Signal Integrity, Impedance and Electrical Models
- Describing Signal-Integrity Solutions in Terms of Impedance
- What Is Impedance?
- Real vs. Ideal Circuit Elements
- Impedance of an Ideal Resistor in the Time Domain
- Impedance of an Ideal Capacitor in the Time Domain
- Impedance of an Ideal Inductor in the Time Domain
- Impedance in the Frequency Domain
- Equivalent Electrical Circuit Models
- Circuit Theory and SPICE
- Introduction to Modeling
- The Bottom Line
In high-speed digital systems, where signal integrity plays a significant role, we often refer to signals as either changing voltages or a changing currents. All the effects that we lump in the general category of signal integrity are due to how analog signals (those changing voltages and currents) interact with the electrical properties of the interconnects. The key electrical property with which signals interact is the impedance of the interconnects.
Impedance is defined as the ratio of the voltage to the current. We usually use the letter Z to represent impedance. The definition, which is always true, is Z = V/I. The manner in which these fundamental quantities, voltage and current, interact with the impedance of the interconnects determines all signal-integrity effects. As a signal propagates down an interconnect, it is constantly probing the impedance of the interconnect and reacting based on the answer.
If we know the impedance of the interconnect, we can accurately predict how the signals will be distorted and whether a design will meet the performance specification, before we build it.
Likewise, if we have a target spec for performance and know what the signals will be, we can sometimes specify an impedance specification for the interconnects. If we understand how the geometry and material properties affect the impedance of the interconnects, then we will be able to design the cross section, the topology, and the materials and select the other components so they will meet the impedance spec and result in a product that works the first time.
Impedance is the key term that describes every important electrical property of an interconnect. Knowing the impedance and propagation delay of an interconnect is to know almost everything about it electrically.
3.1 Describing Signal-Integrity Solutions in Terms of Impedance
Each of the four basic families of signal-integrity problems can be described based on impedance.
Signal-quality problems arise because voltage signals reflect and are distorted whenever the impedance the signal sees changes. If the impedance the signal sees is always constant, there will be no reflection and the signal will continue undistorted. Attenuation effects are due to series and shunt-resistive impedances.
Cross talk arises from the electric and magnetic fields coupling between two adjacent signal traces (and, of course, their return paths). The mutual capacitance and mutual inductance between the traces establishes an impedance, which determines the amount of coupled current.
Rail collapse of the voltage supply is really about the impedance in the power-distribution system (PDS). A certain amount of current must flow to feed all the ICs in the system. Because of the impedance of the power and ground distribution, a voltage drop will occur as the IC current switches. This voltage drop means the power and ground rails have collapsed from their nominal values.
The greatest source of EMI is from common-mode currents, driven by voltages in the ground planes, through external cables. The higher the impedance of the return current paths in the ground planes, the greater the voltage drop, or ground bounce, which will drive the radiating currents. The most common fix for EMI from cables is the use of a ferrite choke around the cable. This works by increasing the impedance the common-mode currents see, thereby reducing the amount of common-mode current.
There are a number of design rules, or guidelines, that establish constraints on the physical features of the interconnects. For example, “keep the spacing between adjacent signal traces greater than 10 mils” is a design rule to minimize cross talk. “Use power and ground planes on adjacent layers separated by less than 5 mils” is a design rule for the power and ground distribution.
Not only are the problems associated with signal integrity best described by the use of impedance, but the solutions and the design methodology for good signal integrity are also based on the use of impedance.
These rules establish a specific impedance for the physical interconnects. This impedance provides a specific environment for the signals, resulting in a desired performance. For example, keeping the power and ground planes closely spaced will result in a low impedance for the power distribution system and hence a lower voltage drop for a given power and ground current. This helps minimize rail collapse and EMI.
If we understand how the physical design of the interconnects affects their impedance, we will be able to interpret how they will interact with signals and what performance they might have.
Impedance is the Rosetta stone that links physical design and electrical performance. Our strategy is to translate system-performance needs into an impedance requirement and physical design into an impedance property.
Impedance is at the heart of the methodology we will use to solve signal-integrity problems. Once we have designed the physical system as we think it should be for optimal performance, we will translate the physical structure into its equivalent electrical circuit model. This process is called modeling.
It is the impedance of the resulting circuit model that will determine how the interconnects will affect the voltage and current signals. Once we have the circuit model, we will use a circuit simulator, such as SPICE, to predict the new waveforms as the voltage sources are affected by the impedances of the interconnects. Alternatively, behavioral models of the drivers or interconnects can be used where the interaction of the signals with the impedance, described by the behavioral model, will predict performance. This process is called simulation.
Finally, the predicted waveforms will be analyzed to determine if they meet the timing and distortion or noise specs, and are acceptable, or if the physical design has to be modified. This process flow for a new design is illustrated in Figure 3-1.
Figure 3-1. Process flow for hardware design. The modeling, simulation, and evaluation steps should be implemented as early and often in the design cycle as possible.
The two key processes, modeling and simulation, are based on converting electrical properties into an impedance, and analyzing the impact of the impedance on the signals.
If we understand the impedance of each of the circuit elements used in a schematic and how the impedance is calculated for a combination of circuit elements, the electrical behavior of any model and any interconnect can be evaluated. This concept of impedance is absolutely critical in all aspects of signal-integrity analysis.