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Duality

Tue Aug 31 2010, 09:59PM

Registered Member #1951 Joined: Sun Feb 01 2009, 01:59PM
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Posts: 105

hello everyone i don't know if i placed it in the right section, but i have a problem, that is math.
frequency in Hz is how Manny times something happens in a second, lets take sound, Hz is two times a second, frequency is 2 Hz.
now i have something that can't happen past 220 ns (nanoseconds) how can i visualize this in terms of frequency can i say not beyond 220MHz? or am i just thinking plane wrong here? cause i have the feeling i am just thinking wrong here.

lets take a switch that can switch, (lol) but can't make smaller passes then 220 ns means it can switch at 220 MHz?

if im not clear please tell me :)

AleSeg

Tue Aug 31 2010, 10:30PM

Registered Member #2727 Joined: Tue Mar 09 2010, 02:39PM
Location: Montevideo - Uruguay
Posts: 33

I don't know if i understand all, but when you speak about frequency you are considering periodical phenomena, and numerically f = 1/T, where T is the period of repetition of the signal in seconds, and f is the freq in Hz. something with a T= 220 ns has a main associated freq of 45.5 MHz.
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big5824

Tue Aug 31 2010, 11:26PM

Registered Member #1687 Joined: Tue Sept 09 2008, 08:47PM
Location: UK, Darlington
Posts: 240

f=1/T, where f is frequency and T is time period of one oscillation. Remember you need both values in SI units

klugesmith

Wed Sept 01 2010, 12:06AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

AleSeg wrote ...

I don't know if i understand all, but when you speak about frequency you are considering periodical phenomena, and numerically f = 1/T, where T is the period of repetition of the signal in seconds, and f is the freq in Hz. something with a T= 220 ns has a main associated freq of 45.5 MHz.
See You

Bzzzt! Decimal point error!

1 / (220 ns) = 4.55 MHz.

Conversely, a frequency of 220 MHz has a period of 4.55 ns. Verstehen Sie?

zhgart

Wed Sept 01 2010, 02:48AM

Registered Member #3156 Joined: Wed Sept 01 2010, 02:19AM
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what is "something that can't happen past 220 ns '?

Duality

Wed Sept 01 2010, 03:52PM

Registered Member #1951 Joined: Sun Feb 01 2009, 01:59PM
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zhgart wrote ...

what is "something that can't happen past 220 ns '?

lets say a switch that can't switch faster then 220 ns.

Mattski

Wed Sept 01 2010, 10:32PM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

R v.d. Tuuk wrote ...

lets take a switch that can switch, (lol) but can't make smaller passes then 220 ns means it can switch at 220 MHz?

Sort of, it depends on the shape of the waveform really. If a switch can switch on and off with a 220ns period then the "fundamental" frequency is indeed 4.5MHz as Klugesmith notes. But in order to have a nice square waveform at 4.5MHz, your switch needs to be working well at odd harmonics of the fundamental frequency: 13.5MHz, 22.5MHz, 31.5MHz, etc. That's because of the fourier series of a square wave. The series is infinite but because you need less amplitude in the higher harmonics, if they are attenuated it can still look pretty square. So if your waveform looks very square with a 220ns period then it could probably switch a sine wave at least at the 5th harmonic (22.5MHz) pretty well.

It's harder to make a square waveform because you need the higher frequency components as well as the fundamental tone. If your transistor is attenuating the higher frequency harmonics then your waveform will have a bigger rise/fall time and maybe some ripple and overshoot.

Look at

which has this nice graphic:

which shows a square wave vs. its fundamental tone, fundamental + 3rd harmonic, fund + 3rd + 5th, and fund + 3rd + 5th, + 7th.

Is this what you're trying to f igure out?

Duality

Thu Sept 02 2010, 06:11PM

Registered Member #1951 Joined: Sun Feb 01 2009, 01:59PM
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Posts: 105

so a square wave is basicly a sine wave with harmonics in it's planes? (just to see if i understood it correct.)
but i figured it out, i wanted to know the frequency if the wave had 220ns inter falls i was doing the math wrong i see, thanks all :)
ow and why do these harmonics have odd numbers? or can harmonics be even numbers like second and forth, what's this phenomena called?

Mattski

Thu Sept 02 2010, 08:25PM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

R v.d. Tuuk wrote ...

so a square wave is basicly a sine wave with harmonics in it's planes? (just to see if i understood it correct.)
but i figured it out, i wanted to know the frequency if the wave had 220ns inter falls i was doing the math wrong i see, thanks all :)
ow and why do these harmonics have odd numbers? or can harmonics be even numbers like second and forth, what's this phenomena called?

Yes, any periodic (repeating) waveform no matter what the shape can be represented as a combination of sinusoids at frequencies which are harmonics of the fundamental frequency of the original wave. This is part of Fourier analysis.

It just so happens to work out for square waves when you do the math that they have all odd harmonics. But that is only true for certain special cases like square waves, triangle waves also have only odd harmonics but in different amounts. Most typical waveforms will be composed of both odd and even harmonics.

radiotech

Fri Sept 03 2010, 05:56AM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

Perhaps the word wave should be explored. A sin or square is the periodic alternation in polarity at the lowest frequency we are considering. 1/f is the time for 1 alternation.
The problem with the square wave is it cannot be depicted on a time line. Time doesnt jump. 1/f - 3/â†¨ is the time for 1 alternation.

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