Personalized speech enhancement (PSE) models can improve the audio quality of teleconferencing systems by adapting to the characteristics of a speaker's voice. However, most existing methods require a separate speaker embedding model to extract a vector representation of the speaker from enrollment audio, which adds complexity to the training and deployment process. We propose to use the internal representation of the PSE model itself as the speaker embedding, thereby avoiding the need for a separate model. We show that our approach performs equally well or better than the standard method of using a pre-trained speaker embedding model on noise suppression and echo cancellation tasks. Moreover, our approach surpasses the ICASSP 2023 Deep Noise Suppression Challenge winner by 0.15 in Mean Opinion Score.