Low frequency analysis of amplifier to obtain lower cut-off frequency

Low frequency analysis of amplifier to obtain lower cut-off frequency:

1. Decibel Unit:

The decibel is a logarithmic measurement of the ratio of one power to another or one voltage to another. Voltage gain of the amplifier is represented in decibels (dBs). It is given by,

Voltage gain in dB = 20 log A_v

Power gain in decibels is given by,

Power gain in dB = 10 log A_p

Where A_v is greater than one, gain is positive and when A_v is less than one, gain is negative. The positive and negative gain indicates that the amplification and attenuation respectively. Usually the maximum gain is called mid frequency range gain is assigned a 0 db value. Any value of gain below mid frequency range can be referred as 0 db and expressed as a negative db value.

Example:

Assume that mid frequency gain of a certain amplifier is 100. Then, Voltage gain = 20 log 100 = 40 db

At f₁ and f₂ A_v = 100/√2 = 70.7

Voltage gain at f₁ = Voltage gain at f₂ = 20 log 70.7 = 37 db

From above figure, it shows that the voltage gain at f₁ and f₂ is less than 3db of the maximum voltage gain. Due to this the frequencies f₁ and f₂ are also called as 3 db frequencies. At f₁& f₂ power gain drops by 3 db. For all frequencies within the bandwidth, amplifier power gain is at least half of the maximum power gain. This bandwidth is also referred to as 3 db bandwidth.

2. Significance of octaves and decades:

The octaves and decades are the measures of change in frequency. A ten times change in frequency is called a decade. Otherwise, an octave corresponds to a doubling or halving of the frequency.

Example:

An increase in frequency from 100 Hz to 200 Hz is an octave.

A decrease in frequency from 100 kHz to 50 kHz is also an octave

At lower and higher frequencies the decrease in the gain of amplifiers is often indicated in terms of db/decades or db/octaves. If the attenuation in gain is 20 db for each decade, then it is indicated by line having slope of 20 db/decade. A rate of -20 db/decade is approximately equivalent to -6db/octave. A rate of -40 db/decade is approximately equivalent to -12db/octave.

3. Midband gain:

It is defined as the band of frequencies between 10 f₁ and 0.1 f₂. It is denoted as midband gain or A_mid.

The voltage gain of the amplifier outside the midband is approximately given as,

Problem:

For an amplifier, midband gain = 100 and lower cutoff frequency is 1 kHz. Find the gain of an amplifier at frequency 20 Hz.

Solution:

Below midband: