HP C, B, 3586A manual Appendix a, Understanding the Decibel Ratio Measuring System

APPENDIX A

UNDERSTANDING THE DECIBEL RATIO MEASURING SYSTEM

The HP3586 will only outputs level measurement in the nonlinear logarithmic system of decibels. This system is widely used to express levels of power in electronic and acoustic measurements because it has the advantage of emphasizing only changes that are significant. In other words, if you had an instrument that measured length in inches but were measuring values around a mile in length and had a reference of 0db equal to a mile, a change of one inch would not look very important in db’s. However if your reference was an inch and you entered a change of a mile, it would look very important in db’s. This system tends to show the importance of significant changes but keeps you from getting concerned about insignificant changes. I hope the discussion below will shed some light on this useful measuring system.

The decibel system is simply a logarithmic ratio system that is used to scale a standard reference value to and then express a real world value such as feet, miles, volts, and watts. Just saying my meter reads a level of 20db doesn’t mean anything in the real world. We have to know what it reads 20db compared to some real world reference or standard. Then when the decibel is transformed back to a linear ratio, that ratio can be multiplied by the reference to get a real value.

As and example, if we have a level of power in decibels of +6db referenced to one miliwatt, 1 mw or .0001 watt, usually shown as +6dbm, then to find out how many miliwatts this represents you first convert the ratio from decibels to a linear ratio which is 4. We’ll show how to compute the linear ratio a little later. You then multiply the ratio by 1 mw to get 4 mw, which is what +6dbm represents. Now as another example, if we have –6dbm and want to convert it into power in miliwatts you use the same procedure to find the ratio but since the it’s a negative db number, you divide the ratio into the reference, i.e. –6dbm = 1mw/4 = .25 mw. This system uses negative decibels to compute numbers less than 1. As another example, which will confuse you now but later you’ll learn how it works, lets find the real value represented of 6db referenced to .775 volts, expressed as +6db.775V. This voltage reference is used by the HP3586 to express voltage levels. When we convert db’s into volts the ratio formula changes so for +6db.775V in volts the linear ration will be 2 and since it was in +db you multiply 2X .775volts to get 1.55 volts. Just read on and this should be clearer.

Now let’s talk a little about how to convert back and forth between the linear ratio for power watts and potential in volts and logarithmic ratio in decibels. We’ll start with the formula for power, which is:

Power ratio in db = 10 log (P/PR)

Where P is the power in watts, miliwatts, horsepower, flea power etc. we want to convert to decibels and PR is the reference power we want to compare it to, both must always be in the same units. To indicate the reference is in miliwatts we use the notation for the units as dbm just like on the HP3586’s display. If we were comparing to one watt we could use the unit dbw, which would let us know we are comparing to one watt.

The logarithmic system we use for decibels are to a base 10. If you aren’t familiar with the logarithmic system, you may want to study a math book or the ARRL Handbook on the subject. In the old days we had to use tables in math books to compute logs and their anti logs but today many inexpensive calculator will do this for you. The log computation of the ratio converts it from a linear ratio to a logarithmic ratio. Multiplying by ten gives us more resolution to make the decibel system better express small changes.

Now to get back from db’s to a real number for power we transpose the above formula to get the following:

P = PR anti log (db/10)

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