analog circuits and systems · 2017. 8. 4. · gyrator based rc oscillators ... of the frequency of...
TRANSCRIPT
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Analog Circuits and Systems Prof. K Radhakrishna Rao
Lecture 33: Transconductor based Oscillator
1
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Review
Gyrator based RC Oscillators Wien Bridge Oscillator Quadrature Oscillator
2
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Review (contd.,)
3
Quadrature oscillator/double integrator oscillator as an LC Oscillator
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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
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Frequency stability of oscillators
5
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Frequency stability of oscillators (contd.,)
Factor that influences the frequency stability of oscillators is active device parameter in oscillator
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Frequency stability of oscillators (contd.,)
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( )( )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
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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+
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Frequency stability of oscillators (contd.,)
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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
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Voltage Controlled Oscillators (VCO)
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Double integrator loop based oscillator integrators are replaced by voltage controlled integrators
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Voltage Controlled Oscillators (VCO) (contd.,)
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( ) ( )
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
= = =∂
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VCO with Amplitude Stabilization
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( )
=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
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Simulation – FM Generator
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Simulation – FSK Generator
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= or at CV 6 3V 10Hz
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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
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LC Oscillators (contd.,)
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( )
+ −⎡ ⎤⎢ ⎥− +⎣ ⎦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
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Hartley Oscillator
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( )
= = +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
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Colpitts Oscillator
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( )
= 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
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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.
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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⎢ ⎥⎝ ⎠ ⎣ ⎦
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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
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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
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Conclusion
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