Symbolic nodal analysis of fully-differential analog circuits

In this paper, a simple element stamp for floating or grounded voltage-controlled voltage sources is proposed. The novelty is that not only the behavior of single-ended, fully-differential and balanced differential operational amplifiers can directly be introduced in the admittance matrix without extra variables, but also the new stamp has few nonzero elements. As a consequence, a reduced and sparse system of equations is built, which means that the computational complexity and memory consumption during the solution of the system of equations by using recursive determinant-expansion techniques are both enhanced. Three analysis examples are used to show that fully-symbolic transfer functions of single-ended, fully-differential and balanced differential analog circuits can be computed by using standard nodal analysis. Furthermore, symbolic expressions for the common-mode rejection ratio of the fully-differential amplifiers are also computed.