Comment on ‘‘AC frequency characteristics of coplanar impedance sensors

In their article, ‘‘AC frequency characteristics of coplanar impedance sensors as design parameters’’, Hong et al. present an analytical model for the calculation of the resistance between two electrodes in a microchannel. However, their measurements fit poorly with their suggested model, and they attribute the discrepancies to electrode thickness and a ‘fringing effect’. In this note we show that the discrepancies are due to the neglected channel height in their model, and that by including two additional transformations, the resistance between two electrodes in a microchannel can be accurately modelled. The cell constant describes the proportionality between the resistivity of the medium in contact with two electrodes and the resulting resistance. The usefulness of the cell constant for microelectrode design optimization has been presented previously. Both these papers treat sensor design for coplanar strip lines in contact with a semi-infinite medium. In order to use the Schwarz–Christoffel (SC) conformal mapping, as described in these papers, the electrodes must be symmetrical about the origin, and the electrode width must be negligible compared to the sample height. In the article by Hong et al., the geometry is such that the height of the channel (30 mm) is not negligible compared to the electrode widths and spacings (20–500 mm) of their device. The approximation of a semi-infinite medium on top of the electrodes therefore fails, since it does not take into account the insulating boundary condition at the top of the channel. We will show in this paper that the large discrepancies between theory and experiment presented by Hong et al. (see Fig. 8 and Fig. 10 in their paper) can be reconciled by appropriate use of conformal mapping for calculation of the cell constant. We introduce two additional conformal mappings that must be performed before the resistance can be analyzed as suggested by Hong. These two conformal mappings are a sinetransformation followed by a bilinear transformation. If we consider the 2D case, the length-wise cross-section of the microchannel can be modelled as a rectangle (Fig. 1(a)). Exploiting the symmetry of the geometry, we can replace the left half of the microchannel with a conductor at the center between the two electrodes. The problem is then to calculate the resistance between the center conductor and one of the active electrodes. Let the geometry of the real microchannel be defined in the Z-plane, with coordinates