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RAE practice questions

Chapter 12: Decibel Notation

Free practice questions on Decibel Notation, chapter 12 of the SARL's Class A manual, for South Africa's Radio Amateur Examination (RAE). Every question has the right answer and an explanation. Sections covered:

  • 12.1 The decibel
  • 12.2 Adding decibels
  • 12.3 Representing losses
  • 12.4 Quick and easy decibel conversions
  • 12.5 Expressing voltage ratios as decibels
  • 12.6 Expressing power Levels in dBW and dBm

80 questions

  1. 1. How is the power gain of an amplifier worked out?
    Show answer

    Output power divided by input power

    Gain is the ratio POut ÷ PIn, so an amplifier that turns 2 W into 20 W has a gain of 10 times; the ratio turned upside down would describe a loss.

  2. 2. A typical amateur receiver has an overall power gain, from its antenna input to its speaker, of about 10¹⁴. What is that in decibels?
    Show answer

    140 dB

    10¹⁴ is a 1 followed by 14 zeros, so it is 14 × 10 = 140 dB; using 20 log, which is meant for voltage ratios, would give 280 dB.

    Try it: dBm, Watts & dB
  3. 3. Which statement about the name of the bel, from which the decibel comes, is correct?
    Show answer

    It honours Alexander Graham Bell, inventor of the telephone

    Telephone engineers at Bell Laboratories first used the bel, naming it after Alexander Graham Bell, the telephone's inventor; wireless telegraphy was Marconi's field, and Hertz has the hertz.

  4. 4. How does the decibel compare in size with the bel?
    Show answer

    It is a tenth of a bel

    The prefix deci means one tenth, so ten decibels make one bel, and the smaller unit turned out to be the handier size.

  5. 5. A gain is quoted as 4 bels. How many decibels is that?
    Show answer

    40 dB

    A decibel is a tenth of a bel, so one bel is 10 dB and 4 bels are 40 dB. Dividing by ten instead, 0,4 dB, treats the decibel as the larger unit.

  6. 6. What does a change of 1 dB in the level of an audio signal correspond to for a listener?
    Show answer

    About the smallest change the ear can notice

    One decibel is about the smallest step in loudness that the ear can detect, so it can just be heard, but it is far short of a doubling.

  7. 7. Which property gives the decibel much of its practical value?
    Show answer

    Its steps match the way the ear judges changes in loudness

    Decibels follow ratios, and the ear judges loudness by ratios too: going from 1 W to 2 W sounds like the same step as 10 W to 20 W. Equal steps in watts would not sound equal.

  8. 8. Which formula gives a power ratio RP in decibels?
    Show answer

    RdB = 10 log₁₀ RP

    For a power ratio, RdB = 10 log₁₀ RP, log₁₀ being the logarithm to the base 10 (log₁₀ 100 = 2, so 100 is 20 dB). 20 log is the voltage formula: voltages must be squared to give powers.

  9. 9. An amplifier turns an input of 2 W into an output of 54 W. Which option is nearest to its gain?
    Show answer

    14 dB

    RP = 54 ÷ 2 = 27 and 10 log₁₀ 27 = 14,3 dB, nearest 14 dB (25 = 100 ÷ 4 is 20 − 6 = 14 dB by the table). 29 dB is 20 log, the voltage formula.

    Try it: dBm, Watts & dB
  10. 10. A signal report says 'S9 plus 20 dB'. How many times the power of an S9 signal does that indicate?
    Show answer

    100

    20 dB is a 1 followed by two zeros, a power ratio of 100, so the signal has 100 times the power of S9. Reading 20 dB as 20 times treats decibels as a plain ratio.

    Try it: dBm, Watts & dB
  11. 11. Two power ratios, each expressed in decibels, are added together. What does this correspond to?
    Show answer

    Multiplying the two ratios

    Decibels are logarithms, and adding logarithms multiplies the numbers behind them; that is why the gains of a chain of stages can simply be added.

