In Chapter 4. we studied the de, l siettc, characteristics of transistors and used these to determine the dc output voltages and currents that resulted from the application of dc inputs. We wish now to investigate ~i tent to which small changes in the input voltage and current cause changes in the corresponding output quantities. We know, for example, that increasing the input voltage (VBE) to an NPN transistor in a CE configuration will cause the input current Is to increase, which will then cause the output current lc to increase, since lc = fJ/· Likewise. decreasing the input voltage causes a decrease in output current. When the input variations are small enough to confine the variation in output voltage and current to the active portion of a transistor’s output characteristics, we say that the device is operating under small-signal conditions. More precisely. we will define small signal operation to occur when the output variations are so small that there is negligible change in the values of the device parameters (a. f3. etc., about which we will mve more to say later). Small-signal operation is studied from the standpoint of the transistor’s behavior as an DC amplifier. Before discussing the ac characteristics of transistors. we will introduce some important general concepts that apply to ail ac amplifiers.

**Amplifier Gain**

When the total change in the output voltage from a device is greater than the total change in the input voltage that caused it, the device is said to be an ac voltage amplifier. The ac Voltage gain, designated Au, is defined to be the ratio of the change in output voltage to the change in input voltage:

Thus, an ac voltage amplifier has A. > 1. Figure 5-1 illustrates the concept. Note carefully in Figure 5-1 that only the ac components of the input and output voltages are used to compute the ac voltage gain. Both the input and output signals are shown superimposed on de levels. but these de values have no bearing on the value

of the ac voltage gain. The rms values of the ac input and output components can also be used to compute Au:

Unless it is necessary to emphasize that we are referring to rms values, we will hereafter drop the rms notation, with the understanding that Vo and Vin mean rms values

AC current gain, A” is defined to be the ratio of the total output current variation to the total input current variation:

A device having A > 1 is an ac current amplifier. In general, an ac amplifier may have Au > 1, or Ai> 1, or both; in other words, it may amplify either voltage or current, or both. The power gain, Ap, is defined to be the ratio of output power to input power, and may be computed as the product of voltage gain and current gain

Although the word gain implies that there is an increase in signal level, it is possible to have a value of gain less than 1. For example, if an amplifier has a voltage gain equal to 0.5, it simply means that the ac output voltage variation is one-half that of the input. In this case, we say that the amplifier attenuates (reduces) the signal voltage applied to it.

**Input and Output Resistance**

The input resistance to an amplifier is the total equivalent resistance at its input terminals. The de input resistance, Rill, is the resistance that a de source would “see” when connected to the input terminals, and the ac resistance, ‘in, is the

resistance that an ac input source would see at the terminals. In either case, the input resistance can be computed as the ratio of mput voltage to input current:

The ac input power can be computed using any of the familiar power relations:

The output resistance of an amplifier is the total equivalent resisance at its output terminals. Output resistance is the same as the The venin equivalent resistance that would appear in series with the output if the amplifier were replaced by its The venin equivalent circuit. Like input resistance, output resistance can be defined as a de resistance Ro, or as an ac resistance, r; Output power can be computed using equation 5-6, by substituting the subscript a (out) for in in each term.

**Example 5-1**

Figure 5-2 shows the conventional symbol for an amplifier: a triangular block with output at the vertex. As shown in the figure, the input voltage to the amplifier is ViII (t) = 0.7 + 0.008 sin 103( V. The amplifier has an ac current gain of 80. If the input current is iill(t) = 2.8 X 10-5 + 4 X 10-6 sin 10Jt A, and the ac component of the output voltage is 0.4 V rms, find (1) Au. (2) Rin; (3) rill, (4) i, (rms), (5) r.; and (6) Ap.

**Solution**

1. ViII (rms) = 0.707(0.008 V-pk) = 5.66 X 10-3 V rrns

2. The de input resistance is the ratio of the de component of the input voltage to the de component of the input current:

Note that the power gain can also be computed in this example as the product of the voltage and current gains: AI’ = AvAi = (70.7)80 = 5656. The small difference

**Source Resistance**

Every signal source has internal resistance (its Thevenin equivalent resistance), which we will refer to as source resistance, rs. When a signal source is connected to the input of an amplifier, the source resistance is in series with the input resistance, r-, of th ~’P9Jinpr,Notice in Figure 5-3 thatr, and rinform a voltage divider across the input to the. amplifier. The input voltage at the ar’np~;::t:”

This example. that when ril/ = lOrs, the vol ~e ~ain is reduced by about 10% and the current gain is reduced by about 90%; when rill = 0.1rs, the voltage gain is reduced by about 90% and the current gain by about 10%.