How does mismatch between stages affect the overall gain flatness of a receiver chain?

In a multi-stage receiver chain, impedance mismatches between adjacent stages create gain ripple that accumulates through the chain, affecting the overall gain flatness: (1) Ripple accumulation: each pair of mismatched interfaces creates its own ripple pattern (amplitude and period). The total receiver gain as a function of frequency is the product of the individual stage gains, each modulated by the mismatch ripple at its interfaces. The ripple from N-1 interface pairs contributes to the overall gain variation. Worst case: all ripples add in phase (this occurs at specific frequencies). Worst-case total ripple ≈ sum of individual pairwise ripples. For 5 interfaces with 0.3 dB ripple each: worst-case total = 1.5 dB. (2) Example receiver chain: antenna (VSWR 1.3) → cable → filter (VSWR 1.5 in, 1.8 out) → LNA (VSWR 1.3 in, 1.5 out) → cable → mixer (VSWR 2.0). Pairwise ripples: antenna-cable-filter: 20×log10((1+0.13×0.2)/(1-0.13×0.2)) = 0.23 dB. Filter-LNA: 20×log10((1+0.28×0.13)/(1-0.28×0.13)) = 0.32 dB. LNA-cable-mixer: 20×log10((1+0.2×0.33)/(1-0.2×0.33)) = 0.58 dB. Total worst case: 1.13 dB. (3) Mitigation: use components with lower VSWR (< 1.3 at each port), add attenuator pads between stages (a 3 dB pad reduces the pairwise ripple by 12 dB but adds 3 dB noise figure), place attenuator pads after the LNA (where the NF impact is divided by the LNA gain), use isolators between stages (for narrow-band systems), and keep interconnects short (to push ripple periods outside the operating band).