44 CHEMICAL SENSORS: TECHNOLOGIES. VOLUME 4: SOLID-STATE DEVICES after the output reaches a stable value. However, in dynamic measurements, the sensor is characterized using a differential equation, which defines its input­output relationship. The input­output relation- ships for zero-order, first-order, and second-order sensors are expressed as follows: Zero-order sensor: First-order sensor: y ( t ) a bx ( t ) (2.6) (2.7) b 1 dy ( t ) b 0 y ( t ) x ( t ) dt d 2 y ( t ) dy ( t ) b 1 b 0 y ( t ) x ( t ) 2 dt dt Second-order sensor: b 2 (2.8) In the above equations, x(t) is the sensor input and y(t) is the sensor output. The zero-order sensor has no energy storage element and therefore the sensor response is instantaneous to any input and hence does not possess any dynamic characteristics. The first-order sensor has one energy storage element, an example of which is a temperature sensor in which the energy storage is the thermal capacity. Typically, a first-order sensor is characterized by its frequency response. The lowest or highest frequency of input to which the sensor can respond is defined as the lower cutoff frequency or upper cutoff frequency, respec- tively. A second-order sensor incorporates two energy storage elements. An accelerometer which consists of a mass and a spring is a classic example of a second-order sensor.