TFE4188 - Lecture 8

Clocks and PLLs

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Goal

Why do we need to generate clocks

Introduction to PLLs

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Why

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Digital

Radio

Energy harvesters

Switched regulators

ADCs

Accurate delay

SC filters

...

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PLL

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A_m(t) \times cos\left( 2 \pi f_{carrier}t + \phi_{m}(t)\right)

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PLL Example

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PLLs need calculation!

#noCowboyDesign

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\phi(t) = 2 \pi \int_0^t f(\tau) d\tau

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Loop gain

\(\frac{\phi_d}{\phi_{in}} = \frac{1}{1 + L(s)}\)

L(s) = \frac{ K_{osc} K_{pd} K_{lp} H_{lp}(s) }{N s}

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Controlled oscillator

K_{osc} = 2 \pi\frac{ df}{dV_{cntl}}

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SUN_PLL_SKY130NM/sim/ROSC/

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Phase detector and charge pump

K_{pd} = \frac{I_{cp}}{2 \pi}

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Loop filter

K_{lp}H_{lp}(s)= K_{lp}\left(\frac{1}{s} + \frac{1}{\omega_z}\right)

K_{lp}H_{lp}(s) = \frac{1}{s(C_1 + C_2)}\frac{1 + s R C_1}{1 + sR\frac{C_1C_2}{C_1 + C_2}}

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Divider

K_{div} = \frac{1}{N}

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Loop transfer function

L(s) = \frac{ K_{osc} K_{pd} K_{lp} H_{lp}(s) }{N s}

Python model

sun_pll_sky130nm/jupyter/pll - interactive

sun_pll_sky130nm/jupyter/pfd

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Summary

Everything on the chip wants a clock, and every clock is a compromise between frequency accuracy (ppm), phase noise and power
A crystal gives the accurate reference; the PLL multiplies it up to the frequency the system needs
PFD turns phase error into pulse width, the charge pump into charge, the loop filter into a control voltage, the oscillator into frequency, and the divider closes the loop
The type-II loop needs its zero: C1 sets the zero with R, C2 cleans the ripple, and the loop bandwidth balances reference noise against VCO noise
Inside the bandwidth the PLL follows the reference; outside, the oscillator is on its own - phase noise plots read exactly that way
SUN_PLL is the whole story in five schematics: ROSC, PFD, charge pump, loop filter, divider

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Would you like to know more?

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SUN_PLL_SKY130NM

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Thanks!

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