高速数字系统设计：互连理论与实践手册

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"高速数字系统设计 - 一本深入探讨高速数字电路系统理论与设计实践的手册，由Stephen H. Hall, Garrett W. Hall 和 James A. McCall合著，是 Wiley-Interscience 出版的一部著作。" 在高速数字系统设计中，关键知识点包括： 1. **高速特性**：随着电子技术的发展，数字系统的工作频率不断提高，这导致了信号传输速度的显著提升。高速系统设计需要考虑信号的上升时间、时钟速率以及数据传输速率等因素，这些因素会直接影响系统的性能和稳定性。 2. **信号完整性（Signal Integrity, SI）**：在高速数字系统中，信号质量至关重要。信号完整性涉及信号在传输过程中保持其原始形状的能力，包括反射、串扰、衰减和噪声等问题。理解和管理信号完整性是高速数字设计的基础。 3. **电源完整性（Power Integrity, PI）**：随着工作频率的增加，电源电压波动和电流瞬态响应对系统性能的影响也越来越大。电源完整性分析确保了系统供电网络的稳定，防止因电源噪声导致的问题。 4. **互连理论**：在高速数字系统中，互连是连接不同组件的关键。互连线的长度、材料、拓扑结构等都会影响信号传输。了解互连理论有助于优化布线策略，减少信号损失和延迟。 5. **电磁兼容性（Electromagnetic Compatibility, EMC）**：高速系统必须满足EMC标准，以防止设备间的电磁干扰。设计时要考虑辐射发射和抗扰度，通过屏蔽、滤波和正确的接地策略来控制电磁场的影响。 6. **设计实践**：书中的设计实践部分可能涵盖仿真工具的使用、PCB设计技巧、测试与验证方法等，这些都是将理论知识应用于实际设计过程中的重要步骤。 7. **时序分析**：高速系统中的时序分析涉及到信号到达时间、时钟同步和时钟偏移等，确保数据正确接收并避免时序错误。 8. **眼图分析**：这是一种评估高速数字信号质量的常用方法，通过观察信号在示波器上形成的“眼图”形状，可以判断信号的清晰度和噪声水平。 9. **差分信号与共模信号**：高速设计中常使用差分信号，因为它们能提供更好的抗干扰能力，并且减少电磁辐射。理解差分信号与共模信号之间的关系对优化设计至关重要。 10. **热管理和散热**：高速设备产生的热量可能影响电路性能。良好的热管理和散热设计是确保系统稳定运行的关键。 "高速数字系统设计"涵盖了从理论到实践的广泛主题，旨在帮助读者理解和解决高速数字电路设计中的挑战。书中可能包含详细的案例研究、实用建议和计算方法，以帮助工程师实现高效、可靠的高速系统。

For maximum accuracy, it is necessary to use one of the many commercially available two-

dimensional electromagnetic field solvers to calculate the impedance of the PCB traces for

design purposes. The solvers will typically provide the impedance, propagation velocity, and

L and C elements per unit length. This is adequate since R and G usually have a minimal

effect on the impedance. In the absence of a field solver, the formulas presented in Figure

2.6 will provide good approximations to the impedance values of typical transmission lines

as a function of the trace geometry and the dielectric constant (ε

). More accurate formulas

for characteristic impedance are presented in Appendix A.

Figure 2.6: Characteristic impedance approximations for typical transmission lines: (a)

microstrip line; (b) symmetrical stripline; (c) offset stripline.

2.3.2. Propagation Velocity, Time, and Distance

Electrical signals on a transmission line will propagate at a speed that depends on the

surrounding medium. Propagation delay is usually measured in terms of seconds per meter

and is the inverse of the propagation velocity. The propagation delay of a transmission line

will increase in proportion to the square root of the surrounding dielectric constant. The time

delay of a transmission line is simply the amount of time it takes for a signal to propagate the

entire length of the line. The following equations show the relationships between the

dielectric constant, the propagation velocity, the propagation delay, and the time delay:

(2.2)

(2.3)

(2.4)

where



= propagation velocity, in meters/second

= speed of light in a vacuum (3 × 10

m/s)

= dielectric constant

PD = propagation delay, in seconds per meter

TD = time delay for a signal to propagate down a transmission line of length x

= length of the transmission line, in meters

The time delay can also be determined from the equivalent circuit model of the transmission

line:

(2.5)

where L is the total series inductance for the length of the line and C is the total shunt

capacitance for the length of the line.

