EE29C Spring 2 Lecture 6: Link Performance Analysis Elad Alon Dept. of EECS Motivation V in, ampl Voff BER = 2 erfc 2σ noise Does eqn. above predict everything? EE29C Lecture 5 2
Traditional Approach Borrowed from computer systems Built to be error free Worst-case analysis Voltage/Time (VT) Budget Also called link budget (especially in wireless) Key: separate random vs. deterministic error sources EE29C Lecture 5 3 Voltage Budget Example EE29C Lecture 5 4
Voltage Budget Example EE29C Lecture 5 5 Timing Budget: Jitter Definitions Like voltage need to separate deterministic (bounded) from random (unbounded) Total jitter (TJ) = Deterministic (DJ) + random (RJ) DJ is measured as peak-to-peak, added linearly RJ is measured as rms For BER = -2, peak-to-peak RJ is 4*RMS value Don t forget that jitter gets filtered too E.g., source synchronous, CDR EE29C Lecture 5 6
Jitter Tolerance Mask Jitter Amplitude (UI) 9. 8.5 8. 7.5 7. 6.5 6. 5.5 5. 4.5 4. 3.5 3. 2.5 2..5..5. CDR Tolerance & XAUI Sinusoidal Jitter Tolerance Mask.UI XAUI Sinusoidal Jitter Mask.875MHz. 22KHz.... Jitter Frequency (MHz) XAUI Mask LV at Vtt-Rx=V & 3.25Gbps Specifies amplitude of sinusoidal jitter (SJ) vs. frequency for which link must maintain BER spec Mask drives CDR loop filter characteristics.ui 2 MHz EE29C Lecture 5 7 Jitter in Source Synchronous Systems EE29C Lecture 5 8
Jitter in Source Synchronous Systems EE29C Lecture 5 9 Issues with Traditional Approach Is worst-case realistic? What if you had taps of residual ISI? Can you really treat timing and voltage noise completely separately? EE29C Lecture 5
Communications Approach Model small deterministic errors as Gaussian Find σ, multiply it to get peak-to-peak value at given BER Works well at low BER (e-3), but EE29C Lecture 5 Issues with Communications Approach log probability [cdf] Cumulative ISI distribution -2-4 -6-8 - 4mV error @ - 25% of eye height 25 5 75 residual ISI [mv] log Steady-State Phase Probability 8 2 4 6 8 phase count Gaussian model breaks at lower probabilities -2-4 -6-8 - CDR phase distribution 9% T symbol 4% T symbol error @ - EE29C Lecture 5 2
A More Modern Approach Use direct noise and ISI statistics Don t treat timing noise separately Integrate with voltage noise sources I.e., need to map from time to voltage Ref: V. Stojanovic, Ph.D. thesis EE29C Lecture 5 3 Residual ISI Generally can t correct for all ISI Equalizers are finite length Even with infinite equalizers, the coefficients are quantized And you may not be able to estimate coefficient values perfectly Need to find distribution of this residual ISI EE29C Lecture 5 4
Generating ISI Distributions voltage [mv] Equalized pulse response 2 5 - -3-2 - 2 sample # probability [pmf] probability [pmf].75.5.25.75.5.25 Convolution -5 [mv] 5 probability [pmf] ISI distribution.75.5.25-25 -5 5 25 voltage [mv] - [mv] EE29C Lecture 5 5 Real ISI Dist.: 5-tap FIR probability distribution of residual ISI.4.3.2. probability distribution of residual ISI.6.2.8.4-6 -4-2 2 4 6 voltage [mv] Data sample distribution -5 - -5 5 5 voltage [mv] Edge sample distribution EE29C Lecture 5 6
