**For some strange reason, many people misunderstand and have difficulty with the**

concept of decibels (abbr. "dB"). That's really a shame because decibels are used in a wide

variety of radio and electronics applications. This form of notation is widely used because it

makes the job of calculating things like gains and losses much easier. By using decibel

notation we can replace multiplication (gains) and division (losses) with addition and

subtraction, respectively.

concept of decibels (abbr. "dB"). That's really a shame because decibels are used in a wide

variety of radio and electronics applications. This form of notation is widely used because it

makes the job of calculating things like gains and losses much easier. By using decibel

notation we can replace multiplication (gains) and division (losses) with addition and

subtraction, respectively.

**The decibel is nothing more than an expression of the ratio between two signals. The**

signals might be voltages, currents or power levels. When rendered in the form of decibel

notation, however, the logarithms of the ratios are used rather than the straight arithmetical

ratios. It is the use of the log of the ratios that makes it possible to replace multiplication and

division calculations with addition and subtraction.

signals might be voltages, currents or power levels. When rendered in the form of decibel

notation, however, the logarithms of the ratios are used rather than the straight arithmetical

ratios. It is the use of the log of the ratios that makes it possible to replace multiplication and

division calculations with addition and subtraction.

**The decibel was originally conceived by the telephone industry to describe audio**

signal gains and losses in telephone circuits. The original unit was named the bel after

Alexander Graham Bell, inventor of the telephone. In most electronics work, however, the

bel proved to be too large a unit, so the decibel (one-tenth of a bel) was adopted as the

standard notation.

signal gains and losses in telephone circuits. The original unit was named the bel after

Alexander Graham Bell, inventor of the telephone. In most electronics work, however, the

bel proved to be too large a unit, so the decibel (one-tenth of a bel) was adopted as the

standard notation.

**Special dB Scales**

**Over the years different segments of the radio and electronics industry have created**

special decibel scales for their own use. All of them are based on the three equations given

above. The differences are in the specified conditions under which the measurements are

made, and the specific level used as a reference point. The standard reference voltage or

power will be placed in the denominator of the equation, and is usually referred to as the "0

dB" reference level. This name comes from the fact that placing the same level in the

numerator produces a ratio of 1:1, or 0 dB. Several different special dB scales are listed

below.

special decibel scales for their own use. All of them are based on the three equations given

above. The differences are in the specified conditions under which the measurements are

made, and the specific level used as a reference point. The standard reference voltage or

power will be placed in the denominator of the equation, and is usually referred to as the "0

dB" reference level. This name comes from the fact that placing the same level in the

numerator produces a ratio of 1:1, or 0 dB. Several different special dB scales are listed

below.

**dBm. These units refer to decibels relative to one milliwatt (1 mW) of power**

dissipated in a 50 ohm resistive impedance (defined as the 0 dBm reference level), and is

calculated from either 10 LOG (PWATTS/0.001) or 10 LOG (PMW). The dBm scale is used in

describing receivers and amplifiers. For example, an input signal or an output signal may be

defined in terms of dBm. Similarly, the noise floor of the receiver may be given in dBm.

dissipated in a 50 ohm resistive impedance (defined as the 0 dBm reference level), and is

calculated from either 10 LOG (PWATTS/0.001) or 10 LOG (PMW). The dBm scale is used in

describing receivers and amplifiers. For example, an input signal or an output signal may be

defined in terms of dBm. Similarly, the noise floor of the receiver may be given in dBm.

**dBmV. This unit is used in television receiver systems in which the system**

impedance is 75 ohms, rather than the 50 ohms normally used in other RF systems. It refers

to the signal voltage, measured in decibels, with respect to a signal level of one millivolt (1

mV) across a 75 ohm resistance (0 dBmv). In many TV specs, 1 mV is the full quieting

signal that produces no "snow" (i.e. noise) in the displayed picture.

impedance is 75 ohms, rather than the 50 ohms normally used in other RF systems. It refers

to the signal voltage, measured in decibels, with respect to a signal level of one millivolt (1

mV) across a 75 ohm resistance (0 dBmv). In many TV specs, 1 mV is the full quieting

signal that produces no "snow" (i.e. noise) in the displayed picture.

**dBmV. This unit refers to a signal voltage, measured in decibels, relative to one**

microvolt (1 mV) developed across a 50 ohm resistive impedance (0 dBmV).

microvolt (1 mV) developed across a 50 ohm resistive impedance (0 dBmV).

**dB (Old). An archaic dB unit used in the telephone industry prior to World War II**

used 6 milliwatts dissipated in a 500 ohm resistive load at the 0 dB reference level.

used 6 milliwatts dissipated in a 500 ohm resistive load at the 0 dB reference level.

**Volume Units (VU). This unit is used in audio work, and largely replaces the old dB**

scale given above. In the VU scale 0 VU is 1 milliwatt dissipated in a 600 ohm resistive

load.

scale given above. In the VU scale 0 VU is 1 milliwatt dissipated in a 600 ohm resistive

load.

