Decibels in Ham Radio: 3 dB, 6 dB, 10 dB and S Units Explained

Decibels in ham radio puzzle almost every beginner. Sooner or later every radio amateur meets the decibel. It appears in the gain of an antenna, in the loss of a coax cable, in the specifications of a receiver, in the report that a friend gives you and in the manual of the amplifier you want to buy. For many people the decibel is a mystery that they accept without understanding, and they nod when somebody says that a change of 3 dB is nothing and 10 dB is a lot. The good news is that you need to remember only a handful of numbers to work with them and to judge an antenna, a cable or an amplifier at a glance. This guide explains what a decibel is, gives the few rules that matter, explains the units with letters after them, such as dBm and dBi, and shows how the S meter on your radio is built from the same logic.

Why We Use a Logarithmic Scale

Radio signals vary over an enormous range. The strongest signal that your receiver can accept is more than a hundred billion times as powerful as the weakest that it can detect. Writing such numbers in watts would be unwieldy, and our ears and eyes respond to differences in proportion, not in absolute amounts. A logarithmic scale compresses the huge range into a small set of numbers and turns multiplication into addition, which is the real reason why engineers prefer it. The Wikipedia article on the decibel describes it as a relative unit based on a base-10 logarithm of a ratio of two power quantities.

The definition is short. The change in decibels between two powers P1 and P2 is ten times the logarithm of their ratio, in other words 10 × log10(P2 / P1). For voltage and current the factor is 20, because power is proportional to the square of the voltage. The decibel is always a ratio, which is a statement of “how many times more or less”, and not an amount of power in itself.

The Numbers to Remember

You can work with decibels without a calculator if you remember the following table.

Two facts follow from this table and they cover most needs. Every 3 dB is a factor of two in power, and every 10 dB is a factor of ten. Because decibels add, you can build any other number from these: 13 dB is 10 plus 3, so it is 10 times 2, which is 20 times. Seven decibels is 10 minus 3, so it is 10 divided by 2, which is 5 times. Nine decibels is three times 3 dB, giving 2 times 2 times 2, which is 8 times. These shortcuts are accurate to within a fraction of a decibel and are all that most operators need.

What an S Unit Is Worth

The S meter reads the strength of the received signal, and each S unit is defined as 6 dB, which is a factor of 4 in power or 2 in voltage. The reference point is S9, which in the IARU recommendation for HF corresponds to a level of -73 dBm at the receiver input, which is a voltage of 50 microvolts across 50 ohms. On the VHF and UHF bands the reference is 20 dB lower, at -93 dBm. Above S9 the meter shows decibels over S9, so S9 plus 20 dB means -53 dBm on HF. Our article on RST reports and S meters explains how this is used in reports, and why the actual meters of many radios are not accurate.

The table helps you to answer a very frequent question: how much does a more powerful amplifier help? If you raise your power from 100 watts to 1500 watts, the ratio is 15, which is about 11.8 dB. The change is about two S units on the meter of the receiving station. If you double the power from 100 to 200 watts, the gain is 3 dB, which is half an S unit and not noticeable in a normal contact. The same reasoning shows why a better antenna is often more economical than a bigger amplifier: 6 dB more gain costs the price of an antenna, but 6 dB more power from an amplifier means a power four times higher, with all that it brings.

Units With Letters After Them

The plain decibel is a ratio. To say how much power there is, we attach a reference, and the letters after “dB” tell us what the reference is.

• dBW: decibels relative to 1 watt. A transmitter of 100 watts is 20 dBW.
• dBm: decibels relative to 1 milliwatt. It is the common unit for weak signals and the article on dBm gives the details. One watt is 30 dBm, 100 watts is 50 dBm and the S9 level on HF is -73 dBm. Always remember that dBm and dBW differ by 30 dB.
• dBi: the gain of an antenna relative to an isotropic radiator. A dipole has a gain of 2.15 dBi.
• dBd: the gain relative to a half-wave dipole. A gain of 0 dBd equals 2.15 dBi. The relation is explained in our guide to dBi and dBd.
• dBc: decibels relative to the carrier, used for the level of harmonics, spurious signals and noise. A harmonic at -60 dBc is 60 dB below the main signal.
• dBμV: decibels relative to one microvolt, used for the voltage at a receiver input.

A Station Example From Start to Finish

A simple example shows how the numbers combine. You have a transmitter of 100 watts, which is 50 dBm. The coax cable to your antenna has a loss of 2 dB on the band that you use, so the power at the antenna is 48 dBm, or about 63 watts. The antenna has a gain of 5 dBi. The effective radiated power in the direction of the main lobe, expressed in the isotropic reference, is 48 + 5 = 53 dBm, which is 200 watts. If you replace the cable with one that has a loss of 0.5 dB, you gain 1.5 dB, a modest improvement of about 40 percent in power but one that costs nothing in the sense of the transmitter. If you change the antenna for one with 8 dBi, the gain over the earlier antenna is 3 dB, which is a doubling of the effective power. Reading the example, you can see that every element in the chain is simply added or subtracted, and the answer is found by arithmetic alone.

