Practice problems

Decibel practice problems

A decibel turns a ratio into a number you can add: +20 dB is ten times the voltage, −3 dB is half the power. These ten problems turn power and voltage ratios into decibels and back, add up a chain of gains, and finish with what −3 dB does to a real signal. Type your answer to check it, and open the working whenever you want it.

The method

dB = 20 × log₁₀(V_out ÷ V_in)

dB = 10 × log₁₀(P_out ÷ P_in)

Voltage ratios use 20 log, power ratios use 10 log
Each ×10 in voltage is +20 dB, each ×2 is about +6 dB, and ×0.707 is −3 dB
Multiply ratios, add decibels: stages in a row add, and losses count as negative
A ratio below 1 is a loss, a negative number of dB

The problems

Type your answer and tap Check. Every one has the working, step by step.

Problem 1 of 10
An amplifier makes a signal's voltage 100 times bigger. What is its gain in decibels?
Show the working
1. For a voltage ratio, dB = 20 × log₁₀(ratio). Each ×10 is +20 dB.
2. 20 × log₁₀(100) = 20 × 2 = 40 dB
Answer: 40 dB
Problem 2 of 10
An amplifier makes a signal's power 1000 times bigger. What is its gain in decibels?
Show the working
1. For a power ratio, dB = 10 × log₁₀(ratio). Each ×10 in power is +10 dB.
2. 10 × log₁₀(1000) = 10 × 3 = 30 dB
Answer: 30 dB
Problem 3 of 10
A microphone preamp gives +26 dB, the cable after it loses 2 dB, and a power amp adds +18 dB. What is the total gain?
Show the working
1. Stages in a row multiply their ratios, so their decibels add. A loss counts as negative.
2. 26 dB − 2 dB + 18 dB = 42 dB
Answer: 42 dB
Problem 4 of 10
A filter lets through half the power it gets. What is that in decibels?
Show the working
1. It's a power ratio, so use 10 × log₁₀.
2. 10 × log₁₀(0.5) ≈ 10 × −0.301 ≈ −3.01 dB, the −3 dB point you'll see on every filter.
Answer: −3.01 dB
Problem 5 of 10
An attenuator leaves 0.2 of the voltage it gets. What is that in decibels?
Show the working
1. It's a voltage ratio, so use 20 × log₁₀. A ratio below 1 gives a negative number: a loss.
2. 20 × log₁₀(0.2) ≈ 20 × −0.699 ≈ −14 dB. Check with the table: ÷10 is −20 dB and ×2 is +6 dB, so ×0.2 is −20 + 6 = −14 dB.
Answer: −14 dB
Problem 6 of 10
An amplifier has a voltage gain of 400. What is that in decibels?
Show the working
1. Split it into ratios from the table: 400 = 100 × 2 × 2.
2. ×100 is 40 dB and each ×2 is 6 dB, so 40 + 6 + 6 = 52 dB.
3. On a calculator, 20 × log₁₀(400) ≈ 52.04 dB.
Answer: 52 dB
Problem 7 of 10
A stage has a voltage gain of 46 dB. What voltage ratio is that?
Show the working
1. Split the decibels into ones from the table: 46 = 20 + 20 + 6.
2. Decibels add, so ratios multiply: ×10 × ×10 × ×2 = ×200.
3. On a calculator, 10 to the power 46 ÷ 20 is about 199.5, so the ratio is about 200.
Answer: 200
Problem 8 of 10
A low-pass filter passes 2 V at low frequencies. At its −3 dB cutoff, what voltage comes out?
Show the working
1. −3 dB is a voltage ratio of about 0.707: half the power.
2. 2 V × 0.707 ≈ 1.41 V
Answer: 1.41 V
Problem 9 of 10
A 50 mV signal goes through an amplifier with 32 dB of voltage gain. What voltage comes out?
Show the working
1. 32 dB = 20 + 6 + 6, so the ratio is about 10 × 2 × 2 = 40. Exactly, 10 to the power 32 ÷ 20 is 39.8.
2. V_out = 50 mV × 39.8 ≈ 1990 mV, which is 1.99 V.
Answer: 1.99 V
Problem 10 of 10
Stretch: an amplifier turns 50 mW of input power into 4 W of output power. What is its power gain in decibels?
Show the working
1. Get both powers in the same unit first: 4 W = 4000 mW, so the ratio is 4000 mW over 50 mW = 80.
2. It's a power ratio, so use 10 × log₁₀.
3. 10 × log₁₀(80) ≈ 10 × 1.903 ≈ 19.0 dB
Answer: 19 dB

Build it in a free lesson

“Decibels and Bode plots” is lesson 5 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 25 before it first.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Decibels and Bode plots” is lesson 5 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 25 before it first.

Or start from the very first lesson, no account needed

Check it with a calculator

The ideas behind it

Questions people ask

When do I use 10 log and when 20 log?

Use 10 × log₁₀ for a power ratio and 20 × log₁₀ for a voltage or current ratio. Power goes with voltage squared, so both give the same dB for the same circuit: doubling the voltage is +6 dB, and that quadruples the power, which is also +6 dB.

Why do decibels add when gains multiply?

A logarithm turns multiplying into adding. So a chain of stages, whose ratios multiply, has a total gain in dB that's just the sum of each stage's dB. Losses count as negative, which is why engineers add up a whole chain with simple sums.

What does −3 dB mean?

Half the power, or about 0.707 of the voltage. Filters and amplifiers quote their bandwidth to the −3 dB points: the frequencies where the output has fallen to 0.707 of its full value.