Silicon neuron is electrical circuit that is analogous to biological neurons. Conventionally, it was designed mainly in the following two attitudes. One is to realize circuitry that is as close to biological neuron as possible, which enlarges circuit size and complexity terribly. Another is to realize simple and compact circuitry that can be utilized to construct large-scale silicon neural network. Because designers ignore the mechanisms underlying the neuronal phenomena, silicon neurons can be quite different from biological ones. We proposed a new design method that utilizes mathematical knowledge on neuronal phenomena, which allows us to design simple circuitry whose operating mechanism is same as biological neuron. Several types of circuits have been and are being implemented to validate its efficiency.