# What Are dB, Noise Floor & Dynamic Range?

Most engineers are probably familiar with or have come across the decibel or dB as a unit of measurement. Its most common use is in the field of acoustics where it is used to quantify sound levels. However, as will be explained in this article, it is also useful for a wide variety of measurements in other fields such as electronics and communications.

One particular use of dB is to quantify the dynamic range and accuracy of an analogue to digital conversion system. This applies to Prosig’s P8000 range of data acquisition hardware where the noise floor, dynamic range and resolution are all specified in terms of dB.

### Decibel (dB)

The decibel is a logarithmic unit of measurement that expresses the magnitude of a physical quantity relative to a reference level. Since it expresses a ratio of two quantities having the same units, it is a dimensionless unit.

### Definition

A decibel is used for the measurement of power or intensity. The mathematical definition is the ratio ($L$) of a power value ($P_1$) to a reference power level ($P_0$) and in decibels is given by:

$L_{db} = 10 log_{10}(\frac{P_1}{P_0})$

When considering amplitude levels, the power is usually estimated to be proportional to the square of the amplitude and so the following can be used:

$L_{db} = 10 log_{10}(\frac{{A_1}^2}{{A_0}^2})$

or

$L_{db} = 20 log_{10}(\frac{{A_1}}{{A_0}})$

Since the decibel is a logarithmic quantity it is especially good at representing values that range from very small to very large numbers. The logarithmic scale approximately matches the human perception of both sound and light.

Like all logarithmic quantities it is possible to multiply or divide dB values by simple addition or subtraction.

Decibel measurements are always relative to given reference levels and can therefore be treated as absolute measurements. That is, if a particular reference value is known then the exact measurement value can be recovered from one of the equations shown above.

The dB unit is often qualified by a suffix which indicates the reference quantity used, some examples are provided in the following section.

### Applications

The decibel is commonly used in acoustics to quantify sound levels relative to a reference. This may be to compare two sound sources or to quantify the sound level perceived by the human ear. The decibel is particularly useful for acoustic measurements since for humans the ratio of the loudest sound pressure level to the quietest level that can be detected is of the order of 1 million. Furthermore, since sound power is proportional to the pressure squared then this ratio is approximately 1 trillion.

For sound pressure levels, the reference level is usually chosen as 20 micro-pascals ($20 {\mu}Pa$), or 2x10-5 Pa. This is about the limit of sensitivity of the human ear.

Note that since the most common usage of the decibel unit is for sound pressure level measurements it is often abbreviated to just dB rather than the full dB(SPL).

The common decibel units used in acoustics are:

 dB(SPL) Sound Pressure Level. Measurements relative to 2x10-5 Pa. dB(SIL) Sound Intensity Level. Measurements relative to 10-12 W/m2 which is approximately the level of human hearing in air. dB(SWL) dB Sound Power level. Measurements relative to 10-12 W.

The human ear does not respond equally to all frequencies (it is more sensitive to sounds in the frequency range from 1 kHz to 4 kHz than it is to low or high frequency sounds). For this reason sound measurements often have a weighting filter applied to them whose frequency response approximates that of the human ear (A-weighting). A number of filters exist for different measurements and applications, these are given the names A,B,C and D weighting. The resultant measurements are expressed, for example, as dBA or dB(A) to indicate that they have been weighted.

In electronics and telecommunication, the decibel is often used to express power or amplitude ratios in order to quantify the gains or losses of individual circuits or components. One advantage of the decibel for these types of measurements is that, due to its logarithmic characteristic, the total gain in dB of a circuit is simply the summation of each of the individual gain stages in dB.

In electronics the decibel can also be combined with a suffix to indicate the reference level used. For example, dBm indicates power measurement relative to 1 milliwatt. The following are some common decibel units used in electronics and telecommunications.

 dBm Power measurements relative to 1mW dBW Power measurements relative to 1W. Note that LdBm = LdBW + 30 W/m2 which is approximately the level of human hearing in air. dBk Power measurements relative to 1kW.Note that LdBm = LdBk + 60 dBV Voltage measurement relative to 1V – regardless of impedance. dBu or dBv Voltage relative to 0.775V and is derived from a 600 Ohm dissipating 0dBm (1mW). dBµ Electric field strength relative to 1µV per meter. dBJ Energy relative to 1 joule. Used for spectral densities where 1 Joule = 1 W/Hz

### Examples

If the numerical value of the reference is undefined then the decibel may be used as a simple measure of relative amplitudes. As an example, assume there are two loudspeakers, one emitting a sound with a power P1 and a second one emitting the same sound at a higher power P2. Assuming all other conditions are the same then the difference in decibels between the two sounds is given by:

