Phase-Locked Loops for High-Frequency Receivers and Transmitters Part 2 by Mike Curtin and Paul O Brien

Transcription

1 Phae-Locke Loop for High- Receiver an Tranmitter Part by Mike Curtin an Paul O Brien The firt part of thi erie of article introuce the baic concept of phae-locke loop (PLL). The PLL architecture an principle of operation wa ecribe an accompanie by an example of where a PLL might be ue in a communication ytem. In thi econ part, we will focu on a etaile examination of two critical pecification aociate with PLL: phae noie an reference pur. What caue them an how can they be minimize? The icuion will inclue meaurement technique an the effect of thee error on ytem performance. We will alo conier output leakage current, with an example howing it ignificance in openloop moulation cheme. oie in Ocillator Sytem In any ocillator eign, frequency tability i of critical importance. We are interete in both long-term an hort-term tability. Longterm frequency tability i concerne with how the output ignal varie over a long perio of time (hour, ay or month). It i uually pecifie a the ratio, f/f for a given perio of time, expree a a percentage or in B. Short-term tability, on the other han, i concerne with variation that occur over a perio of econ or le. Thee variation can be ranom or perioic. A pectrum analyzer can be ue to examine the hort-term tability of a ignal. Figure how a typical pectrum, with ranom an icrete frequency component cauing a broa kirt an puriou peak. f 0 Ranom oie Fluctuation Dicrete Spuriou Signal Figure. Short-term tability in ocillator. The icrete puriou component coul be caue by known clock frequencie in the ignal ource, power line interference, an mixer prouct. The broaening caue by ranom noie fluctuation i ue to phae noie. It can be the reult of thermal noie, hot noie an/or flicker noie in active an paive evice. Phae oie in Voltage-Controlle Ocillator Before we look at phae noie in a PLL ytem, it i worth coniering the phae noie in a voltage-controlle ocillator (VCO). An ieal VCO woul have no phae noie. It output a een on a pectrum analyzer woul be a ingle pectral line. In practice, of coure, thi i not the cae. There will be jitter on the output, an a pectrum analyzer woul how phae noie. To help unertan phae noie, conier a phaor repreentation, uch a that hown in Figure. θ rm ω o V rm V SPK ω m Figure. Phaor repreentation of phae noie. A ignal of angular velocity ω O an peak amplitue V SPK i hown. Superimpoe on thi i an error ignal of angular velocity ω m. θrm repreent the rm value of the phae fluctuation an i expree in rm egree. In many raio ytem, an overall integrate phae error pecification mut be met. Thi overall phae error i mae up of the PLL phae error, the moulator phae error an the phae error ue to bae ban component. In GSM, for example, the total allowe i 5 egree rm. Leeon Equation Leeon (ee Reference 6) evelope an equation to ecribe the ifferent noie component in a VCO. FkT fo LPM 0 log A QL fm 8 () where: L PM i ingle-ieban phae noie enity (Bc/Hz) F i the evice noie factor at operating power level A (linear) k i Boltzmann contant, J/K T i temperature (K) A i ocillator output power (W) Q L i loae Q (imenionle) f O i the ocillator carrier frequency f m i the frequency offet from the carrier Analog Dialogue 33-5 ( 999 Analog Device)

2 For Leeon equation to be vali, the following mut be true: f m, the offet frequency from the carrier, i greater than the /f flicker corner frequency; the noie factor at the operating power level i known; the evice operation i linear; Q inclue the effect of component loe, evice loaing an buffer loaing; a ingle reonator i ue in the ocillator. Phae oie (Bc/Hz) 9B/Octave f f /f flicker noie tranition 6B/Octave Leeon' Equation Applie f 0 / Q L Flat Offet, f m (Hz) Figure 3. Phae noie in a VCO v. frequency offet. Leeon equation only applie in the knee region between the break (f ) to the tranition from the /f (more generally /f γ ) flicker noie frequency to a frequency beyon which amplifie white noie ominate (f ). Thi i hown in Figure 3 [γ = 3]. f houl be a low a poible; typically, it i le than khz, while f i in the region of a few MHz. High-performance ocillator require evice pecially electe for low /f tranition frequency. Some guieline to minimizing the phae noie in VCO are:. Keep the tuning voltage of the varactor ufficiently high (typically between 3 an 3.8 V). Ue filtering on the c voltage upply. 3. Keep the inuctor Q a high a poible. Typical off-the-helf coil provie a Q of between 50 an Chooe an active evice that ha minimal noie figure a well a low flicker frequency. The flicker noie can be reuce by the ue of feeback element. 5. Mot active evice exhibit a broa U-hape noie-figure-v.- bia-current curve. Ue thi information to chooe the optimal operating bia current for the evice. 