6.976 High Speed Communication Circuits and Systems Lecture 16 Noise in Integer-N Frequency Synthesizers

Transcription

1 6.976 High Speed Communication Circuits and Systems Lecture 16 in Integer-N Frequency Synthesizers Michael Perrott Massachusetts Institute o Technology Copyright 23 by Michael H. Perrott

2 Frequency Synthesizer in Wireless Systems From Antenna and Bandpass Filter Z in PC board Mixer trace RF in IF out Z Package o LNA To Filter Interace Reerence Frequency Frequency Synthesizer VCO LO signal Phase o Synthesizer noise has a negative impact on system - Receiver lower sensitivity, poorer blocking perormance - Transmitter increased spectral emissions (output spectrum must meet a mask requirement) is characterized in requency domain

3 Modeling or Frequency Synthesizers PLL dynamics set VCO carrier requency Extrinsic noise (rom PLL) v n (t) Intrinsic noise S out () o Phase v c (t) v in (t) out(t) To PLL PLL has an impact on VCO noise in two ways - Adds extrinsic noise rom various PLL circuits - Highpass ilters VCO noise through PLL eedback dynamics Focus on modeling the above based on phase deviations - Simpler than dealing directly with PLL sine wave output

4 Phase Deviation Model or Analysis PLL dynamics set VCO carrier requency Note: K v units are Hz/V Extrinsic noise (rom PLL) v n (t) Intrinsic noise Φ vn (t) Frequency-domain view S out () o Phase v c (t) v in (t) 2πK v s Φ out 2cos(2π o t+φ out (t)) out(t) To PLL Model the impact o noise on instantaneous phase - Relationship between PLL output and instantaneous phase - Output spectrum (rom Lecture 12)

5 Phase Versus Spurious Phase noise is non-periodic S out () 1 S Φout () dbc/hz - - o o Described as a spectral density relative to carrier power Spurious noise is periodic S out () dbc - - o o Described as tone power relative to carrier power 1 spur 1 d spur 2 2 spur

6 Sources o in Frequency Synthesizers Reerence Jitter Reerence Feedthrough Charge Pump VCO -2 db/dec T 1/T re(t) div(t) PFD e(t) Divider Jitter Extrinsic noise sources to VCO - Reerence/divider jitter and reerence eedthrough - Charge pump noise Charge Pump Divider N Loop Filter v(t) VCO

7 Modeling the Impact o on Output Phase o PLL Divider/Reerence Jitter S Φjit () Reerence Feedthrough S Espur () Charge Pump S Ιcpn () VCO S Φvn () -2 db/dec 1/T Φ jit [k] e spur (t) Ι cpn (t) Φ vn (t) Φ re [k] Φ div [k] α π PFD e(t) I cp Charge Pump 1 N H() Loop Filter v(t) K V j VCO Φ out (t) Divider Determine impact on output phase by deriving transer unction rom each noise source to PLL output phase - There are a lot o transer unctions to keep track o!

8 Simpliied Model PFD-reerred S En () VCO-reerred S Φvn () -2 db/dec 1/T e n (t) Φ vn (t) Φ re [k] Φ div [k] α π PFD e(t) I cp Charge Pump 1 N H() Loop Filter v(t) K V j VCO Φ out (t) Divider Reer all PLL noise sources (other than the VCO) to the PFD output - PFD-reerred noise corresponds to the sum o these noise sources reerred to the PFD output

9 Impact o PFD-reerred on Synthesizer Output PFD-reerred S En () VCO-reerred S Φvn () -2 db/dec 1/T e n (t) Φ vn (t) Φ re [k] Φ div [k] α π PFD e(t) I cp Charge Pump 1 N H() Loop Filter v(t) K V j VCO Φ out (t) Divider Transer unction derived using Black s ormula

10 Impact o VCO-reerred on Synthesizer Output PFD-reerred S En () VCO-reerred S Φvn () -2 db/dec 1/T e n (t) Φ vn (t) Φ re [k] Φ div [k] α π PFD e(t) I cp Charge Pump 1 N H() Loop Filter v(t) K V j VCO Φ out (t) Divider Transer unction again derived rom Black s ormula

11 A Simpler Parameterization or PLL Transer Functions PFD-reerred S En () VCO-reerred S Φvn () -2 db/dec 1/T e n (t) Φ vn (t) Φ re [k] Φ div [k] α π PFD e(t) I cp Charge Pump 1 N H() Loop Filter v(t) K V j VCO Φ out (t) Divider Deine G() as Always has a gain o one at DC - A() is the open loop transer unction o the PLL