**Antenna dB Notation**

Decibel notation is frequently seen in specifications for radio antennas. The gain, the

front-to-back ratio and/or the front-to-side ratio are typically specified in decibels. In the

case of the front-to-back or front-to-side ratios the values are measured by having the

antenna look at a constant power RF source while it is rotated. The signal levels are

measured at the front, side and back so that the ratios can be calculated.

The matter of gain is a little different, however. What do you use as a reference for

antennas? There are two basic forms of gain specification: gain relative to isotropic (dBi)

and gain relative to a dipole (dBd). Gain relative to isotropic (dBi) uses a theoretical construct called an isotropic

radiator, which is a spherical source of RF energy that radiates equally well in all directions.

The available power is distributed equally across the entire surface of the sphere. Gain

antennas distribute the same amount of power over a much smaller portion of the sphere, so

calculations can easily be made. The isotropic gain method is preferred by professional

Decibel notation is frequently seen in specifications for radio antennas. The gain, the

front-to-back ratio and/or the front-to-side ratio are typically specified in decibels. In the

case of the front-to-back or front-to-side ratios the values are measured by having the

antenna look at a constant power RF source while it is rotated. The signal levels are

measured at the front, side and back so that the ratios can be calculated.

The matter of gain is a little different, however. What do you use as a reference for

antennas? There are two basic forms of gain specification: gain relative to isotropic (dBi)

and gain relative to a dipole (dBd). Gain relative to isotropic (dBi) uses a theoretical construct called an isotropic

radiator, which is a spherical source of RF energy that radiates equally well in all directions.

The available power is distributed equally across the entire surface of the sphere. Gain

antennas distribute the same amount of power over a much smaller portion of the sphere, so

calculations can easily be made. The isotropic gain method is preferred by professional

**antenna designers.**

**Gain relative to a dipole (dBd) uses a half wavelength dipole as the reference. When**

both antennas are set up to intercept the same signal, then the gain of the test antenna is

found by measuring the signal levels of both the test antenna and the dipole reference

antenna, and then performing the calculation. The dBd measurement is about 2 dB higher

than the dBi measurement.

both antennas are set up to intercept the same signal, then the gain of the test antenna is

found by measuring the signal levels of both the test antenna and the dipole reference

antenna, and then performing the calculation. The dBd measurement is about 2 dB higher

than the dBi measurement.

**Some dB Lore**

Because radio signals are discussed in decibels some rather odd notions pop up. Let's

take a look at some of those that historically have been quite popular.

Because radio signals are discussed in decibels some rather odd notions pop up. Let's

take a look at some of those that historically have been quite popular.

**The S-Meter Folly. Amateur radio operators and shortwave listeners use the Smeter**

to compare signal strengths. The standard signal reporting system, worked out by

ARRL many years ago, uses S1 through S9, in which S9 represents "...an extremely strong

signal." Receiver S-meters are often calibrated to +60 dB over S-9. What does this mean?

Well, it means that telling someone they are "60-dB over S-9" means that their signal is onemillion

times stronger than an extremely strong signal. Why, that signal level ought to melt

the insulation off your transmission line?

Another S-Meter Folly. Swapping S-meter stories back and forth is basically a

useless exercise. Why? Because there are multiple standards for calibrating S-meters. There

will be a reference input signal level to establish the 0 dB point, and then an increment for

each S-unit. I've seen S-meters calibrated such that 50 mV across the 50-ohm input

impedance constitutes an S-9 signal, while other receivers required 100 mV for an S-9. I've

seen receivers calibrated at 3-dB/S-unit, while others are calibrated at 6-dB/S-unit (more

common).

to compare signal strengths. The standard signal reporting system, worked out by

ARRL many years ago, uses S1 through S9, in which S9 represents "...an extremely strong

signal." Receiver S-meters are often calibrated to +60 dB over S-9. What does this mean?

Well, it means that telling someone they are "60-dB over S-9" means that their signal is onemillion

times stronger than an extremely strong signal. Why, that signal level ought to melt

the insulation off your transmission line?

Another S-Meter Folly. Swapping S-meter stories back and forth is basically a

useless exercise. Why? Because there are multiple standards for calibrating S-meters. There

will be a reference input signal level to establish the 0 dB point, and then an increment for

each S-unit. I've seen S-meters calibrated such that 50 mV across the 50-ohm input

impedance constitutes an S-9 signal, while other receivers required 100 mV for an S-9. I've

seen receivers calibrated at 3-dB/S-unit, while others are calibrated at 6-dB/S-unit (more

common).

**Note: A signal that is "60-dB over S-9" should have an rms input level of**

(pick a standard level) 50 mV ´ 1,000,000 = 50 volts! Wow! That oughta

knock your socks off!

(pick a standard level) 50 mV ´ 1,000,000 = 50 volts! Wow! That oughta

knock your socks off!

