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| Page last updated on:
Sunday, January 15, 2012
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The term ‘RMS’ (root-mean-square) is often encountered in electronics publications. It is the value of a voltage or current waveform, which results in the same power being dissipated in a resistive load. For example, a 240V RMS AC waveform, no matter what its shape, will cause the same power dissipation in a resistor as 240Vdc.
The table below shows the relationship between the RMS and average values for three common waveforms for which the peak value is known. Multiplying the peak value by the factors given in the table will yield the RMS and average values.
Strictly speaking, the average value of a waveform, which is symmetrical about the zero axis, is zero. However, we often need to know the average of the absolute value of a waveform, and this is the value, which the table factors will yield.
Most test equipment does not directly measure RMS values. Meters typically measure average values but are scaled to provide the RMS value of a sine wave. Knowing this, we can convert the indicated reading back to the average value and then convert this to the true RMS value as long as we know the shape of the measured waveform.
| Waveshape |
Multiplying factor to convert peak value to: |
| |
RMS |
Average |
| Sine |
0.707 |
0.637 |
| Square |
1 |
1 |
| Triangle/sawtooth |
0.577 |
0.5 |
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Conversions
| Angstroms/Nanometer |
10 |
| millimetres/inch |
25.4 |
| centimetres/foot |
30.48 |
| metres/yard |
0.914 |
| kilometres/mile |
1.609 |
| grams/ounce |
28.35 |
| kilograms/pound |
0.454 |
| litres/pints |
0.567 |
| litres/gallon |
4.54 |
| litres/cubic foot |
28.32 |
| Joules/Electron Volt |
1.60210x10-19 |
| Watts/Horsepower |
746 |
| Coulombs/Amps Hour |
3600 |
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Temperature conversion
ºC = 5/9 ( ºF-32)
ºF = 32+9/5 ºC
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Handy Constants
| Natural logarithm base |
e |
2.71828 |
| In (x)/log (x) |
|
2.3026 |
| Pi |
( |
3.14159265 |
| Pi (for Basic Programmers) |
ð |
4 x ATN |
| 0dBm |
|
1mW |
| 0dBm voltage in 600 ohms |
|
774.6mV |
| 0dBm voltage on 50 ohms |
|
223.6V |
| DBSPL reference level |
|
20uPa |
| Charge on electron |
e |
1.60210x10-19C |
| Absolute zero |
0K |
-273.16º C |
| Speed of light in Vacuum |
c |
2.997925x108ms-1 |
| Speed of Sound |
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-In air
@ 0 ºC |
|
331.6ms-1 |
-In air
@ 20 ºC |
|
343ms-1 |
-In fresh water
@ 20 ºC |
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1481ms-1 |
-In sea water
@ 13 ºC |
|
1500ms-1 |
Density of air
@ 20 ºC p0 |
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1.293kgm-3 |
Contrary to much popular usage, the decibel (dB) is not actually a unit of any particular quantity, but rather an expression of the ratio between two quantities, such as power, voltage, current and acoustic pressure.
Many sensors, including our own ears respond to stimuli in a logarithmic fashion, allowing them to detect a huge range of intensities. As the dB compares the logarithms of quantities, it agrees with our perceptive comparisons.
To calculate the ratio, in dB, of two power levels, P1 and P2, the formula is:
dB = 10log (P1/P2)
If the quantities are voltages, currents or sound pressure levels, X1 and X2, the formula becomes:
dB = 20log (X1/X2)
If the quantities X1 and X2 are both measured in the same impedances, their dB ratio will be numerically equal to the dB ratio of their equivalent powers. If their impedances Z1 and Z2 are unequal, the dB ratio of their power can be found from:
dB = 20log (X1/X2) + 10log (Z2/Z1)
Negative dB values result when P1 (or X1) is less than P2 (or X2), while positive values indicate that P1 (or X1) is greater than P2 (or X2). Although the dB is not an absolute unit, certain absolute units using the dB scale have been devised. These include dBuV, dBm and dBSPL. dBuV is a logarithmic expression of a voltage compared to 1µV (microvolt). Thus 76dBµV is equivalent to 6.31mV (millivolts). dBm is an expression of a power level compared to 1mW (milliwatt). -20dBm is therefore equivalent to 10µW. Furthermore, because the unit of power, 0dBm represents 775mV in a 600 Ohm impedance but 224mV in a 50 Ohm impedance.
dBSPL is a measure of sound pressure level.
Although usually referred to 20.4µPa (micropascals), other reference levels may be specified. Using 20µPa as a reference, 1 Pascal equates to 93.8dBSPL.4 |
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Re-printed by kind permission of Maplin Electronics
Good Guides - Main Index
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