Consider a voltage amplifier having a frequency response of the single-pole low pass filter with a dc gain of 60 dB and 3 dB frequency of 1000 Hz. Find its gain at 1 MHz

Concept:

For all stable circuits and systems, the product of Gain and Bandwidth is constant always.

Gain × Bandwidth = Constant

The gain in dB is represented as:

Gain (dB) = 20 log₁₀ (Gain)

Calculation:

Given specifications for amplifier are

Gain₁ = 60 dB at 1000 Hz

20 log₁₀(Gain₁) = 60

log₁₀(Gain₁) = 3

Gain₁ = 10³

Case (i): At 1000 Hz

Gain₁ × Bandwidth = 10³ × 1000 Hz

= 10⁶

Case (ii): At 1 MHz

Since the gain bandwidth product is always constant, we can write:

Gain₂ × 1 MHz = 10⁶

Gain₂ × 10⁶  = 106

Gain₂ = 1

In dB, this gain will be:

Gain₂ (dB) = 20 log(1)

Gain2 (dB) = 0 dB

∴ The Gain at 1 MHz is 0 dB