DC Transistor Easy Analysis for Electric Circuits

DC transistor is the most basic power electronic device with several functions.

It is very common of us dealing with electronic products on a daily basis and gets some experience with personal computers.

A basic component for the integrated circuits found in these electronics and computers is the active, three-terminal device known as the transistor.

Transistor

Figure 1. Transistors

This time we will cover only the BJTs, which were the first of the two and are still used today.

Our objective is to learn about BJTs and able to apply the technique developed until now to analyze dc transistor circuits.

Figure 2. Transistors npn and pnp

There are two types of BJTs: npn and pnp, with their circuit symbol as shown in Figure.(2). Each type has three terminals, designated as emitter (E), base (B), and collector (C).

The calculation below has relationship to the transistor characteristic curve.

For npn transistor, the currents and voltages of the transistor are specified as in Figure.(3).

Figure 3. Transistor equivalent circuit

Applying KCL to Figure.(3a) gives

(1)

where I_E, I_C, and I_B are emitter, collector, and base currents, respectively. Similarly, applying KVL to Figure.(3b) gives

(2)

where V_CE, V_EB, and V_BC are collector-emitter, emitter-base, and base-collector voltages. The BJT can operate in one of three modes: active, cutoff, and saturation.

(3)

where α is called the common-base current gain. In Figure.(3), α denotes the fraction of electrons injected by the emitter that is collected by the collector. Also,

(4)

where β is known as the common-emitter current gain. The α and β are characteristic properties of a given transistor and assume constant values for that transistor.

Typically, α takes values in the range of 0.98 to 0.999, while β takes value in the range of 50 to 1000. From Equations.(1) to (4), it is evident that

(5)

and

(6)

These equations show that, in the active mode, the BJT can be modelled as a dependent current-controlled current source.

Thus, in circuit analysis, the dc equivalent model in Figure.(4b) may be used to replace the npn transistor in Figure.(4a).

Since β in Equation.(6) is large, a small base current controls the large current in the output circuit.

Consequently, the bipolar transistor can serve as an amplifier, producing both current gain and voltage gain.

Such amplifiers can be used to furnish a considerable amount of power to transducers such as loudspeakers or control motors.

Figure 4. Transistor equivalent circuit

It should be observed in the following examples that one cannot directly analyze transistor circuits using nodal analysis because of the potential difference between the terminals of the transistor.

Only when the transistor is replaced by the equivalent model can we apply nodal analysis.

Read also : op amp integrator circuit

DC Transistor Example

For better understanding, let us review the example below:
Find I_C, I_B , and vo in the transistor circuit of Figure.(5). Assume that the transistor operates in the active mode and that β = 50.

Figure 5

Solution :
For the input loop, KVL gives

Since V_BE = 0.7 V in the active mode,

But

For the output loop, KVL gives

Note that v_o = V_CE in this case.

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Reference:  Fundamentals of electric circuits by Charles K. Alexander and Matthew N. O. Sadiku