## The Decibel Measurement System

Because of the use of the decibel measurement system in the following paragraphs, you will be introduced to it at this point. Technicians who deal with communications and radar equipment most often speak of the gain of an amplifier or a system in terms of units called DECIBELS (dB). Throughout your electronics career you will use decibels as an indicator of equipment performance; therefore, you need to have a basic understanding of the decibel system of measurement.

Because the actual calculation of decibel measurements is seldom required in practical applications, the explanation given in this module is somewhat simplified. Most modern test equipment is designed to measure and indicate decibels directly which eliminates the need for complicated mathematical calculations. Nevertheless, a basic explanation of the decibel measurement system is necessary for you to understand the significance of dB readings and equipment gain ratings which are expressed in decibels.

The basic unit of measurement in the system is not the decibel, but the bel, named in honor of the American inventor, Alexander Graham Bell. The bel is a unit that expresses the logarithmic ratio between the input and output of any given component, circuit, or system and may be expressed in terms of voltage, current, or power. Most often it is used to show the ratio between input and output power. The formula is as follows: The gain of an amplifier can be expressed in bels by dividing the output (P1) by the input (P2) and taking the base 10 logarithm of the resulting quotient. Thus, if an amplifier doubles the power, the quotient will be 2. If you consult a logarithm table, you will find that the base 10 logarithm of 2 is 0.3; so the power gain of the amplifier is 0.3 bel. Experience has taught that because the bel is a rather large unit, it is difficult to apply. A more practical unit that can be applied more easily is the decibel (1/10 bel). Any figure expressed in bels can easily be converted to decibels by multiplying the figure by 10 or simply by moving the decimal one place to the right. The previously found ratio of 0.3 is therefore equal to 3 decibels.

The reason for using the decibel system when expressing signal strength may be seen in the power ratios in the table below. For example, to say that a reference signal has increased 50 dB is much easier than to say the output has increased 100,000 times. The amount of increase or decrease from a chosen reference level is the basis of the decibel measurement system, not the reference level itself. Whether the input power is increased from 1 watt to 100 watts or from 1,000 watts to 100,000 watts, the amount of increase is still 20 decibels.

Source Level in (dB) to Power Ratio

1 = 1.3

3 = 2.0

5 = 3.2

6 = 4.0

7 = 5.0

10 = 10 = 10 to the 1st power

20 = 100 = 10 to the 2nd power

30 = 1000 = 10 to the 3rd power

40 = 10,000 = 10 to the 4th power

50 = 100,000 = 10 to the 5th power

60 = 1,000,000 = 10 to the 6th power

70 = 10,000,000 = 10 to the 7th power

100 = 10 to the 10th power

110 = 10 to the 11th power

140 = 10 to the 14th power

Examine the information above again, and take particular note of the power ratios for source levels of 3 dB and 6 dB. As the table illustrates, an increase of 3 dB represents a doubling of power. The reverse is also true. If a signal decreases by 3 dB, half the power is lost. For example, a 1,000 watt signal decreased by 3 dB will equal 500 watts while a 1,000 watt signal increased by 3 dB equals 2,000 watts.

The attenuator is a widely used piece of test equipment that can be used to demonstrate the importance of the decibel as a unit of measurement. Attenuators are used to reduce a signal to a smaller level for use or measurement. Most attenuators are rated by the number of decibels the signal is reduced. The technician's job is to know the relationship between the dB rating and the power reduction it represents. This is so important, in fact, that every student of electronics should memorize the relationships in table 2-1 through the 60 dB range. The technician will have to apply this knowledge to prevent damage to valuable equipment. A helpful hint is to note that the first digit of the source level (on the chart) is the same number as the corresponding power of 10 exponent; i.e., 40 dB = 1 ´ 104 or 10,000. A 20 dB attenuator, for example, will reduce an input signal by a factor of 100. In other words, a 100- milliwatt signal will be reduced to 1 milliwatt.

A 30 dB attenuator will reduce the same 100-milliwatt signal by a factor of 1,000 and produce an output of 0.1 milliwatt. When an attenuator of the required size is not available, attenuators of several smaller sizes may be added directly together to reach the desired amount of attenuation. A 10 dB attenuator and a 20 dB attenuator add directly to equal 30 dB of attenuation. The same relationship exists with amplifier stages as well. If an amplifier has two stages rated at 10 dB each, the total amplifier gain will be 20 dB.

When you speak of the dB level of a signal, you are really speaking of a logarithmic comparison between the input and output signals. The input signal is normally used as the reference level. However, the application sometimes requires the use of a standard reference signal. The most widely used reference level is a 1-milliwatt signal. The standard decibel abbreviation of dB is changed to dBm to indicate the use of the 1-milliwatt standard reference. Thus, a signal level of +3 dBm is 3 dB above 1 milliwatt, and a signal level of - 3 dBm is 3 dB below 1 milliwatt. Whether using dB or dBm, a plus (+) sign (or no sign at all) indicates the output signal is larger than the reference; a minus ( - ) sign indicates the output signal is less than the reference.

The student of electronics will encounter the dBm system of measurement most often as a figure indicating the receiver sensitivity of radar or communications equipment. Typically, a radar receiver will be rated at approximately - 107 dBm, which means the receiver will detect a signal 107 dB below 1 milliwatt.

The importance of understanding the decibel system of measurement can easily be seen in the case of receiver-sensitivity measurements. At first glance a loss of 3 dBm from a number as large as - 107 dBm seems insignificant; however, it becomes extremely important when the number indicates receiver sensitivity in the decibel system. When the sensitivity falls to - 104 dBm, the receiver will only detect a signal that is twice as large as a signal at - 107 dBm.

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