Douglas Krantz - Technical Writer - Describing How It Works

Why is the Termination Resistor Equal to the Characteristic Impedance?

By Douglas Krantz | Electroics | 20 minutes of reading

Why is the Termination Resistor Equal to the Characteristic Impedance?


Greetings Douglas,

I had a question about the termination resistor. I understand that it blocks ghost signals but I am confused how the value is determined.

For example, in CAN bus lines the 120 ohm resistor is used between CAN hi and CAN lo. You mentioned that the value of the termination resistor has to be the same value as the characteristic impedance on the lines. However, I do not understand why the value of the termination resistor has to be the same value as the characteristic impedance.

Question 1. How does having the same value termination resistor block the signal from bouncing back to the output of the transmitter?

Question 2. Why does the termination resistor have to be between a differential signal, for example in CAN?

Please give me a simple and detailed explanation as I am still learning and not well versed yet. Thanks again for your site. I really appreciate it.

Thank you, FA

Blocking the Signal versus Soaking Up the Signal

To start with, a termination resistor doesn't really block the signal from bouncing back, the termination resistor soaks up the power of the signal so there isn't anything to bounce back.

There's more explanation on how it works as a few things are described electrically.

Controller Area Network - CAN

The CAN system is a single signal path, it is without t-taps as such, and it has a termination resistor at each end of the path. There can be dozens of modules attached along the CAN signal pathway. Each module can be used to transmit data into the CAN pathway, and each module (when not transmitting) monitors the data on the pathway. When the modules are monitoring, they use so little current that electrically, they may as well not be connected.

Because there are termination resistors at each end, signals can travel along the CAN pathway in either direction from a transmitting module, and not bounce back from either end. Signals cannot travel both directions along any particular part of the pathway at the same time, though, because if they did, the monitoring modules would be receiving two data-signals at the same time. The modules could not tell the difference between two signals at once, so, in other words, the two signals would corrupt each other.

Two wires, CAN Low and CAN High

When there is no data being sent on the CAN pathway, the CAN Low and the CAN High conductors are roughly at the same voltage potential; when compared to each other, the two conductors are at about zero-voltage.

When there is a data-high (usually a digital 1), the CAN Low wire is 2.5-volts lower than the CAN High wire. The difference in voltage between the two wires is 2.5-volts.

When there is a data-low (usually a digital 0), the CAN Low wire is at about the same voltage potential as the CAN High wire. The difference in voltage between the two wires is somewhere around zero-volts.

Basically, when there is data being sent on the CAN pathway, the voltage potential between the two wires rapidly switches between the zero-voltage and the 2.5-volts.

This is a modified differential voltage.

Power Supply - 3.3-Volts or 5.0-Volts

Most of the explanations found on the web talk about the voltage on the two wires in the CAN network as being positive. In order for both wires to be positive, the two wires have to be measured against the negative wire of the power supply.

Power for the CAN modules on the network is commonly either 3.3-volts or 5.0-volts. The modules, being data converters (or data translators), are connected to various types of non-CAN equipment, so this non-CAN equipment cannot be counted on to be able to provide the necessary power for the CAN system itself. The CAN system has to use its own power.

The power supply for the CAN system comes to the modules from either, an extra two wires running alongside the CAN wires (four conductors total) or from separate power supplies for each of the CAN modules.

Electricity is Carried on a Wire

When studying electricity, you are studying the electrical current in a single wire. See: Which Way Does Electricity Flow?

A complete electrical or electronic circuit, however, can be considered a circle. (The word circuit is derived from the word circle.) Because it's a circle, the electricity goes one direction on one half of the circle and goes the other direction on the other half of the circle. I know most people aren't taught to think of the two directions for the electricity this way. However, by going both directions, the electrical current cancels; when looking at the two wires in a circuit, there is no overall current.

When considering the transfer of power from one place to another, instead of thinking of current, think of the two conductors together as a single pathway. The CAN Network System is a Pathway.

Energy (Power or Signal) is Carried by a Pathway

Yes, I know. Watts Law is Watts (Power) equals Current times Voltage. However, at any point in an electrical pathway (the pathway being the two conductors of a circuit), current cancels out to equal zero. Zero Current times whatever Voltage will always equal Zero Watts.

Two major factors are missing from that formula: direction of energy travel, and the speed of light.

In the CAN network, keep in mind that digital signals are a form of energy that is rapidly being turned on and off. The CAN network is carrying digital signals, and the digital signals are traveling from the source to the load at a swiftness somewhere around two-thirds the speed of light.

The Laws of Thermodynamics also come into play.

Energy Cannot be Created or Destroyed

A generator takes energy to turn it, so a generator is not a source of energy. A transformer takes energy to create magnetism inside it, which is used to provide energy at the output of the transformer, so a transformer is not a source of energy. Even the energy from our sun came from somewhere else (sub-atomic forces inside the atoms of the sun), so our sun is not a true source of energy.

Bottom Line: Energy cannot be created or destroyed; it can only be converted.

