sinusoidal carrier

karthikbalaguru hath wroth:

Yep. By definition, a sinusodial waveform is one that doesn't have any harmonics or distortion. It consists only of the fundamental frequency. If you want to minimize interference to other services on other frequencies, a low distortion sine wave carrier is a must.

Yeah, i find that sawtooth wave of constant period contains odd and even harmonics that fall off at -6 dB/octave. Square wave of constant period contains odd harmonics that fall off at -6 dB/octave. Triangle wave, (an integral of square wave) contains odd harmonics that fall off at -12 dB/octave. But, Sine wave does not contain any harmonics or distortion.

Karthik Balaguru

uru hath wroth:

Thx for your info. Thinking over this, i have a strange query :( :( How is it possible that a sinusodial waveform alone doesn't have any harmonics or distortion ?

Thx in advans, Karthik Balaguru

karthikbalaguru hath wroth:

An ideal sine wave has no harmonic distortion by definition. That is, the equation a*sin(wt) only has the fundamental frequency. A real life sine wave has distortion, but you need hardware to detect it.

Regarding the fall off of harmonics, there is some rule of thumb no longer in my brain that relates the harmonic fall off with the number of continuous derivatives of the function. This is the closest I could find on google to the rule of thumb:

the smoother the function, the lower the harmonic levels.

My recollection is the square wave falls off as the 1/n where n is the harmonic. Also the 3rd harmonic of a square wave is stronger than the fundamental. You would need to google fourier series to get reality.

karthikbalaguru hath wroth:

I seem to be doing your homework. This is also the wrong newsgroup for basic communications questions. Any book on basic communications theory will have a page on waveform analysis.

You start with a sine wave. It's strictly the fundamental with no harmonics.

If you add distorition (harmonics), if the harmonics are odd order (3,5,7,9,11,etc), then the waveform will be symmetrical.

If you add distortion (harmonics), if the harmonics are even order (2,4,6,8,10, etc), then the waveform will by asymmetrical.

Exmaples:

If you spend some time with a function generator and spectrum analyzer, you can see the effects of odd and even harmonics on spectra.

If you want to use a computer to see how it works, I suggest you download Sillanumsoft Visual Analyzer. This is a very handy audio oscilloscope, spectrum analyzer, and function generator. You can internally generate a waveform, and see the resulting spectra.

Don't forget to click the "ON" button in the upper left corner.

There are lots of other reasons to use a sine wave to drive a cell phone. In order to get sufficient bits per baud, most modulation methods involve both FM and AM. FM modulation doesn't care about the harmonic content of the synthesizer. AM modulators care and will produce distorted and non-linear garbage if overdriven by harmonic.

In addition, the FCC and other regulatory agencies fail to appreciate harmonics and spurious signals being belched by cell phones. If you remove the modulation, the remaining RF carrier needs to be about clean down to about 0.0001% (about -60dB below peak power) in order to placate the regulatory agency. If you can see the distortion, it will fail.

Interesting Info :):). Thx.

Karthik Balaguru

alaguru hath wroth:

Interesting to know that real life sine wave has distortion :):)

Thx, Karthik Balaguru