Effect of Timing Noise Need to map from time to voltage Voltage noise when receiver clock is off Jittered sampling Ideal sampling Voltage noise Effect depends on jitter magnitude, input sequence, and channel EE29C Lecture 5 7 Effect of Jitter: Decomposition ε k kt b k ε k+ ( k +)T ideal noise Decompose output into ideal + noise Jitter is pulse at front and end of symbol Width of pulse set by jitter magnitude 2 kt ε k b k b k + ( k +)T ε k+ b k EE29C Lecture 5 8
Converting to Voltage bkε k+ ε k b k ε k+ b k b ε k k Variable width pulses annoying to deal with Approximate noise pulses with deltas of same area Channel is low-pass and will filter them anyways EE29C Lecture 5 9 Jitter Propagation Model a k precoder b pulse response ideal k w p( jt) ISI x k + x k â k n vdd PLL H jit (s) noise Channel bandwidth matters jit ISI RX x ( kt + φ + ε ) = φ ) If h(t/2) is small, jitter voltage noise is small EE29C Lecture 5 2 x RX ε k n in T k h jt + 2 εk, k+ impulse RX response sbe i k b k j p ( jt + i j = sbs sbe jitter RX T x ( kt + φi + εk ) = bk j h( jt + + φi ) k k j i k εk+ j j= sbs 2 2 RX T RX ( ε ε ) h( jt + φ )( ε )
Implications Jitter High frequency (period) jitter is bad Changes the energy (area) of the symbol) Uncorrelated noise sources add up Low frequency jitter isn t as bad Just shifts waveform Correlated noise sources partially cancel ε k Rx RX jitter Shifts sequence same as low f jitter EE29C Lecture 5 2 ε k Rx Implications For same source jitter (white) Noise from jitter larger than RX jitter jitter enhanced by channel Bandwidth of jitter sets final magnitude Like any other white noise source Power spectral density [dbv] -3-4 -5-6 Source white jitter Noise from Tx jitter Noise from Rx jitter.5.5 2 2.5 3 frequency [GHz] EE29C Lecture 5 22
Including the CDR Slicer d n deserializer RX dataout d n PD e n data Clk edge Clk Phase control Phase mixer PLL ref Clk d n- e n (late) Need jitter on actual sampling clock Not just jitter from source, PLL EE29C Lecture 5 23 CDR Model Model as a state machine Current phase position is the state Transitions caused by early/late signals Probability.8.6.4.2 Accumulate-reset filter, length 4 p-early p-up p-dn p-no-valid transitions p-late p-hold 5 5 2 25 Phase count On average move to right position But probability of incorrect transition not small EE29C Lecture 5 24
What You Really Care About Final steady-state probability of being in each phase position (state) p dni, p hold, i Probability.8.6 Accumulate-reset filter, length 4 p-up p-dn p-no-valid transitions φ p up, i φ φ i i φ i + φl.4.2 p-early p-late p-hold 5 5 2 25 Phase count Can find using Markov model Fancy way of saying that you iteratively apply the transition probabilities EE29C Lecture 5 25 Result: CDR Phase PDF log Steady-State Probability -5 - -5 5 5 2 25 Phase Count This is the jitter distribution (With nominal phase subtracted out) EE29C Lecture 5 26
ISI and CDR Distributions voltage [mv] 3 2-2PAM - lin. eq -5 - -5-2 -2-25 -3 5 6 7 8 9 time [ps] Vertical slice: ISI distribution @ given time Horizontal weight: CDR phase distribution -3 EE29C Lecture 5 27 Putting It All Together: BER Contours 5 5 tap Tx Eq 5 tap Tx Eq + tap DFE 5-5 -5 margin [mv] 5-5 - -5-2 margin [mv] 5-5 - -5-2 - -25 - -25-5 2 4 6 8 2 4 6 time [ps] Voltage margin @ given BER: -3-5 2 4 6 8 2 4 6 time [ps] Distance from probability contour to threshold () -3 EE29C Lecture 5 28
Model and Measurements -2 log(ber) -4-6 -8 - -2-4 8 6 4 2-2 -4-6 -8 Voltage Margin [mv] EE29C Lecture 5 29