Electricity Can't Go Faster than Light

When a person turns on and off a light switch on the wall, for all practical purposes, the light on the ceiling turns on and off exactly at the same time as the switch.

Speed up the switch turning on and off to some of the digital baud-rates commonly used, and the light on the ceiling turns on and off, not any slower than the switch, but much later than the switch. Even with the short distance between the switch on the wall and the ceiling light, at least at some digital baud-rates, the switch could have turned on and off dozens of times before the light on the ceiling receives the signals.

Because power (which is energy) or signal (which is also energy) isn't instant, it takes time for energy to travel along a path, like a transmission line.

Remember, also, we are not really talking about electricity, we are talking about the movement of energy from one place to another.

See: What is the Difference Between Electricity Flow and Signal or Power Flow?

Signals are energy in motion, and signals on a wire circuit always move from the source of a signal to the load, or the destination.

The Reflected Energy of a Signal is a Second Signal

When the energy (power or signal) is going in two directions at once, there are two sources of energy. If the signal bounces off the end of the wire, for all practical purposes, that signal is a separate signal coming from a separate source.

Bottom Line: When there are reflections on an electrical pathway, there are two or more signals. The CAN system modules can't differentiate between the two signals, so if there are reflections on the pathway, the two (or more) signals corrupt each other.

The Controller Area Network or CAN is a Transmission Line

From the point of view of the two-wire circuit that has a power or signal source, the signal carrying system CAN Network is a transmission line. All transmission lines have an energy source for the power or signal, a pathway (often made up of two conductors), and they have a termination (commonly it's a resistor). Here are just a few examples of two-wire transmission lines:
  • Cable TV - Inner and Outer Conductor (Very low power signal source, 75 Ohm coax cable, 75 Ohm termination resistor)

  • 35,000 Watt TV Station Transmitter - Inner and Outer Conductor (TV transmitter signal {power} source, 50 Ohm ridged coax cable, 50 Ohm antenna that terminates the coax cable). When working on the transmitter, without broadcasting the signal, a dummy load is used instead of an antenna. The dummy load is a 50-Ohm, 35,000-watt resistor.

  • Ethernet Coax 10Base2 Network - Inner Conductor and Outer Conductor (Data signal source, 50 Ohm coax cable, 50 Ohm termination resistor)

  • RS485 Data Communication System - Differential, Side-by-Side Wires - Plus and Minus Conductors, Sometimes with Shield (Data signal source, 100-ohm two conductor circuit, 100-Ohm termination resistors at each end of the differential circuit) Electrically, besides a variation in the characteristic impedance of the circuit, there is very little difference between a CAN network and an RS485 system.

  • Ethernet Twinax Network - Differential, Side-by-Side Wires - Plus and Minus Conductors with an Outer Shield (Data signal source, 78 Ohm dual inner conductor coax cable, 78 Ohm termination resistor)

On a CAN network, the transmitter is somewhere between the two ends of the network, and sends the signal toward both ends of the network. The power (signal) source is basically using two transmission lines, both of them start at the single transmitter, and then they each carry the signal towards their own termination resistors.

Yes, there are a lot of transmitters connected along the CAN Network, but to keep from corrupting each other's data, the transmitters can only be used one at a time. When the transmitters aren't in use, the transmitters are electronically disconnected from the transmission line. At any one time, because the transmitters are being used one at a time, we can consider that there's only one transmitter along with its pair of transmission lines.

Infinite Length Transmission Line

A transmission line isn't defined by its length, so to understand a transmission line, we have to think of it as having infinite length. Looking at the transmission line is a little like looking at a radio transmission in space; once transmitted, the signal goes on forever. Unless something reflects the signal back, the signal will never return.

With a two-wire transmission line, unless something reflects the signal back, like a short in the transmission line or a broken wire (this is theory I'm talking about, not real life), the signal will continue along the transmission line forever.

A transmission line also isn't defined by the electrical resistance of the wire itself, so we have to think of the wire as having absolutely no electrical resistance, whatsoever.

In essence, a "true" transmission line can only be analyzed in theory because "real life" has a finite length to the transmission line, and "real life" has electrical resistance. So, theory will be considered in the next few paragraphs.

Impedance of a Two Wire of a Transmission Line

Figuring out the characteristic impedance of a two-wire transmission line has done in the imagination because a lot of what's involved doesn't occur in real life; even though they're imaginary, these things are affected by real life.

We'll be using a 2.5-volt battery, and a transmission line.
  • The power from the 2.5-volt DC battery we'll pretend lasts forever
  • The length of the transmission line we'll pretend goes on past the edge of the known universe
  • The resistance of the conductors we'll pretend is zero-ohms
  • The voltage charge between the two conductors starts out at zero-volts along the whole transmission line
  • The current in the conductors starts out at zero-current

Connect the 2.5-Volt Battery

Connect the 2.5-volt battery across the two wires at the end of the transmission line.

