Amplifiers

The Transistor Common Emitter Amplifier

A basic transistor amplifier which has the emitter lead in common with the input and output circuits is shown below. The input voltage is between base and emitter and the output voltage between collector and emitter. The voltage V_BB is introduced into the base circuit so that the emitter-base junction is forward-biased for control of the emitter-collector current. The base-to-emitter voltage is referred to as v_be and the base current as i_b. The power supply voltage V_CC is necessary to the circuit to make the collector positive with respect to the emitter and to provide a source for the output current. The collector-to-emitter voltage and collector current are v_ce and i_c, respectively. The resistance R_L is the load. The base current of the transistor controls the current through the collector and through the load resistor.

Output Characteristic Curves

Unfortunately, the resistance of the emitter and collector junctions of transistors are not always constant. Hence, Ohm's Law cannot always be used to express the relationship between the various currents and voltages in a transistor amplifier. For this and other reasons, this information is usually supplied by the manufacturer in graphical form. The figure below shows a graph of the collector (output) characteristics for the common emitter configuration of a transistor. The graph consists of a series of curves. Each curve shows, with the base current held constant, the collector current variation as the collector-to-emitter voltage is changed.

There are particular values for i_b, v_be, i_c, and v_ce even when no signal is applied to the input. The no-signal values of i_b, v_be, i_c, and v_ce are called the quiescent, or average, values and are given the symbols I_B, V_BE, I_C, and V_CE. The point defined by I_C and V_CE on the output characteristic curve is called the quiescent point (Q). The location of the quiescent point on the characteristic curve is an important part of the analysis of an amplifier circuit. The procedure is as follows: First a "load line" is determined for the values of supply voltage V_CC and load resistance R_L which are to be used in the amplifier circuit. Assume that i_b is so small that the collector current i_c = 0. If this were true, the voltage drop across R_L would be zero and v_ce would equal V_CC. This point 1 is plotted on the output characteristic curve (figure above). Then it is assumed that the base current is so large that the transistor becomes a perfect conductor so that v_ce = 0 and i_c = V_CC/R_L. Plot this point 2 on the characteristic curve, and join points 1 and 2 with a straight line as in the figure above. This line is called the load line because it is determined only by the values of the load and V_CC.

For the selected values of V_CC and R_L the resulting values of v_ce and i_c must fall along the load line. The figure above, point Q, shows the no-signal values for V_CE and I_C as determined by the load line and the output characteristic for the selected average base current I_B = 100 µA. The instantaneous base current i_b depends on the sum of base bias current and input signal, and, by moving along the load line, the instantaneous values of v_ce and i_c can be read from the graph for any given value of i_b.

Note that the load line should fall well within the maximum collector-dissipation line. The maximum collector dissipation P_max is a characteristic of the transistor and is usually given in the transistor manuals or catalog descriptions. The maximum collector-dissipation line is drawn by connecting all the points which satisfy the equation I_CV_CE = P_max. The quiescent base current can be estimated by assuming that the base-to-emitter junction is simply the transistor input resistance h_ie. If v_s = 0 (quiescent state), I_B = V_BB/(R_S +h_ie). Often R_S will be very much greater than h_ie so that I_B ≈ V_BB/R_S. Thus the choice of bias voltage will depend on the nature of the signal source. Other methods of biasing will be discussed later.

Transistor Amplifier Characteristics

The change in v_ce or i_c as a result of an input signal (a change in i_b) could be determined by a graphical analysis of the characteristic curves as above for each value of i_b. However, it is much more convenient to analyze the circuit mathematically after substituting an equivalent circuit for the transistor. It is not possible to derive a simple circuit which would replace the transistor for its entire operating range. This is because the characteristic curves of the transistor are not linear, as shown e.g. in the figure above. A linear equivalent circuit is only a valid approximation over small portions of the operating range. In other words, the equivalent circuit will not describe the relationship of the total quantities i_b, v_be, i_c, and v_ce, but it will describe the relationship of the small changes in these quantities. Equations for the various amplifier characteristics may be derived from the equivalent circuit and the mathematical relations used to obtain that circuit. Some of the characteristics (e.g. the voltage and current gains) of the common-emitter amplifier are given below. The actual derivations are not shown here.

