A useful unidirectional sensing device is the photo emitter sensor [15]. A light source is sensitive to the emitter current flowing and alters the resistance of the photo sensor. Both the light source and the photoconductor are packaged in a single four-terminal device. This device provides a large gain and total isolation. A feedback circuit utilizing this device is shown in Figure P4.9(a), and the nonlinear resistance-current characteristic is shown in Figure P4.9(b) for the Raytheon CK1116. The resistance curve can be represented by the equation

where i is the lamp current. The normal operating point is obtained when v0 = 35 V, and vin = 2.0 V.
(a) Determine the closed-loop transfer function of the system.
(b) Determine the sensitivity of the system to changes in the gain, K.
Figure P4.9
Photo sensor system.

0.175 (i0.005)12 ogio R 10 M Ts + I I M 5 100 k E 10k 1 k R2-5000 Photoemitter sensor Constant current source-I 100 2 0 123 4 5 6 78 9 I0 Lamp current (mA)