Electrochemical biosensors and the related concept of redox detection at nanogap electrodes are increasingly explored for ultra-sensitive detection of biomolecules. While experimental demonstrations have been encouraging, the associated design and optimization of electrode geometry, beyond the simple one-dimensional architectures, is inherently challenging from multiple aspects related to numerical complexity. Here we develop a facile simulation scheme to address this challenge using well established electronic circuit analysis techniques that are available as open source-ware. Based on this approach, we show that electrode geometry, especially nano-structured redox electrodes on a planar surface, has interesting implications on the detection limits and settling time of electrochemical biosensors. The methodology we developed and the insights obtained could be useful for electrode optimization for a wide variety of problems ranging from biosensors to electrochemical storage.