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 VCC = +12 V. The transistor quiescent values are to be IC Q = 1 mA and VC E Q = 6 V. Choices

Question

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 [latex]V_{CC} = +12 V[/latex]. The transistor quiescent values are to be [latex]I_{C Q} = 1 mA[/latex] and [latex]V_{C E Q} = 6 V[/latex].

Choices: The transistor used in the design has nominal values of β = 100 and [latex]V_{B E} (on) = 0.7 V[/latex], 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.

Accepted Answer

The collector resistor is found from
[latex]R_{C} = \frac{V_{CC} − V_{C E Q}}{I_{C Q}} = \frac{12 − 6}{1} = 6 k \Omega[/latex]

The base current is
[latex]I_{B Q} = \frac{I_{C Q}}{β} = \frac{1 mA}{100} ⇒ 10 µA[/latex]
and the base resistor is determined to be
[latex]R_{C} = \frac{V_{CC} − V_{B E} (on)}{I_{B Q}} = \frac{12 − 0.7}{10 µA} = 1.13 M \Omega[/latex]
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
[latex]I_{BQ} = \frac{V_{CC} − V_{BE} (on)}{R_{B}} = \frac{12 − 0.7}{1.13 M \Omega} = 10 µA (unchanged)[/latex]
The base current for this circuit configuration is independent of the transistor current gain.
The collector current is
[latex]I_{C Q} = β I_{B Q}[/latex]
and the load line is found from
[latex]V_{C E} = V_{CC} − I_{C} R_{C} = 12 − I_{C}(6)[/latex]
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	[latex]I_{CQ} = 0.50 mA[/latex]	[latex]I_{CQ} = 1 mA[/latex]	[latex]I_{CQ} = 1.5 mA[/latex]
	[latex] V_{CEQ} = 9 V[/latex]	[latex] V_{CEQ} = 6 V[/latex]	[latex] V_{CEQ} = 3 V[/latex]

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 [latex]R_{B}[/latex] 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.

Question 5.14: Objective: Design a circuit with a single-base resistor to m...

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