Extended geometric circuit analysis

Abstract In previous studies, when geometrically analysing a circuit where a single independent voltage or current source is connected to a planar resistive network, the network is expressed as the mosaic of rectangles (which not only symbolize resistors but also represent their resistances, currents, voltages, and powers) (MOR) and the independent voltage or current source corresponds to the full height or width of the MOR, respectively. In this paper, we develop rectangle representations for sources (independent/dependent voltage and current sources) where their aspect ratios are excluded from consideration. Using these representations, we construct an extended MOR (EMOR) based on the assumed current directions in the planar circuit composed of sources and resistors. This EMOR represents the process in which assumed currents start from a reference node, pass through all the elements, and return to the same node in the circuit. The standard EMOR has the top and bottom horizontal sides representing the same reference node with the same voltage and the leftmost and rightmost vertical sides corresponding to two meshes with one-directional (clockwise or counterclockwise) assumed element currents through the reference node (when the planar circuit is drawn on a sphere). The geometric applications of Ohm’s law and Kirchhoff’s current/voltage laws in the EMOR are similar to those (aspect ratio and width/height conservations) in the conventional MOR. We apply this method to a circuit with two parallel batteries, a circuit with independent voltage/current sources and a dependent voltage source, and a transistor amplifier circuit using the transistor’s DC and small-signal equivalent models. To aid readers’ understanding, the process of geometric circuit analysis is presented as a flow of arrows connecting widths and heights of rectangles in the EMOR. The EMOR method is expected to open a new window for electric circuit analysis due to its convenience, efficiency, and the game-like nature.