EECE 380 Lecture, Fall 2003

102 TECHNOLOGY BRIEF: CAPACITIVE SENSORS Capacitive Sensors To sense is to respond to a stimulus. (See Resistive Sensors.) A capacitor can function as a sensor if the stimulus changes the capacitor’s geometry — usually the spacing between its conductive elements — or the dielectric properties of the insulating material situated between them. Capacitive sensors are used in a multitude of applications. A few examples follow. Fluid Gauge The two metal electrodes in (A), usually rods or plates, form a capacitor whose capacitance is di- rectly proportional to the permittivity of the material between them. If the fluid section is of height Hf and A. Fluid tank Air To capacitive bridge circuit C2 Fluid Tank d H − Hf Hf the height of the empty space above it is (H − Hf ), then the overall capacitance is equivalent to two ca- pacitors in parallel, or C2 = Cf + Ca = εf (wHf ) d + εa (H − Hf d , where w is the electrode plate width, d is the spacing between electrodes, and εf and εa are the permittivities of the fluid and air, respectively. Rear- ranging the expression as a linear equation yields C2 = kHf + C0, where the constant k = (εf − εa)w/d and C0 is the capacitance of the tank when totally empty. Using the linear equation, the fluid height can be deter- mined by measuring C2, which can be realized by using a bridge circuit (B). The output voltage Vout is proportional to the deviation between C1 and C2. By setting C1 = C0 (a fixed capacitor) and by connect- ing the tank electrodes to the bridge circuit to form C2, Vout becomes proportional to the fluid height. Vg Vout + − C1 C2 R R + − B. Bridge circuit with 150 kHz ac source TECHNOLOGY BRIEF: CAPACITIVE SENSORS 103 Silicon substrate Electrodes C. Interdigital capacitor Humidity Sensor Thin-film metal electrodes shaped in an interdigi- tized pattern (to enhance the ratio A/d) are fabri- cated on a silicon substrate (C). The spacing be- tween digits is typically on the order of 0.2 µm. The permittivity of the material separating the electrodes D1. Pressure sensor Fluid Conducting Plate Flexible Metallic Membrane Oil Conducting Plate 1 2 3 C1 d1 C2 P P0 d2 varies with the relative humidity of the surrounding environment. Hence, the capacitor becomes a hu- midity sensor. Pressure Sensor A flexible metal diaphragm separates an oil-filled chamber with reference pressure P0 from a second chamber exposed to the gas or fluid whose pres- sure P is to be measured by the sensor (D1). The membrane is sandwiched, but electrically isolated, between two conductive parallel surfaces, forming two capacitors in series (D2). When P > P0, the membrane bends in the direction of the lower plate (D3). Consequently, d1 increases and d2 decreases and, in turn, C1 decreases and C2 increases. The converse happens when P < P0. With the use of a capacitance bridge circuit, such as the one in (B), the sensor can be calibrated to measure the pres- sure P with good precision. D2. Plate Membrane Plate 1 2 C1 C2 d1 d2 3 1 2 3 C1 = C2 P = P0 D3. Plate Membrane Plate 1 2 C1 P C2 d1 d2 3 1 2 3 C1 < C2 P > P0