Page 2 · From the wire up

GMSL Physics

Ten steps from Maxwell to a working link: why a long coax smears bits, and which block in the serializer or deserializer undoes each effect.

Everything GMSL does follows from one fact: a long cable is a frequency-dependent attenuator with a fixed characteristic impedance. Work through what that does to a bit, and each block in the serializer and deserializer appears as the fix for a specific physical problem.

1. The cable is a transmission line

A signal edge travels down the coax as an electromagnetic wave between the center conductor and the shield. Each short slice of cable has series inductance L (the magnetic field around the center conductor) and shunt capacitance C (the electric field across the dielectric). The wave moves at v = 1/√(LC) and sees a characteristic impedance Z₀ = √(L/C).

Z₀ = (60 / √εᵣ) · ln(D/d) v = c / √εᵣFor foamed PE (εᵣ ≈ 1.5) a 50 Ω coax needs D/d ≈ 2.8. The wave moves at about 0.82c, roughly 4 ns per meter, so a 15 m harness is about 60 ns long.

Every few millimeters of coax is a series resistance and inductance and a shunt capacitance and conductance. A wave sees only the ratio √(L/C), so a uniform cable looks like a 50 Ω resistor to the driver, however long it is.

When is a wire a transmission line? When it is long compared with the signal's wavelength. At 3 GHz the wavelength in this cable is about 8 cm, so a 15 m run is around 180 wavelengths. Any impedance change (a connector, a via, an ESD diode's capacitance) reflects part of the wave. The reflection coefficient is

Γ = (Z_L − Z₀) / (Z_L + Z₀) return loss = −20·log₁₀|Γ|A 0.5 pF ESD diode at 3 GHz is a 106 Ω reactance shunted across the line. |Γ| ≈ 0.23, a return loss of only about 13 dB from one small part. This is why GMSL ESD parts are specified below 0.5 pF and why the PCB channel has a return-loss template.

2. The cable loses high frequencies

Two mechanisms dominate, and both rise with frequency.

Skin effect. At high frequency the current's own changing magnetic field pushes it to the conductor surface. It flows in a layer of depth δ = √(ρ / πfμ). For copper δ ≈ 66 µm at 1 MHz and 1.2 µm at 3 GHz. Less copper is carrying current, so resistance rises as √f, and loss in dB rises as √f.
Dielectric loss. The insulation's molecules absorb a fraction tan δ of the field energy each cycle. More cycles per second means more loss: proportional to f.

IL(f) [dB] ≈ ℓ · (a·√f + b·f)ℓ is cable length. GMSL publishes limits rather than lengths: about −21 dB at 3 GHz for a 6 Gb/s channel and −18 dB at 3 GHz for 12 Gb/s, including both PCBs, connectors and the cable.

Illustrative 15 m automotive coax, scaled so loss at 3 GHz is about 21 dB. The dashed curve is the √f skin-effect term; the solid curve adds dielectric loss, which grows linearly with frequency.

At −21 dB the 3 GHz part of the signal arrives with 9% of its amplitude, while content at 100 MHz arrives almost intact. That imbalance is what smears bits.

3. Nyquist: which frequency matters

For NRZ at bit rate R, the fastest pattern is 1010…, a square wave whose fundamental is R/2. That is the Nyquist frequency, and the channel's loss there decides whether the link works. GMSL2 at 6 Gb/s has its Nyquist at 3 GHz; at 3 Gb/s, 1.5 GHz.

To reach 12 Gb/s, NRZ would push Nyquist to 6 GHz, where the illustrative cable above loses about 33 dB instead of 21. GMSL3 instead sends PAM4: four voltage levels, two bits per symbol, 6 GBd. Nyquist stays at 3 GHz.

Same peak-to-peak swing. PAM4 stacks three eyes, so each is one third as tall: a 20·log₁₀(3) ≈ 9.5 dB signal penalty, paid in exchange for halving the symbol rate and therefore the Nyquist frequency.

PAM4 penalty: 20·log₁₀(3) ≈ 9.5 dB NRZ-at-12G extra loss: ≈ 33 − 21 = 12 dBPAM4 wins by a couple of dB on this channel, and much more on real cables, where loss above 3 GHz also comes with worse return loss and crosstalk. The cost is linearity: the driver and receiver must place four levels accurately, and the smaller eyes need tighter noise and more error protection.

4. Intersymbol interference

Send a single 1 and look at what arrives. Low frequencies arrive fast and strong, high frequencies are lost, so the bit arrives late, smaller and stretched over several UI. The tails h₁, h₂, h₃ land on top of the next bits: that is intersymbol interference (ISI). Equalization exists to cancel those tails.

Each received bit is the sum of its own main cursor h₀ and the leftover tails of earlier bits. If enough tails add up the wrong way, a 0 gets read as a 1. The eye diagram closes.

5. Equalization rebuilds the eye

The deserializer undoes the cable's filtering in two stages, both adapted automatically at link lock and tracked over temperature.

Stage	How it works	Trade-off
CTLE (continuous-time linear equalizer)	An analog stage with a zero placed below Nyquist: gain rises with frequency, the inverse of the cable's slope. The flattened channel shortens the pulse response.	It also boosts high-frequency noise and crosstalk. It cannot tell signal from noise.
DFE (decision-feedback equalizer)	After a bit is decided, the receiver knows exactly what tail it will leave (h₁·bit, h₂·bit…). It subtracts those tails from the next samples.	No noise boost, because it feeds back clean decisions. But a wrong decision feeds back the wrong correction, so errors can burst.
TX de-emphasis (on some links)	The transmitter lowers the amplitude of repeated bits relative to transitions, a high-pass filter applied before the cable.	Reduces average signal power arriving at the receiver.

