# Dbm to Watts?

Discussion in 'Homework Help' started by Rickreezi, Aug 13, 2013.

1. ### Rickreezi Thread Starter New Member

Aug 9, 2013
9
0
I am now working on a question that says,

5. A microphone has an output power of 45 dBm, the output power in Watts is;

A. 5.6 mW
B. 31.6 μW
C. 5.6 nW
D. 31.6 nW
E. None of the above

i found the formula to convert dBm to watts which is

P(Watts)= 10^(dB/10)/1000

i dont actually know exactly what is the formula saying apart from the divide by 1000 part because 1watt = 1000mV

10^(-45/10)/1000= 0.0000000316227766 Watts

but then i multiplied the Ans by various submulitples to get me an answer that are in the options. i did 0.0000000316227766 x 10^9(nanowatts)= 31.6nW

is this the correct way of getting the answer?

2. ### MrChips Moderator

Oct 2, 2009
12,636
3,455
10^9 nW = 1 W

Hence that is the correct conversion from W to nW.

3. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
dBm is dB with respect to a reference power of 1 milliwatt = .001 Watt. Your answer is correct. I always get the right answer by writing the definition and doing the algebra.
Code ( (Unknown Language)):
1.
2. -45 dBm = 10*log(Po/Pref), where Pref = 1 mW
3. -45 / 10 = log(Po /.001)
4. -4.5 = log(Po/.001)
5. Po = 10^(-4.5) * .001
6. Po = 3.162e-8
7.
For me is is just easier to start with the definition and do the algebra. Your mileage may vary.

JoeJester, Rickreezi and #12 like this.
4. ### #12 Expert

Nov 30, 2010
16,704
7,354
I've dragged my trees out of the forest dozens of times with the, "back to basics" approach recommended by Papabravo. I must agree with his method.

Papabravo likes this.