# What’s a dB? How is it useful?

I want to share some of my design experiences regarding the usefulness of the dB in engineering designs. It’s obvious that engineers work with numbers daily; some of these numbers may be quite large. In many of these cases we are able to use ratios of two numbers.

**The dB**

The base 10 logarithm begins out journey into what the dB is. It is actually a ratio of two power levels, and so is a quantity without any dimensions. The industry has named the units of dB as ‘Bel’, after Alexander Graham Bell, the telephone inventor. The **deci**bel is commonly used in order to manage the large numbers; ‘deci’ is 1/10. Then we multiply that ultimate power ratio by 10 (this is kind of like multiplying power by 1,000 to get the suffix term milliwatts instead of watts). The following is the equation which converts the ratio of two power levels, P1 and P2, to dB.

**α = 10 x log10(P1/P2) dB where log10 is the base 10 logarithm**

Well, it’s so much more compact and convenient to use logarithms when dealing with extremely small or large numbers.

**A small number**

One common example of a lengthy small number we deal with as engineers is the picowatt which is 10^-12 Watts. So, 1000000000000 picowatts = 1 Watt.

**A large number**

One, very common, term used extensively in today’s technology world is 5G. This wireless standard deals with frequencies up in the millimeter wave spectrum which spans 30 GHz to 300 GHz. So that’s 30,000,000,000 Hz to 300,000,000,000 Hz. These are some very large, cumbersome numbers.

**The dBm**

I would be remiss if I did not discuss here the dBm. There is a reference quantity typically used in RF engineering and telecom known as a dBm which is 1/1,000 of a Watt {the milliWatt (mW) power level} driven into a 50 Ohm load which is a load commonly used in RF. P1 is the power level that will be terminated with that 50 Ohm load.

**Power = 10 x log10 (P1/1mW) dBm**

Remember that the dB and the dBm are two “Ratios” of “power” levels. Voltages are not used in these equations.

**The decibel scale in audio**

Another area that the dB is used is in audio. The human ear has quite a large range of sound levels that it can ascertain. Typically, 0 dB is about the lowest sound level that the human ear can ascertain. Roughly every increase of 10 dB to the ear is perceived as twice as loud.

**dBi: How far can 5G Waves travel? (Reference 1)**

dBi is used to calculate the directional gain of an antenna as compared to an isotropic radiator, an ideal antenna that radiates its power uniformly in all directions. The last letter ‘i’ in the word ‘dBi’ denotes isotropic.

dBi is a value calculated against the antenna input power to determine the directional output power of the antenna.

My friend, Ted Rappaport, is a David Lee/Ernst Weber Chaired Professor of Electrical and Computer Engineering at NYU Tandon School of Engineering and a Professor of Computer Science at New York University’s Courant Institute of Mathematical Sciences. He is also a Professor of Radiology at the NYU School of Medicine. Mr. Rappaport also serves as the founding director of NYU WIRELESS.

In the summer of 2016, a group of New York University students took it upon themselves to investigate just how far 5G millimeter waves could travel in rural southwest Virginia, near the town of Riner.

These students, under the direction of Professor Rappaport, ran a two-day test after erecting a transmitter on the front porch of Professor Rappaport’s mountain home. Next, they selected 36 locations from which to measure any 5G millimeter waves being received from the 5G equipment on the Professor’s front porch. They broadcast at the 73 GHz frequency band with A narrowband CW tone transmitted at a center frequency of 73.5 GHz with a maximum transmit power of 14.7 dBm (28 mW)

The result was that the waves could travel greater than 10 km in that rural area with trees and hills present.

Written for @SupplyFrame

**Reference**

1 Millimeter Wave Wireless Communications: New Results for Rural Connectivity, George R. MacCartney, Jr., Shu Sun, Theodore S. Rappaport, Yunchou Xing, Hangsong Yan, Jeton Koka, Ruichen Wang, and Dian Yu, NYU WIRELESS New York University, Tandon School of Engineering, Oct. 7, 2016