6. Maximize the average power at the tank circuit output. 7. When buffering the VCO, ue evice with the lowet poible noie figure. Cloing The Loop Having looke at phae noie in a free-running VCO an coniere how it can be minimize, we will now conier the effect of cloing the loop (ee Part of the erie) on phae noie. S REF Phae Detector - S Charge Pump K S CP Loop Filter Figure 4. PLL-phae-noie contributor. Figure 4 how the main phae noie contributor in a PLL. The ytem tranfer function may be ecribe by the following equation. Cloe Loop Gain = G = K Kv Z H ( ) G GH Z () VCO K V S VCO S TOT () (3) = (4) Cloe Loop Gain = K K Z v ( ) K K Z v ( ) For the icuion that follow, we will efine S REF a the noie that appear on the reference input to the phae etector. It i epenent on the reference ivier circuitry an the pectral purity of the main reference ignal. S i the noie ue to the feeback ivier appearing at the frequency input to the phae etector. S CP i the noie ue to the phae etector (epening on it implementation). An S VCO i the phae noie of the VCO a ecribe by equation evelope earlier. The overall phae noie performance at the output epen on the term ecribe above. All the effect at the output are ae in an rm fahion to give the total noie of the ytem. Thu: STOT = X Y Z (6) where: S TOT i the total phae noie power at the output X i the noie power at the output ue to S an S REF. Y i the noie power at the output ue to S CP. Z i the noie power at the output ue to S VCO. The noie term at the PD input, S REF an S, will be operate on in the ame fahion a F REF an will be multiplie by the cloe loop gain of the ytem. X = SREF S (5) G (7) GH At low frequencie, inie the loop banwith, GH >> an X = SREF S (8) Analog Dialogue 33-5 ( 999 Analog Device)

3 At high frequencie, outie the loop banwith, G << an X 0 (9) The overall output noie contribution ue to the phae etector noie, S CP, can be calculate by referencing S CP back to the input of the PFD. The equivalent noie at the PD input i S CP /K. Thi i then multiplie by the cloe-loop gain: Y G = SCP (0) K GH Phae oie Meaurement One of the mot common way of meauring phae noie i with a high frequency pectrum analyzer. Figure 6 i a typical example of what woul be een. P S S C (f) = P SSB /P S Finally, the contribution of the VCO noie, S VCO, to the output phae noie i calculate in a imilar manner. The forwar gain thi time i imply. Therefore it contribution to the output noie i: Hz P SSB Z = SVCO () GH f 0 S C (f) in B = 0 log [S C (f)], Bc/Hz f G, the forwar loop gain of the cloe loop repone, i uually a low pa function; it i very large at low frequencie an mall at high frequencie. H i a contant, /. The enominator of the above expreion i therefore low pa, o S VCO i actually highpa filtere by the cloe loop. A imilar ecription of the noie contributor in a PLL/VCO can be foun in Reference. Recall that the cloe-loop repone i a low-pa filter with a 3-B cutoff frequency, B W, enote the loop banwith. For frequency offet at the output le than B W, the ominant term in the output phae noie repone are X an Y, the noie term ue to reference noie, (counter noie), an charge pump noie. Keeping S an S REF to a minimum, keeping K large an keeping mall will thu minimize the phae noie inie the loop banwith, B W. Becaue program the output frequency, it i not generally available a a factor in noie reuction. For frequency offet much greater than B W, the ominant noie term i that ue to the VCO, S VCO. Thi i ue to the high pa filtering of the VCO phae noie by the loop. A mall value of B W woul be eirable a it woul minimize the total integrate output noie (phae error). However a mall B W reult in a low tranient repone an increae contribution from the VCO phae noie inie the loop banwith. The loop banwith calculation therefore mut trae off tranient repone an total output integrate phae noie. To how the effect of cloing the loop on a PLL, Figure 5 how an overlay of the output of a free-running VCO an the output of a VCO a part of a PLL. ote that the in-ban noie of the PLL ha been attenuate compare to that of the free-running VCO. V AVG = 0 f o = MHz Span = 0.00kHz RBW = 00Hz VBW = 00Hz SWP =.60ec Output from VCO in PLL Output from Free-Running VCO Figure 5. Phae noie on a free-running VCO an a PLLconnecte VCO. Figure 6. Phae noie efinition. With the pectrum analyzer we can meaure the pectral enity of phae fluctuation per unit banwith. VCO phae noie i bet ecribe in the frequency omain where the pectral enity i characterize by meauring the noie ieban on either ie of the output ignal center frequency. Phae noie power i pecifie in ecibel relative to the carrier (Bc/Hz) at a given frequency offet from the carrier. The following equation ecribe thi SSB phae noie (Bc/Hz). S C PS ( f) =0 log () P Spectrum Analyzer HP856E (6.5GHz) HP856E (3GHz) HP8563E (6GHz) Reference Output (0Bm, 50 ) Input (50 ) 5 Ω SSB R PFD ADF40 Family TEST SETUP Syntheizer 5 Ω Loop Filter VCO Z() K V / Power Splitter Figure 7. Meauring phae noie with a pectrum analyzer. The 0-MHz, 0-Bm reference ocillator, available on the pectrum analyzer rear-panel connector, ha excellent phae noie performance. The R ivier, ivier, an the phae etector are part of ADF4 frequency yntheizer. Thee ivier are programme erially uner the control of a PC. The frequency an phae noie performance are oberve on the pectrum analyzer. Figure 8 illutrate a typical phae noie plot of a PLL yntheizer uing an ADF4 PLL with a Murata VCO, MQE The frequency an phae noie were meaure in a 5-kHz pan. The reference frequency ue wa f REF = 00 khz (R = 50) an the output frequency wa 880 MHz ( = 9400). If thi were an iealworl PLL yntheizer, a ingle icrete tone woul be iplaye riing up above the pectrum analyzer noie floor. What i iplaye here i the tone, with the phae noie ue to the loop component. The loop filter value were choen to give a loop Analog Dialogue 33-5 ( 999 Analog Device) 3

4 PHASE OISE PLOT 0B per iviion R L = 0Bm V AVG = 34 Span = 5.00kHz RBW = 0Hz VBW = 0Hz SWP =.9ec MKR = -79B MKR oie = Bc/Hz again the baic moel for the PLL which wa icue in Part of thi erie. Thi i hown again in Figure 9. When the PLL i in lock, the phae an frequency input to the PFD (f REF an f ) are eentially equal, an, in theory, one woul expect that there to be no output from the PFD. However, thi can create problem (to be icue in Part 3 of thi erie), o the PFD i eigne uch that, in the locke conition, the current pule from the charge pump will typically be a hown in Figure 0. F REF -KHz -KHz 880MHz KHz KHz F Figure 8. Typical pectrum-analyzer output. banwith of approximately 0 khz. The flat part of the phae noie for frequency offet le than the loop banwith i actually the phae noie a ecribe by X an Y in the ection cloing the loop for cae where f i inie the loop banwith. It i pecifie at a -khz offet. The value meaure, the phae-noie power in a -Hz banwith, wa Bc/Hz. It i mae up of the following:. Relative power in Bc between the carrier an the ieban noie at -khz offet.. The pectrum analyzer iplay the power for a certain reolution banwith (RBW). In the plot, a 0-Hz RBW i ue. To repreent thi power in a -Hz banwith, 0log(RBW) mut be ubtracte from the value obtaine from (). 3. A correction factor, which take into account the implementation of the RBW, the log iplay moe an etector characteritic, mut be ae to the reult obtaine in (). 4. Phae noie meaurement with the HP 856E can be mae quickly by uing the marker noie function, MKR OISE. Thi function take into account the above three factor an iplay the phae noie in Bc/Hz. The phae noie meaurement above i the total output phae noie at the VCO output. If we want to etimate the contribution of the PLL evice (noie ue to phae etector, R& ivier an the phae etector gain contant), the reult mut be ivie by (or 0 log be ubtracte from the above reult). Thi give a phae-noie floor of [ log(9400)] = 65.3 Bc/Hz. Reference Spur In an integer- PLL (where the output frequency i an integer multiple of the reference input), reference pur are caue by the fact that the charge pump output i being continuouly upate at the reference frequency rate. Conier I OUT Figure 0. Output current pule from the PFD charge pump. Although thee pule have a very narrow with, the fact that they exit mean that the c voltage riving the VCO i moulate by a ignal of frequency f REF. Thi prouce reference pur in the RF output occurring at offet frequencie that are integer multiple of f REF. A pectrum analyzer can be ue to etect reference pur. Simply increae the pan to greater than twice the reference frequency. A typical plot i hown in Figure. In thi cae the reference frequency i 00 khz an the iagram clearly how reference pur at ±00 khz from the RF output of 880 MHz. The level of thee pur i 90 B. If the pan were increae to more than four time the reference frequency, we woul alo ee the pur at ( f REF ). -00KHz -00KHz 880MHz 00KHz 00KHz 0B per iviion R L = 0Bm V AVG = 00 Span = 500kHz RBW = 3.0kHz VBW = 3.0kHz SWP = 40m MKR = -75B, 00kHz Figure. Output pectrum howing reference pur. F REF ( REF ) CP e() PFD K Z() - F ( ) Error Detector Loop Filter VCO Feeback Divier K v Figure 9. Baic PLL moel. F O ( O ) Charge Pump Leakage Current When the CP output from the yntheizer i programme to the high impeance tate, there houl, in theory, be no leakage current flowing. In practice, in ome application the level of leakage current will have an impact on overall ytem performance. For example, conier an application where a PLL i ue in openloop moe for frequency moulation a imple an inexpenive way of implementing FM that alo allow higher ata rate than moulating in cloe-loop moe. For FM, a cloe-loop metho work fine but the ata rate i limite by the loop banwith. 4 Analog Dialogue 33-5 ( 999 Analog Device)

5 A ytem that ue open-loop moulation i the European corle telephone ytem, DECT. The output carrier frequencie are in a range of.77 GHz to.90 GHz an the ata rate i high;.5 Mbp. XTAL R Gauian Filter Error Detector Loop Filter VCO CP - PFD K Z() Feeback Divier Figure. Block iagram of open-loop moulation. A block iagram of open-loop moulation i hown in Figure. The principle of operation i a follow: The loop i initially cloe to lock the RF output, f OUT = f REF. The moulating ignal i turne on an at firt the moulation ignal i imply the c mean of the moulation. The loop i then opene, by putting the CP output of the yntheizer into high-impeance moe, an the moulation ata i fe to the Gauian filter. The moulating voltage then appear at the VCO where it i multiplie by K V. When the ata burt finihe, the loop i returne to the cloe loop moe of operation. A the VCO uually ha a high enitivity (typical figure are between 0 an 80 MHz/volt), any mall voltage rift before the VCO will caue the output carrier frequency to rift. Thi voltage rift, an hence the ytem frequency rift, i irectly epenent on the leakage current of the charge pump, CP, when in the high impeance tate. Thi leakage will caue the loop capacitor to charge or icharge epening on the polarity of the leakage current. For example, a leakage current of na woul caue the voltage on the loop capacitor (000 pf for example) to charge or icharge by V/t = I/C ( V/ in thi cae). Thi, in turn, woul caue the VCO to rift. So, if the loop i open for m an the K V of the VCO i 50 MHz/Volt, the frequency rift caue by -na leakage into a 000-pF loop capacitor woul be 50 khz. In fact, the DECT burt are generally horter (0.5 m), o the rift will be even le in practice for the loop capacitance an leakage current ue in the example. However, it oe erve to illutrate the importance of charge-pump leakage in thi type of application. Receiver Senitivity Receiver enitivity pecifie the ability of the receiver to repon to a weak ignal. Digital receiver ue maximum bit-error rate (BER) at a certain rf level to pecify performance. In general, evice gain, noie figure, image noie, an local-ocillator (LO) wieban noie all combine to prouce an equivalent noie figure. Thi i then ue to calculate the overall receiver enitivity. Wieban noie in the LO can elevate the noie level an thu egrae the overall noie factor. For example, wieban phae noie at F LO F will prouce noie prouct at F. Thi irectly impact the receiver enitivity. Thi wieban phae noie i primarily epenent on the VCO phae noie. Cloe-in phae noie in the LO will alo impact enitivity. Obviouly, any noie cloe to F LO will prouce noie prouct cloe to F an impact enitivity irectly. K v F O Receiver Selectivity Receiver electivity pecifie the tenency of a receiver to repon to channel ajacent to the eire reception channel. Ajacentchannel interference (ACI), a commonly ue term in wirele ytem, i alo ue to ecribe thi phenomenon. When coniering the LO ection, the reference pur are of particular importance with regar to electivity. Figure 3 i an attempt to illutrate how a puriou ignal at the LO, having the ame pacing a the channel-pacing frequency, can tranlate energy from an ajacent raio channel irectly onto the. Thi i of particular concern if the eire receive ignal i itant an weak an the unwante ajacent channel i nearby an trong, which can often be the cae. So, the lower the reference pur in the PLL, the better it will be for ytem electivity. Concluion In Part of thi erie we have icue ome of the critical pecification aociate with PLL yntheizer, ecribe meaurement technique, an hown example of reult. In aition, there ha been a brief icuion of the ytem implication of phae noie, reference pur an leakage current. In the final part of thi erie, we will examine the builing block that go to make up a PLL yntheizer. In aition, there will be a comparion between integer- an fractional- architecture for PLL. Acknowlegment The author woul like to acknowlege Brenan Daly of the Analog Device GP RF Application Group in Limerick for the plot of phae noie an reference pur. Reference. Mini-Circuit Corporation, VCO Deigner Hanbook, L.W. Couch, Digital an Analog Communication Sytem, Macmillan Publihing Company, ew York, P. Vizmuller, RF Deign Guie, Artech Houe, R.L. Bet, Phae Locke Loop: Deign, Simulation an Application, 3r eition, McGraw-Hill, D.E. Fague, Open Loop Moulation of VCO for Corle Telecommunication, RF Deign, July D. B. Leeon, A Simplifie Moel of Feeback Ocillator oie Spectrum, Proceeing of the IEEE, Volume 4, February 965, pp LO Figure 3. Ajacent Channel Interference. RF Analog Dialogue 33-5 ( 999 Analog Device) 5