Theory and operation of a single microelectrode voltage clamp

The theory of operation of a discontinuous single-electrode voltage clamp using an ideal microelectrode (infinite response speed) and fixed (current-passing) duty cycle has been previously described. In this paper, the theory is extended by considering a microelectrode which has a finite response speed, by allowing the duty cycle to be variable, and by considering the clamp noise. Formulate are derived for the relationships between the step response, the steady-state error, the steady-state ripple, and the stability, in terms of the cycling frequency, the duty cycle, the open loop gain, and the electrical resistance and capacitance of the microelectrode and the cell membrane. In addition, the amplification of the microelectrode noise by aliasing is analysed, the error due to incomplete decay of the microelectrode voltage is described, and the accuracy of averaging the peak current measurement is established. To achieve the fastest dynamic response and the smallest steady-state error, the cycling period should be made as small as possible, and the open-loop gain should be as large as possible, consistent with stability. Incomplete decay of the microelectrode voltage destabilizes the clamp, and can introduce a significant clamp error. The choice of duty cycle is a compromise between reducing the noise and the step response time while avoiding design problems in the current output circuit. The output noise is amplified by aliasing. It can be minimized for a given output filter cutoff frequency by keeping the cycling frequency as high as possible, and by the use of an anti-aliasing filter whose cutoff frequency must be set for each microelectrode.