The Gain Uncertainty due to Mismatch Calculator determines the minimum and maximum gain variation (Gmin and Gmax) caused by impedance mismatches in RF systems. It accounts for reflections between the source, amplifier, and load, based on their return losses and the amplifier’s gain and isolation. This tool helps RF engineers estimate the worst-case gain ripple in amplifier chains or cascaded systems.
Formulas
P = 10 ^ ((-RLs - RLi) / 20) + 10 ^ ((G - RLl - RLs - ISO) / 20) + 10 ^ ((-RLo - RLl) / 20) Gmin = 20 * log10(1 - P) Gmax = 20 * log10(1 + P)
Parameters
- RLs: Source return loss (dB)
- RLi: Amplifier input return loss (dB)
- RLo: Amplifier output return loss (dB)
- RLl: Load return loss (dB)
- G: Amplifier forward gain (dB)
- ISO: Amplifier reverse isolation (dB)
Outputs
- Gmin: Minimum possible gain (dB)
- Gmax: Maximum possible gain (dB)
- Gain ripple = Gmax – Gmin (dB)
Usage
- Estimate mismatch-induced gain ripple in RF amplifiers and signal chains.
- Evaluate stability margins under imperfect impedance matching.
- Compare amplifier designs and their sensitivity to reflection levels.
Example
Input:
- RLs = 20 dB
- RLi = 18 dB
- RLo = 20 dB
- RLl = 18 dB
- G = 10 dB
- ISO = 30 dB
Step-by-step:
P = 10^((-20 - 18)/20) + 10^((10 - 18 - 20 - 30)/20) + 10^((-20 - 18)/20) = 10^(-1.9) + 10^(-2.9) + 10^(-1.9) ≈ 0.0126 + 0.00126 + 0.0126 = 0.02646 Gmin = 20 * log10(1 - 0.02646) = -0.23 dB Gmax = 20 * log10(1 + 0.02646) = 0.23 dB
Output:
- Gmin = -0.23 dB
- Gmax = +0.23 dB
- Gain ripple = 0.46 dB