New mathematical formulation for designing a fully differential self-biased folded cascode amplifier

One of the most important building blocks in analog circuit design is the operational amplifiers. This is because of their versatility and wide spread usage in many applications such as communications transmitters and receivers, analog to digital converters, or any other application that requires a small signal to be amplified. The basic amplifier topologies are introduced. Then, some operational amplifiers topologies are introduced with some techniques to self bias these amplifiers. The folded cascode fully differential Op-Amp with self bias is presented. This is one of the newest amplifier topologies which provide stable self-biased amplifiers. A new mathematical model for fully differential folded cascode amplifiers is presented and generalized to include the family of fully differential complementary amplifiers. This formulation focuses on deriving detailed design equations for the amplifier gain and frequency response. The equations are verified through time domain and frequency domain simulations of different fabrication processes to ensure the validity of the model across a wide range of processes. The model was verified against TMSC 180nm, 250nm, and 350nm fabrication processes. The new model agrees well with simulations; with 1% error for the amplifier gain and \u3c7% error for amplifier bandwidth. The relatively high error value for the bandwidth is because the model considers the worst case scenario and overestimates the output capacitance. Finally, the algorithm of getting this formulation is extended to include special and commonly used cases. This formulation proved to be very useful in designing stable, self-biased, fully differential folded cascode amplifiers