In an earlier blog post, we reviewed the different kinds of grounds you should familiarize yourself with to successfully install servo drive and servo motor systems. For our next topic in this blog series, we will examine different kinds of interface signaling, when to model cable as a transmission line and how to terminate lines to eliminate reflections.

Signaling

Single-Ended Signaling

A single-ended signal is shown in Figure 1. Gate A from one system is connected to gate B of another system. The input voltage (V_IN) for gate B is relative to the signal ground. The return current from gate A flows through the ground wire back to signal ground. If the cable were to carry multiple signals, the return currents would flow through the same ground wire.

If these currents were large, they could raise the potential of the ground pin on gate A relative to the signal ground and affect noise immunity. A and B signal grounds connected over long distances can create ground loops — especially if the signal grounds are also connected to the earth ground.

Electrical model of a single-ended signal.

Figure 1. Single-ended signal.

Because any noise within the cable appears in the gate B output, single-ended signaling is not recommended for connecting an encoder to a servo drive. Instead, single-ended signaling is primarily used to transfer signals on the same circuit board with a common ground plane.

Differential Signaling

Figure 2 shows an example of differential signaling. Differential signaling involves transmitting two complementary signals — equal in magnitude and opposite in polarity — to a receiver that takes the difference between the two signals.

Gate B is the differential receiver that subtracts the voltage of the negative input from the positive input. As opposed to single-ended signaling, each signal now has its own return current path. Differential signaling is useful because it reduces any noise present on both signals, and it is commonly implemented in twisted pairs for further noise immunity.

The rising and falling edges of digital signals create crosstalk between the wires in a twisted pair cable. But because the electromagnetic emissions from the two wires are equal in magnitude and opposite in polarity, they partially cancel each other and reduce crosstalk.

Electrical model of differential signaling.

Figure 2. Differential signaling.

Because differential signaling can use lower voltages (logic 0 V > +2V, logic 1 V < -2V), in these cases, V_IN is no longer in reference to the ground. However, most standards still require a shared ground to ensure that the signals stay within range of the common-mode voltage rating.

Even though differential signaling uses two wires per signal, it is highly recommended for long-distance signal transfer and systems in environments with high electrical noise.

Transmission Lines and Signal Termination

Rules of Thumb

In motion control systems, the cable connecting the servo drive to the motor or encoder may be 100 meters (m) long or more. Long distances may require you to model the cable as a transmission line. Transmission line modeling involves evaluating wavefront reflections. To determine if you need transmission line modeling, apply the following rules of thumb for analog and digital signals.

Analog
For analog signals, the cable should not be longer than one quarter the wavelength of the highest frequency. A typical sin/cos encoder with 256 periods per revolution and turning at 100 revolutions per second (rev/sec) produces sine waves of around 25 kilohertz (kHz). These sine waves have a wavelength of approximately 8 kilometers (km). This calculation is shown below.

Wavelength $=\frac{\text { Light Speed } \cdot \text { Velocity Factor }}{\text { Frequency }} \approx \frac{300 \cdot 10^6 \cdot 0.65}{25 \cdot 10^3} \approx 8 \mathrm{~km}$

Where:

Light Speed $=300 \cdot 10^6 \mathrm{~m} / \mathrm{s}$

Velocity Factor $=0.65$ for XXX cable

Frequency $=25 \cdot 10^3 \mathrm{~Hz}$

Keep in mind that the velocity factor is necessary because the wavelength is not within a vacuum. For analog encoder signals, it is usually not necessary to treat the cable as a transmission line.

Digital
With digital signals, the propagation delay through the cable should not exceed 10 percent of the signal’s risetime. Assuming a 10-megabits per second (Mbps) transmission rate, a typical RS-422 line driver has a risetime of 10 nanosec (ns). In this case, the cable shouldn’t be longer than approximately 0.2 m. The calculation is shown below.

Max. Cable Length $\approx$ Light Speed $\cdot$ Velocity Factor $\cdot \frac{\text { Risetime }}{10} \approx 300 \cdot 10^6 \cdot 0.65 \cdot 1 \cdot 10^{-9} \approx 0.2 \mathrm{~m}$

For high-speed digital signals, the cable should be treated as a transmission line.

Transmission Line Model

An ideal transmission line is one that features negligible resistance, and it can be modeled as distributed inductance and capacitance as shown in Figure 3. In this model, R_S is the output impedance of the source V_S. Note that the resistor R_T is not yet a part of the circuit.

The wavefront propagating from V_S successively charges each distributed capacitor. The relationship between voltage changes and current changes at any point in the circuit is defined as the characteristic impedance of the line. This relationship is shown below.

$Z=\frac{\Delta V}{\Delta I}$

Where:

Z is characteristic impedance

V is voltage

I is current

Note that the characteristic impedance is not related to transmission line length.

An electrical model of an ideal transmission line featuring negligible resistance.

Figure 3. Ideal transmission line.

Reflections

When a propagating wave encounters a change in impedance, reflections occur at the cable line boundary. For a typical twisted pair, the characteristic impedance (Z) is 120 ohms (Ω). The logic gate at the end of the cable line in Figure 3 has a very high impedance relative to Z and the wave is reflected as shown in Figure 4.

An output square wave encountering impedance changes.

Figure 4. Output square wave encountering impedance changes.

Figure 4 shows the source’s output square wave first encountering a voltage divider composed of R_S and Z impedance. Assuming that RS is equal to Z, the voltages at B and C are half the source voltage. At D, the reflection occurs which adds to the incident wavefront. Then, the reflected wave combines with another wavefront at C. This creates a very distorted wave which can be a serious problem if there is a tap on the line at C. If impedance R_S is not equal to Z, multiple reflections occur. Multiple reflections produce characteristic ringing on the signal as shown in Figure 5.

Current ripple due to multiple reflections.

Figure 5. Current ripple caused by multiple reflections.

Transmission Line Termination

To eliminate reflections, terminate the line with a resistor that has impedance equal to Z — as is the case with R_T in Figure 3. With the additional resistor, a propagating wave does not encounter an impedance discontinuity. Because of the resistor divider of R_S and R_T, the voltage at the load gate is half the source voltage.

The addition of R_T also makes it so the impedance encountered by the source is quite low. With the low impedance, use a driver capable of sourcing the necessary current.

For differential signals, the resistor is placed across the + and – inputs of the differential receiver. With bidirectional bussed signals like CAN, the line is terminated at both ends as in Figure 6. Note the shared ground connection as discussed earlier.

Control model showing terminations at both ends.

Figure 6. Model showing terminations at both ends.

In our next entry in this series, we will discuss cable shielding and consider some installation best practices.

Learn more in our technical note.

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Better Servo Systems — Part II: Signaling and Terminations

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