# FM or TV System Gain-Loss Calculations – TPO for ERP, Coax System & Antenna Gain.

## Dbs for Common Power

Gain or Power Loss

Here is a simple procedure for laying out a method to illustrate Power db gain (or loss), and is easy to perform and easy to remember (both of which are key points). While doing this we can see a little bit of what a "logarithm" is. Simply stated for this instance, we find that the "multiplication factor", as it relates to the "db-gain". i.e. Where the db values increase in a "straight-line", we find that the related "multiplication factor" increases radically (actually "logarithmically"), by basically doubling every 3 db. If we lay out a simple table of just 2 columns, identified first as db gain, and secondly as "Factor (multiplier)", we can begin this simple and understandable task.

The way we do this, is to first establish that 0 db has a "Gain Factor" of 1 (which we will later explain why). ..Next, we need to double the "Gain Factor" for every increase of 3 db. This "doubling" is in essence is one example of a "logarithmic increase in value"... A key point here is that these db gains and their respective "Gain Factors" are actually a continuous circle, where the 10 db restarts at the bottom with the same 0 db, but the "Gain Factor" has increased by 10 times.

Let's start out and see how easy this really works: ... The doubling of the "Gain Factor" from x1 to x8, from 0 db to 9 db in 3 db steps, is pretty straightforward... Adding 3 db to the 9 db would give us 12 db, which when "rolled over" on the chart (where 10 db is represented as 0 db at the bottom), 12 db would be on the chart as 2 db (like 10 db + 2 db).

What happens is that the dbs roll over by simply adding, so that 11 db (which is simply 1 db more than 10 db) is shown as 1 db above 0 db. .. The next "db rollover" would result in 19 db + 1, or ... 20 db!! .. To illustrate this, note that where going db (where we had a "Gain Factor" of x8), 3 db more takes us to the 2 db point (i.e. 9 db + 3 db = 12 db, as 2 db above the 0 db)... Since doubling 8 would give us 16, but rolling over on the chart increases our "Gain Factor" by x10, we can illustrate the 16 as 1.6 instead...

Those relationships are simply accomplished by scientific notation, where a "Gain Factor" of x16 can be expressed as 1.6x10^{1}, and a "Gain Factor" of x21.25 would be expressed in scientific notation as 2.125x10^{1}.

The simplest process for converting db gain to a "Gain Factor", is to strip off the numbers that precede the "basic 1 figure db", use that basic 1 figure db as from the chart, and the number(s) preceding that "basic 1 figure db" as the power of 10.

This means that an antenna which has a 14 db gain would mean (taking the basic 4 db = x2.5 from the chart) that our antenna has a power gain of 2.5x10^{+1}, ... i.e. 25 times...

The thing to remember is that where the dbs roll over by adding, the "Gain Factor" however increases by 10 times, each time that "rollover" occurs.

Think of it like an Odometer (like xxxx.n) where the ".n" represents the "db gain" in each of the Tables below. In that Odometer, when the ".n" goes from ".0" to ".9", and then 0.1 or 0.3 more, we would expect the next number in the adjacent column to pump up by "0.1" or "0.3" above the "0.9". So... 0.0 increasing to 0.9, and then "0.3" more would cause the "0.9" to become "1.2"...... Keep all that in mind as we present these 3 Tables.

Table #1

Db Gain Factor (x) . . 9 8 8 . 7 . 6 4 5 . 4 . 3 2 2 . 1 . 0 1

Table #2

Db Gain Factor (x) . . 9 8 8 6.4 7 . 6 4 5 3.2 4 . 3 2 2 1.6 1 . 0 1

Table #3

Db Gain Factor (x) 10 10 9 8 8 6.4 7 5.0 6 4 5 3.2 4 2.50 3 2 2 1.6 1 1.25 0 1 The reason for the 0 db = 1 , is that any number to the "0" power is equal to "1".

.. Think of it this way, everyone knows that 2^{2}= 4, and 2^{3}=8. .. But also note that as this process is reversed, we find that 2^{1}=2, and 2^{0}=1 !!

Examples:

.... An antenna with a given Power Gain of 5 db and driving it with 15W, means that it would have a "Power Gain Factor" of x3.2, resulting with effectively the same as driving with 48W.

Special Note #1: ... This Process is actually the result of numerical descriptions of the resulting values of powers of 10, ranging from 0.0 to 1.0

in 0.1 steps, where 0 db is actually 10^{0.0}= 1. Continuing this process, we find that 10^{0.1}= 1.25 ..... 10^{0.3 }= 2.0 .... 10^{0.5}= 3.16 ... ....10^{0.7}= 5.0 ... [ note that 7 db correlates to x5 as a "Gain Factor"]

Special Note #2: ... In the opposite way of looking at this, we would say that the "log of 5.0 = 0.7", as the necessary power of 10 required to result in the 5.0..... A Linear Power Amplifier that has a 550W output if driven with 15W, has a "Power Gain Factor" of 36.7. Using scientific notation, this is expressed as 3.67x10

^{1}. We find this approximately at 5.6 db on the chart, and by adding the x10^{1}) to the db we get 15.6 db as the Power Gain (i.e. 5.6 db + 10 db).

When folks use a calculator, it's easy to get confused as to whether to find the "log" of the number in question, or the "anti-log" or "inverse-log". .. By using this chart method (with scientific notation), it's hard to go wrong. But... "Practice helps a lot!".

### One Comment so far:

You must log in to post a comment.

Posted by:*admin*on

*Aug 28, 2012*

[…] your FM or TV System Gain/Loss Calculations including TPO for ERP, Coax System & Antenna Gain. Check it out, more in the works!Tags: antenna, calculator, coax, effective radiaded power, erp, fm, free, […]