maths...

#### Decibels In this section we come across the equations for decibel power and voltage ratios.

The number of decibels increased or decreased is given by either

dB = or dB = P1 = PowerOut P2 = PowerIn similarly V1 = VoltsOut and V2 = VoltsIn

 Example: if the power out is 20 watts and the power in is 10 watts what is the increase in power expressed in dB? You should know that a doubling of power in fact is 3dB increase so let's see what the calculator gives !! 10  20 10  Using a double image of the calculator screen to bring the full input to the calculator you can see the figure comes out at about 3dB what we expected Example: if the power out is 400 watts and the power in is 0.4 watts what is the increase in power expressed in dB? 10  400 0.4  Using a double image of the calculator screen to bring the full input to the calculator you can see the figure comes out at about 30dB what we expected as 30dB represents a 1000 times power increase. If the question was set using voltages then you should now be able to understand how to do the calculation. What is a measured power of 400W expressed in dBW ? Remember dBW = 10 log10 (power in watts) 10  400  Example: What is a measured power of 12dBW expressed in Watts ? For this was have to introduce a secondary key stroke of a previously used key and one you may have forgotten. The shift key (use last when turning off the calculator) and the key which when used "following" (not together with!!) the shift gives "antilog". So what was the question? Example: What is a measured power of 12dBW expressed in Watts ? Remember Power(Watts) = antilog (dBW/10)   12 10  Result 16dBW when rounded up. Example: Your transmitter have a power output of 20dBW and the feeder has a loss of 3dB, the antenna has a forward gain of 9dB. What is your ERP in watts (effective radiated power) ? Now we know that Power(Watts) = antilog dBW/10 so Power(Watts) = antilog ((20-3+9)/10) = 398W rounded up = 400W     20 3 9  10  Result  398W rounded up = 400W The brackets are used as they appear in the formula OR AS NEEDED TO KEEP THE MATH'S RULE TRUE and thus it makes keying the calculator straight forward BUT if you have been taught another way then use it !!

There are more functions to show you but it is hoped that you have taken all the above onboard and it is time to give yourself a coffee / tea break !!!

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