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As thin-film cryotron circuits become faster, the detailed properties of the components themselves have an increasing effect on over-all circuit operation. When a cryotron switches from the superconducting to the resistive state in a fast circuit, its inductive characteristics can change enough to add appreciable delay and dissipation to its driving circuit. The inductive and resistive transition of the component can be accompanied by diamagnetic hysteresis and by eddy-current-damping effects, which add to dissipation and further delay the switching of the component. These component and circuit effects are complex and interrelated, but considerable insight is gained by analyzing separately various portions of the general behavior.