Reflection Loss

For no reflection loss, R_L = R_g, and X_L = X_g. For this condition the power PI! delivered to the load impedance is

The power reflection loss is determined from the ratio of the power transferred to the load impedance under actual circuit conditions to the power that would be transferred under the prescribed conditions for no reflection loss. Dividing equation 50 by equation 51 gives

because R_L = Z_L cos θ_L, and R_g = Z_g cos θ_g. Equation 52 may be written

where k = sqrt(4Z_gZ_L)/(Z_g+Z_L) and sometimes is called the reflection factor.⁴

The reflection loss is defined¹ as

where the reflection loss is in decibels. This equation also can be derived on the basis of the currents flowing under matched and mismatched conditions.⁴ The two vertical lines enclosing a portion of equation 54 indicate that in finding the reflection loss the impedances are combined as complex numbers and that the log is taken of the magnitude of the final value of impedance.

It is common practice to state that two connected circuits are matched when the input impedance of the driven circuit equals the internal impedance of the driving circuit in both magnitude and angle (including sign). Because the condition for matched impedances is not the condition for maximum power transfer (which is that the circuits are conjugate) it is possible to have reflection gains. Reflection losses and gains can be determined from Fig. 21.