Amplifier Low-Frequency Response

By Abe Michelen

From Electronics I Laboratory Manual

A common-emitter amplifier¹ in general will include three coupling capacitors that play an important role in the low-frequency response of the system.  These capacitors are the input and output coupling capacitors² and the emitter biapass capacitor³.

Figure 19.1 shows a typical common-emitter amplifier with a source, V_s (including its source resistance, R_s) and a load, R_L.  The low-frequency response of this amplifier is determined in part by these three capacitors (C_i, C_o and C_E).  The result is essentially a combination of three high-pass filter networks that allow signals having frequencies greater than the cutoff frequency of the dominant network to pass through while attenuating all others.  This frequency is the so-called 3-dB point.  At this frequency, as you should know, the voltage is only 70.7% of the mid-frequency gain, or in decibels, it is the frequency at which the gain is 3-dB below the mid-frequency gain.
Each one of the three capacitors makes a contribution to the overall frequency response of the amplifier.  Each one behaves like the capacitor in a high–pass filter.  Therefore, each one will contribute with a cutoff frequency of its own.  The cutoff frequencies for each capacitor are given by the following equations:

fc_i  The cutoff frequency due to the input coupling capacitor, C_i, is given by

(19.1)

fC_o  The critical frequency due to the output coupling capacitor, C_o, is given by

(19.2)

fc_E  Finally, the cutoff frequency due to the emitter bypass capacitor, C_E, is

(19.3)

Note: The above equations are derived for the circuit shown in Fig. 19.1  where instead of one we have two emitter resistors.  This is called swamping re.  This is a method used to minimize the effect of rewithout reducing the voltage gain to its minimum value.  By doing this we swamp out the effect of reon the voltage gain.  Swamping is, in effect, a compromise between having a bypass capacitor across RE and having no bypass capacitor at all.

For the common-emitter amplifier shown in Fig. 19.1 the voltage gain is given by

		(19.4)

where

(19.5)

and I_E is the quiescent dc emitter current.
The voltage gain in decibels is given by the following equation

Gv = 20 log(Av) dB

(19.6)

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¹ Or basically any other type of amplifier.

² They are important if you want to keep the input and output voltages as pure ac voltages.

³ This is important to produce a high voltage gain.




Source: http://www.globalspec.com/reference/9649/359749/Amplifier-Low-Frequency-Response