  12. 12. An amplifier with a gain of 24 dB is followed by one with a gain of 5 dB. What is their total gain?
    Show answer

    29 dB

    Decibel gains in a chain are simply added, 24 + 5 = 29 dB; multiplying them, as if they were plain ratios, gives the wrong 120 dB.

  13. 13. Two amplifiers in a chain have power gains of 5 and 200. What is their combined gain in decibels?
    Show answer

    30 dB

    The ratios multiply, 5 × 200 = 1000, three zeros, so 30 dB; adding them instead gives 205, which is only about 23 dB.

    Try it: dBm, Watts & dB
  14. 14. Two amplifiers in a chain have power gains of 4 and 30. Which option is nearest to their combined gain?
    Show answer

    21 dB

    4 × 30 = 120 and 10 log₁₀ 120 = 20,8 dB, between 20 dB for 100 and 23 dB for 200, so 21 dB is nearest; adding the ratios to 34 gives about 15 dB.

    Try it: dBm, Watts & dB
  15. 15. Three stages are connected in a chain: the first multiplies the signal power by 100, the second provides 11 dB of gain and the third 14 dB. What is the total gain?
    Show answer

    45 dB

    First turn the first stage into decibels, 100 times being 20 dB, then add: 20 + 11 + 14 = 45 dB; adding the plain 100 to the decibels gives 125.

    Try it: dBm, Watts & dB
  16. 16. An 8 mW signal passes through two amplifiers in a row, each giving 20 dB of gain. What power comes out?
    Show answer

    80 W

    20 dB + 20 dB = 40 dB, a power ratio of 100 × 100 = 10 000, so 8 mW × 10 000 = 80 W. Adding the two ratios, 100 + 100 = 200, gives only 1,6 W.

    Try it: dBm, Watts & dB
  17. 17. Three amplifiers connected one after the other have gains of 10 dB, 20 dB and 30 dB. What overall power ratio do they give?
    Show answer

    1 000 000

    The gains total 10 + 20 + 30 = 60 dB, six zeros, the same as 10 × 100 × 1000 = 1 000 000; adding the three ratios gives only 1110.

    Try it: dBm, Watts & dB
  18. 18. Two amplifier stages each have a gain of 7 dB. What overall power ratio do they give?
    Show answer

    25

    7 dB + 7 dB = 14 dB, and 14 dB = 20 dB − 6 dB, a ratio of 100 ÷ 4 = 25; reading each 7 dB as a ratio of 7 gives the wrong 49.

    Try it: dBm, Watts & dB
  19. 19. A 2 mW signal is applied to an amplifier with a gain of 17 dB. What is the output power?
    Show answer

    100 mW

    17 dB = 10 dB + 7 dB, a ratio of 10 × 5 = 50, so 2 mW × 50 = 100 mW; multiplying by 17, as if it were the ratio, gives 34 mW.

    Try it: dBm, Watts & dB
  20. 20. A power amplifier with a gain of 23 dB is driven with 2 W. What output power does it give?
    Show answer

    400 W

    23 dB = 20 dB + 3 dB, a ratio of 100 × 2 = 200, so 2 W × 200 = 400 W; multiplying 2 by 23 instead gives 46 W.

    Try it: dBm, Watts & dB
  21. 21. A 5 mW signal is applied to an amplifier with a gain of 8 dB. Which option is nearest to the output power?
    Show answer

    30 mW

    8 dB is a power ratio of 6,31, between 5 for 7 dB and 8 for 9 dB, so 5 × 6,31 = 31,5 mW, nearest to 30 mW; reading 8 dB as a ratio of 8 gives 40 mW.

    Try it: dBm, Watts & dB
  22. 22. What is a power ratio of 0,01 in decibels?
    Show answer

    −20 dB

    10 log₁₀ 0,01 = 10 × (−2) = −20 dB, negative because the power falls; without the minus sign it would describe a gain of 100.

    Try it: dBm, Watts & dB
  23. 23. A chain contains amplifiers described by their gains and cables described by their losses, all in decibels. How is the overall gain found?
    Show answer

    Write each loss as a negative gain, then add

    A loss is a negative gain: give each loss a minus sign, then add (20 dB of gain and 7 dB of loss make 13 dB). Adding the figures as they stand counts every loss as a gain.

  24. 24. An amplifier chain has an overall gain of 32 dB. A 10 dB attenuator is then switched in at its input. What is the overall gain now?
    Show answer

    22 dB

    The attenuator counts as a gain of −10 dB, so 32 + (−10) = 22 dB; adding its 10 dB loss as if it were a gain gives 42 dB.

  25. 25. A transmitter delivers 100 W into a feedline with a loss of 2 dB. Which option is nearest to the power that reaches the antenna?
    Show answer

    60 W

    A 2 dB loss leaves 0,63 of the power (1,58 times less), so 100 W × 0,63 = 63 W, nearest 60 W. Half the power, 50 W, is what a 3 dB loss leaves.

    Try it: Feedline Loss
  26. 26. A 4 W signal is fed to an amplifier with 13 dB of gain, followed by a cable with 3 dB of loss. How much power comes out of the cable?
    Show answer

    40 W

    The net gain is 13 + (−3) = 10 dB, a power ratio of 10, so 4 W × 10 = 40 W. Adding the cable's loss as a gain makes 16 dB, a ratio of 40, and 160 W.

    Try it: dBm, Watts & dB
  27. 27. A device leaves the power of a signal exactly unchanged. What is its gain in decibels?
    Show answer

    0 dB

    A ratio of 1 is 10 log₁₀ 1 = 0 dB, and adding 0 dB to a chain changes nothing, just as multiplying by 1 changes nothing.

  28. 28. An amplifier with a gain of 15 dB is followed by an attenuator with a loss of 15 dB. What is their overall gain?
    Show answer

    0 dB

    The loss counts as −15 dB, so 15 + (−15) = 0 dB: a ratio of 1, the signal leaving as strong as it came in. Adding the loss as a gain gives 30 dB.

  29. 29. An attenuator reduces a 4 W signal to 1 mW. What is its loss in decibels?
    Show answer

    36 dB

    The power ratio is 4 ÷ 0,001 = 4000 = 4 × 1000, so the loss is 6 dB + 30 dB = 36 dB; 72 dB would come from 20 log, the voltage formula.

    Try it: dBm, Watts & dB
  30. 30. A 20 W signal is fed into an attenuator with a loss of 26 dB. What power comes out?
    Show answer

    50 mW

    26 dB = 20 dB + 6 dB, a power ratio of 100 × 4 = 400: 20 W ÷ 400 = 50 mW. 20 log, the voltage formula, gives a ratio of 20 and 1 W.

    Try it: dBm, Watts & dB
  31. 31. A signal passes through an amplifier with 20 dB of gain, a filter with 7 dB of loss and a second amplifier with 15 dB of gain. What is the overall gain?
    Show answer

    28 dB

    Write the loss as a gain of −7 dB and add: 20 − 7 + 15 = 28 dB; adding the 7 dB loss as if it were a gain gives 42 dB.

  32. 32. A 15 W transmitter feeds an antenna with 15 dB gain over a dipole through coax with a loss of 5 dB. What is the effective radiated power (ERP)?
    Show answer

    150 W

    The net gain is 15 + (−5) = 10 dB, a ratio of 10, so the ERP is 15 × 10 = 150 W; adding the coax loss as a gain makes 20 dB and 1,5 kW.

    Try it: Link Budget & Path Loss
  33. 33. A 30 W transmitter is connected through a cable with a 4 dB loss to an antenna with 10 dB gain over a dipole. What is the effective radiated power (ERP)?
    Show answer

    120 W

    The net gain is 10 + (−4) = 6 dB, a power ratio of 4, so the ERP is 30 × 4 = 120 W; counting the loss as a gain gives 14 dB and 750 W.