When the battery is first connected, there are three major forces that have to be contended with:
  • Speed of Electricity
  • Inductance of the Wires
  • Capacitance of the Wire

Speed of Electricity - When the 2.5-volts of the battery is first connected, the voltage doesn't instantly get to the whole length of the transmission line; the voltage takes time to travel along the transmission line from the battery. You could say that the front of the traveling wave, where the voltage changes from zero volts and is just starting to build-up, is a wave-front. The wavefront travels along the transmission line at a constant velocity.

Inductance/Capacitance Compromise

Inductance of the Wires - A wire is an inductor. When the 2.5 volts of the battery is first connected, the current isn't allowed to just flow as fast as it wants; the current is impeded by the requirement to induce a magnetic field around the wire.

Capacitance of the Wires - A capacitor is two conductors separated by an insulator. When the 2.5 volts of the battery is first connected, the capacitance between the two wires looks like an immediate, short-term electrical-short to the battery.

But wait. The inductance slows down the current while the capacitance speeds up the current; there is an inductive/capacitive compromise. This compromise, combined with the traveling wave-front means that going into the transmission line from the battery, the electrical current is a continuous, steady-state current.

Steady-State Current and Ohm's Law

Using Ohm's Law, the voltage of the battery, divided by the steady-state current, equals a resistance. Impedance is described in ohms. Impedance is the resistance-capacitance-inductance equivalent of resistance, so the resistance found using Ohm's Law is the impedance of a transmission line.

Termination Resistor

To be a termination resistor, the resistance of the termination resistor is the same value as the impedance of the transmission line. If the termination resistor is used to replace the transmission line at the battery, the current would be exactly that same as was used by the transmission line.

To the electricity running through the transmission line, replacing the last half of the transmission line with a termination resistor looks like a continuation of the transmission line.

To the power traveling along in the transmission line, if the wave-front of energy encounters a termination resistor rather than a continuation of the transmission line, the power just goes into the resistor and heats it up a little. The termination resistor converts the power (energy) from the transmission line into heat energy.

Energy Cannot be Created or Destroyed

Now we have a problem.

Transmission Line - Open End Let's pretend that this theoretical transmission line that goes on forever is cut off, so the ends of the two wires just stop somewhere around the planet Neptune. The battery has been pushing current into the transmission line for a long time; the wave front hasn't reached the wire-cut-off point, and the current going into the transmission line has been very steady.

Keep in mind that electricity is carrying the energy or power. Another point of view is that energy or power creates electricity. Both of these views of energy (or power) and electricity show that electricity alone is not energy or power.

When the electricity of the wave-front hits the end of the line (where the wires have been cut-off), the electrons and positive charges pile up, at least for a very short time. The energy or power doesn't just sit at the end of the line, the energy or power pushes back, forcing the electrons and positive charges back along the wires.

In essence, the energy or power is "reflected" off the open end of the line and heads back toward the source of power (battery).

Transmission Line - Shorted End

Let's pretend that this transmission line isn't "open" somewhere around the planet Neptune, the transmission line is "shorted" somewhere around the planet Neptune.

When the electricity of the wave-front hits the end of the line (where the wires have been shorted together), the energy or power doesn't pile up the electrons and positive charges, the electrons or positive charges continue on their way, but they have taken a "U-turn" at the short.

In essence, the energy or power is "reflected" off the shorted end of the line and heads back toward the source of power (battery).

Termination Resistor

Let's pretend that the transmission line isn't open or shorted somewhere around the planet Neptune. Instead, there's a resistor of the exact resistance in ohms as the transmission line's characteristic impedance in ohms.

When the electricity of the wave-front hist the end of the line (where there's a termination resistor), the electricity thinks that the transmission line just continues on. The termination resistor takes the current and voltage and converts that energy or power (measured in watts) to heat.

In essence, the energy or power isn't reflected, it's just soaked up by the termination resistor.

Wrong Value Termination Resistor

If the termination resistor has more resistance (in ohms) than the characteristic impedance (in ohms) of the transmission line, the electricity of the wave front sees this as a partial-open; some of the energy is converted to heat by the termination resistor, some of the energy is reflected back.

If the termination resistor has less resistance than the characteristic impedance of the transmission line, the electricity of the wave front sees this as a partial short; some of the energy is converted to heat by the termination resistor, some of the energy is reflected back.

The Resistor Ends a Transmission Line

Question 1. How does having the same value terminating resistor block the signal from bouncing back to the output of the transmitter?

A termination resistor doesn't block a signal like a road barrier blocks cars, a termination resistor converts the energy of a signal to heat, which is dissipated into the atmosphere. Once dissipated, there's no energy to bounce back.

Question 2. Why does the termination resistor have to be between a differential signal, for example in CAN?

When a resistor converts electricity to heat, electricity goes through the resistor. In order for electrical current to go through a resistor, the resistor has to connect to two wires. In order to push the current through the resistor, the two wires are required to have different voltages; at least compared to each other, the wires are "differential".

Douglas Krantz

facpdoug@douglaskrantz.com
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