G5B

Decibels, power and RMS

Use dB ratios, add parallel currents, calculate power, and convert between RMS, peak and peak-to-peak to find PEP.

14 pool questions1 on the exam

Syllabus: The decibel; current and voltage dividers; electrical power calculations; sine wave root-mean-square (RMS) values; PEP calculations

3 dB doubles power. 1 dB loses about a fifth.

Decibels compare power as a ratio. +3 dB is two times the power, −3 dB is half. Losses compound: a loss of 1 dB leaves about 79 % of the power, so about 20.6 % is gone.

Every +3 dB roughly doubles power. Every +10 dB multiplies it by 10.

Gain or loss+3 dB

Power in

Loss in dB, power left over. 1 dB loss is about 20.6 % of the power gone.

Loss1 dB

Power lost20.6%

Remember3 dB = ×2 power. 1 dB loss = 20.6 % of the power lost.

Parallel branches: same voltage, currents add

Every branch sees the full source voltage and draws its own current, I = E ÷ R. The source supplies the sum. The smaller resistor takes the bigger share, which is how a current divider splits current. Across series parts, voltage divides instead, with the larger resistor getting the bigger share.

Each branch takes its own current. The source supplies all of them added up.

Branches

Source voltage12 V

RememberTotal current = sum of the branch currents. More branches means more total current.

Power: pick the formula for what you know

Power is P = E × I. Ohm's law (E = I × R) gives two more forms when one of E or I is missing.

Know two things, pick the formula that uses exactly those two.

You know

Voltage (E)400 VResistance (R)800 Ω

You know	Formula	Result
12 V, 0.2 A	P = E × I	2.4 W
400 V, 800 Ω	P = E² ÷ R	200 W
7 mA, 1,250 Ω	P = I² × R, with I = 0.007 A	61 mW
1,200 W, 50 Ω	E = √(P × R)	245 V

Memory hookConvert milliamperes to amperes first, then square.

RMS is the heating value: 0.707 of peak

An AC signal swings between its peak values. Its RMS value heats a resistor exactly like the same DC voltage. For a sine wave:

RMS is the DC-equivalent heating value: 0.707 × peak.

You know the

RMS voltage120 V

RememberRMS = 0.707 × peak. Peak = 1.414 × RMS. Peak-to-peak = 2 × peak.

PEP: power at the crest of the signal

Peak envelope power (PEP) is the power at the highest point of the signal's envelope. A scope reads peak-to-peak, so convert to RMS, then use E² ÷ R.

Four steps from the scope reading to watts.

Signal

Peak-to-peak voltage (50 Ω load)200 V

An unmodulated carrier never changes amplitude, so its PEP equals its average power: ratio 1.00.

RememberPeak-to-peak ÷ 2 × 0.707 = RMS. Then P = E² ÷ R. Steady carrier: PEP = average.

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