### 1. Digital Termination Overview

Unlike systems designed for lower speed applications, in high-speed digital systems, simple passive circuit elements like wires, cables, and chip PCB interconnections can significantly affect signal quality. High-speed digital edges contain frequency components that are several times the effective toggle rate of that signal. For example, a digital edge with a rise time of 1.5 ns contains significant energy in frequencies up to 333 MHz, regardless of toggle rate. When designing systems using digital waveform generator/analyzers, you must have a basic understanding of both transmission lines and termination so that you can maximize signal quality and minimize the effects of signal reflections.

The signals in the following figures show identical digital waveforms generated by an digital device. The left figure shows a properly terminated waveform where the test system was designed with a careful understanding of both transmission lines and termination. The second figure shows a waveform from an unterminated system where transmission line effects and termination were not considered.

Figure 1. (a.) Properly Terminated Digital Channel (b.) Improperly Terminated Digital Channel

Consider the following key areas when designing your test system:

· Z_{s}—The impedance at the source of the transmission line

· Z_{0}—The characteristic AC impedance of the transmission line

· Z_{t}—The impedance at the destination of the transmission line

By carefully controlling these three elements of your system, you can achieve the best possible results. Leaving these three elements uncontrolled can result in the type of signal distortion shown in the improperly terminated signal and produce the following results:

· Signals that exceed specified high-level and low-level thresholds (overshoot and undershoot)

· Signals that have false edges (ringing)

· Signals that have reduced operating margins (degraded eye diagram caused by inter-symbol interference)

· Potential physical damage or overheating of driver/receiver components in extreme cases

### 2. Transmission Lines

In lower frequency (slow edge rate) applications, you can assume that small wires interconnecting devices do not affect system performance, and that every point in a wire has the same voltage as every other point for any instance in time. At lower frequencies, this "lumped" circuit model is valid. However, as frequency content increases, even the small geometries of typical wire dimensions become a significant portion of the signal wavelengths, in which case the small inductance and capacitance become electrically significant impedances. What constitutes a significant proportion of the wavelength? While this value changes for different applications, for digital circuits, a good general rule is that if the propagation delay in a wire or interconnect is greater than 1/6 of the rise time of the digital signal, then the "lumped" circuit analysis assumption is no longer valid and you should analyze the interconnect as a transmission line.

For calculation purposes, you should understand the concept of electrical length (l). Electrical length is defined as the distance that a signal can travel in an electrical medium during the time that it takes for one rise or fall time, whichever is longer. Using the concept of electrical length, the general rule of the previous paragraph can be rephrased as follows: If the physical length of a wire or electrical interconnect is greater than 1/6 of the electrical length of a signal propagating on that wire, the system must be analyzed as a transmission line. Velocity is defined as the rate at which an electrical wave propagates in the transmission medium. Using this value you can calculate electrical length in one of the following ways:

*l(in) = Velocity(in/ns) • t _{rise}*

*l(in) = t _{rise}(ns)/t_{pd}(ns/in)*

where *t _{rise}* is the rise/fall time of the digital edge, and

*t*is the propagation delay of the edge in the transmission line.

_{pd}For example, the NI SHC68-C68-D2 shielded cable has a t_{pd} of 165 ps/inch. On an __NI 655 X digital device__, t

_{rise}for a high-speed digital signal can be as low as 1.5 ns. Therefore, the electrical length is 9 inches (t

_{rise}/t

_{pd}= 1.5/.165 = 9 in.), and any trace lengths longer than 1.5 inch (9 inch/6) should be treated as a transmission line. Since this cable is significantly longer than 1.5 inches, NI considers this cable to be a transmission line and designed the cable to have a controlled 50 Ω characteristic impedance cable.

**Note:** While the propagation delay number in the previous example is specific to the NI SHC68-C68-D2 cable, if you do not know the specific propagation delays for your interconnects, when using the NI digital waveform generator/analyzer, assume that you are working with transmission lines for any wire or interconnect longer than 1 to 2 inches.

Figure 2 gives a simple diagram of a basic single-ended transmission line. A voltage source (V_{s}) generates a digital edge with an impedance of Z_{s} looking "into" the transmission line. The transmission line itself has some low characteristic AC impedance (Z_{0}) to ground, typically 50 Ω for most test systems. The end of the transmission line is most commonly terminated through an impedance (Z_{t}) to ground at the destination.

Figure 2. Diagram of a Basic Single-ended Transmission Line

Practically, termination at only one end of the transmission line is often adequate and is more commonly used. However, for high-precision applications, termination at both the source and the load end of the transmission line yields the best results.

