IDEAL TRANSMISSION-LINE FUNDAMENTALS - Advanced Signal Integrity for High-Speed Digital Design - page 114

Following the method used to derive equations (2-132) and (2-133) leads to the
definition of the reflection and transmission coefficients:

v r
v i =

Z 02 − Z 01

≡ (3-102)

Z 02 + Z 01

v t
v i =

2 Z 02
Z 02

T ≡ = 1 + (3-103)

+ Z 01

The reflection coefficient is a measure of how much is reflected back off the inter-
section between the two impedance regions, and the transmission coefficient tells
how much of the wave is transmitted . If the reflection coefficient is zero, it means
that the characteristic impedances in the two regions are identical. If the charac-
teristic impedances are not equal, the reflection coefficient will be finite. If the
impedance discontinuity is infinite, such as an open circuit, the signal propagating
on transmission line A will be reflected 100%, as shown in Figure 3-28a. This
is easy to show simply by taking the limit of (3-102) as Z 02 goes to infinity:

open = 1 (3-104)

Incident wave

Γ = 1

Reflected wave

R

∼

Z 0

(a)

In cident wave

Γ = − 1

Reflected wave

R

∼

Z 0

(b)

Figure 3-28 Reflections caused by (a) open- and (b) short-circuit termination.