Two 1-km fibers are spliced together. Each fiber has a 5-dB loss, and the splice adds 1 dB of loss. If the power entering is 2 m W, then how much power is delivered to the end of this combined transmission line?
Total loss = -5 + -5 + -1 = -11 db
10*Log(Po/Pi) = -11 db.
10*Log(Po/2) = -11
Log(Po/2) = -1.1
Po = 2*10^-1.1 = 0.159 mW.
Well, well, well, we've got a little fiber splicing situation going on here, huh? Alright, let's put on our clown hats and do some calculations!
So, each fiber has a 5-dB loss, and the splice adds 1 dB of loss, making it a total of 6 dB loss. Now, let's convert 6 dB into a linear scale because, let's be honest, we don't want any more confusion than necessary. Remember, we're trying to bring some clarity here, folks!
Converting 6 dB to a linear scale, we use the formula: linear value = 10^(dB/10). Applying this formula, we get a linear value of approximately 0.501.
Now, since the power entering the fibers is 2 mW, we need to multiply it by the linear value of 0.501 to find the power delivered to the end of this fiber-filled adventure. So, 2 mW multiplied by 0.501 equals approximately 1.002 mW.
So, after all the fiber losses and the clowning around, approximately 1.002 mW of power is delivered to the end of this combined transmission line. Voila!
To calculate the total power delivered to the end of the combined transmission line, we need to consider the losses in each fiber and the splice.
Given:
- Each fiber has a 5 dB loss.
- The splice adds 1 dB of loss.
- The power entering is 2 mW.
Step 1: Convert the power from milliwatts (mW) to decibels (dB).
The formula to convert power from mW to dB is:
dB = 10 * log10(P / P0)
Since P0 is a reference power (usually 1 mW), we can simplify the formula to:
dB = 10 * log10(P)
Converting the power entering from 2 mW to dB:
P_in_dB = 10 * log10(2)
P_in_dB = 10 * 0.3010
P_in_dB = 3.010 dB
Step 2: Calculate the total loss in the two fibers.
Since each fiber has a 5 dB loss, the total loss for two fibers would be:
Total_loss_fibers = 2 * 5 dB
Total_loss_fibers = 10 dB
Step 3: Calculate the total loss including the splice.
Total_loss = Total_loss_fibers + 1 dB
Total_loss = 10 dB + 1 dB
Total_loss = 11 dB
Step 4: Calculate the power delivered to the end of the combined transmission line.
Using the formula to convert power from dB back to mW:
P_out_dB = P_in_dB - Total_loss
P_out_dB = 3.010 dB - 11 dB
P_out_dB = -7.990 dB
P_out = 10^(P_out_dB/10) (using the inverse of the dB to mW conversion formula)
P_out = 10^(-7.990/10)
P_out ≈ 0.0796 mW
Therefore, the power delivered to the end of the combined transmission line is approximately 0.0796 mW.
To find the power delivered to the end of the combined transmission line, we need to calculate the total loss experienced by the signal as it travels through the fibers and splice.
Given:
- Length of each fiber = 1 km
- Loss per km = 5 dB
- Splice loss = 1 dB
- Power entering = 2 mW
First, let's calculate the total loss in the fibers. Since each fiber has a length of 1 km, and the loss per km is 5 dB, the total loss in each fiber is 5 dB/km * 1 km = 5 dB.
Next, let's calculate the total loss including the splice. The total loss is the sum of the loss in the fibers and the splice loss, which is 5 dB + 1 dB = 6 dB.
Now, let's convert the power from dB to milliwatts (mW). We can use the formula:
Power (in mW) = 10^(Power (in dB) / 10)
Applying this formula, the power loss in milliwatts is:
Loss (in mW) = 10^(Total Loss (in dB) / 10) = 10^(6 / 10) = 3.981 mW
Finally, to calculate the power delivered to the end of the combined transmission line, we subtract the loss from the initial power:
Power delivered (in mW) = Power entering (in mW) - Loss (in mW) = 2 mW - 3.981 mW = - 1.981 mW
Note that the result is negative, indicating that the transmitted power is lower than the initially supplied power. In this case, the power delivered to the end of the combined transmission line is approximately -1.981 mW.