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The concept of using a long mismatched transmission line to measure noise parameters has been known for some time. However, it has been limited to narrow-bandwidth applications, and a wide-band extension has never been reported. In order to measure the cryogenic noise parameters of a wide-band low-noise amplifier (LNA), a wide-band frequency-variation method is proposed. In this method, the four noise parameters at each frequency are derived numerically from a set of matched and mismatched noise temperatures measured within a surrounding frequency-sampling window. By scanning this frequency-sampling window, noise parameters over a wide frequency range can be obtained. Since this approach can be easily incorporated into existing noise measurement systems, a tuner is not required, and the technique can be applied to a cryogenic amplifier. This paper details the theory, implementation, and verification of this new method. The measured noise parameters of a cryogenic wide-band LNA are presented.