resonance
frequency of the crystal and is given by:
C
o
LC
f
2
1


57. Unijunction Oscillator
 The unijunction transistor
can be used in what is
called a relaxation relaxation
oscillatoroscillator as shown by
basic circuit as follow.
The unijunction oscillator
provides a pulse signal
suitable for digital-circuit
applications.
Resistor R
T and capacitor
C
T
are the timing
components that set the
circuit oscillating rate
UJT

58. Unijunction Oscillator
 Sawtooth wave
appears at the
emitter of the
transistor.
This wave shows the
gradual increase of
capacitor voltage

59. Unijunction Oscillator
 The oscillating frequency is calculated as
follows:
 where, η = the unijunction transistor intrinsic
stand- off ratio
 Typically, a unijunction transistor has a
stand-off ratio from 0.4 to 0.6
 

1/1ln
1
TT
o
CR
f