Power vs. Bandwidth

Question

A 10 watt transmitter is transmitting a 700 hz tone in a 3 kHz wide band. If the power is increased to 1000 watts will that not increase the bandwidth if the data (700Hz tone) remains constant? What I am asking is this. Does the bandwidth become wider if the power is increased and the data transmitted stays the same? It seems to me like it must become wider. If the power is increased with the data remaining constant the power must go somewhere and I contend that it goes into increasing the bandwidth of the signal. I do not want to factor in noise or any changes in receiver characteristics. Just power vs. bandwidth.

Simply a 3kHz wide bandwidth saturated with 700 Hz tone and the power is increased from 10 watts to 1000 watts. Thank you.

Answer 1

Unless there is a defect in the transmitting station, the transmitted bandwidth always stays the same when the power is increased.

That is true even if the power is increased from 1 microwatt to 1 megawatt, if that were possible.

Having said that, when you or I are listening to a 10 watt station and its power increases to 1000 watts (or more), its bandwidth may appear to increase. This could be due to several reasons, and I'll list only a few here.

• A linear amplifier is switched on, and it introduces more distortion than the 10W transmitter.
• Portions of the signal that were below your receiver's noise threshold are now audible.
• Due to the increased signal power at your preamp or receiver, the latter overloads and the bandwidth in your receiver increases. Same thing can happen in your noise blanker

Answer 2

"A rising tide lifts all boats equally." Since bandwidth is measured in relation to the signal's peak amplitude, linear amplification alone should not increase the signal's bandwidth. Generally speaking, all frequencies produced by your source that fall in the amplifier bandwidth will increase by at least the gain of the amplifier. The amplifier's inherent nonlinearity will distort the input to some degree, which may increase some noise components more than others and even produce new noise components that will increase the signal bandwidth. Of course, operating the amplifier outside its specified limits will produce undesired products like "splatter."

We must be careful with our terms when talking about signals and bandwidth. The generator and the detector each has its own "bandwidth."

In theory, a "700Hz tone" has zero bandwidth. In reality, all processes are subject to random fluctuations and nonlinear behaviors that increase the bandwidth from this ideal. Inasmuch as an oscillator is an (imperfect) amplifier with positive feedback, noises that appear in the output are fed back to the input, resulting in self-mixing products that appear as noise in a spectrogram. (In fact, the "noise" of random fluctuations is what gets the oscillation process going in the first place!) Even a crystal oscillator produces "noise sidebands" that generally diminish with frequency difference from the carrier. The "bandwidth" of this real world "pure tone" depends on many factors including: component selection and construction; circuit design and implementation; environmental noises like vibration and power supply variations.

The detector measures the power that is present in its bandwidth. A wider detector will capture more of the generator's noise power than will a narrowband detector. Combining the properties of the generator with the properties of the detector gives meaning to your statement, re: "700Hz tone in a 3kHz bandwidth" but doesn't relate to the signal's bandwidth as a function of its amplitude.