Clock Skew

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The preceding timing analysis example is simpli?ed for ease of presentation byassuming that the source and destination ?ops in a logic path are driven by thesame clock signal. Although a synchro- nous circuit uses a common clock forall ?ops, there are small, nonzero variances in clock timing at individual ?ops.Wiring delay variances are one source of this nonideal behavior. When a clocksource drives two ?ops, the two wires that connect to each ?ops clock input areusually not identical

FIGURE 1.16 Hypothetical logic circuit.

Figura 1.16 Hypothetical logic circuit.

in length. This length inequality causes one ?ops clock to arrive slightly before orafter the other ?ops clock.
Clock skew is the term used to characterize differences in edge timing betweenmultiple clock inputs. Skew caused by wiring delay variance can be effectivelyminimized by designing a circuit so that clock distribution wires are matched in length.A more troublesome source of clock skew arises when there are too many clockloads to be driven by a single source. Multiple clock drivers are necessary in thesesituations, with small variations in electrical characteristics between each driver.These driver variances result in clock skew across all the ?ops in a synchronousdesign. As might be expected, clock skew usually reduces the frequency at whicha synchronous circuit can operate. Clock skew is subtracted from the nominalclock period for setup time analysis purposes, because the worst-case scenarioshown in Fig. 1.17 must be considered. This scenario uses the same logic circuit inFig. 1.16 but shows two separate clocks with 1 ns of skew between them.
The worst timing occurs when the destination ?ops clock arrives before that of thesource ?op, thereby reducing the amount of time available for the D-input to stabilize.Instead of the circuit having zero margin with a 20-ns period, clock skew increasesthe minimum period to 21 ns. The extra 1 ns compensates for the clock skew torestore a minimum source to destination period time of 20 ns. A slower circuitsuch as this one is not very sensitive to clock skew, especially after backing off to40 MHz for timing margin as shown previously. Digital systems that run at relativelylow frequencies may not be affected by clock skew, because they often havesubstantial margins built into their timing analyses. As clock speeds increase, themargin decreases to the point at which clock skew and interconnect delay becomeimportant limiting factors in system design.
Hold time compliance can become more dif?cult in the presence of clock skew.The basic problem occurs when clock skew reduces the source ?ops apparent tCOfrom the destination ?ops perspective, causing the destinations input to changebefore tH is satis?dhe. Such problems are more prone in high-speed systems,but slower systems are not immune. Figura 1.18 shows a timing diagram for acircuit with 1 ns of clock skew where two ?ops are connected by a short wirewith nearly zero propagation delay. The ?ops have tCO = 2 ns and tH = 1.5 ns.A scenario like this may be expe- rienced when connecting two chips that arenext to each other on a circuit board. In the absence of clock skew, thedestination ?ops input would change tCO after the rising clock edge, exceeding tHby 0.5 ns. The worst-case clock skew causes the source ?op clock to arrivebefore that of the destination ?op, resulting in an input change just 1 ns after therising clock edge and violating tH. Solutions to skew-induced tH violations includereducing the skew or increasing the delay be- tween source and destination.Unfortunately, increasing a signals propagation delay may cause tSUviolations in high-speed systems.

FIGURE 1.17 Clock skew in?uence on setup time analysis.

Figura 1.17 Clock skew in?uence on setup time analysis.

FIGURE 1.18 Hold-time violation caused by clock skew.

Figura 1.18 Hold-time violation caused by clock skew.

Hold time may not be a problem in slower circuits, because slower circuits oftenhave paths between ?ops with suf?ciently long propagation delays to offsetclock skew problems. megjithatë, even slow circuits can experience hold-timeproblems if ?ops are connected with wires or components that have smallpropagation delays. It is also important to remember that hold-time complianceis not a function of clock period but of clock skew, tCO, and tH. Prandaj, aslow system that uses fast components may have problems if the clock skewexceeds the difference between tCO and tH.
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Synchronous Timing Analysis

