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 ACFinding 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

00.22 0.44 0.64 0.82 0.98 1.11 1.21.241.27

1.24

1.2

1.11

0.98

0.82

0.64

0.44

0.22

0-0.22

-0.44

-0.64

-0.82

-0.98

-1.11

-1.2

-1.26

-1.28

-1.26

-1.2

-1.11

-0.98-0.82 -0.64 -0.44 -0.22

0

-2

-1.5

-1

-0.5

0

0.5

1

1.5

21 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

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.

N

VRMS

N

0

2

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

RMSPeak VV 414.1

PeakPeak

RMS VV

V 707.414.1

PeakPtoP VV 2Remember:

Converting Peak Voltage to RMS

VoltsPeak VoltsPeak-to-Peak RMS

17 ? ?

? 240 ?

? ? 120

RMS to Power

• Convert Peak or Peak-to-Peak voltage to RMS.

• Then:

R

VPEP RMS

2

RMS to Power

VoltsPeak-to-Peak Load PEP

200 50 ?

? 50 1000

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

• 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

LN 10log

LN 10

Logarithms and Anti-log

1

2log10 P

PdB

NL log

NL 10

dB and Power Ratio Calculations

1

2log10 10 P

PdB

10101

2 dB

P

PePowerChang

dB and Power Ratio Calculations

P1 P2 P2/P1 dB

- - +2 ?

- - ½ ?

- - ? -3

- - ? +3

100 500 ? ?

100 50 ? ?

100 2000 ? ?