Assignment 1 - Questions

Question 1 - Bridge circuits are very important in instumentation applications. They often form part of transucer circuits. Their main utility lies in the fact that they can measure small changes in resistance accurately.

Consider the wheat stone bridge circuit in Figure 1.

Figure 1: Wheatstone bridge with 2 variable resistors

1. Derive the expression of the output voltage V_o of figure 1 where V_B is the applied voltage.

2. Comment on the linearity of the measurement circuit.

Depending on the application, different configuratons of bridge circutis can be used. Another such circuit is as shown in figure 2.

Figure 2: Wheatstone bridge with 2 variable resistors II

1. Derive the expression of the output voltage V_o of figure 2 where V_B is the applied voltage.

2. Comment on the linearity of the measurement circuit.

In some applications, the bridge circuit is driven by a constant current soure rather tha a voltage source. Figure 3 is one such configuration.

Figure 3: Current Driven wheatstone bridge with 4 variable resistors

1. Derive the expression of the output voltage V_o of figure 3 where I_B is the drive current.

2. Comment on the linearity of the measurement circuit.

3. Describe a scenario where driving a bridge circuit with a constant current source is more advantageous than driving the circuit with a constant voltage source.

Consider the bridge circuit in fig 1. If it is driven with a constant voltage with magnitude 2 × V_B what effect will it have on the accuracy of the measurement circuit as compared with when it is driven by a constant voltage of magnitude V_B.

Question 2 - An unmanned submarine is equipped with temperature and depth measuring instruments and has radio equipment that can transmit the output readings of these instruments back to the surface. The submarine is initially floating on the surface of the sea with the instrument output readings in steady state. The depth-measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 25 seconds. The water temperature on the sea surface, T₀, is 20degreesC and the temperature T_x at a depth of x metres is given by the relation:

T_x = T_o - 0.01x

1. If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5 metres/second, draw a table showing the temperature and depth measurements reported at intervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error in each temperature reading.

2. What temperature does the submarine report at a depth of 1000 metres?

Question 3 - Optocouplers are extremely useful devices. One of the main applications of optocouplers is to electrically isolate 2 or more parts of a circuit. This serves a number of purposes for example it can be used to isolate sensitive instruments ground loop noise and switching noise in industrial settings.

Read the datasheet "Optocoupler, Photodarlington Output, High Gain, with Base Connection" provided for the Vishay 4N32 and 4N33 series optocoupulers carefully and answer the following questions:

1. What is the maximum rated total power disspation of the device?

2. What transistor configuration is used for the output of the device?

3. If the device is used to drive a counter for a digital signal in an industrial instrument, what is the maximum signal frequency for which the optocoupler may be used reliably?