What is the effective radiated power of a repeater with a 50 watts transmitter output, considering 4 dB feedline loss, 3 dB duplexer and circulator loss, and 6 dB antenna gain?

To calculate the effective radiated power (ERP) of a repeater with the given specifications, you need to consider the transmitter output, loss components, and the antenna gain.

Start with the transmitter output power, which is 50 watts. Next, you need to deduct the losses from the transmission system and then account for the antenna gain.

1. Calculate the Total Losses:

• Feedline loss: 4 dB

• Duplexer and circulator loss: 3 dB

• Total loss = 4 dB + 3 dB = 7 dB

2. Convert the dB Loss to Power Factor:

A loss of 7 dB can be converted to a power factor using the formula:

[

\text{Power factor} = 10^{\frac{\text{Loss (dB)}}{10}} = 10^{\frac{7}{10}} \approx 5.012

]

This means that you lose about a factor of 5.012 in power due to the losses.

3. Calculate the Output Power After Losses:

The effective power after applying the total loss from the transmitter output