Decibels, Bels, and Telephone Bells – Dick Bird G4ZU/F6IDC

When, as a young apprentice, I first started work in a radio research laboratory, the transistor was something of a novelty. An expensive and rather fragile novelty. I learned, rather to my surprise, that electrons have the habit of flowing, not as one might have imagined, from positive to negative, but from negative to positive, and that it is only “holes” which take the conventional route.To make life even more difficult some transistors were PNP and others NPN. If, by mistake, you connected the battery supply the wrong way round, there was no second chance.

They were damaged beyond repair, and there were rather dirty looks from the big Boss. Personally I much preferred the good old vacuum tubes, which would take plenty of punishment, and could be relied on to give visible signs of distress when really ill-treated. First of all, nice red-hot anodes, then a blue fluorescent glow and, finally, a quite impressive internal firework display.

One of my jobs was to go down to the store-keeper and collect various bits and pieces, which were scribbled out on a piece of paper, so that there would be no mistake. I must have seemed pretty green, because one day, just for fun, someone added to my list a 1mA fuse, a 75 ohm 25 KW resistor and six decibels. Thus began my indoctrination into the mysteries of electronics. I was told that Graham Bell, who founded the Bell Telephone Company, was getting complaints of unacceptable delays at the central telephone exchange when trying to put through long distance calls. The operators would apparently crank the handle of the ringing magneto like mad, but for some reason or other, the bell just didn’t seem to ring at the other end.

Graham Bell decided that he would have to lay down some sort of limit for the line loss on long distance circuits. He chose as his standard, a power loss of 10 to 1 and with typical modesty, he decided to call this standard the Bel. It should be noticed that the Bel is a power ratio, so if two telephone subscribers, each with a line loss of 1 Bel were trying to communicate, one with the other, the total line loss would be not 10 + 10, but 10 x 10 i.e., a power loss of 100:1. It might be simpler if we just said a loss of 2 Bels, because if there happened to be any additional losses, either in Bels, or fractions of a Bel, to be taken into account these could all be added together, (not multiplied) when calculating the total circuit loss.

With radio communication, few of us would be willing to contemplate losses of 2 Bels, or even just 1 Bel, (10 watts left out of the 100 watts from our transceiver), so it is more convenient for us to use the term Decibel (db) which is one tenth of a Bel. Ten Decibels loss, -10db, or ten Decibels gain +10db, if we are talking about the power gain of a linear amplifier, or of a rotary beam, therefore indicates a power of 10 to 1. Strictly speaking, with an antenna, it is not really sufficient to say that it has a power gain of 1.

Ten db means a power gain of ten to one relative to some reference standard. We must specify this standard, otherwise ten db in this present case can have no real significance. Most of us have a pretty good idea of what can be expected from a half-wave dipole, and it can therefore serve as a useful standard for comparison purposes.

So with antennas, in order to be really clear as to what we are talking about, we should use the term dbd (the suffix d indicates that the quoted gain is relative to that given by a half-wave dipole. Radio amateurs do quite often try to estimate the performance of some new wonder beam, just by switching over to a dipole and asking for comparative signal reports.

A short-wave listener could conduct similar tests, just on reception by switching antennas, and noticing relative “S” meter readings on a number of local and DX signals. Either way, if you want to know the relative gain in decibels, (db) you will need to know just how many decibels there are to an “S” point. This can vary considerably from one make of receiver to another (and even between two receivers of identical make straight from the factory!)

As a general guide, I would suggest about 4 to 5 db per “S” point is quite a good guess for around mid scale (S9) but could be way out up in the 9+20 or 9+60 region.

Let’s face it, most transceivers in good condition will produce a readable output with input signals of only 1 or 2 microvolts. If the calibration was a true 6 db per S point, as often suggested in the maker’s handbook, S9 would be close to a millivolt, and 9+60 would represent 1000mv, ie. nearly one volt coming down the feed-line! Our 250 KW TV station ten miles away, would be hard pushed to provide my TV receiver with a one volt signal even when using high gain antennas at both ends.

