In this article, the standard theoretical model accounting for a double barrier quantum well resonant tunneling diode (RTD) connected to a direct current source of voltage is simplified by representing its current-voltage characteristic with an analytically approachable, anti-symmetric N-shaped function. The time and variables involved are also transformed to reduce the number of parameters in the model. Responses observed in previous, more physically accurate studies are reproduced, including slow-fast dynamics, excitability, and bistability, relevant for spiking signal processing. A simple expression for the refractory time of the excitable response is derived and shown to be in good agreement with numerical simulations. In particular, the refractory time is found to be directly proportional to the circuit's intrinsic inductance. The presence or absence of bistability in the dependence of the parameters is also discussed thoroughly. The results of this work can serve as a guideline in prospective endeavors to design and fabricate RTD-based neuromorphic circuits for power and time-efficient execution of neural network algorithms.