Analog Circuits and Systems Prof. K Radhakrishna Rao

Lecture 33: Transconductor based Oscillator

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Review

  Gyrator based RC Oscillators   Wien Bridge Oscillator   Quadrature Oscillator

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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

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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

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

Voltage Controlled Oscillators (VCO)

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Double integrator loop based oscillator integrators are replaced by voltage controlled integrators

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

= = =∂

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

Simulation – FM Generator

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Simulation – FSK Generator

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= 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

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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

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

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

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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