What is the equation for IRC?

What is the equation for IRC?

• A. IRC (%) = [(Z2 - Z1)/(Z2 + Z1)] x 100
• B. IRC (%) = [(Z2 - Z1)/(Z2 + Z1)]^2
• C. IRC (%) = [(Z2 - Z1)/(Z2 + Z1)]^2 x 100
• D. IRC (%) = [(Z1 - Z2)/(Z2 + Z1)]^2 x 100

Answer: (C)

When there’s an impedance mismatch between two parts of a circuit, not all of the incident signal is transmitted—some is reflected. The voltage reflection coefficient that describes this mismatch is Γ = (Z2 − Z1) / (Z2 + Z1). To express how much of the incident power is reflected, you use the square of the magnitude of that reflection coefficient and convert it to a percentage. That gives IRC (%) = [(Z2 − Z1) / (Z2 + Z1)]^2 × 100. This form shows why the square and the 100 are needed: squaring relates to power (not voltage), and the 100 turns the fraction into a percent. The other forms either omit the 100 or the squaring, which would misrepresent reflected power as a percent or as a voltage ratio. The common convention uses the Z2 − Z1 difference in the numerator, so the standard expression is the squared ratio times 100.

When there’s an impedance mismatch between two parts of a circuit, not all of the incident signal is transmitted—some is reflected. The voltage reflection coefficient that describes this mismatch is Γ = (Z2 − Z1) / (Z2 + Z1). To express how much of the incident power is reflected, you use the square of the magnitude of that reflection coefficient and convert it to a percentage. That gives IRC (%) = [(Z2 − Z1) / (Z2 + Z1)]^2 × 100. This form shows why the square and the 100 are needed: squaring relates to power (not voltage), and the 100 turns the fraction into a percent. The other forms either omit the 100 or the squaring, which would misrepresent reflected power as a percent or as a voltage ratio. The common convention uses the Z2 − Z1 difference in the numerator, so the standard expression is the squared ratio times 100.