Analog Circuits and Systems Prof. K Radhakrishna Rao
Lecture 33: Transconductor based Oscillator
1
Review
Gyrator based RC Oscillators Wien Bridge Oscillator Quadrature Oscillator
2
Review (contd.,)
3
Quadrature oscillator/double integrator oscillator as an LC Oscillator
Review (contd.,)
4
( ) ( )
( )
33 3
22 20
3 C 2R C 2R 0
3and C 2R 3;2RC
ω − ω =
ω = ω =
( )( ) ( )
3
i 3 22 20
2 8g 11 2sCR 1 3 C 2R
− −= = =+ − ω
Ring oscillator using opamp inverters
Frequency stability of oscillators
5
Frequency stability of oscillators (contd.,)
Factor that influences the frequency stability of oscillators is active device parameter in oscillator
6
Frequency stability of oscillators (contd.,)
7
( )( )i
2
0 0
2a
1
3sCRg3s1 1 3sCR sCRGB
9 4.51 1R GB GB1 3;R RC RC
=⎛ ⎞+ + +⎜ ⎟⎝ ⎠
ω ω− −+ = ω = =
( )
⎛ ⎞+⎜ ⎟
⎝ ⎠=+ +
= + = ω =when at
when influences the gain
2
1i 2 2 2
2i 0
1
R1 sCRR
g1 3sCR s C R
R 1g 1 1 3R RC
GBs
ω φ=ω
ω⎛ ⎞φ = =⎜ ⎟⎝ ⎠
V V
V
0
0
where2Q3 1;QGB 3
Frequency stability of oscillators (contd.,)
i
0 02 2 2
2 20 0 00 0
0a
0
g in a BFP embedded amplifier is s sK KQ Q
Ks s s s Ks s1 1 1GB Q Q GB Q
K1GBQ
ω ω≅
⎛ ⎞ ⎛ ⎞⎛ ⎞+ + + + + +⎜ ⎟ ⎜ ⎟⎜ ⎟ ω ω ωω ω⎝ ⎠ ⎝ ⎠ ⎝ ⎠ω
ω =ω+
8
Frequency stability of oscillators (contd.,)
9
ω ω ω⎛ ⎞ω = ≅ ω − =⎜ ⎟ω⎛ ⎞ ⎝ ⎠+⎜ ⎟⎝ ⎠
0 0 0a 0
0
Higher the Q of the BPF circuit lower is the sensitivity of the frequency of oscillation to the GB of the opamp.
KK12 GBQ 2GBQK1
2 GBQIf therefore a crystal which has very high
ωω φ ⎛ ⎞= φ = =⎜ ⎟ω ⎝ ⎠V V V 0
0
Q used instead of LC, frequency of oscillation rarely deviates from that of the crystal frequency.
3 1where ;Q2Q GB 3
Voltage Controlled Oscillators (VCO)
10
Double integrator loop based oscillator integrators are replaced by voltage controlled integrators
Voltage Controlled Oscillators (VCO) (contd.,)
11
( ) ( )
RC in oscillator gets replaced by
Such a VCO should however have an amplitude
stabilization scheme to maintain the condition for oscillation throughout. This is not an easy
propos
R
C
C0
R
VRCV
V1RC V RC
ω = ⇒
( ) ( )
ition. Therefore, sine wave VCOs are not
normally preferred to non-sinusoidal VCOs.
VCO sensitivity rad/sec per volt.0 0VCOC R C
1KV V RC V∂ω ω
= = =∂
VCO with Amplitude Stabilization
12
( )
=π
= + π
= Ω = µ
c0
C
Vf20 RC
V 5 2sin 20 VR 5k ;C 0.1 F = ± =at 0 Cf 159Hz 63.6Hz V 5V
Simulation – FM Generator
13
Simulation – FSK Generator
14
= or at CV 6 3V 10Hz
LC Oscillators
( ) ( ) ( )Δ = ω = ω
Δ = + + −i o
Transcondutor as active element embedded
in a passive network made up of R L and C
For the oscillator determinant of the two-port network at
p p is the loop-gain
of the two-p
0
s L l l
0p p 1 g whereg
( ) ( )+ −∴ = ω = ω
i
ort network
Admittance at any port of the
network = p
at ; port admittance at
any port is always zero
s l
l 0
p 1 gg 1
15
LC Oscillators (contd.,)
16
( )
+ −⎡ ⎤⎢ ⎥− +⎣ ⎦Δ = + + + =
ω = ωat and if they are inductive
has to be capacitive and vice-versa.
i f f
m f o f
i o f i o m
0
i o f
Y Y Yg Y Y Y
YY Y Y Y g 0
Y Y Y
Hartley Oscillator
17
( )
= = +ω ω
= ω
ω =+
=
Frequency
Condition
i o1 2 2
f
01 2
2m 2
1
1 1 1Y ;Yj L j L R
Y j C1
L L C
L g RL
Colpitts Oscillator
18
( )
= ω = ω +
=ω
ω =
+
=
Frequency
Condition
i 1 o 22
f
01 2
1 2
1m 2
2
1Y j C ;Y j cR
1Yj L
1C C
LC C
C g RC
Crystal Oscillator
Crystal is a vibrating mechanical resonant system with an equivalent electrical resonant circuit shown
It is mainly a series resonant circuit with very high Q value ranging from 104 to 106.
Crystals are available with resonant frequencies ranging from hundreds of kHz to tens of MHz.
19
Crystal Oscillator (contd.,)
It is represented as
Mainly used for generation of precision frequency clock signals The impedance function of a crystal is given by
( )( )
2
2s ss
2 2p
0 2s p pp
s s 1 1Q
Z ss s 1s C 1
Q
⎡ ⎤+ +⎢ ⎥ωω⎢ ⎥⎣ ⎦=⎡ ⎤ω⎛ ⎞⎢ ⎥× + +⎜ ⎟ω ωω⎢ ⎥⎝ ⎠ ⎣ ⎦
20
Crystal Oscillator (contd.,)
Series resonance frequency
Parallel resonance frequency
where
The quality factors are
As is very close to the quality facto
s1 1
1 0 1 1p s s
1 1 0 0 0
0 1
p 1s 1s p
1 1
p s
1L C
C C C C1 » 1L C C C 2CC C
LLQ ;QR R
ω =
⎛ ⎞+ω = = ω + ω +⎜ ⎟
⎝ ⎠
ωω= =
ω ω
?
r will be close to p sQ Q
21
Crystal Oscillator (contd.,)
Crystal can act as an inductor, capacitor or resistor at w0
It can act as a series resonance circuit or a parallel resonance circuit
22
Conclusion
23
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