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
    12,418
    3,355
    10^9 nW = 1 W

    Hence that is the correct conversion from W to nW.
     
  3. Papabravo

    Expert

    Feb 24, 2006
    10,135
    1,786
    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
    16,250
    6,746
    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.
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