Why does a square waveform require more bandwidth then a sine waveform for transmission?

Answer 1

A sine wave is used for transmission - and not a square or triangular wave - because a sine wave is the most efficient waveform to use and also because it can be generated using normal copper windings in alternator rotors and stators without needing much, if any, "wave shape improvement" equipment.

The deliberate production of either square or triangular waves would waste a huge amount of energy, both in the power generation plant and in the many Transformers used in the power distribution network. Read some Electrical Power Technology books to find out more!

Answer 2

Because a sine wave is just a sine wave. Its bandwidth requirement is just its frequency.

A square wave consists of a sine wave of the same frequency as the square wave and all the odd harmonics to infinity. Since no transmission system has infinite bandwidth, it follows that it is not possible to transmit a square wave perfectly.

To prove, consider a one square wave. using this formula:

BW= f0/Q ,

where f0 is the center frequency of the square wave and Q is the quality factor.An ideal square wave does not fall -3dB because it is flat on top. Thus f1 and f2 is infinite , Q=0 (infinitely wide), thus the bandwidth is infinite.

Answer 3

A square wave is mathematically the sum of an infinite number of sinewaves. A 2kHz squarewave is composed of a basic sinewave known as a fundamental, having a frequency of 2kHz, plus an infinite number of all odd harmonics. An odd harmonic has a frequency of an odd number mulitplied by the fundamental. So the 3rd harmonic has a frequency of 6kHz, the 5th harmonic has a frequency of 10kHz, and so fourth for the 7th, 9th, 11th, 13th.......to infinity, harmonics. So every squarewave, regardless of frequency, has a bandwidth of infinity.

Answer 4

Let's compare a 1kHz sine wave and a 1kHz square wave.

The former consists of only one component - it's a sine wave.

The square wave consists of the sum of many sine waves. There is the fundamental of 1kHz and an infinite series of odd harmonics, each successive one having an amplitude equal to a fraction of the fundamental equal to the harmonic's order.

What does that mean?

Lets's explain.

The third harmonic has an amplitude a third of the fundamental's, the fifth harmonic an amplitude of a fifth of the fundamental's, the seventh harmonic an amplitude of one seventh of the fundamental's ... etc.

So you see, a 1kHz sine requires a bandwidth of only 1kHz, but a 1kHz square wave, if it's shape is to be preserved, requires a bandwidth of up to at least 9kHz, the higher the better.