Pseudoresistive networks and the pseudovoltage-based cocontent

Using the concept of a transistor as a pseudoresistor, many resistive networks can be mapped to transistor based equivalents. Pseudoresistors are two-terminal circuit elements whose current is a function of the instantaneous difference in the pseudovoltage across the two terminals, where the pseudovoltage is a nonlinear function of the voltage at each terminal. A transistor with fixed gate and bulk voltages is a linear pseudoresistor between the drain and source over a wide range of currents including strong and weak inversion. Motivated by this, we extend the cocontent, defined for two-terminal resistors, to the pseudovoltage-based (PVB) cocontent, defined for two terminal pseudoresistors. We show that the PVB cocontent has similar properties as the cocontent in characterizing the DC-operating points of transistor networks and their stability, but under more restrictive conditions. As examples, we derive the total PVB cocontent for several neuromorphic circuit networks including the diffuser grid, a linear pseudoresistive network, and the winner-take-all circuit of Lazzaro, a nonlinear pseudoresistive network. This work establishes that these circuits can be viewed in terms of function minimization, which may lead to better intuition about their operation as well as the development of new circuit architectures.