In the recent past, Physically Unclonable Functions (PUFs) have been proposed as a way of implementing security in modern ICs. PUFs are hardware designs that exploit the randomness in silicon manufacturing processes to create IC-specific signatures for silicon authentication. While prior PUF designs have been largely digital, in this work we propose a novel PUF design based on transfer function variability of an analog push-pull amplifier under process variations. A differential amplifier architecture is proposed with digital interfaces to allow the PUF to be used in digital as well as mixed-signal SoCs. A key innovation is digital stimulus engineering for the analog amplifier that allows 2X improvements in the uniqueness of IC signatures generated over arbiter-based digital PUF architectures, while maintaining high signature reliability over +/- 10 % voltage and -20 to 120 degree Celsius temperature variation. The proposed PUF is also resistive to model building attacks as the internal analog operation of the PUF is difficult to reverse-engineer due to the continuum of internal states involved. We show the benefits of the proposed PUF through comparison with a traditional arbiter-based digital PUF using simulation experiments.