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  • In this final chapter, we're going to look into optimizing

  • digital systems to make them smaller, faster,

  • higher performance, more energy efficient, and so on.

  • It would be wonderful if we could

  • achieve all these goals at the same time and for some circuits

  • we can.

  • But, in general, optimizing in one dimension

  • usually means doing less well in another.

  • In other words, there are design tradeoffs to be made.

  • Making tradeoffs correctly requires

  • that we have a clear understanding of our design

  • goals for the system.

  • Consider two different design teams:

  • one is charged with building a high-end graphics

  • card for gaming, the other with building the Apple watch.

  • The team building the graphics card

  • is mostly concerned with performance

  • and, within limits, is willing to trade-off cost and power

  • consumption to achieve their performance goals.

  • Graphics cards have a set size, so there's a high priority

  • in making the system small enough to meet the required

  • size, but there's little to be gained in making it smaller

  • than that.

  • The team building the watch has very different goals.

  • Size and power consumption are critical since it has fit

  • on a wrist and run all day without leaving scorch marks

  • on the wearer's wrist!

  • Suppose both teams are thinking about pipelining

  • part of their logic for increased performance.

  • Pipelining registers are an obvious additional cost.

  • The overlapped execution and higher t_CLK

  • made possible by pipelining would

  • increase the power consumption and the need

  • to dissipate that power somehow.

  • You can imagine the two teams might

  • come to very different conclusions

  • about the correct course of action!

  • This chapter takes a look at some of the possible tradeoffs.

  • But as designers you'll have to pick and choose which tradeoffs

  • are right for your design.

  • This is the sort of design challenge

  • on which good engineers thrive!

  • Nothing is more satisfying than delivering more

  • than anyone thought possible within the specified

  • constraints.

  • Our first optimization topic is power dissipation,

  • where the usual goal is to either meet a certain power

  • budget, or to minimize power consumption while meeting

  • all the other design targets.

  • In CMOS circuits, there are several sources

  • of power dissipation, some under our control, some not.

  • Static power dissipation is power

  • that is consumed even when the circuit is idle,

  • i.e., no nodes are changing value.

  • Using our simple switch model for the operation of MOSFETs,

  • we'd expect CMOS circuits to have zero static power

  • dissipation.

  • And in the early days of CMOS, we

  • came pretty close to meeting that ideal.

  • But as the physical dimensions of the MOSFET have shrunk

  • and the operating voltages have been lowered,

  • there are two sources of static power dissipation in MOSFETs

  • that have begun to loom large.

  • We'll discuss the effects as they appear in n-channel

  • MOSFETs, but keep in mind that they appear in p-channel

  • MOSFETs too.

  • The first effect depends on the thickness of the MOSFET's gate

  • oxide, shown as the thin yellow layer in the MOSFET diagram

  • on the left.

  • In each new generation of integrated circuit technology,

  • the thickness of this layer has shrunk,

  • as part of the general reduction in all the physical dimensions.

  • The thinner insulating layer means

  • stronger electrical fields that cause a deeper inversion

  • layer that leads to NFETs that carry more current, producing

  • faster gate speeds.

  • Unfortunately the layers are now thin enough

  • that electrons can tunnel through the insulator,

  • creating a small flow of current from the gate to the substrate.

  • With billions of NFETs in a single circuit,

  • even tiny currents can add up to non-negligible power drain.

  • The second effect is caused by current flowing

  • between the drain and source of a NFET that

  • is, in theory, not conducting because V_GS is less

  • than the threshold voltage.

  • Appropriately this effect is called sub-threshold conduction

  • and is exponentially related to V_GS -

  • V_TH (a negative value when the NFET is off).

  • So as V_TH has been reduced in each new generation

  • of technology, V_GS - V_TH is less negative

  • and the sub-threshold conduction has increased.

  • One fix has been to change the geometry of the NFET

  • so the conducting channel is a tall, narrow fin with the gate

  • terminal wrapped around 3 sides, sometimes referred

  • to as a tri-gate configuration.

  • This has reduced the sub-threshold conduction

  • by an order-of-magnitude or more,

  • solving this particular problem for now.

  • Neither of these effects is under the control of the system

  • designer, except of course, if they're free to choose an older

  • manufacturing process!

  • We mention them here so that you're aware that newer

  • technologies often bring additional costs that then

  • become part of the trade-off process.

  • A designer does have some control over the dynamic power

  • dissipation of the circuit, the amount of power

  • spent causing nodes to change value

  • during a sequence of computations.

  • Each time a node changes from 0-to-1 or 1-to-0,

  • currents flow through the MOSFET pullup and pulldown networks,

  • charging and discharging the output node's capacitance

  • and thus changing its voltage.

  • Consider the operation of an inverter.

  • As the voltage of the input changes,

  • the pullup and pulldown networks turn on and off,

  • connecting the inverter's output node to VDD or ground.

  • This charges or discharges the capacitance of the output

  • node changing its voltage.

  • We can compute the energy dissipated

  • by integrating the instantaneous power associated

  • with the current flow into and out of the capacitor

  • times the voltage across the capacitor over the time taken

  • by the output transition.

  • The instantaneous power dissipated

  • across the resistance of the MOSFET channel

  • is simply I_DS times V_DS.

