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The interaction between an HVDC converter and the saturation characteristic of a converter transformer can lead to a type of harmonic instability widely known as converter transformer core saturation instability. The paper presents a linearised direct frequency domain analysis of the mechanism behind this instability. Using linearised converter transfer functions and transformer saturation characteristics on AC and DC system equivalents, the system equations are solved to describe the phenomenon. A measure of the level of stability, saturation stability factor, is derived and utilised to predict the system dynamics. The analysis is verified by dynamic simulation of several systems.