Launching Into a Line

Matched Load Has No Reflected Step

A matched load has reflection coefficient zero. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A matched load has the same impedance as the line

The line and load are both 4 ohms, so the reflection numerator is zero.

Zload−Zline=4 − 4=0Z_{\text{load}}-Z_{\text{line}}=4\,-\,4=0
Matched boundaryEqual impedances make the reflection coefficient zero.incidentreflectedline 4 ohmload 4 ohmGamma 0in 12 Vback 0 V

Zero coefficient means no reflected step

The reflected voltage is 0 volts, so the echo from this boundary is erased.

Γ=0,V−=0 V\Gamma=0,\quad V_{-}=0\ \text{V}
No reflected stepThe matched case renders a zero reflected voltage.incidentreflectedline 4 ohmload 4 ohmGamma 0in 12 Vback 0 V