dB

A knowledge of dB is, in my opinion, necessary when discussing antennas. dB is a power ratio. It can, however, be calculated by using either power or voltage.

When comparing two powers the definition of a dB is:  

dB = 10 Log P1/ P2

P1/P2 is the power ratio. If P1 is 2 times P2, than P1 is 3 dB more than P2.

When comparing two voltage ratios the definition of dB is:

dB = 20 Log V1/V2   Where V1/ V2 is the voltage ratio.

When working with radio signals we can measure the field strength of a signal in volts or more usually in microvolts.   A strong signal may be 50 microvolts. This is taken as 50 microvolts across a 50 ohm load. We almost always use 50 ohms as our reference impedance.

With our radio receivers we typically have S-meters that are some what calibrated to read S-9 when there is a 50 microvolt signal present at the antenna terminals. 

If that signal was decreased to 25 microvolts we would see the S-meter go down. How much would it go down? 

Well we decreased the voltage by 1/2. How many dB would that be?  dB = 20 Log V1/V2 turns out to be 6dB. But what is we used power? How much would the power change is the voltage were cut in half? Well it would be reduced by 1/4. That’s because in our 50 ohm load, if we reduce the voltage by 1/2 we also decrease our current by 1/2. Also the formula from ohms law is Power = V squared divided by R. The power varies with the square of the voltage. 

Decreasing our voltage by 1/2 is the same as reducing our power by 1/4. So using our dB formula for power we get 

dB = 10 Log P1/P2 = 10 Log 4 = 6 dB.

With S-meters we try and calibrate them so that the S-unit is 6dB. So if we reduce our power in half we go down 3 dB and if we decrease outer power by one fourth we go down 6 dB or one S-unit.

So 50 microvolts is S-9 and 25 microvolts is S-8.  My 1963 Drake 2B receiver used 30,000 microvolts to set the S-meter to 60dB over S9.    Although not exact the rule of thumb is a power change by a factor of two is a two dB change and a voltage change by a factor of two is a 6 dB change.  If it takes 100 watts of power from your transmitter to be S-9 on a receiver, reducing your power to 25 watts will drop you to S-8. That means if 100 watts is creating a 50 microvolt signal at the receiver reducing power to 25 watts creates 25 microvolts at the same receiver.  

We can measure signal strength in microvolts and compare signal strengths is dB. We can get the dB by knowing either the power levels or the voltage levels. 

When we are measuring voltage we can use microvolts directly or we can also use dB referenced to 1 microvolt. 

We can say “1 microvolt “ or use the equivalent by saying “zero dB above a microvolt”.

We can say 50 microvolts or 34 dB above a microvolt.

Going from 1 microvolt to 50 microvolts is an increase of 34 dB. Since an S-unit is 6 dB, the difference between 50 microvolts and 1 microvolt (34 dB) is almost 6 S-units. 

30 dB would be 5 S-units and 36 dB would be 6 S-units. 

So S-units, power, dB, and signal strength are all related and just different ways to express the same thing. There are times that one way may be more appropriate than the other.

Measuring voltages is usually easy and from that you can convert to dB because dB is usually easier to work with.  However you must always state the reference level any time you use dB. dB signifies a change and you must know a change from what!

Basically you need to know that one S-unit on your radio is a 6 dB change. That 6 dB change equates to a power increase or decrease of four times. It does not matter if that is 1 watt to 4, 10 watts to 40, 100 watts to 400 watts or 1000 watts to 4000 watts. The result will always be that the S-meter moves only 1 S-unit!

In a similar matter increasing or decreasing power four times only increases or decreases the field strength (voltage) by a factor of two.

When looking at antenna plots and specifications you must have a feel for dB. The difference in signal strength from the front to the back of an antenna will be stated in dB.  If the signal off the front of an antenna is 10 dB stronger than the signal off the back or opposite direction, that is more than two S- units difference. 

The power ratio of 10 times is exactly 10 dB. The power ratio of 2 times is approximately 3 dB. It is actually 3.01 dB. We always drop the .01 and just say 3 dB.