© H. Heck 2008Section 6.11 Module 6:Advanced Issues Topic 1:Projections, Limits, Barriers OGI EE564 Howard Heck

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.12 Where Are We? 1.Introduction 2.Transmission Line Basics 3.Analysis Tools 4.Metrics & Methodology 5.Advanced Transmission Lines 6.Multi-Gb/s Signaling 1.Projections, Limits, & Barriers 2.Differential Signaling 3.Equalization Techniques 4.Modulation Techniques 7.Special Topics

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.13 Contents Shannon’s Limit Differential Signaling Exploiting Moore’s Law  Pre-emphasis  Equalization  Adaptive Techniques Simultaneous Bi-directional Signaling Summary References

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.14 Shannon’s Limit Shannon’s Capacity Theorem describes the upper limit of the information rate that can be passed through a given channel. This theorem is widely accepted throughout the scientific community and has never been exceeded in practice. The data rate through a channel is given by Where D = data rate [bits/second] S = symbol rate [symbols/second] B = # of bits per symbol [bits/symbol] [6.1.1]

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.15 Shannon’s Limit #2 Using a sinc pulse as the symbol achieves the maximum possible symbol rate within a given bandwidth.  i.e. the sinc pulse gives maximum spectral efficiency at the expense of the need for perfect timing (i.e. no jitter).  The timing constraint prevents its use real systems. [6.1.2] The symbol rate with a sinc pulse is given by Time domain Frequency domain 1 GHz Sinc pulse

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.16 Shannon’s Limit #3 Shannon’s theorem states that the maximum number of bits per symbol that can be transmitted without error is given by: [6.1.4] From equation [6.1.4], we see that the maximum data rate is limited by the bandwidth of the channel and by the signal-to-noise ratio (SNR). [6.1.3] Equation [6.1.3] assumes that the noise is Gaussian. Combining the previous equations, we get the following expression for the maximum data rate:

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.17 Example Limit Calculation Break the channel into multiple bands. Calculate noise floor.  ISI due to losses, reflections, crosstalk  Supply noise Calculate capacity per band and sum them. Gaussian noise ISI, Supply + Other

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.18 Example FR4 Capacity vs. Line Length Line length [cm] Data Rate [Gb/s] Differential Single Ended Shannon

Projections, Limits, Barriers EE 564 © H. Heck 2008 Section 6.19 Summary Shannon’s Theorem gives us the ability to project theoretical limits on data rate for a given interconnect channel.  Data rate is ultimately a function of signal-noise ratio. It doesn’t tell us how to attain them.