Two 1 km fibers are spliced together. Each fiber has a 5 db loss and the splice adds the 1 db of loss. If the power entering is 2mW, then how much power is delivered to the end of this combined transmission line ?
To calculate the power delivered to the end of the combined transmission line, we need to consider the losses in each fiber and the splice.
Given:
- Length of each fiber = 1 km
- Loss in each fiber = 5 dB
- Loss in the splice = 1 dB
- Power entering = 2 mW
First, let's convert the power from milliwatts (mW) to decibels (dB). The conversion formula is:
Power (dB) = 10 * log10(Power (mW))
Here, we can calculate the power entering in dB:
Power (dB) = 10 * log10(2) ≈ 3 dB
Now, let's calculate the total loss in the fibers and the splice.
Loss (dB) = Loss in Fiber 1 (dB) + Loss in Fiber 2 (dB) + Loss in Splice (dB)
= 5 dB + 5 dB + 1 dB
= 11 dB
Next, we can calculate the power at the end of the combined transmission line by subtracting the total loss from the initial power:
Power at the end (dB) = Power entering (dB) - Loss (dB)
= 3 dB - 11 dB
= -8 dB
Finally, let's convert the power at the end back to milliwatts:
Power at the end (mW) = 10^(Power at the end (dB) / 10)
= 10^(-8 / 10)
≈ 0.1585 mW
Therefore, the power delivered to the end of the combined transmission line is approximately 0.1585 milliwatts (mW).