The voltage gain could be approximated by the equation

where β is the transistor current gain and h_ie is the transistor input resistance in the common-emitter circuit. The minus sign indicates that the output voltage is 180° out of phase from the input voltage.

The current gain A_i is approximately

Again the minus sign is an indication of the phase reversal between the input and output signals.

The power gain A_p is simply the product of the current and voltage gains

The power gain does not include power losses in the signal source or in transferring the output signal to a load other than R_L. It is simply the ratio of the signal power dissipated in R_L to the signal power dissipated in the transistor input resistance h_ie.

The input resistance R_in is

The output resistance R_out could be approximated by the equation

where h_oe is the conductance between the collector and emitter. As this equation indicates, the output resistance R_out is in this case the resistance that the transistor as a power source presents to the load R_L. The output resistance of the entire amplifier circuit as seen by a device attached to the output terminals v_ce would actually be R_out in parallel with R_L.

The common-emitter amplifier is thus shown to possess the properties of voltage gain, current gain, phase reversal of the input signal, low input resistance, and high output resistance.

Transistor Biasing

The use of a separate power source for the input and output circuits of the transistor amplifier is costly and inconvenient. Methods of providing the proper bias voltages from a single power source have, therefore, been devised. One of the most widely used bias systems is the voltage-divider type shown in the figure below (see the Types of Bias section for more info). Fixed bias is provided in this circuit by the voltage-divider network consisting of R_B1, R_B2, and the collector supply voltage (V_CC). Resistor R_E, which is connected in series with the emitter, provides the emitter with self-bias. A large capacitor bypassing R_E will alleviate the loss in gain for AC signals.

Quiescent Point Determination

After it has been concluded that widely used transistor amplifiers could have a resistance in the emitter circuit and a voltage divider in the base, it is suitable to learn how to determine the quiescent point for such circuits. First, the load line is drawn in the usual way (see the graph of output characteristics above), care being taken to use R_E + R_L in calculating the current for V_CE = 0. Now the circuit of figure above is redrawn considering the voltage divider as a series battery V_BB and resistor R_B (see Thevenin's theorem). It is first approximated that the emitter and the base have very nearly the same potential (V_E = V_B ≈ V_BB) and that I_E is very nearly I_C. Therefore, I_C ≈ V_BB/R_E. Looking at the load line to find the value of I_B corresponding to this value of I_C, one can improve on the approximation by correcting the base voltage to V_BB - I_BR_B. Use this value of the base voltage to calculate a better value for I_C. Usually this second approximation is sufficiently accurate.

Example of Transistor Bias Design

An example of how to go about determining reasonable resistance values for a transistor-amplifier circuit is given here. First, choose the desired quiescent point from the transistor's collector-characteristic curve. Evaluate from the characteristics or look up values for β, h_ie, and h_oe in datasheets. Assume that, at the desired quiescent point (I_C = 1 mA, V_CE = 5 V), β = 55, h_ie = 2720 Ω, and h_oe = 14 μS. Choose R_L according to gain requirements and impedance matching, high values for current gain, moderate values for voltage gain with moderate output impedance. For this example R_L = 25 kΩ. R_B should be larger than h_ie to prevent excessive signal loss through the bias divider. Therefore, choose R_B = 25 kΩ. For good stability choose R_E = R_B/5 = 5 kΩ. The required DC supply voltage is then (assuming I_E ≐ I_C)

The bias voltage V_BB should equal the base voltage plus the voltage drop I_BR_B. V_BB is thus

where V_BE = 0.7 for silicon transistors. V_BB can also be calculated as

Parallel combination of R_B1 and R_B2 is R_B

Solving the two previous simultaneous equations for the bias resistors, R_B1 = 142 kΩ and R_B2 = 30.3 kΩ. The formulas derived previously for the voltage- and current-gain of the transistor amplifier apply also to this circuit. The amplifier output resistance is 1/h_oe in parallel with R_L. The amplifier input resistance is h_ie in parallel with R_B.

Note: The current through the voltage divider R_B1, R_B2 should be at least 10 × I_B. In our case the current through R_B2