What happens when two channels of equal power, but different frequencies, are combined for transport over a network?

When two channels of equal power but different frequencies are combined, the resulting total power of the combined channels is 3 dB over that of either channel. This increase occurs due to the way power levels are expressed in decibels (dB). When two signals are combined, their powers are additive.

To elaborate, when you have two equal power signals, coherent addition in decibels results in an increase of 3 dB. This is mathematically represented as follows: if each channel has a power of P, the combined power can be calculated as:

[

P_{total} = P + P = 2P

]

In dB, this translates to:

[

10 \log_{10}(2P / P) = 10 \log_{10}(2) \approx 3 \text{ dB}

]

This outcome highlights that combining two unequal signals can yield a net increase in power because decibels measure power in a logarithmic scale. Since the channels are of different frequencies, they do not interfere with each other destructively, which keeps the total energy being transported over the network at a higher level than that of a single channel.