    Try it: Link Budget & Path Loss
  34. 34. A 30 W transmitter feeds an antenna with 8 dB gain over a dipole through coax with a loss of 3 dB. Which option is nearest to the effective radiated power (ERP)?
    Show answer

    90 W

    Net gain 8 − 3 = 5 dB, a ratio of 3,162 (between 2 for 3 dB and 4 for 6 dB): 30 × 3,162 = 94,9 W, nearest 90 W. The loss taken as a gain gives 380 W.

    Try it: Link Budget & Path Loss
  35. 35. A feedline has a loss of 1,5 dB. Which option is nearest to the share of the power fed in that reaches the antenna?
    Show answer

    70 %

    A loss of 1,5 dB leaves 0,71 of the power, nearest 70 %: half of 3 dB is the square root of 2, and 1 ÷ 1,41 = 0,71. 50 %, half, is what 3 dB leaves.

    Try it: Feedline Loss
  36. 36. A transmitter's 200 W reaches the antenna as 20 W. What is the loss in the feedline?
    Show answer

    10 dB

    The power ratio is 200 ÷ 20 = 10, and 10 log₁₀ 10 = 10 dB, written as a loss without a minus sign. 20 dB comes from 20 log, the voltage formula; subtracting the watts gives 180.

    Try it: dBm, Watts & dB
  37. 37. What is the quick way to convert a power ratio such as 10, 100 or 1000 into decibels?
    Show answer

    Count the zeros and multiply by 10

    Every zero is another factor of 10, worth 10 dB, so a ratio with three zeros is 30 dB; counting digits overstates it by 10 dB.

  38. 38. An amplifier has a power gain of 5. What is this in decibels?
    Show answer

    7 dB

    The table of common ratios gives 7 dB for a power ratio of 5; 14 dB would come from 20 log, which is used for voltage ratios.

    Try it: dBm, Watts & dB
  39. 39. What is a power gain of 40 in decibels?
    Show answer

    16 dB

    40 = 4 × 10, and multiplying ratios means adding decibels, 6 dB + 10 dB = 16 dB; multiplying the decibels, 6 × 10, gives the wrong 60.

    Try it: dBm, Watts & dB
  40. 40. The power of a signal is doubled. By about how many decibels has it risen?
    Show answer

    3 dB

    A power ratio of 2 is 3 dB, a figure worth remembering; 6 dB means four times the power, which is what doubling the voltage gives.

    Try it: dBm, Watts & dB
  41. 41. What is a power ratio of 100 000 in decibels?
    Show answer

    50 dB

    100 000 is a 1 followed by five zeros, so it is 5 × 10 = 50 dB; counting all six digits instead of only the zeros gives 60 dB.

    Try it: dBm, Watts & dB
  42. 42. What is a power ratio of 0,25 in decibels?
    Show answer

    −6 dB

    0,25 is 1 ÷ 4, so its decibel value is that of 4 with the sign reversed, −6 dB, a loss; +6 dB would be a gain of 4.

    Try it: dBm, Watts & dB
  43. 43. What is a power ratio of 8 in decibels?
    Show answer

    9 dB

    8 = 2 × 2 × 2, three doublings of 3 dB each, so 3 + 3 + 3 = 9 dB; 18 dB is what 20 log would give for a voltage ratio of 8.

    Try it: dBm, Watts & dB
  44. 44. What power ratio does 19 dB stand for?
    Show answer

    80

    19 dB = 10 dB + 9 dB, and 9 dB is three doublings (2 × 2 × 2 = 8), so the ratio is 10 × 8 = 80. Adding the ratios, 10 + 8, gives 18.

    Try it: dBm, Watts & dB
  45. 45. What is a power ratio of 16 in decibels?
    Show answer

    12 dB

    16 = 4 × 4, so 6 dB + 6 dB = 12 dB; 24 dB is the 20 log figure, which belongs to a voltage ratio of 16.

