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

Question

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 [latex]I_{S} = 10^{−12} A[/latex] is available

Accepted Answer

From the design in Chapter 1, the diode voltage is given by
[latex]V_{D} = 1.12 − 0.522 \left( \frac{T}{300} \right) [/latex]
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
[latex]V_{D} = V_{B E} + I_{C} R_{E} [/latex] (5.49)
We can write
[latex]I_{C} = I_{S ^{e^{V_{B E} /V_{T}}}} [/latex] (5.50)
so that Equation (5.49) becomes
[latex]\frac{V_{D} − V_{B E}}{R_{E}} = I_{S^{e^{V_{B E} /V_{T}}}} [/latex] (5.51)

and
[latex]V_{O} = 15 − I_{C} R_{C} [/latex] (5.52)
From Chapter 1, we have the following

T (°F)	[latex]V_{D} (V) [/latex]
0	0.6760
40	0.6372
80	0.5976
100	0.5790

If we assume that [latex]I_{S} = 10^{−12} A[/latex] for the transistor, then from Equations (5.50), (5.51), and (5.52), we find

T (°F)	[latex]V_{BE} (V) [/latex]	[latex]I_{C} (mA)[/latex]	[latex]V_{O} (V)[/latex]
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

Question 5.DA.6: DIODE THERMOMETER WITH A BIPOLAR TRANSISTOR Objective: Incor...

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