## What’s the Difference between dB and dBm and dB_{mW}?

If you are like most amateurs, you look at dB specifications and then you see dBm specifications and you wonder what it all means. You should, therefore not feel alone. You may have visited various websites where it is all painted for you in straightforward terms, but you still feel mystified. Join the crowd.

Our approach to this is to work in stages. First, we will present what each is individually from 50,000 feet. We will show how each is a representation of the same thing but from different references. We will then push down a little, doubling back, giving a little more detail into that one, and do likewise for the other. It will therefore be a little back-and-forth.

## Preface

In most cases, it is safe to say that things in electronics that appear complicated are your friend such as is the case with the Smith Chart. These things make life easy for you. While this is certainly the case with the deciBel, it is generally the exception for the amateur radio operator unless you are doing tasks such as determining what adjacent channel rejection is required for your ham shack or repeater station. But even so, there could be no amateur radio without the dB so get with the program.

## What is dB

If you want to explore the nature of the quantified decibel or dB, please look here. On this page, we start at the ground level and work our way up a little to manipulate decibels to our advantage. If you are already familiar with working with dB, you can skip the webpage linked above.

## Can you Mix-and-Match dB with dBm?

The decibel (dB) and the dBm are of the same blood but of different reference. You can mix and match as long as your audience understands that you know what you are doing. But nevertheless, it is a bad idea as explained below.

The decibel, or dB, is a relative measure. It is used to compare two measures of the same units. The units could be volts or jellybeans and everything in between. But the ratios must be of the same units. But there is nothing to fix their absolute value.

The dBm (described in detail below), however, is referenced to 1 milliwatt. The “m” in the dBm serves to reference 1 milliwatt. It is also acceptable to label this figure as dB_{mW}. But the ratio units will be in Watts while the resulting value will be unitless.

Suppose, as in the illustration above, we sum the quantity -90dBm with 70dB. The sum would be unitless except for being a decibel. But which decibel should it be? Should it be a dB or a dBm? We have to consider the nature of the components. The -90dBm is a fixed quantity. Its fixed value is 1pW (1e-12 Watts).

-90dBm = 10 log_{10}(Power/1milliWatt)

1mW * 10^{[-90/10]} = 1 pW

While the equation in and of itself does not give a reference for the 70dB, it can only make sense if it is with reference to the other component of the equation. That means that it must be a dBm though it is not specified as such. Thus, it is a bad idea to mix and match dBs with dBms.

## Relative Measure

The deciBel, in and of itself, is a relative measure. It acts on ratios. It can give a gain of output vs input. This is a huge aspect of amateur radio.

By way of example, consider the gain of a receiver. Its input is from an antenna. Consider the example of a strong signal, S9, which is defined by the IARU (International Amateur Radio Union) as representing 50uV delivered at the receiver’s antenna input S-meter. S9 is a relative measure used by the IARU as a reference and therefore assigned a value of 0dB. Signals stronger than 50uV will have dB values greater than zero (positive values) and signals of smaller voltages than 50uV will have negative dB values.

This is a case where a dB can have an absolute measure but it is by convention, not a definition. It must be recognized that the “dB” in this case came from an S-meter. We cannot make the reverse trip from dB to the S-meter unless the dB value has been defined to be relative to the S-meter convention of the IARU.

## dB Loss for 25uV

Using the above example, let us suppose that our signal from the antenna dropped to 25u Volts. What S-value should the receiver’s S-Meter show? This represents half of the earlier signal. I never learned how to spell very well. How do you spell the word “ratio”? We have a ratio of 25uV relative to 50uV. Our signal dropped by a half or a unitless index of 0.5.

dB loss = 20 log(25/50) = -6dB

That can be expressed as a loss of 6dB or a gain of -6dB. Both ways are exactly the same. It is merely six of one and a half-dozen of the other.

The dB loss, an expression of the ratio of one signal magnitude to the other is therefore generally given as:

dB loss = 20 log (V_{1}/V_{reference})

## Expected S-Meter Reading

The IARU has defined that a 6dB change in signal represents one click or notch in the S-scale. An increase in the signal magnitude of 6dB raises an S-meter reading of S4 to S5. A 6dB decrease in signal (-6dB) changes an S-meter reading of S4 to S3.