    Try it: dBm, Watts & dB
  46. 46. What is a power ratio of 0,04 in decibels?
    Show answer

    −14 dB

    0,04 = 4 × 0,01, so add 6 dB and −20 dB to get −14 dB; giving the 6 dB for the 4 a minus sign too leads to the wrong −26 dB.

    Try it: dBm, Watts & dB
  47. 47. What power ratio does 33 dB stand for?
    Show answer

    2000

    33 dB = 30 dB + 3 dB, so the ratios multiply, 1000 × 2 = 2000; adding them, 1000 + 2, gives the wrong 1002.

    Try it: dBm, Watts & dB
  48. 48. What power ratio does −24 dB stand for?
    Show answer

    0,004

    −24 dB = −30 dB + 6 dB, so the ratio is 0,001 × 4 = 0,004, a loss; dropping the minus sign gives a gain of 250 instead.

    Try it: dBm, Watts & dB
  49. 49. What power ratio does 4 dB stand for?
    Show answer

    2,5

    4 dB = 10 dB − 6 dB, and subtracting decibels divides the ratios, 10 ÷ 4 = 2,5; subtracting the ratios, 10 − 4, gives the wrong 6.

    Try it: dBm, Watts & dB
  50. 50. An amplifier raises the power of a signal from 200 mW to 4 W. What is its gain?
    Show answer

    13 dB

    RP = 4 ÷ 0,2 = 20 = 2 × 10, so the gain is 3 dB + 10 dB = 13 dB; 26 dB would be 20 log, the formula for voltage ratios.

    Try it: dBm, Watts & dB
  51. 51. A signal's power rises from 20 mW to 1,2 W. Which option is nearest to the gain?
    Show answer

    18 dB

    RP = 1,2 ÷ 0,02 = 60 and 10 log₁₀ 60 = 17,8 dB, so 18 dB is nearest; 36 dB comes from 20 log, the voltage formula.

    Try it: dBm, Watts & dB
  52. 52. Which option is nearest to a power ratio of 0,07 expressed in decibels?
    Show answer

    −12 dB

    10 log₁₀ 0,07 = −11,5 dB, between −13 dB for 0,05 and −10 dB for 0,1, so −12 dB is nearest; 20 log 0,07 would give about −23 dB.

    Try it: dBm, Watts & dB
  53. 53. An amplifier has a gain of 38 dB. Which option is nearest to its power ratio?
    Show answer

    6300

    38 dB = 30 dB + 8 dB, a ratio of 1000 × 6,31 = 6310, nearest 6300 (8 dB is 6,31, between 5 for 7 dB and 8 for 9 dB). 20 log, the voltage formula, gives only 79.

    Try it: dBm, Watts & dB
  54. 54. Which option is nearest to a power ratio of 3000 expressed in decibels?
    Show answer

    35 dB

    10 log₁₀ 3000 = 34,8 dB, nearest 35 dB: 3000 lies between 2500 (34 dB) and 4000 (36 dB). 70 dB comes from 20 log, the voltage formula; 30 dB ignores the 3.

    Try it: dBm, Watts & dB
  55. 55. What is a power ratio of 0,5 in decibels?
    Show answer

    −3 dB

    0,5 is 1 ÷ 2, so it is the 3 dB of a doubling with the sign turned over: −3 dB, half the power. Without the minus sign, 3 dB would be a gain of 2.

    Try it: dBm, Watts & dB
  56. 56. The voltage across a fixed resistance is doubled. By what factor does the power it dissipates increase?
    Show answer

    4

    With R fixed, P = V² ÷ R, so doubling V multiplies the power by 2² = 4, which is 6 dB; a factor of 2 would mean power simply followed voltage.

  57. 57. Which formula gives a voltage ratio RV in decibels, both voltages being across the same resistance?
    Show answer

    RdB = 20 log₁₀ RV

    Power is proportional to V², so 10 log₁₀ RV² = 20 log₁₀ RV, which is why voltage ratios take 20 where power ratios take 10.

