Learning Library · Signals and oscilloscopes · 5
Impedance matching
At high frequencies a cable is not just a wire. It has a characteristic impedance, usually 50 Ω for test equipment, and a pulse travelling down it only stays put in the load if the load has the same impedance. Any mismatch sends part of the pulse back.
Top: the voltage along the cable. Yellow travels toward the load, blue travels back. Bottom: what a scope at the source end records over one round trip.
The reflection coefficient
Γ is the fraction of the incoming voltage that comes back. A matched load gives Γ = 0 and nothing returns. An open circuit gives Γ = +1, so the full pulse comes back the same way up. A short gives Γ = −1, so it comes back inverted. Everything else lands in between.
RF datasheets usually quote one of those two instead of Γ. A VSWR of 1.5 means about 4 % of the power reflects, and a return loss of 20 dB means 1 %.
When does it matter?
Reflections matter once the cable is long compared with the signal's edges. A common rule of thumb treats a cable as a transmission line once its one-way delay is more than about a sixth of the signal's rise time. Signals in coaxial cable travel at roughly two-thirds the speed of light, about 20 cm per nanosecond, so a 1 m cable has a round trip of about 10 ns.
Try this
- Pick Open. The echo returns at full height and the same polarity, one round trip after the original pulse.
- Pick Short. The echo returns at full height, inverted.
- Pick Matched. The pulse disappears into the load and the scope at the source sees nothing come back.
- Set the load to 75 Ω on a 50 Ω cable, a common mix-up with video cable. Γ is 0.2: a fifth of the voltage, 4 % of the power, comes back.
Most oscilloscopes have a 1 MΩ input, which is an open circuit as far as a 50 Ω cable is concerned. When you drive a scope from a 50 Ω generator through coax, use the scope's 50 Ω input setting if it has one, or a 50 Ω feed-through terminator. Otherwise reflections distort fast edges and the amplitude reads double what the generator says.
See the echo for yourself. Oscilloscopes and generators for signal-integrity work.
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