PeaktoPeak RMS Voltage and Power Alternating Current Defined

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 0. 809 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 = 0. 9006 V. • The actual RMS voltage is 0. 707 of the peak voltage. • The actual RMS of a wave with peak voltage of 1. 27 V = 0. 897 V (not bad for rounding error). • The simple average was 0. 809 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 0. 707 times the peak voltage. • AC volt meters measure RMS voltage!!!!!

Converting Peak Voltage to RMS Remember:

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

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

RMS to Power Volts. Peak-to-Peak Load PEP 200 50 ? ? 50 100 75 ?

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 • Basic log formula: • Anti-log formula • 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.

Logarithms and Anti-log

d. B and Power Ratio Calculations

d. B and Power Ratio Calculations P 1 100 100 P 2 500 50 2000 P 2/P 1 +2 ½ ? ? ? d. B ? ? -3 +3 ? ? ?