  58. 58. The voltage across a load rises from 4 V to 40 V while the load resistance stays the same. By how much has the power risen, in decibels?
    Show answer

    20 dB

    RV = 40 ÷ 4 = 10, and 20 log₁₀ 10 = 20 dB, matching the power ratio of 10² = 100; using 10 log on a voltage ratio gives 10 dB.

    Try it: dBm, Watts & dB
  59. 59. The voltage across a load rises from 2 V to 6 V, the resistance staying the same. Which option is nearest to the rise in power?
    Show answer

    10 dB

    RV = 6 ÷ 2 = 3 and 20 log₁₀ 3 = 9,5 dB, as the power rises nine times, so 10 dB is nearest; 10 log 3, about 5 dB, treats RV as a power ratio.

    Try it: dBm, Watts & dB
  60. 60. A 40 dB attenuator is inserted in a line carrying 50 V RMS, with the impedances unchanged. What voltage comes out?
    Show answer

    0,5 V

    For voltage, 40 dB is a ratio of 100, since 20 log₁₀ 100 = 40, so 50 ÷ 100 = 0,5 V; dividing by the power ratio of 10 000 gives 5 mV.

    Try it: dBm, Watts & dB
  61. 61. An 11 dB attenuator is inserted in a line carrying 30 V RMS, with the impedances unchanged. Which option is nearest to the output voltage?
    Show answer

    8 V

    For voltage, 11 dB is a ratio of 3,55, between 2 for 6 dB and 4 for 12 dB, so 30 ÷ 3,55 = 8,45 V, nearest to 8 V; the power ratio 12,6 would give 2,4 V.

    Try it: dBm, Watts & dB
  62. 62. An amplifier with equal input and output resistances has a gain of 60 dB. If 1 mV is applied to its input, what is the output voltage?
    Show answer

    1 V

    60 dB is a power ratio of 1 000 000 but a voltage ratio of only √1 000 000 = 1000, so 1 mV × 1000 = 1 V; using the power ratio gives 1 kV.

    Try it: dBm, Watts & dB
  63. 63. Why is it usually better to work with power ratios than voltage ratios when using decibels?
    Show answer

    Voltage figures in decibels are confusing and can mislead

    Decibels really describe power, and a voltage ratio gives the right figure only across equal resistances, so voltage decibels easily mislead. One change gives the same decibels either way: neither is easier to add.

  64. 64. An amplifier with equal input and output resistances turns a 5 µV signal into 50 mV. What is its gain?
    Show answer

    80 dB

    RV = 50 mV ÷ 5 µV = 10 000, and with equal resistances the gain is 20 log₁₀ 10 000 = 80 dB; 10 log would give only 40 dB.

    Try it: dBm, Watts & dB
  65. 65. What does a voltage ratio expressed in decibels describe?
    Show answer

    The ratio of the powers they would deliver into a load

    Decibels always express a power ratio: for voltages, that of the powers they would deliver into the same load, hence 20 log, as power goes with V². The voltages alone are not what is described.

  66. 66. A signal of 20 µV appears across the 50 Ω input resistance of an amplifier. What input power does it deliver?
    Show answer

    8 pW

    P = V² ÷ R = (20 × 10⁻⁶)² ÷ 50 = 400 × 10⁻¹² ÷ 50 = 8 × 10⁻¹² W = 8 pW; forgetting to square V gives 0,4 µW.

    Try it: dBm, Watts & dB
  67. 67. An amplifier has an input resistance of 1 kΩ and drives a 4 Ω load. An input of 2 V gives 20 V across the load. What is its power gain?
    Show answer

    44 dB

    PIn = 2² ÷ 1000 = 4 mW, POut = 20² ÷ 4 = 100 W: 25 000 times, 14 + 30 = 44 dB. 4 mW taken as 4 W gives 14 dB; 20 log ignores the resistances.

    Try it: dBm, Watts & dB
  68. 68. What RMS voltage across a 50 Ω load delivers a power of 2 W?
    Show answer

    10 V

    P = V² ÷ R gives V² = P × R = 2 × 50 = 100, so V = √100 = 10 V. Forgetting the square root leaves 100 V; 0,04 is P ÷ R.

