Neuromorphic circuits using emerging memory technologies have recently gained popularity since they facilitate dense integration with reduced design complexity. In this work, we introduce a simplified modeling approach for the analysis of threshold switch (TS) based neuron circuits where, under given constraints, we represent the TS device as a nonlinear resistor in series with a parasitic inductor. As a result, we define the current of the TS as its state variable. In order to demonstrate the feasibility of the proposed approach, we analyze the conventional Leaky Integrate and Fire (LIF) neuron circuit along with two of its modified variants. We validate the accuracy of the provided analysis and key predictions through numerical simulation results. As a significant contribution, we demonstrate the effectiveness of the proposed method in modifying the nullclines of the TS based LIF neuron and qualitatively align them with the nullclines of a 2nd order biologically plausible neuron model.