High-speed Serial Interface

Lect. 10 – Charge-pump PLL

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PLL Review

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Clock Signal Generation Frequency Synthesis

PLL Review

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Frequency Demodulation

(FM signal)

(Recovered message)

(PLL output)

Limitation of PLL with PD– Narrow linear phase detection range

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AB

VPD

A

BVPD

A

BVPD

Phase Frequency Detector (PFD)

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Vin

Vout

UP

DOWN

UP-DOWN

2π-2π

Duration of (UP-DOWN)

PFD Implementation

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Subtraction and integrationSubtraction Integration

Subtraction

Integration

Voltage modeusing OP amplifiers

Current modeusing charge pump

Charge Pump PLL

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Charge Pump Transfer Function

– Charging (or discharging) time for phase error during one period= 2– Integrated voltage = = 2– Transfer function = 2

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Transfer function of PD + Charge pump + LF

Charge pump

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21

1 1( )2 CP VCOH s I K

s C

( )H s

( )H s

0 dB

-180

ω

ω

-40dB/decade

Feedback Stability• Negative feedback system

– It is unstable when denominator of closed loop transfer function is equal to 0.

– Criteria for unstable condition is;

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H(s)

G(s)

= ( )1 + ( ) ( )

Adder+

-

= −1 0 @∠ − 180°

Charge-pump PLL

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Open loop gain:

12

1

11( )2 CP VCO

sRCH s I Ks C

( )G s

( )G s

0 dB

-180

ω

ω

-90

-40dB/decade

-20dB/decade

zero

Large ripple during transient

Charge-pump PLL

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Ripple reduction with small C2 (≈C1/10)Simplification as 2nd-order system

Stability• Transfer function for charge-pump PLL

– : damping factor– : natural frequency

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= (2 + )/ + 2 + = 2 2 , = 2

Stability

– Poles of transfer function:

– Location of poles are defined by

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+ 2 + = 0= − ± − 1Location of poles Damping

=0 2 imaginary Undamped (oscillation)

0< <1 2 complex conjugate Underdamped

=1 2 real (same) Critically damped

>1 2 real Overdamped

Step Response• x-axis is normalized;

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Undamped

OverdampedCriticallyDamped

Frequency Response

– Transfer function vs. various damping factor.– Large peaking for small damping factor

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Stability

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• Damping factor– Use of = 0.707 is popular even though it is underdamped

because settling time is shorter than = 1

Phase Margin– Open-loop transfer

= 2 ( + 1 )– Gain vs. Phase Margin?

– Zero location vs. Phase Margin

– Damping Factor vs. Phase Margin?

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Phase Margin• Phase margin enhances as loop gain increases

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Magnitude [dB]

Phase [deg]

-90

-180

Phase Margin • Phase margin enhances as zero freq. decreases

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Magnitude [dB]

Phase [deg]

-90

-180

Phase Margin

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• Damping factor vs. phase margin– It is OK to use one of both for stability analysis.

http://www.scribd.com/doc/57004703/86/Relationship-Between-Damping-Ratio-and-Phase-Margin