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The common-emitter (CE) amplifier provides an output voltage that is 180° out of phase with the input voltage, as shown in Figure 9-1. This voltage phase shift can be explained as follows:
Since the output current is in phase with the input voltage, the input and output voltages are 180° out of phase.
 Figure 9-1. Common-emitter input and output voltages.
The ac emitter resistance (
The process used to determine the value of The ac current gain of a transistor is different than its dc current gain. This is because the two values are measured differently, as illustrated in Figure 9.4 of the text. As shown in that figure,  and  Note that transistor spec sheets list
Coupling and Bypass Capacitors Amplifiers are often cascaded (connected in series) to increase gain. Each amplifier within the cascade is referred to as a stage, and the overall circuit is referred to as a multistage amplifier. Coupling capacitors are used to provide ac coupling and dc isolation between the stages of an amplifier. They are also used to couple an amplifier to its signal source and load, as shown in Figure 9-2. The coupling capacitors prevent the source and load from affecting the dc biasing of the transistor. Note that coupling capacitors are normally high-value components that provide little reactance at the lowest operating frequency of the circuit.  Figure 9-2. Coupling and bypass capacitors.
The bypass capacitor (shown in Figure 9-2) is connected in parallel with the emitter resistor. The result of this connection is to provide an ac ground at the emitter terminal of the transistor. This has the effect of increasing the circuit voltage gain (as explained later in the chapter). Note that the bypass capacitor is normally a high-value component that provides little reactance at the lowest circuit operating frequency. The typical common-emitter waveforms are illustrated in Figure 9.10 of the text. Note that there is no change in
AC Equivalent Circuits The ac equivalent of any amplifier is derived by:
The complete process is demonstrated in Example 9.2 of the text.
Amplifier Gain Voltage gain is the factor by which ac signal voltage increases from the amplifier input to the amplifier output. Stated mathematically,
Since The ac equivalent of the amplifier in Figure 9-2 is shown in Figure 9-3. As shown in the figure, the total ac resistance in the collector circuit equals
where 
Figure 9-3. The ac equivalent of Figure 9-2.
The ac emitter resistance of the transistor ( The current gain (
Gain and Impedance Calculations If the load on an amplifier opens, the ac resistance in the collector circuit increases. As a result, the voltage gain of the circuit increases. This concept is illustrated in Figure 9.16 of the text. The input impedance of a CE amplifier equals the parallel combination of the base biasing resistor(s) and the input impedance to the transistor base. For example, the input impedance of the amplifier in Figure 9-3 is found as
where When the values of
The calculation of To calculate the total power gain of a multistage amplifier, you must first determine the values of
Multistage voltage gain calculations are demonstrated in Examples 9.11 and 9.12 of the text.
Swamped Amplifiers A swamped amplifier reduces variations in voltage gain by increasing the ac resistance of the emitter circuit. The swamped amplifier is also referred to as a gain-stabilized amplifier. A swamped amplifier is shown in Figure 9-4. The resistor labeled   Figure 9-4. A swamped (gain-stabilized) amplifier. When the amplifier is designed so that
The effect of swamping on amplifier input impedance is demonstrated in Examples 9.15 and 9.16 of the text. H-parameters Hybrid parameters, or h-parameters, are transistor characteristics that are measured under specific conditions. The four h-parameters, which are listed on most transistor spec sheets, are summarized in Table 9-1. TABLE 9-1
The parameters listed are measured as shown in Figure 9.23 of the text. The values of
When the parameters are listed as maximum and minimum values, the geometric average of the two is used. In many cases, h-parameters are provided using graphs like those shown in Figure 9.26 of the text. When using these graphs:  .The h-parameter analysis of a CE amplifier is demonstrated in Example 9.19.
Amplifier Troubleshooting There are several appoaches that can be taken to troubleshooting multistage amplifiers. One such approach is to begin at the final stage output and work back toward the input. (This approach makes sense when you consider that many electronic systems contain two or more signal paths that are combined at later stages. By working your way back from the final output, you can trace through multiple signal paths without having to test them all.) One problem that is common to CE amplifiers is nonlinear distortion. Nonlinear distortion is characterized by asymmetrical alternations of the amplifier output, as shown in Figure 9.29 of the text. Nonlinear distortion is most commonly caused by driving the transistor in an amplifier into the nonlinear operating region of its base curve.
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).
) of a transistor is a dynamic value (like zener impedance) that is used only in ac calculations. For a small-signal amplifier, the value of 
is demonstrated in Example 9.1 of the text.
as 
and 
as 
. 
, due to the presence of the bypass capacitor (which effectively shorts the ac component of the emitter voltage to ground).
, the voltage gain of a CE amplifier also equals the ratio of ac collector resistance to ac emitter resistance. 
. Since the emitter resistor is shorted in the ac equivalent circuit, the total ac emitter resistance equals 
. Therefore, the voltage gain of the amplifier can be found as
. The complete procedure for calculating the voltage gain of a CE amplifier is demonstrated in Example 9.4 of the text.
) of a CE amplifier is lower than the value of 
for the transistor, because of the current dividers in the base and collector circuits. The power gain of a CE amplifier equals the product of current gain (
). 
. Note that the value of 
is given as 
on the spec sheet of a transistor. The calculation of 
for a CE amplifier is demonstrated in Example 9.9 of the text.
for a CE amplifier is demonstrated in Example 9.10.
for each stage. Then, the total current gain (
) is found as the product of the individual stage gains. The same holds true for the total voltage gain (
). Finally, the overall power gain can be found using
is not bypassed, so it is a part of the ac equivalent circuit for the amplifier. For the circuit shown, the total ac emitter resistance is (
). 
, the effects of any change in 
on voltage gain are minimized. This principle is demonstrated in Example 9.14 of the text. Note that the addition of a swamping resistor also has the effect of increasing the base input impedance of the transistor, as given in the following relationship:
, as follows: