Tutorial 5: PLL, solutions

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1 TSE03 Itegrated Radio Frequecy Circuit 08 /6 Problem (9. Coure book) Tutorial 5: PLL, olutio Determie the cloed-loo trafer fuctio, the damig factor ζ, ad the atural frequecy ω for the frequecy-multilyig PLL how below. φ i F() R φ V V cot C M Solutio: F ( ) C R C R C The cloe loo Trafer Fuctio: i i M M ( ) ( R C ) M R C M R C M M RC R C R C M R C M LPF LPF M

2 TSE03 Itegrated Radio Frequecy Circuit 08 /6 Problem (9.3 Coure book) Suoe the charge-um PLL how below i deiged with ζ =, ad a loo badwidth of ωi/5, ad a tuig rage of 0 %. Aume Vcot ca vary from 0 to VDD. Prove that the voltage dro acro the loo filter reitor reache roughly.6πvdd if o ecod caacitor i ued. Solutio: From (9.0) ad (9.) I C R I C From (9.8), the time cotat of the loo i 4 R I ad the loo badwidth i i 5 R I 4 From the tuig rage aumtio, we have (V cot,max -V cot,max ) =0%*w i () () From () ad (): V DD RI 0. i R I 4 V 5 0. DD.6V DD

3 TSE03 Itegrated Radio Frequecy Circuit 08 3/6 Problem 3 Let u coider deigig a commo ource ower amlifier for a battery-oerated ortable device. We aume the baic ecificatio: - 30 dbm ut ower i to be delivered to the atea (ZL = 50 Ω), which correod to RL i the figure. - VDD, the ower uly voltage i.5 V. Deed o the battery ad alo i limited by the MOSFET breakdow voltage. a) How much ut ower i dbm ca we achieve with modifyig the amlifier?, where V i the eak voltage over the traitor VDD. Awer: V =.5 V, RL = 50 Ω => PL =.5 / (*50) = W = 8 dbm. b) How high uly do we eed to reach 30 dbm ut ower? Awer: PL = 30 dbm = W. = = 0 V Achievig thi take everal batterie i erie. Alo, 0 V uly will create high voltage over the traitor - 0 V, why? - which i much higher tha tadard CMOS traitor ca hadle. We eed to tet aother way to reach 30 dbm ut ower. c) What load (RL) ca give 30 dbm ut ower? Awer: => RL = 3. Ω. We eed a imedace traformatio etwork (ometime called a matchig etwork, but ot trictly correct) at the amlifier ut. d) Let u deig a traformatio etwork that traform the 50 Ω load to the 3. Ω load the ower amlifier wat to ee to deliver 30 dbm to the load. Which etwork() from the book, below, ca do the job? Which oe i bet uited for our exitig amlifier?

4 TSE03 Itegrated Radio Frequecy Circuit 08 4/6 Awer: (a) ad (b) ca be ued, we wat to traform 3. Ω to 50 Ω, i.e. Re {Zi} < RL. If C i the exitig circuit i ot very large (BFC), it will alo be art of the traformatio etwork. Eaier maybe to elect (b) ice we alo eed a erie C (ay value) to block DC curret to flow from VDD to RL. e) Maybe we ca ue the bodwire at the ut of the amlifier ( from the chi to the ackage), the etwork (a) i how it will look like. (But we eed to add a large C alo a the DC block omewhere before the load.) Calculate L ad C value for GHz uig traformatio (a) above. Let Q of the traformatio etwork be very high. Ca we ue a bodwire? Awer: See ectio.5.3 i the book: Settig the imagiary art to 0: So, C i give by (.8) with Zi = 3. Ω, ad L by (.8), whe the Q value i high. C = = 6.4 F. L = 0.99 H. A mm igle bodwire i aroud H. Ye, the L of the matchig etwork ca be a bodwire!

5 TSE03 Itegrated Radio Frequecy Circuit 08 5/6 Problem 4 Comute the maximum efficiecy of the cacode PA how here. Aume M ad M early tur off but their drai curret ca be aroximated by iuoid. Awer: The efficiecy (drai efficiecy) i The voltage i ode X will wig betwee (almot) 0 ad *VDD. PL = (VDD/) / ( Ri) where Ri i the aaret imedace i the matchig etwork from ode X. ID = VDD / Ri => = 50 %. The efficiecy i the ame for a cacode a for a igle traitor.

6 TSE03 Itegrated Radio Frequecy Circuit 08 6/6 Homework I the PLL how below, derive the ut-to-oie V oie trafer fuctio. F() V oie φ i R C φ Awer: F ( ) C R C R C ( ) H ( ) Voie( ) F( ) ( RC ) ( R C ) ( ( RC ) ( R C ) )

ECEN689: Special Topics in Optical Interconnects Circuits and Systems Spring 2016

ECEN689: Special Topics in Optical Interconnects Circuits and Systems Spring 2016 EEN689: Special Topic i Optical Itercoect ircuit ad Sytem Sprig 06 Lecture 6: Limitig mplifier (L) Sam Palermo alog & Mixed-Sigal eter Texa &M Uiverity oucemet & geda Multi-tage limitig amplifier Badwidth