$10 log \left(\frac{P_2}{P_1}\right)$

If the second speaker produces twice as much power than the first, the difference in dB is

$10 log \left(\frac{P_2}{P_1}\right) = 10log2 = 3dB$

If the second had 10 times the power of the first, the difference in dB would be

$10 log \left(\frac{P_2}{P_1}\right) = 10log10 = 10dB$

If the second had a million times the power of the first, the difference in dB would be

$10 log \left(\frac{P_2}{P_1}\right) = 10log1000000 = 60dB$

Note that if both speakers produce the same power then the difference in dB would be

$10 log \left(\frac{P_2}{P_1}\right) = 10log1 = 0dB$

This illustrates some common features of the dB scale irrespective of the measurement type:

• A doubling of power is represented approximately by 3dB and a doubling of amplitude by 6dB.
• A halving of power is given by -3dB and a halving of amplitude by -6dB
• 0dB means that the measured value is the same as the reference. Note that this does not mean there is no power or signal.

### Noise floor

Any practical measurement will be subject to some form of noise or unwanted signal. In acoustics this may be background noise or in electronics there are often things like thermal noise, radiated noise or any other interfering signals. In a data acquisition measurement system the system itself will actually add noise to the signals it is measuring. The general rule of thumb is: the more electronics in the system the more noise imposed by the system.

In data acquisition and signal processing the noise floor is a measure of the summation of all the noise sources and unwanted signals generated within the entire data acquisition and signal processing system.

The noise floor limits the smallest measurement that can be taken with certainty since any measured amplitude cannot on average be less than the noise floor.

In summary, the noise floor is the level of background noise in a signal, or the level of noise introduced by the system, below which the signal that’s being captured cannot be isolated from the noise.

Figure 1

As shown in Figure 1 the noise floor is better than -120 dB.

Figure 2 shows that only signals above the noise floor can be measured with any degree of certainty. In this case the signal level of -100dB at 20KHz could be measured. If however, the noise floor increased above the -120dB level then it would become more difficult to measure this signal.

For example, it is possible for the human ear to hear a very low sound such as a pin drop or a whisper. However, this is only possible if the noise floor or background noise of the particular environment is very low such as in a soundproof or quiet room. It would not possible to hear or discriminate such low levels in a noisy room.

Figure 2

Various techniques are employed by the Prosig P8000 data acquisition system in order to ensure that the noise floor of the equipment is kept as low as possible. These include signal-processing functions as well as practical features such as the ability to disable cooling fans during acquisition scans.

### Dynamic range and resolution

Dynamic range is a term used to describe the ratio between the smallest and largest signals that can be measured by a system.

The dynamic range of a data acquisition system is defined as the ratio between the minimum and maximum amplitudes that a data acquisition system can capture.

In practice most Analogue to Digital Converters (ADC) have a voltage range of ± 10V. Sometimes amplification may be applied to signals before they are input to an ADC in order to maximize the input voltages within the available ADC range.

The resolution of a measurement system is determined by the number of bits that the ADC uses to digitise an input signal. Most ADCs have either 16-bit or 24-bit resolution. For a 16-bit device the total voltage range is represented by 216 (65536) discrete digital values. Therefore the absolute minimum level that a system can measure is represented by 1 bit or 1/65536th of the ADC voltage range. For a system with a voltage range of ±10V then the smallest voltage that the system can distinguish will be:

20 / 65536 = 0.3 mV

In decibels this dynamic range is therefore expressed as:

20 Log10 (65536) = 96dB

Therefore for a 16-bit ADC the dynamic range is 96dB. Using the same calculations the dynamic range of a 24-bit ADC is 144dB.

The noise floor of a measurement system is also limited by the resolution of the ADC system. For example, the noise floor of a 16-bit measurement system can never be better than -96dB and for a 24-bit system the lower limit is limited to -144 dB. In practice, however, the noise floor will always be higher than this due to electronic noise within the measurement system.

Modern data acquisition systems, such as the Prosig P8000, employ a number of sophisticated digital signal processing techniques to improve the amplitude resolution and thereby allow low amplitude data, such as noise floor signals, to be measured with greater precision and with greater accuracy.

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#### James Wren

Application Engineer & Sales Manager at Prosig
James Wren is an Application Engineer and the Sales Manager for Prosig Limited. James graduated from Portsmouth University in 2001, with a Masters degree in Electronic Engineering. He is a member of the Institution of Engineering and Technology. He has been involved with motorsport from a very early age with special interest in data acquisition. James is a founder member of the Dalmeny Racing team.