12 Parameterize Transer Functions in Terms o G() PFD-reerred noise VCO-reerred noise

13 Parameterized PLL Model PFD-reerred S En () VCO-reerred S Φvn () -2 db/dec 1/T e n (t) Φ vn (t) o α π N G() o 1-G() Φ npd (t) Divider Control Φ c (t) o Frequency Setting (assume noiseless or now) Φ n (t) Φ nvco (t) Φ out (t) PFD-reerred noise is lowpass iltered VCO-reerred noise is highpass iltered Both ilters have the same transition requency values - Deined as o

14 Impact o PLL Parameters on Scaling PFD-reerred S En () 1/T e n (t) VCO-reerred S Φvn () -2 db/dec Φ vn (t) Radians 2 /Hz α π N 2 S en () S Φvn () o α π N G() o 1-G() Φ npd (t) Divider Control Φ c (t) o Frequency Setting (assume noiseless or now) Φ n (t) Φ nvco (t) Φ out (t) PFD-reerred noise is scaled by square o divide value and inverse o PFD gain - High divide values lead to large multiplication o this noise VCO-reerred noise is not scaled (only iltered)

15 Optimal Bandwidth Setting or Minimum PFD-reerred S En () 1/T e n (t) VCO-reerred S Φvn () -2 db/dec Φ vn (t) Radians 2 /Hz ( o ) opt α π N 2 S en () S Φvn () o α π N G() o 1-G() Φ npd (t) Divider Control Φ c (t) o Frequency Setting (assume noiseless or now) Φ n (t) Φ nvco (t) Φ out (t) Optimal bandwidth is where scaled noise sources meet - Higher bandwidth will pass more PFD-reerred noise - Lower bandwidth will pass more VCO-reerred noise

16 Resulting Output with Optimal Bandwidth PFD-reerred S En () 1/T e n (t) VCO-reerred S Φvn () -2 db/dec Φ vn (t) Radians 2 /Hz ( o ) opt α π N 2 S en () S Φvn () Φ npd (t) Divider Control Φ c (t) o Frequency Setting (assume noiseless or now) o α π N G() Φ n (t) o 1-G() Φ nvco (t) Φ out (t) Radians 2 /Hz S Φnpd () ( o ) opt S Φnvco () PFD-reerred noise dominates at low requencies - Corresponds to close-in phase noise o synthesizer VCO-reerred noise dominates at high requencies - Corresponds to ar-away phase noise o synthesizer

17 Analysis o Charge Pump Impact Charge Pump S Ιcpn () VCO S Φvn () -2 db/dec PFD-reerred e n (t) Ι cpn (t) Φ vn (t) Φ re [k] Φ div [k] α π PFD e(t) I cp Charge Pump We can reer charge pump noise to PFD output by simply scaling it by 1/I cp H() Loop Filter 1 N Divider v(t) K V j VCO Φ out (t)

18 Calculation o Charge Pump Impact Charge Pump S Ιcpn () VCO S Φvn () -2 db/dec PFD-reerred e n (t) Ι cpn (t) Φ vn (t) Φ re [k] Φ div [k] α π PFD e(t) I cp Charge Pump Contribution o charge pump noise to overall output noise 1 N Divider H() Loop Filter v(t) K V j VCO Φ out (t) - Need to determine impact o I cp on S Icpn ()

19 Impact o Transistor Current Value on its I bias I d 2 i dbias M 1 M 2 i d 2 W L current bias C big current source Charge pump noise will be related to the current it creates as Recall that g do is the channel resistance at zero V ds - At a ixed current density, we have

20 Impact o Charge Pump Current Value on Output Recall Given previous slide, we can say - Assumes a ixed current density or the key transistors in the charge pump as I cp is varied Thereore - Want high charge pump current to achieve low noise - Limitation set by power and area considerations

21 Impact o Synthesizer on Transmitters S x () S y () reduction o SNR out-o-band emission IF RF x(t) y(t) out(t) S out () close-in phase noise Synthesizer LO ar-away phase noise Synthesizer noise can be lumped into two categories - Close-in phase noise: reduces SNR o modulated signal - Far-away phase noise: creates spectral emissions outside the desired transmit channel This is the critical issue or transmitters

22 Impact o Remaining Portion o Transmitter S x () S y () reduction o SNR out-o-band emission IF x(t) y(t) RF PA Band Select Filter To Antenna out(t) S out () close-in phase noise Synthesizer LO ar-away phase noise Power ampliier - Nonlinearity will increase out-o-band emission and create harmonic content Band select ilter - Removes harmonic content, but not out-o-band emission

