Here’s your chance to convert light into electricity using simple operational circuits. You can apply a similar approach to develop instruments that measure other physical variables in the environment, such as temperature and pressure.

You use an *input transducer* to turn a physical variable into an electrical variable. A *photoresistor* is an input transducer that converts light energy into a change in resistance, resulting in a change in the current flowing in the circuit. The light is, in fact, an electrical signal.

Suppose you’re dealing with a photoresistor that has a resistance value between 20 MW in total darkness and 20 kW in bright light. If the photoresistor is a linear device, then doubling the amount of light doubles the amount of voltage. You can therefore model a photoresistor as a variable resistor that changes resistance according to the amount of light.

The following figure shows a photoresistor and a complete design of an operational-amplifier (op-amp) circuit to produce an output voltage *v*_{O}*.*

Use circuit analysis to show that the op-amp output voltage *v** _{O}* is 0 volts in total darkness and 5 volts in bright light. In other words, show that the voltage range of the output varies from 0 to 5 volts. Here’s how:

Determine the output voltage

*v*_{2}from the transducer.To determine the range of the output

*v*from the transducer (that is, the voltage across Terminals A and B), you can use the voltage divider equation. This equation sets the output voltage equal to the input voltage multiplied by the ratio of the resistance of the output device (_{2}*R*_{2}) to the total series resistance (*R*_{1}+*R*_{2}):Determine the lower bound of

*v*_{2}.The lower bound of the output voltage

*v*_{2}occurs in bright light, when the photoresistor’s resistance is at a minimum. When*R*_{2}= 20 kW, the lower voltage*v*_{2}is_{L}Determine the upper bound of

*v*_{2}.The upper bound of the output voltage

*v*_{2}occurs when the photoresistor’s resistance is highest. In total darkness,*R*_{2}= 20 MW = 20,000 kW , so the upper voltage*v*_{2}is_{U}The voltage of

*v*_{2 }ranges from 5 to 10 volts.Simplify the transducer (the source circuit) using the Thévenin technique.

The Thévenin technique reduces a source circuit to one single resistor

*R*_{T}*v*_{T}*.*By using the Thévenin equivalent to simplify the transducer, you get a Thévenin voltage*v*_{T}*R*that varies from 10 kW to 20 kW._{T}Analyze the op-amp circuit (inverting summer).

The op-amp circuit in the following figure is a typical configuration of an inverting op-amp summer circuit. In this circuit, you have two inputs: one coming from the transducer and another coming from a voltage source of –10 volts. The equation for the inverting operational amplifier is

Because the voltage range of *v*_{2 }varies between 5 and 10 volts, the output voltage range of the inverting summer goes from 0 to 5 volts.