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Logic elements, including ?ip-?ops and gates, are physical devices that have ?niteresponse times to stimuli. Each of these elements exhibits a certain propagation delaybetween the time that an input is presented and the time that an output is generated.As more gates are chained together to create more complex logic functions, theoverall propagation delay of signals between the end points increases. Flip-?ops aretriggered by the rising edge of a clock to load their new state, requiring that the inputto the ?ip-?op is stable prior to the rising edge. Similarly, Një ?ip-?ops output stabilizesat a new state some time after the rising edge. In between the output of a ?ip-?opand the input of another ?ip-?op is an arbitrary collection of logic gates, as seen inthe preceding synchronous counter circuit. Synchronous timing analysis is the studyof how the various delays in a synchronous circuit combine to limit the speed at whichthat circuit can operate. As might be expected, circuits with lesser delays areable to run faster.
A clock breaks time into discrete intervals that are each the duration of a singleclock period. From a timing analysis perspective, each clock period is identical tothe last, because each rising clock edge is a new ?op triggering event. Prandaj,timing analysis considers a circuits delays over one clock period, betweensuccessive rising (or falling) clock edges. Knowing that a wide range of clockfrequencies can be applied to a circuit, the question of time arises of how fast theclock can go before the circuit stops working reliably. The answer is that the clockmust be slow enough to allow suf?cient time for the output of a ?op to stabilize,for the signal to propagate through the combinatorial logic gates, and for the inputof the destination ?op to stabilize. The clock must also be slow enough for the ?opto reliably detect each edge. Each ?op circuit is characterized by a minimumclock pulse width that must be met. Failing to meet this minimum time can result inthe ?op missing clock events.
Timing analysis revolves around the basic timing parameters of a ?op: input setuptime (tSU), input hold time (tH), and clock-to-out time (tCO). Setup time speci?esthe time immediately preceding the rising edge of the clock by which the input mustbe stable. If the input changes too soon before the clock edge, the electrical circuitrywithin the ?op will not have enough time to properly recognize the state of the input.Hold time places a restriction on how soon after the clock edge the input
may begin to change. Again, if the input changes too soon after the clock edge, itmay not be properly detected by the circuitry. Clock-to-out time speci?es howsoon after the clock edge the output will be updated to the state presented at theinput. These parameters are very brief in duration and are usually measured innanoseconds. One nanosecond, abbreviated ns, is one billionth of a second.In very fast microchips, they may be measured in picoseconds, or one trillionthor a second. Consistent terminology is necessary when conducting timing analysis.Timing is expressed in units of both clock frequency and time. Clock frequency,or speed, is quanti?ed in units of hertz, named after the twentieth century Germanphysicist, Gustav Hertz. One hertz is equivalent to one clock cycle per secondone transition from low to high and a second transition from high to low. Units ofhertz are abbreviated as Hz and are commonly accompanied by pre?xes that denotean order of magnitude. Commonly observed pre?xes used to quantify clockfrequency and their de?ni- tions are listed in Table 1.13. Unlike quantities of bytesthat use binary-based units, clock frequency uses decimal-based units.

Units of time are used to express a clocks period as well as basic logic elementdelays such as the aforementioned tSU, tH, and tCO. As with frequency, standardpre?xes are used to indicate the order of magnitude of a time speci?cation. megjithatë,rather than expressing positive powers of ten, the exponents are negative.Table 1.14 lists the common time magnitude pre?xes employed in timing analysis.

