Reflections in a CAN-FD bus: the Γ coefficient explained

Guide · updated on 2026-11-10

When a wave meets an impedance different from the line's characteristic impedance, part of it comes back. On a CAN pair we always mean the differential characteristic impedance, typically 120 Ω, with L′ and C′ per metre referred to the differential mode of the pair, not to a single wire.

The basic formulas

Z_{0, diff} ≃ \sqrt{\frac{{𝐿′}_{diff}}{{𝐶′}_{diff}}} v = \frac{1}{\sqrt{𝐿′ 𝐶′}} = NVP \cdot c

These hold for an ideal or low-loss line, which is a good approximation for CAN cables. In general the impedance also depends on resistive and dielectric losses, and therefore on frequency:

Z_{0} (ω) = \sqrt{\frac{𝑅′ + j ω 𝐿′}{𝐺′ + j ω 𝐶′}}

NVP is a property of the cable, not of CAN. With NVP = 0.76:

\frac{1}{v} = \frac{1}{0.76 \cdot c} \approx 4.39 ns/m

The reflection coefficient Γ

Γ = \frac{Z_{L} - Z_{0}}{Z_{L} + Z_{0}} V_{refl} = Γ \cdot V_{inc}

Load at the end of the line	Γ
Z_L = Z₀ (matched)	0
Open circuit	+1
Short circuit	−1
Unterminated receiver (R_ID ≫ Z₀)	≈ +1

A 120 Ω termination in parallel with a receiver's differential input resistance, on a 120 Ω line, gives:

Z_{L} = 120 Ω ∥ R_{ID} \Rightarrow Γ = - \frac{60 Ω}{R_{ID} + 60 Ω}

R_ID	Z_L	Γ
12 kΩ	118.8 Ω	−0.0050
30 kΩ	119.5 Ω	−0.0020
60 kΩ	119.8 Ω	−0.0010
100 kΩ	119.9 Ω	−0.0006

In every realistic case the terminated end is practically matched. Note the difference between a receiver at the end of a line, which is a terminal load, and an ordinary node connected to the backbone through a stub: there the reflection comes from the impedance discontinuity at the branch point, with the stub, the node's input impedance and its parasitic capacitance all contributing.

When transmission-line effects matter

They become relevant when the one-way propagation delay is no longer negligible compared with the edge time. A common screening rule is:

2 t_{pd} ≳ \frac{t_{r}}{3} \Leftrightarrow t_{pd} ≳ \frac{t_{r}}{6} \Rightarrow ℓ_{crit} = \frac{v \cdot t_{r}}{6}

With NVP = 0.76 (4.39 ns/m):

Rise time t_r	Critical length ℓ_crit
5 ns	≈ 0.19 m
10 ns	≈ 0.38 m
20 ns	≈ 0.76 m
40 ns	≈ 1.52 m
50 ns	≈ 1.90 m

It is a screening criterion, not a physical threshold. It shows the key point for CAN-FD: whether you need a distributed model depends mainly on the transceiver's rise and fall times, not on the nominal bit rate.

Parasitic capacitance

A lumped capacitance on CANH/CANL does not change the characteristic impedance of the cable, which depends on its geometry and materials. It adds a local discontinuity whose impedance falls with frequency:

Z_{C} = \frac{1}{j ω C}

Every extra capacitance adds to the total capacitive load of the bus. It can slow the edges, create local impedance discontinuities and reflections, and reduce the timing margin at the sample point. This is why low-capacitance ESD protection is preferred for CAN-FD, especially at higher data rates; vendor guidance commonly suggests keeping the diode capacitance below about 15 pF, and lower is better. Capacitance is not the only criterion: also check working voltage, polarity, clamping voltage, dynamic resistance, ESD rating and the layout of the protection.

From Γ to what you see on the bus

Γ only tells you how much of an edge is reflected at one discontinuity. On the bus it shows up as overshoot, undershoot, ringing and a longer settling time, and the question that matters is whether the differential voltage is clearly above or below the receiver thresholds when each node samples. That is what the simulator lets you see: the waveform at any point and the voltage margin at each receiver's sample point. Full bit-timing analysis (oscillator tolerance, transceiver delays and asymmetry, TDC) is outside its scope.

A pre-layout and what-if tool: it does not replace SPICE, measurements or compliance testing. See the technical disclaimer.

Try it on your own bus.

Draw the topology, pick the bit rate and check the voltage margin at every receiver's sample point. It runs in your browser: your topologies and files are never uploaded.

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