# Timing Methodologies (cont d) Registers. Typical timing specifications. Synchronous System Model. Short Paths. System Clock Frequency

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1 Registers Timing Methodologies (cont d) Sample data using clock Hold data between clock cycles Computation (and delay) occurs between registers efinition of terms setup time: minimum time before the clocking event by which the must be stable (T su ) hold time:minimum time after the clocking event until which the must remain stable (T h ) Sequential Logic 1 Sequential Logic 2 Typical timing specifications Synchronous System Model Positive edge-triggered flip-flop setup and hold times minimum clock width propagation delays (low to high, high to low, max and typical) Register-to-register operation Perform operations during transfer Many transfers/operations occur simultaneously " 0 Combinational 1 Logic &! Sequential Logic 3 Sequential Logic 4 System Clock Frequency Short Paths Register transfer must fit into one clock cycle reg tpd + C.L. tpd + reg tsu < Tclk Use maximum delays Find the critical path Longest register-register delay 0 Combinational 1 Logic Can a path have too little delay? Yes: Hold time can be violated tpd > th Use min delay (contamination delay) Fortunately, most registers have hold time = 0 But there can still be a problem! Clock skew 0 0 t su t h t su t h C.L. t pd Sequential Logic 5 Sequential Logic 6

2 Cannot make clock arrive at registers at the same time If skew > 0: tpd > th + tskew Clock skew can cause system failure Can you fix this after you ve fabbed the chip? Cannot make clock arrive at registers at the same time If skew > 0: tpd > th + tskew Clock skew can cause system failure Can you fix this after you ve fabbed the chip? t t su t h t skew t su t h skew Sequential Logic 7 Sequential Logic If skew < 0: tclk > reg tpd + CL tpd + reg tsu + tskew Can you fix this after fab? 0 1 C.L. If skew < 0: tclk > reg tpd + CL tpd + reg tsu + tskew Can you fix this after fab? 0 1 C.L. 0 0 C.L. tpd C.L. tpd 1 1 t skew t su t h Sequential Logic 9 t skew t su t h Sequential Logic 10 Nasty Example Correct behavior assumes that all storage elements sample at exactly the same time Not possible in real systems: clock driven from some central location different wire delay to different points in the circuit Problems arise if skew is of the same order as FF contamination delay Gets worse as systems get faster (wires dont improve as fast) 1) distribute clock signals against the data flow 2) wire carrying the clock between two communicating components should be as short as possible 3) try to make all wires from the clock generator be the same length => clock tree What can go wrong? How can you fix it? (A) /2 (B) Sequential Logic 11 Sequential Logic 12

3 Other Types of Latches and Flip-Flops Comparison of latches and flip-flops -FF is ubiquitous simplest design technique, minimizes number of wires preferred in PLs and FPGAs good choice for data storage register edge-triggered has most straightforward timing constraints Historically J-K FF was popular versatile building block, often requires less total logic two s require more wiring and logic can always be implemented using -FF Level-sensitive latches in special circumstances popular in VLSI because they can be made very small (4 T) fundamental building block of all other flip-flop types two latches make a -FF Preset and clear s are highly desirable System reset " & " & () " & & Sequential Logic 13 Sequential Logic 14 What About External Inputs? Sampling external s Internal signals are OK Can only change when clock changes External signals can change at any time Asynchronous s Truly hronous Produced by a different clock This means register may sample a signal that is changing Violates setup/hold time What happens? (A) (B) 0 0 0/1? 1 1 Sequential Logic 15 Sequential Logic 16 Synchronization failure Calculating probability of failure Occurs when FF changes close to clock edge the FF may enter a metastable state neither a logic 0 nor 1 it may stay in this state an indefinite amount of time this is not likely in practice but has some probability, * ++, * ** Sequential Logic 17 For a single synchronizer Mean-Time Between Failure (MTBF) = exp ( tr / τ ) / ( T0 f a ) where a failure occurs if metastability persists beyond time tr tr is the resolution time - extra time in clock period for settling Tclk - (t pd + T CL + t setup ) f is the frequency of the FF clock a is the number of hronous changes per second applied to the FF T0 and τ are constaints that depend on the FFs electrical characteristics (e.g., gain or steepness of curve) example values are T0 =.4s and τ = 1.5ns (sensitive to temperature, voltage, cosmic rays, etc.). Must add probabilities from all synchronizers in system 1/MTBFsystem = Σ 1/MTBFsynch Sequential Logic 1

4 Metastability What does this circuit do? What s wrong with this? clk Example changes at 1 MHz system clock of 10MHz, flipflop (t pd + t setup ) = 5ns MTBF = exp( 95ns / 1.5ns ) / (.4s ) = 25 million years if we go to 20MHz then: MTBF = exp( 45ns / 1.5ns ) / (.4s ) = 1.33 seconds! And we re not even doing any logic! Must do the calculations and allow enough time for synchronization Sequential Logic 19 Sequential Logic 20 What does this circuit do? Guarding against synchronization failure How much better is this? Give the register time to decide Probability of failure cannot be reduced to 0, but it can be reduced Slow down the system clock? Use very fast technology for synchronizer -> quicker decision? Cascade two synchronizers? * * Can you do better? Sequential Logic 21 Sequential Logic 22 Stretching the Resolution Time Sampling Rate Also slows the sample rate and transfer rate How fast does your sample clock need to be? A B C /2 Sequential Logic 23 Sequential Logic 24

5 Sampling Rate Sampling Rate How fast does your sample clock need to be? f() > 2f() A B C What if sample clock can t go faster? If clock is not available, no solution(?) If clock is available (e.g. video codec) (A) (A) (B) (C) Sequential Logic 25 Sequential Logic 26 Increasing sample rate Another Problem with Asynchronous s The problem is the relative sample rate Slow down the clock! What goes wrong here? (Hint: it s not a metastability thing) What is the fix? Sequential Logic 27 Sequential Logic 2 More Asynchronous s Important Rule! What is the problem? What is the fix? Exactly one register makes the synchronizing decision C. L. 2 2 Sequential Logic 29 Sequential Logic 30

6 More Asynchronous s More Asynchronous s Can we hronous data values with several bits? How can we hronous data values with several bits? A B C A B C (A)[7:0] x00 xff Sequential Logic 31 (B)[7:0] (C)[7:0] x00 x00 x00/xff xff xff x00 x00 x00 xaa xff!! Sequential Logic 32 What Went Wrong? Sending Multiple ata Bits Each bit has a different delay Wire lengths differ Gate thresholds differ river speeds are different Register delays are different Rise vs. Fall times Clock skews to register bits Bottom line data skew is inevitable aka Bus Skew Longer wires => More skew What is the solution?? Must send a clock with the data Waits until data is stable e-skewing delay f() > 2 f() Sequential Logic 33 Sequential Logic 34 Sending Multiple ata Bits Sending Multiple ata Bits Balancing path delays... What s wrong with this solution? What s the right way to do it? The right way to do it... Sequential Logic 35 Sequential Logic 36

7 Sending Multiple ata Bits Slightly different alternative... EN Sequential Logic 37

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