Low-Frequency Response of Amplifiers

Voltage-divider BJT amplifier configuration

The various capacitors which effect the response of the voltage-divider BJT amplifier configuration in the low-frequency region are as follows.
Effect of Input Coupling Capacitor: Ci is the input-coupling capacitor and is connected between the applied input source and the active device. The capacitor Ci forms an RC network as shown in figure below.

Determining the effect of input-coupling capacitor on the low-frequency response

R_i is the input resistance of the amplifier as seen by the source and is given by parallel combination of R₁, R₂ and hie.

The voltage V_i applied to the input of the active device is calculated by using the voltage-divider rule. Therefore, voltage V_i is given by

At mid- and high frequencies the reactance of capacitors C_i and C_o will be sufficiently small to permit a short-circuit approximation. Therefore, the input voltage at mid-band frequencies (V_i-mid) is given by

The cut-off frequency established by the capacitor Ci is given by

At f_LCi the voltage V_i will be 0.707 times the voltage V_i-mid assuming that C_i is the only capacitive element effecting the low-frequency response. Effect of the Output-Coupling Capacitor: Co is the output-coupling capacitor and is connected between the output of the active device and the active load. Figure below shows the simplified configuration highlighting the effect of Co on the low-frequency response of the amplifier.

Determining the effect of output-coupling capacitor on the low-frequency response

R_o is the total output resistance and is given by

The cut-off frequency as established by C_o is given by

The output voltage Vo will be 70.7% of its mid-band value at the frequency f_LCo assuming that Co is the only capacitive element controlling the low-frequency response. Effect of Bypass Capacitor: Figure below shows the network as seen by the bypass capacitor C_E.

Determining the effect of bypass capacitor on the low-frequency response

The value of the equivalent resistance R_e is given by

where,

The cut-off frequency as established by resistance R_e and capacitor C_E is given by

The input- and the output-coupling capacitors and the bypass capacitors affect only the low-frequency response. At the mid-band frequency range, they are considered as short-circuit equivalent and do not affect the gain at these frequencies.

If the lower cut-off frequencies offered by the different capacitors are far apart, then the highest cut-off frequency due to the capacitors essentially determines the lower cut-off frequency of the entire system. If the individual lower cut-off frequencies are near to each other, then the effect will be to raise the lower cut-off frequency of the entire system, that is, there is an interaction between the capacitive elements resulting in increased overall lower cut-off frequency for the entire system.

In the case of FET amplifiers also, there are three capacitors that affect the low-frequency response, namely, the coupling capacitor Ci between the source and the FET, the coupling capacitor Co between the active device and the load and the source capacitor C_S.

JFET-based amplifier

The lower cut-off frequencies due to coupling and the source capacitors is given below. Effect of Input-Coupling Capacitor: Figure below shows the equivalent network seen by the input-coupling capacitor C_i.

Determining the effect of input-coupling capacitor on the low-frequency response

The cut-off frequency as determined by the capacitor C_i is given by

In most of the applications, the value of resistor R_G is much larger than the value of the resistor Rsignal. Therefore, the low-cut off frequency (f_LCi) is primarily determined by the values of resistor R_G and capacitor C_i. Effect of Output-Coupling Capacitor: Figure below shows the network as seen by the output-coupling capacitor.

Determining the effect of output-coupling capacitor on low-frequency response

The output resistance (R_o) is determined by

The resulting cut-off frequency f_LCo is given by

Effect of Source Capacitor: The equivalent network seen by the source capacitor C_S is shown in figure below.

Determining the effect of source capacitor on the low-frequency response

The equivalent resistance as seen by the capacitor CS is given by

As the value of resistance rd is very large, assuming rd =∞ we get

The cut-off frequency due to the capacitor C_S is defined as