Question 5.DA.6: DIODE THERMOMETER WITH A BIPOLAR TRANSISTOR Objective: Incor...
DIODE THERMOMETER WITH A BIPOLAR TRANSISTOR
Objective: Incorporate a bipolar transistor in a design application that enhances the simple diode thermometer design discussed in Chapter 1.
Specifications: The electronic thermometer is to operate over a temperature range of 0 to 100 °F.
Design Approach : The output-diode voltage developed in the diode thermometer
in Figure 1.48 is to be applied to the base–emitter junction of an npn bipolar transistor to enhance the voltage over the temperature range. The bipolar transistor will be held at a constant temperature
Choices: Assume an npn bipolar transistor with I_{S} = 10^{−12} A is available
From the design in Chapter 1, the diode voltage is given by
V_{D} = 1.12 − 0.522 \left( \frac{T}{300} \right)
where T is in kelvins.
Consider the circuit shown in Figure 5.64. We assume that the diode is in a vari-able temperature environment while the rest of the circuit is held at room temperature. Neglecting the bipolar transistor base current, we have
V_{D} = V_{B E} + I_{C} R_{E} (5.49)
We can write
I_{C} = I_{S ^{e^{V_{B E} /V_{T}}}} (5.50)
so that Equation (5.49) becomes
\frac{V_{D} − V_{B E}}{R_{E}} = I_{S^{e^{V_{B E} /V_{T}}}} (5.51)
and
V_{O} = 15 − I_{C} R_{C} (5.52)
From Chapter 1, we have the following
| T (°F) | V_{D} (V) |
| 0 | 0.6760 |
| 40 | 0.6372 |
| 80 | 0.5976 |
| 100 |
0.5790 |
If we assume that I_{S} = 10^{−12} A for the transistor, then from Equations (5.50), (5.51), and (5.52), we find
| T (°F) | V_{BE} (V) | I_{C} (mA) | V_{O} (V) |
| 0 | 0.5151 | 0.402 | 4.95 |
| 40 | 0.5092 | 0.320 | 7.00 |
| 80 | 0.5017 | 0.240 | 9.00 |
| 100 | 0.4974 | 0.204 | 9.90 |
Comment: Figure 5.65(a) shows the diode voltage versus temperature and Fig-
ure 5.65(b) now shows the output voltage versus temperature from the bipolar transistor circuit. We can see that the transistor circuit provides a voltage gain. This voltage gain is the desired characteristic of the transistor circuit.
Discussion: We can see from the equations that the collector current is not a linear function of the base–emitter voltage or diode voltage. This effect implies that the transistor output voltage is also not exactly a linear function of temperature. The line drawn in Figure 5.65(b) is a good linear approximation. We will obtain a better circuit design using operational amplifiers in Chapter 9