23 Why is Out-o-Band Emission A Problem? Transmitter 1 Desired ( Channel) Interering Channel Relative Power Dierence (db) Transmitter 2 Base Interering Station ( Channel ) Desired Channel Near-ar problem - Interering transmitter closer to receiver than desired transmitter - Out-o-emission requirements must be stringent to prevent complete corruption o desired signal

24 Speciication o Out-o-Band Emissions Maximum RF Output Emission M 2 M 3 M 1 M RF Integration Bandwidth = R Hz Channel Spacing = W Hz Maximum radiated power is speciied in desired and adjacent channels - Desired channel power: maximum is M - Out-o-band emission: maximum power deined as integration o transmitted spectral density over bandwidth R centered at midpoint o each channel oset

25 Calculation o Transmitted Power in a Given Channel R Hz R Hz S x ( mid ) S x ( mid ) mid mid For simplicity, assume that the spectral density is lat over the channel bandwidth - Actual spectral density o signal oten varies with requency over the bandwidth o a given channel Resulting power calculation (single-sided S x ()) Express in db ( Note: db(x) = 1log(x) )

26 Transmitter Output Versus Emission Speciication Piecewise Constant Approximation o Transmitter Output Spectrum Emission Speciication RF Output Y +X 2 Y +X 3 Y Y +X 1 RF Channel Spacing = W Hz Maximum RF Output Emission M 2 M 3 M 1 M RF Integration Bandwidth = R Hz Channel Spacing = W Hz Channel Spacing = W Hz Assume a piecewise constant spectral density proile or transmitter - Simpliies calculations Issue: emission speciication is measured over a narrower band than channel spacing - Need to account or bandwidth discrepancy when doing calculations

27 Correction Factor or Bandwidth Mismatch Piecewise Constant Approximation o Transmitter Output Spectrum Emission Speciication RF Output Y +X 2 Y +X 3 Y Y +X 1 RF Channel Spacing = W Hz Maximum RF Output Emission M 2 M 3 M 1 M RF Integration Bandwidth = R Hz Channel Spacing = W Hz Channel Spacing = W Hz Calculation o maximum emission in oset channel 1

28 Condition or Most Stringent Emission Requirement Piecewise Constant Approximation o Transmitter Output Spectrum Emission Speciication RF Output Y +X 2 Y +X 3 Y Y +X 1 RF Channel Spacing = W Hz Maximum RF Output Emission M 2 M 3 M 1 M RF Integration Bandwidth = R Hz Channel Spacing = W Hz Channel Spacing = W Hz Out-o-band emission requirements are unction o the power o the signal in the desired channel - For oset channel 1 (as calculated on previous slide) - Most stringent case is when Y maximum

29 Table o Most Stringent Emission Requirements Piecewise Constant Approximation o Transmitter Output Spectrum Emission Speciication RF Output Y +X 2 Y +X 3 Y Y +X 1 RF Channel Spacing = W Hz Maximum RF Output Emission M 2 M 3 M 1 M RF Integration Bandwidth = R Hz Channel Spacing = W Hz Channel Spacing = W Hz Channel Oset Mask Power M M 1 M 2 M 3 Emission Requirements (Most Stringent) Y = M (or most stringent case) X 1 = M 1 -M + db(w/r) db X 2 = M 2 -M + db(w/r) db X 3 = M 3 -M + db(w/r) db

30 Impact o Synthesizer on Transmitter Output IF Input RF Output M M +X 2 IF RF oset Synthesizer Spectrum (dbc) dbc IF RF PA To Antenna X 2 dbc LO LO Band Select Filter oset Consider a spurious tone at a given oset requency - Convolution with IF signal produces a replica o the desired signal at the given oset requency

31 Impact o Synthesizer Phase (Isolated Channel) IF Input RF Output M M +X 2 IF RF oset Synthesizer Spectrum (dbc) dbc IF RF PA To Antenna X 2 dbc LO LO Band Select Filter oset Consider phase noise at a given oset requency - Convolution with IF signal produces a smeared version o the desired signal at the given oset requency For simplicity, approximate smeared signal as shown

32 Impact o Synthesizer Phase (All Channels) IF Input RF Output M IF M +X 1 M +X 2 M +X 3 RF Channel Spacing = W Hz Synthesizer Spectrum (dbc) dbc IF RF PA To Antenna X dbc X 1 dbc X 2 dbc X 3 dbc LO LO Band Select Filter Channel Spacing = W Hz Partition synthesizer phase noise into channels - Required phase noise power (dbc) in each channel is related directly to spectral mask requirements Exception is X set by transmit SNR requirements

33 Synthesizer Phase Requirements Synthesizer Spectrum (dbc) dbc IF RF PA To Antenna X dbc X 1 dbc X 2 dbc X 3 dbc LO LO Band Select Filter Channel Spacing = W Hz Impact o channel bandwidth (oset channel 1) Overall requirements (most stringent, i.e., Y = M ) Channel Oset Emission Requirements (Most Stringent) Maximum Synth. Phase (Most Stringent) Y = M set by required transmit SNR 1 2 X 1 = M 1 -M + db(w/r) db X 2 = M 2 -M + db(w/r) db X 1 - db(w) dbc/hz X 2 - db(w) dbc/hz 3 X 3 = M 3 -M + db(w/r) db X 3 - db(w) dbc/hz

34 Example DECT Cordless Telephone Standard Standard or many cordless phones operating at 1.8 GHz Transmitter Speciications - Channel spacing: W = MHz - Maximum output power: M o = 25 mw (24 ) - Integration bandwidth: R = 1 MHz - Emission mask requirements

35 Synthesizer Phase Requirements or DECT Using previous calculations with DECT values Channel Oset Mask Power Maximum Synth. Power in Integration BW Maximum Synth. Phase at Channel Oset MHz MHz MHz 24 set by required transmit SNR -8 X 1 = dbc -92 dbc/hz -3 X 2 = dbc -114 dbc/hz -44 X 3 = dbc -128 dbc/hz Graphical display o phase noise mask Synthesizer Spectrum (dbc) -92 dbc/hz -114 dbc/hz LO -128 dbc/hz Channel Spacing = MHz

36 Critical Speciication or Phase Critical speciication is deined to be the one that is hardest to meet with an assumed phase noise rollo - Assume synthesizer phase noise rolls o at -2 db/decade Corresponds to VCO phase noise characteristic For DECT transmitter synthesizer - Critical speciication is -128 dbc/hz at MHz oset Synthesizer Spectrum (dbc) dbc Phase Rollo: -2 db/dec -92 dbc/hz -114 dbc/hz Critical Spec. LO -128 dbc/hz Channel Spacing = MHz

37 Receiver Blocking Perormance RF Input Band Select Filter Must Pass All Channels IF Output Channel Filter Bandwidth LNA RF Band Select Filter IF Channel Filter To IF Processing Stage Synthesizer Synthesizer Spectrum (dbc/hz) dbc LO Radio receivers must operate in the presence o large intererers (called blockers) Channel ilter plays critical role in removing blockers Passes desired signal channel, rejects intererers

38 Impact o Nonidealities on Blocking Perormance RF Input Band Select Filter Must Pass All Channels IF Output Channel Filter Bandwidth Synthesizer and Mixer/LNA Distortion Produce Inband Intererence LNA RF Band Select Filter IF Channel Filter To IF Processing Stage Synthesizer Blockers leak into desired band due to - Nonlinearity o LNA and mixer (IIP3) - Synthesizer phase and spurious noise Synthesizer Spectrum (dbc/hz) dbc LO Phase (dbc/hz) Spurious (dbc) In-band intererence cannot be removed by channel ilter!

39 Quantiying Tolerable In-Band Intererence Levels RF Input Band Select Filter Must Pass All Channels IF Output Min SNR: 15-2 db Channel Filter Bandwidth Synthesizer and Mixer/LNA Distortion Produce Inband Intererence LNA RF Band Select Filter IF Channel Filter To IF Processing Stage Synthesizer Synthesizer Spectrum (dbc/hz) dbc LO Phase (dbc/hz) Spurious (dbc) Digital radios quantiy perormance with bit error rate (BER) - Minimum BER oten set at 1e-3 or many radio systems - There is a corresponding minimum SNR that must be achieved Goal: design so that SNR with intererers is above SNR min

40 Impact o Synthesizer on Blockers RF Input IF Output Y db RF oset IF Synthesizer Spectrum (dbc) dbc RF IF LO LO Synthesizer passes desired signal and blocker - Assume blocker is Y db higher in signal power than desired signal

41 Impact o Synthesizer Spurious on Blockers RF Input IF Output Y db SNR: -X-Y db X db RF oset IF Synthesizer Spectrum (dbc) dbc RF IF Spurious Tone X dbc LO LO oset Spurious tones cause the blocker (Y db) (and desired) signals to leak into other requency bands - In-band intererence occurs when spurious tone oset requency is same as blocker oset requency - Resulting SNR = -X-Y db with spurious tone (X dbc)

