Novel closed form expressions for the error vector magnitude (EVM) are presented. The expressions combine the in-phase quadrature (IQ) amplitude and phase imbalances and the DC offsets along with the phase noise. Both the Gaussian and the Tikhonov probability density functions are utilised for the oscillator phase noise distribution. The explicit conditions when the EVM computations based on the Tikhonov distribution converge to a Gaussian based are investigated. Furthermore, the application of the proposed EVM expressions is demonstrated by including phase noise masks, providing a direct means to the phase locked loop/voltage controlled oscillator design parameters. The measurements are used to validate the proposed expressions.