**Low Frequency Response of BJT Amplifier:**

For analysis, we will consider the loaded voltage-divider BJT bias configuration. But the results can be applied to any configuration. For the network shown in Fig. 15.14 the capacitors C_{in}, C_{out} and C_{E} will determine the low frequency response of BJT Amplifier.

Now we will examine the impact of each independently.

**Effect of C**_{in} on Frequency Response of Amplifier:

_{in}on Frequency Response of Amplifier:

Since C_{in} is normally connected between the applied source and the active device, the general form of the R-C combination is established by the network shown in Fig. 15.15.

The total resistance is now (R_{s} + R_{in}) and the cutoff frequency is

At mid or high frequencies, the reactance of the capacitor C_{in} will be considerably small to allow a short-circuit approximation for the element. The relation between V_{in} and V_{s} is given as

At f_{Li}, input voltage V_{in} will be 0.707 times the value determined by above Eq. (15.38), assuming that C_{in} is the only capacitive element that controls the Low Frequency Response of BJT Amplifier.

For the network given in Fig. 15.14, in analysis of the effects of C_{in}, we must assume that the capacitors C_{E} and C_{out} are performing their de-signed function or the analysis becomes too unwieldy, that is, that the magnitudes of the reactances of C_{out} and C_{E }allow using a short-circuit equivalent as compared to the magnitude of the other series impedances. Using this hypothesis, the ac equivalent network for the input section of the circuit shown in Fig. 15.14 will become as shown in Fig. 15.16.

The value of R_{in} is given by the equation

The voltage V_{in} applied to the input of device can be determined by using voltage-divider rule and is given as

Thus with the decrease in frequency, the reactance of the capacitor C_{in} increases, some of the signal or source voltage is lost across the input capacitor C_{in} and the voltage V_{in} applied to the input of the device is reduced resulting in decrease in output voltage and hence the gain.

**Effect of C**_{out }**on Frequency Response of Amplifier****:**

_{out }

Since the output capacitor is normally connected between the output of the active device and the load, the R-C configuration determining the lower cutoff frequency due to C_{out} will appear as given in Fig. 15.17. From Fig. 15.17, the total series resistance is now R_{out} + R_{L} and the cutoff frequency due to C_{out} is given by equation

Ignoring the effects of C_{in} and C_{E}, the output voltage will be 70.7% of its midband value at f_{Lo}. For the network shown in Fig. 15.14, the ac equivalent network for the output section with V_{in} = 0, will appear as shown in Fig. 15.18.

The value of R_{out} is given by the equation

**Effect of C**_{E }on Frequency Response of Amplifier:

_{E }on Frequency Response of Amplifier:

For determination of frequency f_{Le}, the network “seen” by C_{E }must be determined as illustrated in Fig. 15.19.

Once the level of R_{e} is determined, the cutoff frequency due to C_{E} can be computed from the relation

For the network shown in Fig. 15.14, the ac equivalent as ‘seen’ by C_{E }will be as given in Fig. 15.20.

The value of R_{e} is given by the equation

where R′_{s} = R_{s} || R_{1} || R_{2}

The effect of C_{E} on the gain is best described in a quantitative manner by recalling that the gain for the configuration shown in Fig. 15.21 is given as

The maximum gain will obviously be for R_{E} = 0 Ω. At low frequencies, with the bypass capacitor C_{E} is its “open-circuit” equivalent state, all of R_{E} appears in the above voltage gain equation, resulting in minimum gain.

With the increase in frequency, the reactance of capacitor C_{E} decreases, reducing the parallel impedance of R_{E} and C_{E} until the resistor R_{E} is effectively “shorted out” by C_{E}. The result is a maximum or midband gain given by equation A_{v} = -R_{C}/r_{e}. At f_{LE} the gain will be 3 dB down the midband value determined with R_{E} “shorted out.”