# As an RF engineer, do you really use “dB”?

### As an RF engineer, do you really use “dB”?

In our work, the unit “dB” is often used. Such as insertion loss, return loss, power, we often use xx dB, or xx dBm to describe. Of course, it’s easy for your peers to understand what you mean, but for a layman, it sounds like you’re confused: what are you talking about?

In our work, the unit “dB” is often used. Such as insertion loss, return loss, power, we often use xx dB, or xx dBm to describe. Of course, it’s easy for your peers to understand what you mean, but for a layman, it sounds like you’re confused: what are you talking about?

In previous articles, we have also introduced the concept of “dB” many times, including calculation methods. Today, let’s talk about the concept of dB again. I hope it will become clearer and clearer. It is best to let all the old and young. Ha ha!

What is dB?

The Chinese name of dB is called decibel, which has both transliteration and meaning translation. We took the “bel” after the full English name of dB “decibel” as “bei”, and then used the preceding deci as “point”. The popular explanation is one-tenth of Bell. Isn’t this a bit of a light? It turns out that the “bei” in the decibel is called “Bell” the whole time, to commemorate the inventor of the telephone: Alexander Graham Bell. Such an important radio frequency unit, of course, is a matter of course for Bell, the originator of the telephone. We know that Alexander Graham Bell, in addition to being a great inventor, was an acoustic physiologist and teacher of the language of the deaf, and in the process of studying sound he invented the telephone. When studying sound, the scale of sound is defined – Bell: When the intensity of the sound increases tenfold, the increase in the loudness of the sound is called 1 Bell. It is a unit used to compare power levels or sound intensities in electrical communication and corresponds to a 10 to 1 intensity ratio. Since the bell is a huge number, the tenth of the bell: the decibel comes out: when the intensity of a sound increases by a factor of 10 0.1, the increase in the loudness of the sound is called 1 decibel. In other words, a tenth of a bell is called a decibel. It is a unit used to measure the intensity of sound or the power level of an electrical signal by comparing it to a given level on a logarithmic scale.

On the decibel scale, the lowest audible sound (near complete silence) is 0 dB. 10 times the impact sound is 10 dB. A sound 100 times stronger than near complete silence is 20 dB. A sound 1,000 times stronger than near complete silence is 30 dB.

In RF design, dB is the base-10 logarithm of a ratio.

The Mathematical Basis of Logarithms vs Exponentials

In high school mathematics, we have come to know logarithms and exponents, two complementary numbers.The exponent of a number refers to how many of the numbers are multiplied together, for example

The logarithm refers to how many given numbers are multiplied together to get another number. So here is a correspondence:

That is: the multiplication of 3 2s is 8, and the base 2 logarithm of 8 is 3.

Since the two descriptions are the same, why do you have to do a logarithm when you have an exponent?

Let’s look at the following table of logarithms in base 10: if expressed in numerical terms, it is either very large or very small, but when expressed in logarithms, it becomes: 3, 2, 1, 0, -1, -2, -3. Addition, subtraction, multiplication and division within ten will not be wrong if you close your eyes.

More importantly, after converting to logarithms, the original multiplication and division operations can be turned into simple addition and subtraction. Wouldn’t it be simpler.

Why use logarithms? Laziness may be the main motivating factor for inventors.

If you are not convinced, do the math: In an RF receiver system, it is known that the gain of the antenna is x5.7, the gain of the low noise amplifier is x7.5, the mixer is x4.6, and the loss of the filter is x4.6. is x0.43, …, what is the gain of the whole link? Very simple, are these gain values ​​multiplied together? 5.7*7.5*4.6*0.43*12.8*8.7*35.6=?

tell me your answer. I knocked on the calculator for a long time, and the result was: 335229.032752. If the signal received by this antenna is 0.02354mW, what is the output signal power?

Isn’t that annoying enough.

But what if we change the gain in the link to dB?

Then the total gain of this link is: 0.76+0.88+0.66-0.37+1.11+0.94+1.55=? Don’t knock the calculator, I believe many people already have the answer: 5.53 dB. Then if we change the received signal power to dBm: -16.2819dBm. The output signal power is -16.28dBm+5.53dB=10.75dBm. Isn’t this calculation process easier?

That’s why RF engineers prefer to use dB – it’s just too good.

dB in RF design

Since dB is so easy to use, can we use it casually in the process of using it? For example, when a three-port power divider is used as a combiner, and a 30dBm signal is input to each of the two input ports, what is the power of the output port? 30dBm+30dBm=60dBm?

In addition to this, there is another thing to pay attention to is, the difference between Voltage gain and power gain?

The dB of the voltage gain is 20 times the base 10 logarithm of the ratio of the output voltage to the input voltage.

The dB of power gain is 10 times the logarithm of the ratio of output power to input power.

Why is this? Because in RF design, we mainly target RF power, and if we insist on using it for voltage, we must start with the relationship between power and voltage:

That is, the power gain is the square of the voltage gain, and this square gives the previous coefficient of 10 a factor of 2 in the logarithmic calculation.

Having said that, do you have any questions?