Question

a signal goes through two amplification stages. the first stage has a gain of A₁=75 v/v, and the second has a gain of A₂=14 v/v. find the total gain and express it in db.

Answer 1

The total gain of the signal going through two amplification stages is 1050 v/v and can be expressed as approximately 60.66 dB.

Step-by-step explanation:

To find the total gain of the signal going through two amplification stages, we can multiply the gains of each stage together. In this case, the first stage has a gain of A₁=75 v/v, and the second stage has a gain of A₂=14 v/v. Therefore, the total gain is A₁ × A₂ = 75 × 14 = 1050 v/v.

To express the total gain in dB, we can use the formula: Gain(dB) = 20 × log₁₀(Gain).

Using this formula, we can calculate the total gain in dB: Gain(dB) = 20 × log₁₀(1050) ≈ 60.66 dB.

When a signal goes through two amplification stages with gains A₁ = 75 v/v and A₂ = 14 v/v respectively, the total gain (Atotal) is the product of the two gains, which gives Atotal = A₁ × A₂ = 75 × 14 = 1050 v/v.

To express this total gain in decibels (dB), the formula 20 × log₁₀(Atotal) is used. Therefore, the total gain in dB is 20 × log₁₀(1050) ≈ 60.4 dB.