**CBer's Folly. In the early days of Citizens Band the transceivers used vacuum tube**

technology. It was quite common for CBers to boost the power of their rigs by either

changing the DC power supply voltage to all elements of the tubes, or (more common)

upping the positive voltage applied to the screen grid of the power amplifier tube. A

common modification of one series of models raised the power from the legal 5-watts to a

whopping (and illegal) 7-watts. The gain in dB is 10 LOG (7/5) = 1.46 dB. OK, so now they

have an illegal rig, but have they accomplished anything? Let's see.

technology. It was quite common for CBers to boost the power of their rigs by either

changing the DC power supply voltage to all elements of the tubes, or (more common)

upping the positive voltage applied to the screen grid of the power amplifier tube. A

common modification of one series of models raised the power from the legal 5-watts to a

whopping (and illegal) 7-watts. The gain in dB is 10 LOG (7/5) = 1.46 dB. OK, so now they

have an illegal rig, but have they accomplished anything? Let's see.

**The S-unit on receivers is usually defined (loosely) as the smallest change that is**

easily noted by the average listener. If the conservative 3-dB/S-unit applies, then 1.46 dB

represents around half an S-unit...or about half the change that the other person can detect

with their ears! What a waste. The reliability of those circuits was reduced, the owner

exposed to legal sanctions, all for a change that no one could detect. Wow...that's smart!

Ham's Folly. Knock the CBers and you gotta knock hams as well. I once owned a

1,200-watt linear amplifier. A friend of mine also had the same model, but he traded his in

on a 2,000-watt linear amplifier. He claimed "I'm really getting out now!" Was he? The gain

at the other end would be 10 LOG (2,000/1,200) = 2.2 dB...or a bit less than an S-unit.

easily noted by the average listener. If the conservative 3-dB/S-unit applies, then 1.46 dB

represents around half an S-unit...or about half the change that the other person can detect

with their ears! What a waste. The reliability of those circuits was reduced, the owner

exposed to legal sanctions, all for a change that no one could detect. Wow...that's smart!

Ham's Folly. Knock the CBers and you gotta knock hams as well. I once owned a

1,200-watt linear amplifier. A friend of mine also had the same model, but he traded his in

on a 2,000-watt linear amplifier. He claimed "I'm really getting out now!" Was he? The gain

at the other end would be 10 LOG (2,000/1,200) = 2.2 dB...or a bit less than an S-unit.

**Because of the way power changes and signal strength are related, the FCC for a**

long time restricted commercial and broadcasting stations to power increases of at least fives

times the old level. Thus, a 500-watt station would not normally be allowed to go to 1,000-

watt, but rather a minimum of 2,500-watts. Or the "standard" 1,000-watt local AM station

might go to 5,000-watts. A 5:1 change results in 6.9 dB increase, so it's about two S-units.

As to me and my friend? I kept my money in the bank while he spent his...and no

one could tell the difference between our signals.

long time restricted commercial and broadcasting stations to power increases of at least fives

times the old level. Thus, a 500-watt station would not normally be allowed to go to 1,000-

watt, but rather a minimum of 2,500-watts. Or the "standard" 1,000-watt local AM station

might go to 5,000-watts. A 5:1 change results in 6.9 dB increase, so it's about two S-units.

As to me and my friend? I kept my money in the bank while he spent his...and no

one could tell the difference between our signals.

**The Huge, Monster VSWR Loss. Hams and SWLs spend a lot of time and money**

reducing the VSWR of antennas to as close to 1:1 as humanly possible. But there is a point

of diminishing returns. According to one method of calculating VSWR mismatch loss, a

2.5:1 VSWR could be as much as 1.43 dB or as little as 0.89 dB. Big deal! How does that

affect an S-meter? The reason for reducing the VSWR for solid-state transmitters is the

sensitivity of the transistors in the output, not the loss.

reducing the VSWR of antennas to as close to 1:1 as humanly possible. But there is a point

of diminishing returns. According to one method of calculating VSWR mismatch loss, a

2.5:1 VSWR could be as much as 1.43 dB or as little as 0.89 dB. Big deal! How does that

affect an S-meter? The reason for reducing the VSWR for solid-state transmitters is the

sensitivity of the transistors in the output, not the loss.

**In general, the only people who have to worry a lot about tweeking a system to**

squeeze out every fractional decibel of signal are those who work with extremely weak

signals. Radio astronomers, for example, go to great lengths to get as much gain as possible,

and reduce losses to the bare minimum. But then again, they are dealing with power levels

most conveniently measured in millimicronanofemtowatts. Mere mortals can worry a little

less and get on with the prospect of enjoying our hobby!

squeeze out every fractional decibel of signal are those who work with extremely weak

signals. Radio astronomers, for example, go to great lengths to get as much gain as possible,

and reduce losses to the bare minimum. But then again, they are dealing with power levels

most conveniently measured in millimicronanofemtowatts. Mere mortals can worry a little

less and get on with the prospect of enjoying our hobby!

**From:**

Joseph J. Carr

Universal Radio Research

6830 Americana Parkway

Reynoldsburg, Ohio 43068

Joseph J. Carr

Universal Radio Research

6830 Americana Parkway

Reynoldsburg, Ohio 43068