42 Impact o Synthesizer Phase on Blockers RF Input IF Output Y db SNR: -X-Y db X db RF oset IF Synthesizer Spectrum (dbc) dbc RF IF X dbc LO oset LO Same impact as spurious tone, but blocker signal is smeared by convolution with phase noise - For simplicity, ignore smearing and approximate as shown above

43 Blocking Perormance Analysis (Part 1) RF Input Y db In-Channel IF Output SNR: -X-Y db RF oset IF Synthesizer Spectrum (dbc) dbc RF IF X dbc LO oset LO Ignore all out-o-band energy at the IF output - Assume that channel ilter removes it - Motivation: simpliies analysis

44 Blocking Perormance Analysis (Part 2) Y 1 db RF Input Y 2 db RF In-Channel IF Output SNR min : 15-2 db Channel Filter Bandwidth = W Hz IF Inband Intererence Produced by Synth. Phase Synthesizer Spectrum (dbc) Channel Spacing dbc RF IF X dbc X 1 dbc X 2 dbc LO Channel Spacing LO Consider the impact o blockers surrounding the desired signal with a given phase noise proile - SNR min must be maintained - Evaluate impact on SNR one blocker at a time

45 Blocking Perormance Analysis (Part 3) Y 1 db RF Input Y 2 db RF In-Channel IF Output SNR min : 15-2 db Channel Filter Bandwidth = W Hz IF Inband Intererence Produced by Synth. Phase Synthesizer Spectrum (dbc) Channel Spacing dbc RF IF Channel Oset X dbc X 1 dbc X 2 dbc LO Channel Spacing Relative Blocking Power Y 1 db Y 2 db Y 3 db LO Maximum Synth. Power at Channel Oset db X = -SNR min dbc X 1 = -SNR min -Y 1 dbc X 2 = -SNR min -Y 2 dbc X 3 = -SNR min -Y 3 dbc Derive using the relationship SNR = -X-Y db >= SNR min

46 Blocking Perormance Analysis (Part 4) Y 1 db RF Input Y 2 db RF In-Channel IF Output SNR min : 15-2 db Channel Filter Bandwidth = W Hz IF Inband Intererence Produced by Synth. Phase Synthesizer Spectrum (dbc) Channel Spacing dbc RF IF X dbc X 1 dbc X 2 dbc LO LO Convert power to spectral density Channel Spacing Channel Oset Relative Blocking Power Y 1 db Y 2 db Y 3 db Maximum Synth. Power at Channel Oset db X = -SNR min dbc X 1 = -SNR min -Y 1 dbc X 2 = -SNR min -Y 2 dbc X 3 = -SNR min -Y 3 dbc Maximum Synth. Phase at Channel Oset X - db(w) dbc/hz X 1 - db(w) dbc/hz X 2 - db(w) dbc/hz X 3 - db(w) dbc/hz

47 Example DECT Cordless Telephone Standard Receiver blocking speciications - Channel spacing: W = MHz - Power o desired signal or blocking test: Minimum bit error rate (BER) with blockers: 1e-3 Sets the value o SNR min Perorm receiver simulations to determine SNR min Assume SNR min = 15 db or calculations to ollow - Strength o intererers or blocking test

48 Synthesizer Phase Requirements or DECT RF Input RF In-Channel IF Output SNR min : 15 db Channel Filter Bandwidth W = 1.73 MHz IF Inband Intererence Produced by Synth. Phase Synthesizer Spectrum (dbc) Channel Spacing = 1.73 MHz dbc RF IF X dbc X 1 dbc X 2 dbc X 3 dbc LO LO Channel Spacing = 1.73 MHz Channel Oset Relative Blocking Power Maximum Synth. Power at Channel Oset Maximum Synth. Phase at Channel Oset MHz MHz MHz db X = -15 dbc Y 1 = 15 db Y 2 = 34 db Y 3 = 4 db X 1 = -3 dbc X 2 = -49 dbc X 3 = -55 dbc -77 dbc/hz -92 dbc/hz -111 dbc/hz -117 dbc/hz

49 Graphical Display o Required Phase Perormance Mark phase noise requirements at each oset requency Synthesizer Spectrum (dbc) dbc Phase Rollo: -2 db/dec LO -92 dbc/hz -111 dbc/hz Critical Spec dbc/hz Calculate critical speciication or receive synthesizer - Critical speciication is -117 dbc/hz at MHz oset Lower perormance demanded o receiver synthesizer than Channel Spacing = MHz transmitter synthesizer in DECT applications!