    Try it: dBm, Watts & dB
  69. 69. What do the units dBW and dBm mean?
    Show answer

    Decibels relative to 1 W, and to 1 mW

    dBW states a power as decibels above or below 1 W, and dBm as decibels above or below 1 mW, so 0 dBW is a thousand times 0 dBm.

  70. 70. In the Radio Spectrum Regulations, in which unit are the power limits for amateur transmissions given?
    Show answer

    dBW

    The regulations give amateur power limits in dBW, decibels relative to 1 W, instead of in watts as they once did.

  71. 71. A power level is given as 30 dBW. How many watts is that?
    Show answer

    1 kW

    30 dBW is 30 dB, a ratio of 1000, above 1 W, so 1000 W = 1 kW; 1 W is what 30 dBm, referred to 1 mW, would be.

    Try it: dBm, Watts & dB
  72. 72. What is a power of 1 mW expressed in dBW?
    Show answer

    −30 dBW

    1 mW is a thousandth of 1 W, three zeros below the reference, so −30 dBW; 0 is its value in dBm, which uses 1 mW as the reference.

    Try it: dBm, Watts & dB
  73. 73. How much power is 40 dBm?
    Show answer

    10 W

    40 dBm is 40 dB, a ratio of 10 000, above 1 mW, so 10 000 mW = 10 W; reading it as 40 dBW would give 10 kW.

    Try it: dBm, Watts & dB
  74. 74. Which of these power levels is the greatest?
    Show answer

    10 dBW

    10 dBW is 10 W, whereas 30 dBm and 0 dBW are both 1 W and 20 dBm is only 0,1 W, so the bigger number in dBm misleads.

    Try it: dBm, Watts & dB
  75. 75. Which option is nearest to a power of 350 W expressed in dBW?
    Show answer

    25 dBW

    10 log₁₀ 350 = 25,4, so 350 W is 25,4 dBW, between 23 dBW (200 W) and 26 dBW (400 W) and nearest to 25 dBW; 55 is roughly its value in dBm.

    Try it: dBm, Watts & dB
  76. 76. A signal generator is set to −90 dBm. What is its output power?
    Show answer

    10⁻¹² W

    −90 dBm is 90 dB, nine zeros, below 1 mW, so 10⁻⁹ × 10⁻³ = 10⁻¹² W; taking 1 W as the reference instead gives 10⁻⁹ W.

    Try it: dBm, Watts & dB
  77. 77. Which is the best estimate of the weakest signal that most amateur receivers can detect?
    Show answer

    About −130 dBm

    Most amateur receivers detect about −130 dBm, 130 dB below 1 mW: 10⁻¹⁶ W. −13 dBm is some 50 µW, an enormous signal, and −130 dBW would be a thousand times stronger than −130 dBm.

  78. 78. What prevents an actual power, such as 100 W, from being given in plain decibels?
    Show answer

    Decibels express a ratio, which needs a reference

    Decibels compare two powers, so a power on its own needs a fixed reference: 100 W is 20 dB above 1 W, written 20 dBW. Losses and other ratios are in decibels too, not only gains.

  79. 79. A signal of 10 dBm passes through an amplifier giving 23 dB of gain. What level comes out?
    Show answer

    33 dBm

    A gain in decibels adds to a level in dBm: 10 dBm + 23 dB = 33 dBm, still measured from 1 mW. Multiplying the figures, 10 × 23, gives the wrong 230 dBm.

    Try it: dBm, Watts & dB
  80. 80. A transmitter delivers 20 dBW into a feedline with a loss of 2 dB, feeding an antenna with a gain of 8 dB over a dipole. What is the ERP?
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    26 dBW

    Decibels add along the path, the loss counting as a negative gain: 20 dBW − 2 dB + 8 dB = 26 dBW. Adding the feedline's 2 dB as a gain gives 30 dBW.

    Try it: Link Budget & Path Loss