Peak-to-Peak, RMS Voltage, and Power

Alternating Current Defined In alternating current (ac), electrons flow back and forth through the conductor with some periodicity.

AC Vocabulary

Power Power is the ability to do work. Work is basically making something move. –Force over a distance. or –Pressure over a distance. If something doesn’t move, there is no work produced. Heat produced is also a measure of work.

Power in Electricity The force is Voltage. The things being moved are electrons. Power therefore is Voltage times Current. Power is measured in Watts.

Power in DC 12 volts pushing 2 amps = 24 W (watts) 1.5 volts pushing 300 milli amps = 450 milli W This is great for dc, but what about ac when the voltage and current are constantly changing?

Power in AC Finding the Effective Voltage The voltage used in power calculations in ac is the equivalent dc voltage value that would do the same amount of work (or heat). A simple average of ac voltage is not quite good enough. A weighted average called Root Mean Square (RMS) is more accurate.

RMS versus Simple Average

Simple Average of AC Need to consider the sign change or the average voltage will = 0. Simple average of this wave is V. The simple average does not consider the “weight” that should be given to the higher voltage segments where more work (heat) is produced.

RMS Voltage – The Equivalent DC Value “Weighted” average of the higher voltages. Takes into account the negative and positive values: Square individual values, add them up, take the average, then take the square root of the average.

RMS of Our AC Wave Root Mean Square calculation = V. The actual RMS voltage is of the peak voltage. The actual RMS of a wave with peak voltage of 1.27 V = V (not bad for rounding error). The simple average was V (10% too low).

Okay – Important Points about RMS RMS is the equivalent value of dc voltage to do the same work. RMS is used in Power and Ohms Law formulas. The RMS voltage is times the peak voltage. AC volt meters measure RMS voltage!!!!!

Converting Peak Voltage to RMS Remember:

Converting Peak Voltage to RMS Volts Peak Volts Peak-to-Peak RMS 17?? ?240? ??120

RMS to Power Convert Peak or Peak-to-Peak voltage to RMS. Then:

RMS to Power Volts Peak-to-Peak LoadPEP 20050? ? ?

Logarithms Used to deal with very large and very small numbers in electronics. Commonly used to compare input to output power (gain either positive or negative). Advantage of using logs – gain of component parts of a system are additive.

Logarithms and Anti-log The anti-log is the reverse or opposite of the log. It is sometimes handy to have the formulas for log and anti-log side by side to help keep everything straight. The variables in the two formulas represent the same values. Basic log formula: Anti-log formula

Logarithms and Anti-log

dB and Power Ratio Calculations

P1P1 P2P2 P 2 /P 1 dB --+2? --½? --?-3 --? ?? 10050?? ??