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# Dynamics with AC input

Transistor circuit (common-emitter configuration) is commonly used for voltage amplification, as shown in the example below.

Here we assume and , and . Given the input voltage , the base current can be found by the input characteristic plot as shown below:

From the plot above we see that the voltage between B and E is a superposition of DC component and an AC component :

The resistance, the reciprocal of the slope of the curve around , is approximately . Correspondingly the base current is also a superposition of a DC component and an AC component with an amplitude :

(Why can't we get ?)

The output characteristic plot is shown below:

Note that the value is . The load line is the straight line that goes through the two points

The collector current and the output voltage can be found either algebraically or graphically:
• Find output current:

• Find output voltage:

Note:

• The AC sinusoidal component of the input voltage is amplified times.
• The sinusoidal component of the output voltage ( ) is out of phase compared to that of the input signal ( ), i.e., the CE transistor circuit is a reverse amplifier.
• If the DC component of the input voltage, and thereby, the base current is either too low or too high, the positive or negative peaks of the sinusoidal component may exceed the linear range of the output characteristic plot and sever distortion of the output voltage may result as shown below:

Switch Circuit

From the current-voltage plot of the output characteristics, we see that the operation of a transistor can be in one of the three possible regions:

• Linear region: When the input voltage is about , the transistor works in the linear range where the collector current is proportional to base current . Amplification takes place in the linear region due to this relationship.
• Cutoff region: When the input voltage (possibly negative), and is close to zero. The transistor is said to be cut off.
• Saturation region: When the input voltage is higher than , will significantly increase (due to the exponential relationship between and ). But as the maximum value of is restricted by the voltage supply and the collector and emitter resistors ( ), the linear relationship no longer holds. In this case, the transistor is said to be saturated and .
Severe distortion in output will be caused if a transistor amplification circuit is working near either the cutoff or the saturation region, as can be seen in the following sections.

Example

Assume , , . Given the input voltage or , find the output voltage .

• , the forward bias of BE PN-junction is insufficient for it to conduct current, we have , , . The transistor is cutoff (the switch is open or open-circuit).
• , the BE PN-junction is forward biased, from the input characteristics, we can find , here assumed to be , then , . The transistor is in linear region.
• , the BE junction is forward biased, from the input characteristics, we can find , here assumed to be . If the linear relationship could hold, then we have , . But this result is obviously wrong, we realize the transistor is actually in the saturation region (the switch is closed or short-circut), in which the linear relation no longer holds. In fact, it is impossible for the transistor to draw from the voltage source, as the maximum current is only . In this case, can be determined on the output characteristics to be about (intersection of load line and the curve corresponding to ), and .
Conclusion: a change in input from 0.2V to 0.8V switches the output current from 0 to about 10 mA, and the output voltage from 15V to 0.2V, and the transistor is in cut-off, linear, and saturation region, respectively. is only valid when the transistor is in the linear region.

Next: DC Biasing Up: ch4 Previous: Bipolar Junction Transistor (BJT)
Ruye Wang 2014-04-15