The same reasoning applies to the loss of the cable. A coax with a loss of 3 dB sends only half of the power to the antenna, and our article on coaxial cable types shows the losses per hundred feet at different frequencies. A mismatch causes a loss which is described in dB too. A high SWR can mean that a part of the power is reflected, and the explanation of the meter reading is given in the article on what an SWR meter tells you.

Noise, Sensitivity and Signal to Noise

The decibel is also the language of the receiver. The thermal noise floor in a bandwidth of 1 Hz is -174 dBm, and in a bandwidth of 2.4 kHz it is -174 + 34 = -140 dBm. A receiver with a noise figure of 10 dB has a floor of -130 dBm, and a signal at -123 dBm is 7 dB above the noise. The ratio of signal to noise is a difference of two levels in dBm, and this is how weak-signal modes are rated. If a mode can decode a signal at -20 dB signal to noise, in a given reference bandwidth, you know that it can work with a signal that is 20 dB below the noise in that bandwidth. The method is also used in the link budgets of VHF and satellite links, where the losses of the path are added to the gains of the antennas.

The same arithmetic applies to the dynamic range of a receiver, the difference in dB between the weakest signal that it can hear and the strongest that it can handle without distortion. A value of 100 dB or more means that a signal that is 100 dB above the noise floor can be accepted. These figures can be added or subtracted, and that is why they are so convenient when comparing the specifications of two radios.

Practice Problems With Answers

A few exercises make the rules stick. First, your antenna gives 6 dB more than the old one. What is the change in power? Six dB is two steps of 3 dB, so the effective power is four times higher. Second, a signal changes from S5 to S9. How many decibels is that? Four S units of 6 dB each give 24 dB, a factor of about 250 in power. Third, a cable loses 1.5 dB at your frequency, and the run is doubled. The new loss is 3 dB, so half of the power is lost. Fourth, a preamplifier gives 15 dB of gain and the cable between the preamplifier and the receiver loses 1 dB. The net gain is 14 dB, which is a factor of 25 in power. Fifth, a harmonic is 50 dB below a 100 watt carrier. Fifty dB is a factor of 100,000, so the harmonic power is one milliwatt. Do these on paper a few times and you will find that you can answer the same questions in your head when you read a review or compare two antennas.

Common Mistakes

• Adding decibels of different kinds. You can add a gain in dB to a level in dBm, but you cannot add two levels in dBm; the sum of two powers requires a conversion back to watts.
• Mixing power and voltage factors. A doubling of voltage is +6 dB, and a doubling of power is +3 dB.
• Confusing dBi with dBd. The difference of 2.15 dB matters when you compare two antennas from different makers.
• Trusting the S meter. Many meters are not calibrated, and a reading of S9 on one radio can be several decibels away from the same signal on another.
• Treating 3 dB as small. It is a factor of two in power. A loss of 3 dB in the cable is the loss of half of the transmitter output.

The Bottom Line

A decibel is a ratio on a logarithmic scale: 3 dB is a factor of two in power, 10 dB is a factor of ten, 6 dB is one S unit, and because decibels add, any other value can be built from these. Units with letters give the reference: dBm relative to a milliwatt, dBi relative to an isotropic antenna, dBd relative to a dipole, dBc relative to a carrier. Use decibels to judge an antenna gain, a cable loss, an amplifier upgrade or a receiver specification at a glance. A power increase from 100 to 1500 watts is about 12 dB, two S units, and a loss of 3 dB in the cable takes away half of the power.

Frequently Asked Questions

What does 3 dB mean?

It means a change in power by a factor of two. +3 dB doubles the power and -3 dB halves it.

How many dB is one S unit?

One S unit is 6 dB, which is a factor of four in power or two in voltage. S9 is conventionally -73 dBm on HF.

What is the difference between dBm and dBW?

dBm is referred to one milliwatt and dBW to one watt, so the same power is 30 dB higher in dBm than in dBW.

Is dBi the same as dBd?

No. dBi is referred to an isotropic radiator and dBd to a half-wave dipole. A value in dBi is 2.15 higher than the same gain in dBd.

How much does a 1500 watt amplifier help over 100 watts?

The ratio is 15, which is about 11.8 dB, or a little less than two S units at the receiving end.

Why are decibels used instead of plain ratios?

The range of radio signals is huge, and decibels turn multiplication into addition. A chain of gains and losses becomes a simple sum.