EE 435 Lecture 42. Phased Locked Loops and VCOs

Transcription

1 EE 435 Lecure 42 d Locked Loops and VCOs

2 Basis PLL Archiecure Loop Filer (LF) Volage Conrolled Oscillaor (VCO) Frequency Divider N Applicaions include: Frequency Demodulaion Frequency Synhesis Clock Synchronizaion Noise filering (exreme) Tracking and calibraed filers.. One of he mos widely used analog blocks Many SoC sysems include muliple PLLs Closely relaed o Delay Locked Loop (DLL)

3 Basis PLL Archiecure Loop Filer (LF) Volage Conrolled Oscillaor (VCO) Frequency Divider N Applicaions by subcaegory: Clock and Daa Recovery Recovering signals when SNR <<<1 Timing generaors in digial sysems

4 Desired Operaion of PLL Loop Filer (LF) Volage Conrolled Oscillaor (VCO) Frequency Divider N =V M sin(ω IN +φ IN ) Desired oupu when locked: =V X sin(nω IN +φ OUT ) Relaionship beween V M and V X is of lile concern Frequency relaionship is criical φ OUT is ofen of criical oo Waveshape of and is ofen of lile concern May be highly disored or even square waves

5 Desired Operaion of PLL Loop Filer (LF) Volage Conrolled Oscillaor (VCO) Frequency Divider N =V M sin(ω IN + φ IN ) Desired oupu when locked: =V X sin(nω IN +φ OUT ) Some Terminology of PLLs Locked / Unlocked Locked when assumes desired value Lock Range f LLOW < f IN < f LHIGH If locked, will remain locked for f IN in lock range Capure Range f CLOW < f IN < f CHIGH If unlocked, will lock for f IN in capure range Free-running frequency frequency of VCO when no locked Harmonic/Subharmonic Lock

6 Desired Operaion of PLL =V M sin(ω IN + φ IN ) =V X sin(nω IN +φ OUT ) Loop Filer (LF) Volage Conrolled Oscillaor (VCO) Frequency Divider N Capure range always less han lock range f LLOW < f CLOW <f CHIGH < f LHIGH Loop filer conrols capure and lock range Jier in VCO oupu srongly dependen upon lock range (large lock range resuls in high jier, low lock range in low jier) Loop filer is ofen dynamic wih wide bandwidh prior o lock and narrow BW afer lock

7 Concepual Operaion of PLL Consider a signal expressed as V=V M sin(φ) If he signal is sinusoidal, can express he argumen φ as φ=ω+θ Taking he ime derivaive, we obain d d Taking he Laplace Transform, we have S s

8 Concepual Operaion of PLL When locked, PLL can be modeled as a linear sysem Small-signal s-domain analysis when PLL is locked Φ sin K PD sin sfb V,I TLF s Loop Filer (LF) V LF K VCO s Volage Conrolled Oscillaor (VCO) Φ sfb Frequency Divider N Φ sout V LF sout sfb K PD sin sfb V T s V LF V LF N sout K s Noe: Dimensions of variables in loop are no he same VCO T PLL s Solving, we obain sout sin T s K K KVCOK s+tlf s N LF PD VCO PD

9 Ofen he LF is low order Example: Assume N=1 and T LF 1 s = 1+RCs Φ sin K PD sin sfb V,I TLF s Loop Filer (LF) V LF K VCO s Volage Conrolled Oscillaor (VCO) Φ sfb Frequency Divider N Φ sout T PLL s TLF s KPDK VCO KPDKVCO s+t s K K s 1+RCs +K K LF VCO PD VCO PD T PLL s KPDK RC 1 K s s + RC VCO K RC 2 VCO PD

10 Ofen he LF is low order Example: Assume N=1 and T LF 1 s = 1+RCs Φ sin K PD sin sfb V,I TLF s Loop Filer (LF) V LF K VCO s Volage Conrolled Oscillaor (VCO) Φ sfb Frequency Divider N Φ sout KPDKVCO TPLL s RC 2 1 KVCOKPD s s + RC RC 2 1 KVCOKPD 2 KVCOKPD 0 2 s s + s s RC RC Q RC Q RCK K VCO PD

11 Volage Conrolled Oscillaors Many differen VCOs can be used Volage Conrolled Oscillaor (VCO) n=3 Im I 0 s I s I s 0 0 X ou Re I 0 Inegraor-Based VCO Im n=3 ω 0 Re I 0 s+ I 0 s+ I 0 s+ X ou I 0 Lossy Inegraor-Based VCO Δα

12 Volage Conrolled Oscillaors Volage Conrolled Oscillaor (VCO) V DD V DD V ou V in M 1 C X V B CX V ou V in V ou V in M 3 M 1 C X V B CX V ou V in V CTRL V CTRL I m1 0d s g sc X I s g sc +g 0d m1 X m3 Inegraor-based VCO Lossy Inegraor-based VCO

13 Volage Conrolled Oscillaors Relaxaion Oscillaor Derived VCO R R Volage Conrolled Oscillaor (VCO) C C R 1 R 2 M 2 -V X V X V SATH V X -V X V SATL T Can have eiher riangle wave or square wave oupus

14 s Many differen s can be used Some Popular Circuis Analog Muliplier Exclusive OR Gae Sample and Hold Charge Pump I X DIV Φ sin Φ sfb Logic I 1 I 2 I OUT I X Charge-pump based Average I OUT is he average phase

15 s Many differen s can be used I X DIV Φ sin Φ sfb Logic I 1 I 2 I OUT -90 o 90 o Δ Average I OUT is he average phase I X Region of Operaion Δ -90 o 90 o 180 o Δ -180 o -90 o 90 o 180 o Region of Operaion Region of Operaion

16 s I 1 I 2 Δ0 I X DIV Φ sin Φ sfb Logic I 1 I 2 I X I OUT I 1 I 2 Δ>0 Average I OUT is he average phase I 1 Δ<0 I 2

17 s I 1 I 2 Δ0 I X DIV Φ sin Φ sfb Logic I 1 I 2 I X I OUT I 1 I 2 Δ>0 Average I OUT is he average phase I 1 I 2 Δ<0 Vulnerable o dead zone problem

18 Loop Filers Many differen s can be used Ofen he loop filer is firs or second order Usually he loop filer circui is very simple TLF s Loop Filer (LF) I IN C R V I OUT INAVG TLF s R 1+RCs Basic firs-order LF wih average curren difference as inpu

19 Wha is he phase of a signal? V 1 =V M1 sin(ω 1 + φ 1 ) V 2 =V M2 sin(ω 2 + φ 2 ) K PD ( φ 1 -φ 2 ) Assume ω 1 = ω 2 =ω If V I can be expressed as V 1 =V M1 sin(ω+ φ 1 ) he phase is φ 1 Bu wha is he phase if ω is ime varying? Or wha is he phase if his funcional form does no really characerize V()? Or wha if ω 1 ω 2? Wha does a phase deecor do if he wo inpus are no a he same frequency?

20 Wha is he phase of a signal? V 1 =V M1 sin(ω 1 + φ 1 ) V 2 =V M2 sin(ω 2 + φ 2 ) /Frequency K PD ( φ 1 -φ 2 ) Mos s are acually /Frequency s Large oupu when frequency difference exiss Also provides oupu when phase difference exiss afer frequencies are mached

21 End of Lecure 42