All the power in the observable universe expressed in milliwatts ...

Foundations of Amateur Radio

Foundations of Amateur Radio

If you've been following my amateur radio journey, you'll have likely noticed that I've been straying from the fold. The words I use for power have been changing. I've reduced references to Watt and increased use of the term decibel.

Initially this was incidental, recently it's been more of a deliberate decision and I'd like to explain how this came to be. It starts with representing really big and really small numbers.

Let's start big.

On 14 September, 2015 the first direct observation of gravitational waves was made when a pair of black holes with a combined estimated weight of 65 solar masses merged. The signal was named GW150914, combining "Gravitational Wave" and the observation date to immortalise the event.

Following the collision, it was estimated that the radiated energy from the resulting gravitational waves was 50 times the combined power output of all the light from all the stars in the observable universe. As a number in Watts, that's 36 followed by 48 zeros. If you're curious, there's even a word for that, 36 Quindecillion Watts.

Now let's look at small. The typical signal strength received from a GPS satellite, like say by your phone, is about 178 attowatts, or in Watts, 0.000 and so on, in all, 13 zeros between the decimal point and then 178.

What if I told you that the energy associated with the collision of those two black holes could be expressed in comparison with a milliwatt. Remember, this collision emitted more energy than all the output of light from all the stars in the observable universe. The expression for all that power is 526 dBm.

Similarly, the tiny received GPS signal can be expressed as -127.5 dBm.

Just let that sink in. All the power in the observable universe through to the minuscule power received by the GPS in your phone, all expressed between 526 dBm and -127.5 dBm, and not a zero in sight.

As I mentioned, the unit dBm relates to a milliwatt. As a starting point, let me tell you that 1 Watt is 1,000 milliwatts and is represented by 30 dBm.

The decibel scale doesn't work quite the same as other number ranges you might be used to. Adding the value 3 doubles its size and adding the value 10 increases its size by a factor 10.

For example, to double power from 1 Watt or 30 dBm, add 3 and get 33 dBm, which is the same as 2 Watts. If you want to increase 1 Watt by a factor 10, again, starting with 30 dBm, add 10 and get 40 dBm which is 10 Watts. Similarly, 50 dBm is 100 Watts and 60 dBm is 1,000 Watts.

Going the other way, halving power, remove 3. So taking 3 from 60 dBm is 500 Watts or 57 dBm. Dividing power by a factor 10 works the same, take 10. So 47 dBm is 50 Watts and 37 dBm is 5 Watts.

If you get lost, remember, dBm relates to a milliwatt. 1 Watt is 1,000 milliwatts and is represented by 30 dBm. Divide by a factor 1,000, remove 30 and end up with 0 dBm, which is the same as 1 milliwatt. I'll say that again, 0 dBm is the same as 1 milliwatt.

It takes a little getting used to, but you can do some nifty things. For example, remove 10 to get a tenth of a milliwatt, or -10 dBm.

This same process of adding and subtracting applies in other ways too. Attenuation, or making a signal weaker, and amplification, or making a signal stronger can use the same rules.

For example, if you apply 3 dB of attenuation, you're making the signal 3 dB weaker, or halving it, so you subtract 3 dB from your power output. If your amplifier is rated at 6 dB gain, you're quadrupling the output and you add 6 dB to your power output.

Similarly, if you talk about the gain of an antenna, you add it. If the gain is 20 dBi, you add it to the power output. You can use this for coax loss calculations as well. A 100m length of RG-58 at 28 MHz has a loss of 8 dB. You can directly subtract this from the power output of the transmitter and know precisely how much power is making it to the antenna.

There's more. The radio amateur S9 signal strength on HF, something which we consider to be a strong signal, can be expressed as -73 dBm or a very small fraction of a milliwatt. An S8 signal is 6 dB weaker, or -79 dBm. A 20 over 9 report is -53 dBm. I will point out that this is at 50 Ohm.

As a result, we now have a continuous scale for all the elements in the transmission chain between the transmitter and the receiver.

While I'm here, I've already mentioned that negative dBm readings relate to fractions of a milliwatt, so values between 0 and 1.

This highlights one limitation of this scale. We cannot represent 0 Watts. Mind you, that doesn't happen all that often. The thermal noise floor in space at 1 Hz bandwidth, that's at 4 kelvins, is -192.5 dBm, which practically means the minimum level of power we need to express. It's also a good value to remember because if you're doing funky calculations and you end up with a number less than -192.5 dBm, you can pretty much guarantee that you've probably made a boo-boo.

0 Watts using the dBm scale is represented by negative infinity, or essentially a division by zero error, really not defined, so there's that.

I'm Onno VK6FLAB