### 3. Characteristic Impedance

The characteristic impedance of a transmission line largely influences the transient response of a signal passing through it. The physical properties of the transmission line materials determine this characteristic impedance. For example, the dielectric of the insulators and the cross sectional geometry of a cable determine the capacitance. Likewise, the inductance of the cable is a function of the length and the properties of the dielectric. The characteristic impedance is a function of both this inductance and capacitance. Manufacturers of cables provide the specification for the characteristic impedance of that cable, along with how it behaves over environmental extremes.

Once again, it is critical that the characteristic impedance be matched to the source impedance. If the impedance is not matched, the resulting signal at the load is greatly distorted in both time and amplitude. Any time you disrupt the geometry described above, it results in impedance mismatches and resulting reflections. For example, at the interfaces or boundaries between the cables and the devices, you should use connectors designed to maintain this characteristic impedance (coaxial connectors). Screw terminals, tees in the transmission line, or wire stubs are not recommended.

**Caution:** Failure to use the connectors designed for these cables may result in impedance mismatches.

### 4. Signal Reflections

A digital rising or falling edge is a step function that can be modeled as a high-frequency wavefront. As the wavefront travels along the transmission line, it acts as a purely AC signal, encountering the characteristic impedance (Z_{0}) of the transmission line. When the wavefront reaches the end of the path, if a mismatch between Z_{0} and the termination (Z_{t}) exists, portions of the wave are reflected. As the wave reflects back along the transmission line, it eventually reaches the original source impedance (Z_{s}). If a mismatch exists between the transmission line characteristic impedance (Z_{0}) and Z_{s}, then portions of the wave are re-reflected. The superposition of these reflected waves can cause significant signal degradation.

Reflection caused by an impedance mismatch at the end of a transmission line is quantified by the reflection coefficient. Reflection coefficient Γ is given by:

Γ = *V _{r}/V_{i} = (Z_{t} - Z_{0})/(Z_{t} + Z_{0})*;

where *V _{r}* is the reflected voltage,

*V*is the incident voltage,

_{i}*Z*is the terminating impedance, and

_{t}*Z*is the characteristic impedance of the transmission line. For example, by applying this formula, you can calculate that when a 3.3 V wave, traveling down a 50 Ω characteristic medium hits a 1 kΩ load impedance:, the reflection coefficient Γ

_{0}_{t}is equal to (1 kΩ - 50 Ω)/(1 kΩ + 50 Ω), or .90, and V

_{r}equals 0.9 x 3.3 V = 2.97 V. Thus, the reflected wave V

_{r}is almost the same magnitude as the incident wave. At the load, this condition only has the effect of giving an erroneous voltage—assuming that the circuit was calibrated with a 50 Ω load originally. While nearly the entire signal is reflected back, this reflection is eliminated at the source because the source and the transmission line are matched.

However, should the transmission line/cable be mismatched from the source and the load, the mismatch causes a scenario of multiple reflections resulting in aberrations at the load similar to what is shown in the improperly terminated signal in figure 1b.

**Note:** NI *strongly* recommends that you take great care to ensure that the source impedance of the system is matched as closely as possible to the characteristic impedance of the transmission line. For generation operations, the source impedance is inside the NI device and is handled by the hardware architecture. For acquisition operations, however, you control the source impedance of the system. You should create a source impedance as close to the characteristic impedance of your device as possible.

### 5. Types of Termination

There are several forms of line termination, including parallel, series, and differential. Parallel termination matches the characteristic impedance of the medium at the end of the line, squelching the wavefront at the destination (Z_{t} = Z_{0}). Differential termination is a variation of parallel termination used for differential transmission lines. Many electrical standards, such as emitter-coupled logic (ECL) and LVDS, require that traces are routed differentially. As such, parallel termination is used between the two modes of the differential trace. Series termination places series impedance equal to the characteristic impedance at the source of the transmission line. This termination prevents the source from re-reflecting any reflections from an unterminated transmission line. It also prevents reflections from the transmission line to the source at the entry (Z_{S} = Z_{0}). Practically, termination at only one end of the transmission line is often adequate and is more commonly used.

### 6. Relevant NI Products

Customers interested in this topic were also interested in the following NI products:

- High-Speed Digital I/O
- Industrial Digital I/O
- Logic Analyzers
- Modular Instruments (digital multimeters, digitizers, switching, etc...)
- Digital Waveform Editor
- LabVIEW Graphical Programming Environment
- SignalExpress Interactive Software Environment

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page