Aside from basic ?op timing characteristics, timing analysis must take intoconsideration the ?nite propagation delays of logic gates and wires thatconnect ?op outputs to ?op inputs. All real components have nonzeropropagation delays (the time required for an electrical signal to move from aninput to an output on the same component). Wires have an approximatepropagation delay of 1 ns for every 6 in of length. Logic gates can havepropagation delays ranging from more than 10 ns down to the picosecond range,depending on the technology being used. Newly designed logic circuits shouldbe analyzed for timing to ensure that the inherent propagation delays of the logicgates and interconnect wiring do not cause a ?ops tSU and tH speci?cations tobe violated at a given clock frequency.
Basic timing analysis can be illustrated with the example logic circuit shownFig. 1.16. There are two ?ops connected by two gates. The logic inputs shownunconnected are ignored in this instance, because timing analysis operates on asingle path at a time. In reality, other paths exist through these unconnected inputs,and each path must be individually analyzed. Each gate has a ?nite propagationdelay, tPROP , which is assumed to be 5 ns for the sake of discussion. Each ?ophas tCO = 7 ns, tSU = 3 ns, and tH = 1 ns. For simplicity, it is assumed that thereis zero delay through the wires that connect the gates and ?ops.
The timing analysis must cover one clock period by starting with one rising clockedge and ending with the next rising edge. How fast can the clock run? The ?rstdelay encountered is tCO of the source ?op. This is followed by tPROP of the twologic gates. Finally, tSU of the destination ?op must be met. These parametersmay be summed as follows:
tCLOCK = tCO + 2 ? tPROP + tSU = 20 ns
The frequency and period of a clock are inversely related such that F = 1/t. A 20-nsclock period corresponds to a 50-MHz clock frequency: 1/(20 ? 109) = 50 ? 106.Running at exactly the calculated clock period leaves no room for design margin.Increasing the period by 5 ns reduces the clock to 40 MHz and provides headroomto account for propagation delay through the wires.
Hold time compliance can be veri?ed following setup time analysis. Meeting a ?opshold time is often not a concern, especially in slower circuits as shown above.The 1 ns tH speci?cation is easily met, because the destination ?ops D-input willnot change until tCO + 2 ? tPROP = 17 ns after the rising clock edge. Actualtiming parameters have variance associated with them, and the best-casetCO and tPROP would be somewhat smaller numbers. megjithatë, there is somuch margin in this case that tH compliance is not a concern.
Hold-time problems sometimes arise in fast circuits where tCO and tPROPare very small. When there are no logic gates between two ?ops, tPROP canbe nearly zero. If the minimum tCO is nearly equal to the maximum tH, thesituation should be carefully investigated to ensure that the destination?ops input remains stable for a suf?cient time period after the active clock edge.

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Monitor Settings

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Today’s CRT monitors (those with television-like picture tubes) can handle the highest settings computer users are likely to want to use. If you run into a situation, megjithatë, in which an old monitor is displaying unusable video, it is possible that the Windows video settings exceed the capabilities of the monitor. You will have to diagnose the source of the problem. If you are able to read the text that appears on screen as the system is starting but the video becomes distorted and unreadable once Windows starts up, then the settings are most likely too high for the monitor. If the image is distorted from the moment you start up the computer, then it is possibly a video adapter issue. If it is the former, you will have to start Windows in Safe Mode, which will give you basic settings that almost all monitors will work with. While in Safe Mode, set the Display Properties to a lower setting and restart Windows. At this point, you might very well decide to get a new monitor that can display higher settings rather than live with a low resolution. You can try to find the monitor’s specifications on the Web and set the Display Properties accordingly. If you can’t find this information, which is possible, you’ll have to try lower settings until you find a combination that works.

The monitor itself will have settings for shape and size of the picture, brightness and contrast, and others. In addition, virtually all monitors manufactured for the last several years have an energy saving system. When the video signal from the computer stops, the monitor goes into a low-power state, and the power indicator light begins to blink or turns from green to orange. Some monitors, megjithatë, show a test pattern or no-video message in certain circumstances such as when the power comes back on after a failure and the computer is still off.

Refresh Rate

A monitor (or television, for that matter) produces a picture by having an electron beam scan a grid of microscopic light-emitting elements. The refresh rate is the rate at which the beam scans all the elements the entire screen once. The rate is expressed in Hertz (Hz), which means cycles per second, so that a rate of 60 Hz means that the electron beam scans the screen 60 times every second. Rates that are too low have noticeable flicker. If the rate is set too high for a given monitor, the video can be unusable and the monitor can be damaged. The higher the refresh rate, the less apparent the flicker will be. Rates of 70 Hz or higher should provide flicker-free video for most people. The refresh rate should be set only as high as necessary to minimize flicker higher rates, even if all the components support it, can cause other problems such as reduced contrast. To adjust the refresh rate, follow Tutorial 8.2.

Tutorial 8.2: Setting the Refresh Rate

Note that some systems don’t have a refresh rate setting.

  1. Follow Steps 1 dhe 2 of Tutorial 8.1 to access the Settings page of Display Properties.
  2. Click the Advanced button.
  3. Click the Monitor tab (if there is one).
  4. Click the down arrow next to the frequency and select a new frequency.

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