The Transistor as an Amplifier

When the DC operating point Q is in the active region, the transistor can act as an amplifier to AC signals. For such purpose, Q should be set midway between Q_sat and Q_cutoff to allow for the maximum possible voltage excursions.

Let's analyse this by considering an AC source v_in added to the circuit of Figure 96, see Figure 104 (please note that this is not a practical circuit; just one we use here to teach ideas).

**Figure 104:** Basic transistor amplifier.
$\begin{figure} \begin{center} \epsfig{file=images/bjtimg13.eps}\end{center}\end{figure}$

We will use the AC hybrid- $\pi$ model from Section 8.2.4. It is convenient to re-draw the circuit showing only the AC signals, Figure 105. Here, the DC sources have been zeroed out; the AC component does not see them.

**Figure 105:** AC equivalent circuit for the circuit of Figure 104.
$\begin{figure} \begin{center} \epsfig{file=images/bjtimg14.eps}\end{center}\end{figure}$

By KVL around the left loop we get

$\begin{displaymath}v_{in} = i_b(R_B + r_\pi) \end{displaymath}$

and solving for the base current we get

$\begin{displaymath}i_b = \frac{v_{in}}{R_B + r_\pi} = \frac{v_{in}}{R_B + (\beta +1)r_e} . \end{displaymath}$

Next, KVL around the right loop gives the AC collector voltage as

v_c = - i_c R_C

and from (88) we get

$\begin{displaymath}v_c = - \beta R_C i_b . \end{displaymath}$

Combining these equations gives

$\begin{displaymath}v_c = - \frac{\beta R_C}{R_B + (\beta +1)r_e} v_{in} . \end{displaymath}$

(99)

Equation (99) says that the input voltage v_in is amplified at the output (i.e. collector voltage v_c) by a gain factor

$\begin{displaymath}A = - \frac{\beta R_C}{R_B + (\beta +1)r_e} \end{displaymath}$

(100)

Note the minus sign, indicating that it is an inverting amplifier. (Also, note that if $\beta$ is very large and R_B is not too high, the gain A equals -R_C/r_e approximately.)

It is instructive to visualise the operation of the amplifier on the load line. When v_in=0 the transistor is at the DC operating point Q. As v_in increases, the operating point moves up and to the left along the load line, and when v_in decreases it moves down and to the right, Figure 106. Clipping of the waveform will occur if the operating point reaches either of the extremes Q_sat or Q_cutoff.

**Figure 106:** AC movement around the DC operating point for the circuit of Figure 104.
$\begin{figure} \begin{center} \epsfig{file=images/bjtimg30.eps}\end{center}\end{figure}$

Exercise. Determine the maximum value of v_in before clipping occurs.

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