Spreadsheet explains decibels as voltage and power

Spreadsheet explains decibels as voltage and power
Termination resistors and the ratio units of voltage and power -- dB -- are interrelated topics. The dB units can refer to voltage or power, and conversions between voltage dB units and power dB units must specify a value of termination resistance, because voltage and power differ by a factor of resistance.

Texas Instruments has produced a tool to perform dB calculations for designers; to provide definition of commonly used dB units, and information about important dB relationships. This tool can be accessed through the Mixed Signal and Analog portion of the Texas Instruments Home page, in the "Amplifiers and Comparators" box, on the "Engineer Design Utilities" Selection. The direct link to the utility is: http://focus.ti.com/download/utilities/db_calc.xls

The utility is written in Microsoft Excel format. When the user downloads the utility from the TI web site, it will automatically open if Excel is installed on the user's computer. The calculator sheet displays by default. It is shown below in Figure 1.

Figure 1. dB Calculators

dB Calculator

There are five separate calculators on this page. They are grouped under the titles "voltage", "power", "voltage conversions", "power conversions" and "power to voltage conversions". These will be covered individually. User inputs are in yellow boxes -- calculator outputs are in blue boxes.

Voltage Calculator

The unit "dB" is a ratio -- in this case of one voltage to another. One voltage is designated as a "reference", and the other an "input" -- the calculator will then do the ratio.

Power Calculator

In the case of power, dB is a ratio of one power to another. One power is designated as a "reference", and the other an "input" -- the calculator will then do the ratio.

Voltage Conversions

The basic unit dB is simply a ratio. It is often times expressed with some sort of suffix, some of which define the reference voltage. The new unit (for example dBV) therefore defines absolute values of voltage instead of a ratio. It can therefore be converted to and from other voltage units, such as Vrms.

The voltage conversion section has two lines that operate independently:

A Vrms line

A dBV line

Simply enter the quantity in the yellow box -- the calculator performs the conversion to indicated units.

Power Conversions

As stated above - the basic unit dB is simply a ratio. It is often times expressed with some sort of suffix, some of which define the reference voltage. The new unit (for example dBm) therefore defines absolute values of voltage instead of a ratio. It can therefore be converted to and from other voltage units, such as Watts.

The voltage conversion section has two lines that operate independently:

A Watts line

A dBm line

Simply enter the quantity in the yellow box -- the calculator performs the conversion to indicated units.

Voltage and Power Conversions

Conversions between dissimilar units, such as voltage and power, require an additional factor -- the termination resistor. Power is equal to:

The squared factor on voltage can be handled by simple scaling (see the definition worksheet section below) because dB is logarithmic. The resistive factor, however, must be entered by the user in the "Termination" box. This value of resistance is used by all three calculators in the voltage and power conversion section. Once the termination resistor value has been entered, the three lines in the voltage and power conversion section operate independently:

A Vrms line

A dBV line

A dBm line

Simply enter the quantity in the yellow box -- the calculator performs the conversion to indicated units.

Definition and Useful Relations Worksheets

The "definitions" and "useful relations" worksheets can be reached by their tabs on the dB calculator. No calculations are done on these worksheets, however. They are reproduced in Figures 2 and 3 as a handy reference.

The reader may recognize the basic unit is not dB -- or decibel, but it is "bel". As originally used, the bel represented the power ratio between the strength or intensity (power), of two sounds, and was named after the great inventor Alexander Graham Bell. Thus a power ratio of 10:1 = 1 bel, 100:1 = 2 bels, and 1000:1 = 3 bels. Therefore, the bel represents a logarithmic relationship, since the logarithm of 100 to the base 10 is 2 (corresponding to 2 bels), the logarithm of 1000 to the base 10 is 3 (corresponding to 3 bels), etc.

The decibel, then, is just a tenth of a bel. Over a period of time, the scale of the dB proved to be much more useful to electronics designers than that of the bel, and the bel has fallen into disuse as a result.

The decibel is a ratio of two voltages or powers. As such, in order to convert to a level of voltage, a reference must be stated as well as the dB measurement. In many cases, however, the user will encounter a decibel with a suffix. These suffixes are used to attach a reference unit -- voltage or power -- to the decibel so that the reference level does not have to be explicitly stated.

Unfortunately, not all suffixes are standardized. DBu, and dBv, are particularly problematic. Also -- a prominent speaker manufacturer has claimed one of the combinations, as well as the direct broadcast satellite people. Designers can use more common units such as dBm with confidence, but should carefully review the context of some of the other dB reference units.

Figure 2. Definition Worksheet

The primary usefulness of the dB unit is its ability to span broad dynamic ranges without the use of scientific notation. It is also useful because, as a logarithm, it is possible to multiply and divide power and voltage ratios by addition and subtraction. These relationships, as well as others are defined in Figure 3.

Figure 3. Useful Relation Worksheet

With the proper understanding, decibels are a useful and elegant way of defining voltage and power ratios, and even absolute values of voltage and power. With the dB calculation and definition tool available from Texas Instruments, there is no reason why a designer should be confused about decibel units. Hopefully, the reader is encouraged to download the tool and use it as a valuable resource.