Differential Signalling, Common-Mode Rejection, and Where to Put the Terminator

A single-ended bus compares a signal wire against a ground reference. Every volt of noise between the two ends of the wire, every ground potential difference between two enclosures, and every supply droop from a motor starting appears directly at the receiver input as if it were signal. Over a few metres on one board that is tolerable. Over tens of metres between cabinets it is not, and the answer is to stop referencing the signal to ground at all.

Two wires, one difference, no reference

A differential driver produces two outputs that move in opposite directions: when one goes up, the other goes down. The receiver takes the difference. Anything that shifts both wires together — a ground offset, a common-mode noise voltage coupled from a nearby cable, a supply rail moving — cancels in the subtraction, provided the receiver can handle the range over which the two wires move together.

The cancellation is not perfect, because the receiver’s input divider is not perfectly matched and the two wires do not couple identically to the noise source. The measure of how well it works is common-mode rejection, expressed as a ratio and improving with the balance of the input network. A well-balanced receiver tolerates tens of volts of common-mode difference while resolving a differential swing of a couple of volts, and the tolerated range is a specified parameter rather than a property of the ideal subtraction.

Twisting the pair is the other half. Noise couples into both wires as a common-mode voltage only if both wires see the same electric field, and a twist makes the two wires occupy nearly the same average position along the cable, so the induced voltages match. A twisted pair without termination still suffers reflections; termination without a twist still couples noise as a differential signal when the wires separate. Both are required.

The result is a physical layer whose reach is limited by loss and by the common-mode range rather than by the noise margin of a single threshold. RS-485 specifies a common-mode range of roughly minus seven to plus twelve volts, which is enough to cover the ground potential difference between buildings on a shared earth. The same electrical idea, with different levels and a different termination convention, is what classical CAN uses.

Reflections, and why a resistor fixes them

A cable is a transmission line. Its characteristic impedance for a twisted pair used in these buses is typically around 100 to 120 ohms, and the exact value depends on the twist, the insulation, and the conductor spacing. When a driver launches an edge into a line that is not terminated at the far end, the energy arrives, finds no load to absorb it, and reflects back. The reflected edge arrives at the receiver later, superimposed on the signal, and the receiver sees a step, a dip, or a double edge depending on the timing.

The cure is a resistor equal to the characteristic impedance, placed at the end of the line, which absorbs the arriving energy instead of reflecting it. A line terminated at both ends with the characteristic impedance looks like a pure resistance to the driver, and an edge launched into it settles without reflection.

The consequence for the driver is that it must be able to drive the parallel combination. Two 120-ohm terminators at the ends of a line present 60 ohms to a driver at the middle, and the driver must source enough current into that load to develop the required differential voltage. For a bus with a specified differential level of about two volts, the current is a few tens of milliamps, which is why these transceivers are specified with a minimum load resistance and why adding extra termination degrades the signal rather than improving it.

The placement rule follows. The terminator belongs at the physical end of the cable, not at the transceiver pin. A stub of untwisted wire between the transceiver and the terminator is a short transmission line of uncontrolled impedance, and it produces a reflection of its own. On a backplane, the terminators belong at the two extreme ends of the bus, and every other node taps in with the shortest possible stub.

CAN’s version of this is split termination: two resistors of half the value in series, with the midpoint tied to a capacitor to ground. The series pair still presents the correct differential load, and the midpoint gives a low-impedance path to ground for common-mode energy, which improves emissions. The split also gives a convenient bias point for the recessive state, where both wires sit at the same voltage.

Biasing the idle state

A differential bus with no driver connected has both wires floating at whatever the cable leakage allows. The receiver’s differential input is then undefined, and a floating line can produce noise at the receiver output, which a protocol interprets as a stream of edges.

The fix is a bias network: a resistor from one wire to the supply and one from the other wire to ground, sized so that the differential voltage across the pair at idle exceeds the receiver’s threshold with margin. These bias resistors are large compared with the terminators, hundreds of ohms, so they do not load the driver significantly, and they are normally fitted at one point on the bus rather than at every node. Fitting them at multiple points puts them in parallel and changes the termination.

CAN handles this differently: the recessive state is defined as both wires sitting at approximately half the supply, and the transceiver provides that bias internally through high-value resistors rather than relying on external parts. The split termination’s capacitor then gives the common-mode energy a low-impedance path to ground without disturbing the differential load.

The interaction between bias and termination is where the arithmetic gets tight. A bus with the correct terminators and no bias reads as noise when no node is transmitting. A bus with the correct bias and no terminators rings on every edge. A bus with bias networks at several nodes has their resistances in parallel, and the effective differential load is no longer the cable impedance.

Ground, shield, and the connection that is not there

A differential pair removes the need for a shared signal reference, but it does not remove the need for a ground path. The transceivers on both ends have a ground pin, and the common-mode voltage between them must stay inside the specified range. That requires a ground conductor in the cable, and it is why RS-485 cable has a third conductor alongside the pair.

The ground conductor carries the current that would otherwise appear as common-mode voltage, and it should be a dedicated wire rather than the cable shield. Using the shield as the ground return puts shield currents through the same conductor that is supposed to intercept noise, and it makes the shield part of the circuit.

The shield itself is normally connected at one end only. Connecting both ends creates a loop whose area encloses the building’s magnetic field variations, and the resulting circulating current couples noise into the pair. The single-ended connection still intercepts electric field noise, because the shield does not need to carry current to do that. Where both ends must be connected for radio-frequency reasons, the connection at one end is made through a capacitor, which presents a low impedance at high frequency and an open circuit at the frequencies where ground loops matter.

None of this is visible to the protocol layer. A CAN controller reports a bus-off condition when the transceiver delivers enough errors, and the cause may be a missing terminator, a common-mode voltage outside the range, or a cable that is simply too long. The diagnostic path from the protocol symptom back to the physical cause is what error counters and fault confinement describes from the controller side.

How length and rate trade

The propagation delay of a twisted pair is roughly five nanoseconds per metre, and the round trip doubles it. A bus of a hundred metres therefore has a round-trip delay of about one microsecond. For CAN, the arbitration and acknowledge mechanism requires that a node which transmits a bit and expects to read it back within the same bit time can do so, which means the round-trip delay plus the transceiver delays must fit inside the propagation segment of one bit.

At 1 Mbit/s a bit is one microsecond long, and a hundred-metre bus consumes essentially the entire bit in round trip, leaving nothing for the transceivers and the sampling point. That is why classical CAN at 1 Mbit/s is conventionally limited to a bus of about forty metres, and why 125 kbit/s supports several hundred metres. The relationship is not a rule of thumb about cable quality; it is the timing budget of the arbitration loop.

RS-485 has a looser constraint because it is a master-slave arrangement with no bit-level arbitration read-back, so the limit is set by loss and by the receiver’s ability to resolve an attenuated signal. At low rates, lengths of over a kilometre are achievable with a suitable cable and a single terminator pair, and the dominant loss is the direct-current resistance of the conductors rather than high-frequency attenuation.

The differential bus is therefore the right answer when the wire leaves the enclosure, when the ground potential between the ends is unknown, or when the length exceeds what a single-ended line can carry at the required rate. Inside one board, over a few centimetres, a single-ended bus with a shared ground is simpler and needs no terminators, no bias, and no common-mode budget. Choosing between them is a question about the physical environment, not about which protocol is better.

The number that decides it is usually capacitance or length: a few hundred picofarads of load for a single-ended bus, against a twisted pair terminated at both ends for a differential one. Above that boundary, no amount of driver strength substitutes for a proper transmission line.