Standing Wave on a Transmission Line

Incident and reflected sine waves form position-dependent voltage amplitudes on an open-ended line.

Circuit operation

Four identical 50 Ω sections each delay the signal 2.5 ns. Together they form a quarter-wave line at 25 MHz. RL = 1 GΩ approximates an open load; the source resistance absorbs returning energy.

Expected behavior

$$\Gamma_L=\frac{R_L-Z_0}{R_L+Z_0}\approx+1$$ $$\beta\ell=2\pi fT_D=\frac\pi2$$

After startup, the load is a voltage antinode near 2 V peak. The input is near a voltage node, while the midpoint is near √2 V peak. The fixed chart shows settled cycles. No animation is needed: the simultaneous traces sample three physical positions.

Reading the results

The first voltage probe is green and the second is red. Current probes start with blue. The schematic opens fitted to its extents. The transient runs for 400 ns with a maximum step of 0.2 ns. Compare sending and receiving waveforms with time-axis cursors. The table uses the same probe order.

Try a change

Set V1 to 12.5 MHz; the same physical line is now half as long electrically, changing the standing-wave pattern. Restore the saved values after comparison.

Model limits

Each line is ideal and lossless: Z0 and TD are independent of frequency. Conductor and dielectric loss, dispersion, radiation, connectors, and breakdown are omitted. Line length is represented by propagation delay; the drawing is not a physical length scale. These examples describe differential line voltage relative to the shared return conductor.

References: Single-stub matching, distributed filter principles.