Question 5.14: Objective: Design a circuit with a single-base resistor to m...
Objective: Design a circuit with a single-base resistor to meet a set of specifications.
Specifications: The circuit configuration to be designed is shown in Figure 5.51(b). The circuit is to be biased with V_{CC} = +12 V. The transistor quiescent values are to be I_{C Q} = 1 mA and V_{C E Q} = 6 V.
Choices: The transistor used in the design has nominal values of β = 100 and V_{B E} (on) = 0.7 V, but the current gain for this type of transistor is assumed to be in the range 50 ≤ β ≤ 150 because of fairly wide fabrication tolerances. We will assume, in this example, that the designed resistor values are available.
The collector resistor is found from
R_{C} = \frac{V_{CC} − V_{C E Q}}{I_{C Q}} = \frac{12 − 6}{1} = 6 k \Omega
The base current is
I_{B Q} = \frac{I_{C Q}}{β} = \frac{1 mA}{100} ⇒ 10 µA
and the base resistor is determined to be
R_{C} = \frac{V_{CC} − V_{B E} (on)}{I_{B Q}} = \frac{12 − 0.7}{10 µA} = 1.13 M \Omega
The transistor characteristics, load line, and Q-point for this set of conditions are shown in Figure 5.52(a).
Trade-offs: In this example, we will assume that the resistor values are fixed and will investigate the effects of the variation in transistor current gain β.
The base current is given by
I_{BQ} = \frac{V_{CC} − V_{BE} (on)}{R_{B}} = \frac{12 − 0.7}{1.13 M \Omega} = 10 µA (unchanged)
The base current for this circuit configuration is independent of the transistor current gain.
The collector current is
I_{C Q} = β I_{B Q}
and the load line is found from
V_{C E} = V_{CC} − I_{C} R_{C} = 12 − I_{C}(6)
The load line is fixed. However, the Q-point will change. The transistor Q-point values for three values of β are given as:
| β | 50 | 100 | 150 |
| Q-point values | I_{CQ} = 0.50 mA | I_{CQ} = 1 mA | I_{CQ} = 1.5 mA |
| V_{CEQ} = 9 V | V_{CEQ} = 6 V | V_{CEQ} = 3 V |
The various Q-points are plotted on the load line shown in Figure 5.52(b). In this figure, the collector current scale and load line are fixed. The base current scale changes as β changes.
Comment: In this circuit configuration with a single base resistor, the Q-point is not stabilized against variations in β; as β changes, the Q-point varies significantly. In our discussion of the amplifier in Example 5.13 (see Figure 5.50), we noted the importance of the placement of the Q-point. In the following two examples, we will analyze and design bias-stable circuits.
Although a value of 1.13 MΩ for R_{B} will establish the required base current,this resistance is too large to be used in integrated circuits. The following two examples will also demonstrate a circuit design to alleviate this problem.
