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A KY converter has the characteristics of non‐pulsating output current, low‐output voltage ripple and no right‐half plane zero in continuous conduction mode which can overcome the drawbacks of the conventional boost and buck–boost converters. However, when the KY converter is implemented into an integrated circuit, its discontinuous conduction mode (DCM) operation cannot be avoided due to a small‐inductor value. The boundary for the DCM operation region, DCM dc voltage and small‐signal transfer functions are proposed, which fill the gap of the DCM operation theory for the KY converter. Simulation results, using MATLAB and Cadence, are provided to verify the deduced DCM operation theory of the KY converter. The DCM closed‐loop controller design can be achievable in future. [ABSTRACT FROM AUTHOR]