EE290C Spring Lecture 5: Equalization Techniques. Elad Alon Dept. of EECS 9" FR4 26" FR4. 9" FR4, via stub.

Transcription

1 EE29C Spring 211 Lecture 5: Equalization Techniques Elad Alon Dept. of EECS Link Channels Attenuation [db] " FR4, via stub 9" FR4 26" FR4-6 26" FR4, via stub frequency [GHz] EE29C Lecture 5 2

2 Inter-Symbol Interference Channel is band-limited I.e., dispersive (low pass) Short TX pulses get spread out Low latency Also get reflections Z mismatches, connectors, etc. Longer latency pulse response Tsymbol=16ps ns EE29C Lecture 5 3 Why ISI Matters 1.8 Eye Diagram Amplitude Symbol time First sample doesn t even reach RX threshold Suffers ISI from all previous zero bits Middle sample hardly different from first.2 trailing ISI (from previous symbol) and.1 leading ISI (from next symbol) EE29C Lecture 5 4

3 Equalization + = Basic goal is to flatten channel response I.e., in time domain, get back our nice clean pulse For low-pass channel, equalizer boosts high frequencies EE29C Lecture 5 5 History Equalization been around for a very long time What makes electrical interfaces unique: Performance Power and area constraints EE29C Lecture 5 6

4 Equalizer Types More alphabet soup CTLE, ZFE, DFE, RX FIR, MMSE, Three basic distinctions: Linear vs. Non-Linear Continuous Time vs. Discrete Time Minimize ISI vs. Minimize ISI + Noise EE29C Lecture 5 7 Continuous Time Linear Equalizer (CTLE) EE29C Lecture 5 8

5 CTLE Implementation, Limitations EE29C Lecture 5 9 Linear FIR EE29C Lecture 5 1

6 Transmitter FIR Example Tx Data Anticausal taps.7.5 Unequalized Equalization Pulse End of Line Voltage.3.1 Causal taps time (ns) EE29C Lecture 5 11 Setting the Coefficients Assume channel response is known for now See later how to estimate it Most basic approach: zero-forcing (ZFE) Single-bit Channel Response Equalized Response EE29C Lecture 5 12

7 ZFE Setting Formulation (Math ) EE29C Lecture 5 13 Zero-Forcing : Desired Response EE29C Lecture 5 14

8 Final Coefficients: Least Squares EE29C Lecture 5 15 Transmitter FIR Revisited Tx Data Anticausal taps.7.5 Unequalized Equalization Pulse End of Line Voltage.3.1 Causal taps time (ns) Can t generally use ZFE result directly TX has a peak swing constraint At same max. swing, RX amplitude reduced Is this a problem? EE29C Lecture 5 16

9 The Fundamental Issue: Noise Attenuation [db] equalized unequalized -2 frequency [GHz] ZFE eliminates ISI But increases magnitude of noise relative to signal Noise enhancement Particularly bad on channels with notches TX/RX eq. needs large atten./gain EE29C Lecture 5 17 An Alternate Approach: MMSE Don t just cancel ISI Find optimal balance between noise and ISI Minimum Mean Squared Equalizer: EE29C Lecture 5 18

10 MMSE vs. ZFE, Limitations MMSE allows residual ISI But amplifies noise less Normalized Amplitide Unequalized ZFE MMSE Symbol Number Unfortunately, MMSE not so straightforward to apply in links Harder to adapt (more later) Noise may not be known EE29C Lecture 5 19 Good News: There Is Another Way Once you know which bit was transmitted You also know exactly what ISI that bit will cause Why not directly cancel the ISI you know is coming? Symbol time Amplitude EE29C Lecture 5 2

11 Decision Feedback Equalization (DFE) RX_in Pulse response time FIR Filter Key advantage: no noise enhancement Feedback signal based on perfect digital bits ISI subtracted based on those bits EE29C Lecture 5 21 DFE Issues Only handles postcursors May still need linear (feedforward) filter for pre-cursors RX_in What happens when RX makes a mistake? EE29C Lecture 5 22

12 DFE Issues: Timing RX_in Need to do all of the following in at most 1UI: Resolve the (small) bit Scale the bit by the coefficient Sum the new analog value EE29C Lecture 5 23 Pulse Shape Interaction RX_in Ideal DFE would actually settle within.5ui Otherwise affects edge position FIR filter can have same issue Fixing it requires an over-sampled (fractional) equalizer EE29C Lecture 5 24

13 Fractional Equalization Normalized Amplitude Symbol-spaced 2x Oversampled Symbol Number EE29C Lecture 5 25