Digital Signal Integrity:Modeling and Simulation with Interconnects and Package.pdf
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1、Chapter 2SIGNAL INTEGRITYDigital systems rely on signaling from drivers to receivers to pass information be-tween their components. Reliable signaling is achieved when the signaling specifica-tions are met under full adverse noise conditions as well as device behavior variationsdue to both process d
2、eviations in device manufacturing and normal changes overthe operating temperature. A breakdown in communication leads to glitches whereunintended or incorrect data is transferred, a situation called false signaling.Critical data paths within systems often contain safeguards against false signal-ing
3、, and the primary system for this is data redundancy through parity. Parity canenable the system to detect small-scale signaling failures, while an error correctionscheme can be optionally included to correct data faults detected using parity in-formation. However, parity and error correction cannot
4、 be relied upon to make anoisy system stable and reliable. In addition, it is often not practical in terms ofcost or performance to include parity and error correction on every circuit.Superimposed on the desired signals are unwanted waveforms (i.e., noise) gener-ated from many sources. The principa
5、l sources are crosstalk, impedance mismatch,simultaneous switching noise, and multiple reflections. Each can be independentlycharacterized to facilitate an understanding of the mechanisms that degrade signalquality and to help guide design decisions. In real systems, all act simultaneouslyand requir
6、e detailed circuit simulation to obtain good estimates of the total wave-form on each signal line.5556Signal IntegrityChapter 22.1Transmission LinesA transmission line is a two-conductor interconnect (so that it can carry signalfrequency components down to DC) that is long compared to the conductor
7、crosssection and uniform along its length. Because many interconnects are dominatedby long runs over unbroken ground planes (to minimize radiation and EMI suscep-tibility), they can be accurately modeled as transmission lines, and much of signalintegrity analysis is based on them.If a short length o
8、f a transmission line is considered, then the lumped approxi-mation applies and the transmission line can be modeled, as shown in Figure 2.1,with series resistance and inductance and with shunt capacitance and conductance.Applying Kirchhoffs voltage law around the loop, thenv(z + z,t) v(z,t) = Ri(z,
9、t) Ldi(z,t)dt.(2.1)Similarly, Kirchhoffs current law applied at z + z yieldsi(z + z,t) i(z,t) = Gv(z + z,t) Cdv(z + z,t)dt.(2.2)Divide through by z and let z 0, then (2.1) and (2.2) transform from differenceequations to the differential equationsi(z + z,t)v(z + z,t)z + zzLRG+v(z,t)i(z,t)CFigure 2.1.
10、 Lumped model of a short length of a transmission line.Section 2.1.Transmission Lines57v(z,t)z= ri(z,t) )i(z,t)t(2.3)andi(z,t)z= gv(z,t) cv(z,t)t,(2.4)where the lumped component values transition to the per-unit-length quantities r,), c, and g due to normalization by z. Simultaneous solution of the
11、transmissionline equations (2.3) and (2.4) yields the voltage and current at any point on thetransmission line.2.1.1Time-Domain SolutionTransmission lines for digital signaling often have low losses. For example, the effectof half an Ohm of loss on a 50 transmission line driven with a 50 driver is n
12、egligi-ble for most applications. To facilitate investigations of the effects of various systemimperfections on signal integrity, losses will be neglected. The lossless transmissionline equations are recovered from (2.3) and (2.4) by setting r = g = 0 yieldingv(z,t)z= )i(z,t)t(2.5)andi(z,t)z= cv(z,t
13、)t.(2.6)An important property of the lossless transmission line is that pulses propagateundistorted along the length of the line. Consider an arbitrary waveform such as theone in Figure 2.2, where the wave shape is described by the function f() with anindependent variable. Since there are no losses
14、and no frequency dependence to ) orc, the waveform must move down the line unchanged in shape (see section 2.1.3 fora proof) and can be described mathematically by f(z,t) = f() = f(z t), where = z t. A maximum or minimum of the waveform occurs when /t = 0, sot= 0 =dzdt ,58Signal IntegrityChapter 2f(
15、 )Figure 2.2. Arbitrary waveform for propagation down a transmission line.or =dzdt,indicating that the maximum or minimum point is moving in the +z direction withvelocity .The partial derivatives in (2.5) and (2.6) can be rewritten in terms of by notingthatz=z=(z t)z=andt=t= ,thenv()= )i()(2.7)andi(
16、)= cv().(2.8)Eliminatingi()between (2.7) and (2.8) and cancellingv()yields =1)c,(2.9)Section 2.1.Transmission Lines59so the velocity of an arbitrary pulse can be directly computed from the per-unit-length inductance and capacitance of the transmission line. Integrating (2.7) withrespect to while ass
17、uming that no static charge is on the transmission line (sothat the integration constant vanishes), thenv() =?)ci(),where (2.9) is used. Therefore, the voltages and currents of an arbitrary waveformon a lossless transmission line are in phase and related by the impedanceZo=?)c,called the characteris
18、tic impedance of the transmission line.For a transmission line of length d, the time for a wave to travel the length ofthe line is called the delay or the time of flight (TOF) and can be computed asTOF = d)c.(2.10)The lossless transmission line is completely specified by its characteristic impedance
19、and delay. Note that) = ZoTOFd(2.11)andc =1ZoTOFd.(2.12)The analyses can be repeated with = z +t with identical results, except thatthe waveform travels in the z direction with velocity = 1/)c and the voltageand current are related byv() = Zoi().Effective Dielectric ConstantSince the TOF can be foun
20、d given the length of a transmission line and the velocityof a wave on it, the velocity is often the unknown parameter that must be found.60Signal IntegrityChapter 2In a transmission line where the electric and magnetic fields are completely encasedin a dielectric with dielectric constant -r, then t
21、he velocity is =co-r,(2.13)where co= 3108m/s is the velocity of a wave in a vacuum (-r= 1) which is alsocalled the free-space speed of light. For transmission lines such as stripline, dualstripline, embedded microstrip, and coax, the velocity is easily computed once thedielectric constant of the fil
22、ler material is known.When the electric and magnetic fields run through two dielectrics, the wave stillpropagates with some velocity. Generalizing (2.13) yields =co-eff,where -effis an effective dielectric constant. For a transmission line like microstrip,the two dielectrics are air with -r= 1 and t
23、he substrate. The effective dielectricconstant must lie between these two, and since most of the field is below the stripin the substrate, the effective dielectric constant must be closer to the dielectricconstant of the substrate than to that of air.Effective dielectric constants are convenient bec
24、ause they offer a handy shortcutin many situations and can be easily estimated for approximate calculations. Forexample, if -r= 4 for the substrate in microstrip, then -eff 3.For the lossless case, the formulas in (2.11) and (2.12) are easily modified forthe effective dielectric constant to be) =Zo-
25、effco(2.14)andc =-effZoco.(2.15)2.1.2Directional IndependenceThe analysis of lossless transmission lines can be carried further to show that twowaveforms traveling in opposite directions do not interact. Let v+denote a voltageSection 2.1.Transmission Lines61waveform launched in the +z direction, whi
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