Circuit and electrochemical models of supercapacitor electrical energy storage devices are related via their energy dissipation. A method for the synthesis of linear, low-order finite dimensional circuits from nonlinear infinite dimensional electrochemical partial differential equations is analysed with this method involving discretisation, linearisation, model order reduction and circuit synthesis. It is shown that a circuit with three time constants sufficiently captures the input/output response of the electrochemical model. Using absolute stability, the local nature of the resistance of the nonlinear electrochemical model is shown. The problem of supercapacitor design is also discussed, with the device capacitance and resistance being linked to its electrochemical parameters.