# Conversion of transmitter power from Watts into dB

I've been practicing problems relating to the dB conversion and came across this interesting example problem.

In the above example Tx power is defined in Watts and the conversion from the Watts to dB is done. However, so far according to my understanding of the definition of dB, is defined in relative to receiver power too. But in the above example the calculation was done just by considering the Tx power.

Can some one enlighten me? If I'm understanding it wrong or the example is wrong?

Thanks to @MBaz who pointed out my mistake: dBm and dBW are unitless, but they relate to a reference of 1 mwatt, and 1 Watt.

The question has an error, as well as the answer. Watts does not convert to dB, it converts to dBW. (i) should be as follows:

find (i) the transmit power in dBm and dBW.

The reason behind that is that dB is a ratio, while dBm and dBW are ratios with a reference to 1 mWatt and 1 Watt, respectively, and you can use them to recover an absolute value of the power.

For example, the signal to noise ratio is a measure of how strong a signal is compared to the noise. In the linear scale it is written as:

$\frac{\text{Signal Power (in watts or miliwatts)}}{\text{Noise Power (in watts or miliwatts)}} = SNR (\text{unitless})$

or in logarithmic domain:

$\text{Signal Power (in dBW or dBm)}-\text{Noise Power (in dBW or dBm)} = SNR (\text{in dB})$

So the correct answer to (i) is

TX power = $10\log(50)=17\text{ dBW}=17+30=47\text{ dBm}$

• Thanks for your answer. From your answer, let's say if I've signal power -1 dB and noise power is -90dBm. Will my SNR now be in -91dB ? Or should I convert the noise power and signal power into same units (dBm or dB) – Agni Mar 18 '16 at 11:19
• You just made the same mistake. You mean, you have a signal power of -1 dBW, not 1 dB because dB is a ratio and a ratio is unit-less, while power has a unit: Watts. Anyways, the answer to this question is that you must have them both in the same unit. First you convert -1 dBW to 29 dBm, or the noise power -90 dBm to -120 dBW. Then, you can find the SNR, which will be 29 dBm - ( - 90 dBm ) = -1 dBW - ( -120 dBW ) = 119 dB. – user304584 Mar 18 '16 at 11:46
• I understand your point that Signal Power and Noise power must be in same units (dBW or dBm). But I understand from standard definition of RSSI(Signal Power) that signal power value is measured in decibels from 0 to -120.The closer this value to zero,stronger the signal. What confuses me is what to do when I've a signal power in dB? – Agni Mar 18 '16 at 13:11
• @user304584 I disagree on one point: dBW and dBm are unitless. The letter after dB are indications of what is the reference unit (1 W and 1 mW), but they're still unitless ratios. – MBaz Mar 18 '16 at 13:59
• @PBCR The signal power has units of watts. You can represent those watts as dBW (referenced to 1 W) or dBm (referenced to 1mW). – MBaz Mar 18 '16 at 15:40