6. AC coupling and why the data is scrambled

A series capacitor at each end blocks DC. That removes the ground offset between camera and ECU and lets DC power share the wire. It also makes the link a high-pass filter. With 0.1 µF between two 50 Ω terminations, τ = C·(50 + 50) = 10 µs, a corner near 16 kHz.

A long run of identical bits is a DC level, and a high-pass filter lets DC droop toward zero: the baseline wanders and the decision threshold drifts. At 6 Gb/s, 1,000 identical bits last 167 ns and droop by 167 ns / 10 µs ≈ 1.7%. Harmless once, harmful if the data's average keeps shifting. So the serializer scrambles the bitstream with a pseudo-random sequence (or uses a DC-balanced code). The result has near-zero average, a bounded run length, and enough transitions for the next step.

7. The clock travels inside the data

There is no clock wire. The deserializer's clock-and-data-recovery (CDR) circuit is a phase-locked loop that compares each data transition with its local clock edge and nudges the phase until it samples in the middle of the eye. It needs transitions to do this, which the scrambler guarantees. Because the clock is recovered from the same wire as the data, cable skew does not exist as a problem.

The cost is jitter. The CDR loop bandwidth sets how much: a wide loop tracks the transmitter's wander (good) but passes more of its high-frequency jitter (bad). Reference-clock noise and supply noise on the PLL show up directly as a smaller eye, which is why GMSL datasheets give strict supply-ripple limits on the PLL rails.

8. Full duplex on one wire

The coax is linear, so waves going in opposite directions pass through each other without interacting. At the deserializer's pin, the voltage is the sum of the forward wave arriving from the camera and the reverse wave it is sending itself. Two things let it separate them.

Band edges from the GMSL2 channel limits quoted in ST AN6331. The two directions overlap between roughly 100 and 400 MHz, so each end also subtracts its own transmitted signal (echo cancellation). The PoC network has to be invisible across the whole span.

Frequency. The reverse channel is 32 times slower than forward at 6 Gb/s; most of its energy sits around 94 MHz and below, while the forward signal's energy sits up near 3 GHz. Filtering does most of the separation.
Echo cancellation. Where the bands overlap, the transmitter knows exactly what it sent. A replica, shaped to match the hybrid and the near-end reflections, is subtracted from the received signal. Any reflection the canceller cannot model (a bad connector farther down the cable) stays in as noise. That is the second reason the return-loss limits are tight.

9. Power over coax (PoC)

The camera's DC supply rides on the center conductor and returns on the shield. A bias-T at each end puts it there and takes it off.

A bias-T. The series capacitor passes the signal and blocks DC from the PHY. The inductor chain passes DC and must block the signal. No single inductor covers 2 MHz to 3.5 GHz, because every real inductor turns capacitive above its self-resonant frequency, so a large, a medium and a GHz-range element are stacked with the fastest one nearest the signal line. Values are illustrative.

How much impedance is enough? The PoC branch hangs across a 50 Ω line that sees 25 Ω (source and load in parallel). For a shunt impedance Z across a matched line:

S₂₁ = 2Z / (2Z + Z₀) S₁₁ = −Z₀ / (2Z + Z₀)Z = 1 kΩ: 0.2 dB insertion loss, −32 dB return loss. Z = 200 Ω: 1.0 dB loss, −19 dB return loss. Every dB lost here comes straight out of the equalizer's margin.

PoC design constraint	Physics	Consequence
Low-frequency edge (~2 MHz)	\|Z\| = 2πfL. 1 kΩ at 2 MHz needs about 80 µH.	A large inductor, and large inductors have big parasitic capacitance.
Self-resonance	Winding capacitance resonates with L; above that frequency the part looks like a capacitor and shorts the signal.	Stack smaller inductors and a ferrite toward the signal node to cover the GHz range.
DC current	Core flux ∝ current. Near saturation, permeability and L collapse.	Pick I_sat well above the camera's peak current, including inrush. Check L at full current, not at zero bias.
Voltage drop	Cable center, shield and inductor DCR in series. Example: 15 m × ~0.1 Ω/m + 2 Ω of inductors ≈ 3.5 Ω; at 0.25 A that is ~0.9 V.	Send 12 V or more and regulate in the camera. Budget the drop at cold-crank minimum.
Hot plug and faults	Cable capacitance plus L rings on connection; a pinched cable shorts center to shield.	Current limit and fault reporting on the supply. GMSL parts include line-fault detection for open and short.

10. Errors: from SNR to BER

After equalization, the decision is a comparison against a threshold in the presence of Gaussian noise. With eye half-height V and noise σ, Q = V/σ and

BER = ½ · erfc(Q / √2) Q ≈ 7.0 → 10⁻¹² Q ≈ 7.9 → 10⁻¹⁵At 6 Gb/s, BER 10⁻¹² is one error every ~3 minutes. That is why every GMSL packet carries a CRC: errors are rare but certain, and the system must detect them. GMSL3's PAM4 eyes are a third as tall, so the same noise gives a much lower Q, which is why PAM4 links lean on stronger coding.

Thirty-second version

The cable is a 50 Ω line that loses about 20 dB at 3 GHz. So: keep Nyquist at 3 GHz (NRZ at 6 Gb/s, PAM4 at 12), equalize the loss (CTLE then DFE), AC-couple and scramble so the ground offset and DC power are invisible and the CDR always sees edges, separate the slow reverse channel by frequency plus echo cancellation, and feed power through inductors that look open from 2 MHz to 3.5 GHz.