How do I calculate the worst case mismatch loss between two components with known VSWR values?

The worst-case mismatch loss between two components with known VSWR values occurs when the reflected waves combine with the worst possible phase relationship. The calculation involves: (1) Convert VSWR to reflection coefficient for each component: Gamma_1 = (VSWR_1 - 1) / (VSWR_1 + 1). Gamma_2 = (VSWR_2 - 1) / (VSWR_2 + 1). (2) Calculate worst-case mismatch loss: ML_worst = -10 × log10(1 - (Gamma_1 × Gamma_2)²) (assuming the reflection phases produce maximum cancellation of delivered power). However, the more commonly used formula for the mismatch uncertainty limits: ML_max = -10 × log10((1 - Gamma_1 × Gamma_2)²) (maximum loss when reflections add constructively). ML_min = -10 × log10((1 + Gamma_1 × Gamma_2)²) should be negative meaning gain (maximum gain when reflections add constructively in the forward direction). But for physical consistency the total mismatch loss range is: ML = -10 × log10(1 - Gamma_1²) - 10 × log10(1 - Gamma_2²) is the combined mismatch loss from both reflections independently. The interaction term creates the uncertainty range: ±20 × log10(1 ± Gamma_1 × Gamma_2). (3) Example: Component 1: VSWR = 2.0 → Gamma_1 = 0.333. Component 2: VSWR = 1.5 → Gamma_2 = 0.200. Individual mismatch losses: ML_1 = -10×log10(1 - 0.111) = 0.51 dB. ML_2 = -10×log10(1 - 0.040) = 0.18 dB. Total individual: 0.69 dB. Interaction uncertainty: ±20×log10(1 ± 0.333×0.200) = ±20×log10(1 ± 0.067) = ±0.58 dB. Worst case total loss: 0.69 + 0.58 = 1.27 dB. Best case: 0.69 - 0.58 = 0.11 dB. (4) Simplified approach: for most engineering purposes, the worst-case mismatch loss is approximately: ML_worst ≈ -10 × log10(1 - Gamma_1 × Gamma_2)² / ((1 - Gamma_1²)(1 - Gamma_2²)). This accounts for both the individual losses and the interaction term.