So don’t take “S” meter readings too seriously, or give DX stations ridiculous signal reports. S 9 should be enough to satisfy most people. Even then, to say, “You are S 9 but I didn’t get my signal report or your name and QTH”, might sound somewhat stupid.

Just like any other antenna, the signal from a dipole can be affected by height above ground and ground conductivity. So, to be rather more precise, it would be better if we used as our reference standard, a dipole in free space. This is the sort of dipole we have in mind when we use the term 6db. (not a dipole a couple of feet off the ground!) The design of multi-element beam antennas is these days normally done by computer, and to eliminate various unknown quantities such as ground conductivities and dielectric constant, we start off by calculating the gain of our beam antenna in free space, relative to a dipole also in free space. (6db)

To be really precise we should correct this theoretic gain to take account of any resistive losses in matching systems, loading inductors, traps, baluns, etc., and also make allowance for feeder loss, but this would not be good for publicity purposes, because even without these corrections, free-space figures are not generally over-impressive. Of recent years there has been a tendency towards the use of an isotropic radiator as a reference rather than a dipole in free space. Instead of 6db we can then say 8.15 dbi! What is this mysterious isotropic radiator? If you can imagine a loss-free, point source in free space, radiating uniformly in all directions on a spherical wave-front, that is about as close as we can get.

One interesting point about an isotropic radiator is that it is not frequency sensitive, and has exactly the same gain regardless of whether we are thinking in terms of HF, VHF, UHF, or micro-waves. This is very convenient in computer work, because our reference remains constant, whether we are designing HF or micro-wave antennas. If someone asked me off the cuff the length of a half-wave dipole for 20GHz I would have to do some hard thinking! Seeing that the isotropic radiator is an infinitely small point source, it will come as no surprise when I suggest that physically larger antennas can show quite a substantial gain as compared to that of an isotropic radiator. Unlike the isotropic radiator, the dipole does not radiate uniformly in all directions. It is this directivity which produces the gain.

Off the tips of a half-wave dipole, there is very little radiation, and in this direction it would show a loss relative to an isotropic radiator. In general, the gain of an antenna increases progressively as we restrict the radiation into a more and more narrow segment, rather like a searchlight beam. Putting a reflector behind a dipole might increase the signal in a forward direction by 4dbd (relative to an unaided dipole), but there would, at the same time, be a loss of signal to the rear.

Quite possibly, a loss of 10db or even more, to make a front to back ratio of around 14db. If we chose to quote the gain of this simple two-element beam relative, not to the dipole, but to an isotropic radiator, we could add 2.15 to the 4dbd gain, and say the forward gain was 6.15dbi. The back to front ratio however, being a ratio, and nothing more, would remain unchanged at 14db.

This 6.15dbi gain obviously sounds very much more impressive than 4db, and you can now see why, for publicity purposes, manufacturers prefer to quote “dbi” rather than dbd gain figures. I am not suggesting that there is deliberate deception on their part. Their consultants and designers, hoping to please the big boss, will also come up with the rather flattering dbi gain figures which come out of the computer, rather than converting them to dbd.

On its own the term 6.15db gain tends to be a rather meaningless expression if we happen to be talking about antennas. To make real sense, we need to be told whether it is dbd or dbi gain. If you will bear with me, there are still one or two further complications which can arise when we are talking about antenna gain. For example , there is a substantial difference between the gain of an antenna in free space, as compared with an antenna at normal height above ground.

It may come as a surprise to many people that as you raise an antenna to greater and greater height, you will get a lower angle of radiation, but the power gain in the main radiation lobe can sometimes fall off by as much as 5 to 6db. My little V5 antenna at a height of 20 feet, has quite a useful forward gain of 12.3 dbi and a good front to back ratio. Computer analysis shows that, if raised to a height of 200 feet (almost in free space) the gain in the main lobe would fall to less than 8dbi. It makes you think!

Dick Bird (G4ZU/F6I) – September 1994

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