Which expression correctly gives the reflection coefficient magnitude between two media with impedances Z1 and Z2?

Which expression correctly gives the reflection coefficient magnitude between two media with impedances Z1 and Z2?

• A. Magnitude of the ratio |(Z2−Z1)/(Z2+Z1)|^2
• B. |(Z2−Z1)/(Z2+Z1)|
• C. Magnitude of the ratio |(Z2+Z1)/(Z2−Z1)|^2
• D. (Z2−Z1)/(Z2+Z1)

Answer: (A)

At a boundary between two media, the amplitude reflection coefficient for a wave is Γ = (Z2 − Z1)/(Z2 + Z1). The magnitude of this amplitude is |Γ|, but the portion of incident energy that is reflected (the reflected intensity) is |Γ|^2. Since Z1 and Z2 are real impedances here, |Γ|^2 = |(Z2 − Z1)/(Z2 + Z1)|^2. This is why the expression in option A is the appropriate one when referring to the reflected power. The other forms correspond to the amplitude alone, the reciprocal, or the ratio without squaring, which do not represent the reflected power.

At a boundary between two media, the amplitude reflection coefficient for a wave is Γ = (Z2 − Z1)/(Z2 + Z1). The magnitude of this amplitude is |Γ|, but the portion of incident energy that is reflected (the reflected intensity) is |Γ|^2. Since Z1 and Z2 are real impedances here, |Γ|^2 = |(Z2 − Z1)/(Z2 + Z1)|^2. This is why the expression in option A is the appropriate one when referring to the reflected power. The other forms correspond to the amplitude alone, the reciprocal, or the ratio without squaring, which do not represent the reflected power.