For a total transmit power (Pt) of 1000 W, determine the energy per bit (Eb) for a transmission rate of 50 Mbps.

Question

For a total transmit power [latex](P_{t})[/latex] of 1000 W, determine the energy per bit [latex](E_{b})[/latex] for a transmission rate of 50 Mbps.

Accepted Answer

[latex]T_{b}=\frac{1}{f_{b}}=\frac{1}{50\,×\,10^{6}\,bps}=0.02\,×\,10^{-6}s[/latex]

(It appears that the units for [latex]T_{b}[/latex] should be s/bit, but the per bit is implied in the definition of [latex]T_{b}[/latex], time of bit.)
Substituting into Equation 4 yields

[latex]E_{b}= P_{t}T_{b}[/latex] (4)

[latex]E_{b}=1000\,J/s\, (0.02 × 10^{-6} s/bit) = 20\,μJ[/latex]

(Again the units appear to be J/bit, but the per bit is implied in the definition of [latex]E_{b}[/latex], energy per bit.)

[latex]E_{b}=\frac{1000\,J/s}{50\,×\,10^{6}\,bps}= 20\,μJ[/latex]

Expressed as a log with 1 joule as the reference,

[latex]E_{b}=10\log(20 × 10^{-6}) = −47\,dBJ[/latex]

It is common to express [latex]P_{t}[/latex] in dBW and [latex]E_{b}[/latex] in dBW/bps. Thus,
[latex]P_{t}[/latex] = 10 log 1000 = 30 dBW
[latex]E_{b} = P_{t}[/latex] − 10 log [latex]f_{b} = P_{t}\, − \,10\log (50 × 10^{6})[/latex]
= 30 dBW − 77 dB = −47 dBW/bps
or simply −47 dBJ.

Question 14.2: For a total transmit power (Pt) of 1000 W, determine the ene......

Related Answered Questions

Verified Answer:

Verified Answer:

A coherent binary phase-shift-keyed (BPSK) transmitter operates at a bit rate of 20 Mbps. For a probability of error P(e) of 10^-4, a. Determine the minimum theoretical C/N and Eb/N0 ratios for a receiver bandwidth equal to the minimum double-sided Nyquist bandwidth. b. Determine the C/N if the ...

Verified Answer:

For an equivalent noise bandwidth of 10 MHz and a total noise power of 0.0276 pW, determine the noise density and equivalent noise temperature. ...

Verified Answer:

Convert noise figures of 4 dB and 4.1 dB to equivalent noise temperatures. Use 300 K for the environmental temperature. ...

Verified Answer:

For an earth station transmitter with an antenna output power of 40 dBW (10,000 W), a back-off loss of 3 dB, a total branching and feeder loss of 3 dB, and a transmit antenna gain of 40 dB, determine the EIRP. ...

Verified Answer:

An earth station is located in Houston, Texas, which has a longitude of 95.5°W and a latitude of 29.5°N. The satellite of interest is RCA’s Satcom 1, which has a longitude of 135°W. Determine the azimuth angle and elevation angle for the earth station. ...

Verified Answer: