The paper describes an analytic theory of the IMPATT diode, based on the well known Read model. The inclusion of finite avalanche pulse width and space-charge effects in the treatment yields a relatively simple theory that compares well with a computer simulation such as that of Scharfetter and Gummel, or the University College London full-simulation program. The use of such diode admittance calculations in the prediction of oscillator locking characteristics is described. The circuit of a reflection-type locked oscillator is analysed for steady-state conditions and stability limits. After allocation of practical parameter values to the theory, the resulting predicted variation of locked output power with frequency shows good agreement with experimental measurements on a low-power X band IMPATT oscillator.