## 12dB Loss Given X Volts

Let us now algebraically rearrange the above equation to solve for a relative voltage

dB loss/20 = log (V_{1}/V_{reference})x

10^{(dB loss/20)} = V_{1}/V_{reference}

**V _{1} = V_{reference} * 10^{(dB/20)}**

## What is a “Noise Factor’?

Noise factor is a measure of a signal degradation to noise ratio in a device. It is the ratio of the signal to noise ratio (SNR) at the input to the SNR at the output. A device will always add noise and that without exception. Therefore, because the noise at the output will always be higher than the noise at the input, the noise factor (ratio) is always less than unity but greater than zero. While a noise factor can be expressed in dB, it can often be expressed as a simple ratio. The noise figure (described below) is generally more suitable for specifying a device’s noise characterization.

## What is a “Noise Figure” Specification?

This question is taken directly from the FCC pool questions for the Extra Class exam (E4C04). But in order to properly address this question, it is necessary to first understand that there is such a thing as a universal noise minimum that a perfect receiver (they don’t exist) will have.

## A Noise Floor

There exists in the environment, electrical noise, dependent on temperature, that has been present from the creation of the earth–a *noise floor*. The name “noise floor” is very appropriate since there can be no noise anywhere on planet earth that is less than this noise. A radio receiver is capable of amplifying that noise. Therefore, any signal in the atmosphere that has a magnitude less than this environmental “noise floor” cannot be heard from even the finest and most expensive exotic equipment. The earth’s “noise floor” will swamp it out. The power of this environmental noise is dependent on the environmental temperature and the frequency bandwidth of interest. Its equation is given as

P = (kTB)^{0.5}

Where P is power in Watts, k is Boltzmann’s constant in Joules/^{o}K, T is temperature in ^{o}K, and B is bandwidth in Hertz. The temperature is defined to be 290^{o}K which is about room temperature.

Having this equation in hand, we can quantify the smallest noise possible that a radio receiver can exhibit since the only variable open to specification is the bandwidth, B. Let B=1 Hz. This is going to be an absolute measurement so it shall be in units of dBm.

P (J.Hz) = 1.38e-23J/^{o}K * 290 ^{o}K * 1 Hz = 4.00e-21 J.Hz

dBm = 10 log_{10} (4.00e-21/1e-3) = -174 dBm

This is an important concept to understand because it is universal and therefore forms an absolute minimum noise for all radio communications on a global scale. You will see -174 dBm in many places, including the FCC pool questions (E4C05 as of the pool in 2023). It also appears as a wrong answer for question E4C06.

Let’s apply all this to FCC pool question E4C06.

## What is the FCC Pool Question E4C06 Testing You On?

Question E4C06 is very cleverly written. It beats around the bush depending on your knowledge to get at the real question. It would have been simpler if the question asked you what the noise level is with a bandwidth of 400 Hz. After all of that mumbo-jumbo above, that was all that the question was asking.

But how did it go about asking the question? You had to know that

- a 0 dB SNR is where the two relative figures are equal.
- an unmodulated carrier is a sine wave.
- automatic gain control would throw unknowns into the equation.
- in CW mode, all we are looking at is a carrier.

## Hunt Around on the Web About E4C06

When you hunt around on the web, you will find different ways to solve for the correct answer which are quite complicated. When you find these, please note that there is no explanation given for what those equations are doing. This is called “cook-bookery.” You should learn to hate cookbooks. They will get you into trouble and keep you from learning and you will always be striving for creativity by looking to see what somebody else was able to do.

## A “Noise Floor Extension”

Agilent Technologies PXA Spectrum Analyzers offer a new feature called Noise Floor Extensin or NFE. This is state-of-the art technology and beyond the interest of the amateur community. However, it promises to facilitate receiver capabilities beyond what is possible today. For a fuller explanation of this technology and noise technology in general, please visit the RF Cafe website.