It should be noted that equations (2.2) through (2.4) assume that no magnetic materials are

present, such that µ

= 1, and thus effects due to magnetic materials can be left out of the

formulas.

The delay of a transmission line depends on the dielectric constant of the dielectric material,

the line length, and the geometry of the transmission line cross section. The cross-sectional

geometry determines whether the electric field will stay completely contained within the

board or fringe out into the air. Since a typical PCB board is made out of FR4, which has a

dielectric constant of approximately 4.2, and air has a dielectric constant of 1.0, the resulting

"effective" dielectric constant will be a weighted average between the two. The amount of the

electric field that is in the FR4 and the amount that is in the air determine the effective value.

When the electric field is completely contained within the board, as in the case of a stripline,

the effective dielectric constant will be larger and the signals will propagate more slowly than

will externally routed traces. When signals are routed on the external layers of the board as

in the case of a microstrip line, the electric field fringes through the dielectric material and the

air, which lowers the effective dielectric constant; thus the signals will propagate more

quickly than those on an internal layer.

The effective dielectric constant for a microstrip is calculated as follows [Collins, 1992

(2.6)

(2.7)

where ε

is the dielectric constant of the board material, H the height of the conductor above

the ground plane, W the conductor width, and T the conductor thickness.

2.3.3. Equivalent Circuit Models for SPICE Simulation

In Section 2.3 we introduced the equivalent distributed circuit model of a transmission line,

which consisted of an infinite number of RLCG segments cascaded together. Since it is not

practical to model a transmission line with an infinite number of elements, a sufficient

number can be determined based on the minimum rise or fall time used in the simulation.

When simulating a digital system, it is usually sufficient to choose the values so that the time

delay

of the shortest RLCG segment is no larger than one-tenth of the

minimum system rise or fall time. The rise or fall time is defined as the amount of time it

2.4. LAUNCHING INITIAL WAVE AND TRANSMISSION LINE

REFLECTIONS

The characteristics of the driving circuitry and the transmission line greatly affect the integrity

of a signal being transmitted from one device to another. Subsequently, it is very important

to understand how the signal is launched onto a transmission line and how it will look at the

receiver. Although many parameters will affect the integrity of the signal at the receiver, in

this section we describe the most basic behavior.

2.4.1. Initial Wave

When a driver launches a signal onto a transmission line, the magnitude of the signal

depends on the voltage and source resistance of the buffer and the impedance of the

transmission line. The initial voltage seen at the driver will be governed by the voltage divider

of the source resistance and the line impedance. Figure 2.8

depicts an initial wave being

launched onto a long transmission line. The initial voltage V

will propagate down the

transmission line until it reaches the end. The magnitude of V

is determined by the voltage

divider between the source and the line impedance:

(2.8)

Figure 2.8: Launching a wave onto a long transmission line.

If the end of the transmission line is terminated with an impedance that exactly matches the

characteristic impedance of the line, the signal with amplitude V

will be terminated to ground

and the voltage V

will remain on the line until the signal source switches again. In this case

the voltage V

is the dc steady-state value. Otherwise, if the end of the transmission line

exhibits some impedance other than the characteristic impedance of the line, a portion of the

signal will be terminated to ground and the remainder of the signal will be reflected back

down the transmission line toward the source. The amount of signal reflected back is

determined by the reflection coefficient, defined as the ratio of the reflected voltage to the

incident voltage seen at a given junction. In this context, a junction is defined as an

impedance discontinuity on a transmission line. The impedance discontinuity could be a

section of transmission line with different characteristic impedance, a terminating resistor, or

the input impedance to a buffer on a chip. The reflection coefficient is calculated as

(2.9)

impedance of the line, and Z

the impedance of the discontinuity. The equation assumes that

the signal is traveling on a transmission line with characteristic impedance Z

and

encounters an impedance discontinuity of Z

. Note that if Z

= Z

, the reflection coefficient is

zero, meaning that there is no reflection. The case where Z

= Z

is known as matched

termination.

As depicted in Figure 2.9

, when the incident wave hits the termination Z

, a portion of the

signal, V

iρ

, is reflected back toward the source and is added to the incident wave to produce

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