Current Wave
How Current Propagates Along a Transmission Line
When a generator drives a transmission line, energy does not appear instantly at the load. Charge accelerates into the near end and a disturbance propagates outward at the line's phase velocity, typically 60 to 95 percent of the speed of light depending on the dielectric. The current wave is the moving picture of that charge flow: at every position z and instant t the conductor carries a current I(z, t) whose envelope travels along the line. The same physics that produces the voltage wave produces the current wave, and the two are inseparable because they are coupled by the per-unit-length inductance and capacitance described in the telegrapher equations.
For a lossless line carrying a single forward wave, the current and voltage are simply proportional, I = V / Z0, and perfectly in phase. The proportionality constant is the characteristic impedance, a real number set by the geometry of the conductors rather than the length of the line. This is why a long, perfectly terminated cable looks resistive to the source even though it stores no steady energy: the forward current wave continually delivers V times I watts into the line, and a matched load absorbs all of it.
Reality is rarely matched. At any impedance discontinuity, part of the wave reflects. The reflected current is the feature that confuses many engineers, because it does not simply mirror the reflected voltage. To keep power flowing in the correct physical direction, the backward current wave must satisfy I- = −V- / Z0. The minus sign means a positive voltage reflection (an open circuit) produces a negative current reflection, so currents cancel at an open end while voltages add.
Incident, Reflected, and Total Current
The total current at a point is the superposition of the incident and reflected current waves. Because of the sign reversal, the current standing-wave envelope is the inverse of the voltage envelope: wherever the voltage is maximum the current is minimum, and the two patterns are spatially offset by exactly a quarter wavelength. A short circuit forces a current antinode (maximum) and a voltage node at the termination; an open circuit forces a current node and a voltage antinode. Engineers exploit this quarter-wave offset directly in matching networks and in slotted-line measurements.
Governing Relationships
I(z) = (V+/Z0) e−jβz − (V+/Z0) Γ e+jβz
Local current to voltage ratio:
I+ = V+ / Z0 and I− = −V− / Z0
Average power carried by the wave:
Pavg = ½ × Re(V × I*) = |V+|2 / (2 Z0)
Where V+ = forward voltage amplitude, Γ = reflection coefficient, β = 2π/λ = phase constant, Z0 = characteristic impedance. Example: V+ = 10 V on a 50 Ω line → I+ = 0.2 A and Pavg ≈ 1 W.
Current Behavior at Common Terminations
| Termination | Γ | Current at load | Voltage at load | Pattern at load end |
|---|---|---|---|---|
| Matched (Z0) | 0 | V+/Z0 (traveling) | V+ (traveling) | No standing wave |
| Short circuit | −1 | Maximum (antinode) | 0 (node) | Current antinode |
| Open circuit | +1 | 0 (node) | Maximum (antinode) | Current node |
| ZL > Z0 | 0 to +1 | Below incident | Above incident | Partial standing wave |
| ZL < Z0 | −1 to 0 | Above incident | Below incident | Partial standing wave |
Frequently Asked Questions
Why does the reflected current wave change sign while the reflected voltage wave does not?
Both waves carry power in their direction of travel, so the voltage-to-current ratio must equal +Z0 forward and −Z0 backward. Writing I− = −V−/Z0 keeps the reflected power flowing toward the source. That is why an open end (Γ = +1) gives a voltage maximum but a current minimum, and the current and voltage envelopes sit a quarter wavelength apart.
How do I calculate the current wave amplitude from the voltage wave and Z0?
For a single traveling wave, I = V / Z0. A 10 V forward wave on a 50 Ω line gives a 0.2 A forward current and about 1 W of average power, |V+|2/(2 Z0). With reflection present, I(z) = (V+/Z0)(e−jβz − Γ e+jβz), so the reflected term subtracts and the result depends on the magnitude and phase of Γ.
Where are the current maxima located on a shorted versus an open line?
A short circuit (Γ = −1) forces a current maximum and a voltage zero at the termination; an open circuit (Γ = +1) forces a current zero and a voltage maximum. Current maxima then repeat every half wavelength back from the load, always offset a quarter wavelength from the nearest voltage maximum. That offset is what makes quarter-wave transformers work.