  • Here's the power calculation using the energy integral

  • for the 1-to-0 transition of the output node,

  • where we're measuring I_DS using the equation for the current

  • flowing out of the output node's capacitor: I = C dV/dt.

  • Assuming that the input signal is a clock signal of period

  • t_CLK and that each transition is taking half a clock cycle,

  • we can work through the math to determine that power dissipated

  • through the pulldown network is 0.5 f C VDD^2,

  • where the frequency f tells us the number

  • of such transitions per second,

  • C is the nodal capacitance, and VDD (the power supply voltage)

  • is the starting voltage of the nodal capacitor.

  • There's a similar integral for the current dissipated

  • by the pullup network when charging the capacitor and it

  • yields the same result.

  • So one complete cycle of charging then discharging

  • dissipates f C V-squared watts.

  • Note the all this power has come from the power supply.

  • The first half is dissipated when the output node is charged

  • and the other half stored as energy in the capacitor.

  • Then the capacitor's energy is dissipated as it discharges.

  • These results are summarized in the lower left.

  • We've added the calculation for the power dissipation

  • of an entire circuit assuming N of the circuit's nodes change

  • each clock cycle.

  • How much power could be consumed by a modern integrated circuit?

  • Here's a quick back-of-the-envelope estimate

  • for a current generation CPU chip.

  • It's operating at, say, 1 GHz and will have 100 million

  • internal nodes that could change each clock cycle.

  • Each nodal capacitance is around 1 femto Farad

  • and the power supply is about 1V.

  • With these numbers, the estimated power consumption

  • is 100 watts.

  • We all know how hot a 100W light bulb gets!

  • You can see it would be hard to keep the CPU from overheating.

  • This is way too much power to be dissipated

  • in many applications, and modern CPUs

  • intended, say, for laptops only dissipate

  • a fraction of this energy.

  • So the CPU designers must have some tricks up their sleeve,

  • some of which we'll see in a minute.

  • But first notice how important it's been to be able to reduce

  • the power supply voltage in modern integrated circuits.

  • If we're able to reduce the power supply voltage from 3.3V

  • to 1V, that alone accounts for more than a factor of 10

  • in power dissipation.

  • So the newer circuit can be say, 5 times larger and 2 times

  • faster with the same power budget!

  • Newer technologies trends are shown here.

  • The net effect is that newer chips would naturally

  • dissipate more power if we could afford to have them do so.

  • We have to be very clever in how we use more and faster MOSFETs

  • in order not to run up against the power

  • dissipation constraints we face.

  • To see what we can do to reduce power consumption,

  • consider the following diagram of an arithmetic and logic unit

  • (ALU) like the one you'll design in the final lab in this part

  • of the course.

  • There are four independent component modules,

  • performing the separate arithmetic, boolean, shifting

  • and comparison operations typically found in an ALU.

  • Some of the ALU control signals are

  • used to select the desired result in a particular clock

  • cycle, basically ignoring the answers produced

  • by the other modules.

  • Of course, just because the other answers aren't selected

  • doesn't mean we didn't dissipate energy in computing them.

  • This suggests an opportunity for saving power!

  • Suppose we could somehowturn offmodules whose outputs we

  • didn't need?

  • One way to prevent them from dissipating power is to prevent

  • the module's inputs from changing,

  • thus ensuring that no internal nodes would change

  • and hence reducing the dynamic power dissipation of theoff

  • module to zero.

  • One idea is to put latches on the inputs to each module,

  • only opening a module's input latch if an answer was required

  • from that module in the current cycle.

  • If a module's latch stayed closed,

  • its internal nodes would remain unchanged,

  • eliminating the module's dynamic power dissipation.

  • This could save a substantial amount of power.

  • For example, the shifter circuitry has

  • many internal nodes and so has a large dynamic power

  • dissipation.

  • But there are comparatively few shift operations in most

  • programs, so with our proposed fix,

  • most of the time those energy costs wouldn't be incurred.

  • A more draconian approach to power conservation

  • is to literally turn off unused portions of the circuit

  • by switching off their power supply.

  • This is more complicated to achieve,

  • so this technique is usually reserved

  • for special power-saving modes of operation,

  • where we can afford the time it takes to reliably power

  • the circuity back up.

  • Another idea is to slow the clock (reducing the frequency

  • of nodal transitions) when there's nothing for the circuit

  • to do.

  • This is particularly effective for devices

  • that interact with the real world,

  • where the time scales for significant external events

  • are measured in milliseconds.

  • The device can run slowly until an external event needs

  • attention, then speed up the clock

  • while it deals with the event.

  • All of these techniques and more are

  • used in modern mobile devices to conserve battery power

  • without limiting the ability to deliver bursts of performance.

  • There is much more innovation waiting

  • to be done in this area, something you may be

  • asked to tackle as designers!

  • One last question is whether computation

  • has to consume energy?

  • There have been some interesting theoretical speculations about

  • this questionsee section 6.5 of the course notes to read

  • more.

In this final chapter, we're going to look into optimizing

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B2 中上級

8.2.1 消費電力 (8.2.1 Power Dissipation)

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    林宜悉 に公開 2021 年 01 月 14 日
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