do harmonics exist?

[harryr]

I understand that I can do a Fourier Transform on a waveform
in the time domain to identify frequency components which
can be combined to reconstruct the waveform in the time domain.

Now, say I have a component in the frequency domain at for example, 30 MHz.
If I excite the box that is creating the time domain waveform and place an antenna ajacent to the box and connected to a receiver which is tuned to 30MHz, will it measure a 30 MHZ signal?

 

[SolderingGunslinger]

The answer to the question posed in the title of your post is a resounding YES.

After reading the post, I have come to the conclusion that I need to go and find an epistemology web board.

I remain,
The Old Soldering Gunslinger

 

[VEBill]

Yes. In fact on a good day you might even get a QSL card from someone in a land far, far away.

 

[harryr]

S.Gunslinger
Thanks for your response.
I would like to make sure you understood my question.
I'm not doubting your response but if that's true, I need you or someone to answer another question.
Clarification of my previous post, if needed.
The time domain waveform that I have was not created by combining sine waves at different freuqencies. I understand that can be done.
The time domain waveform was created by closing a switch connecting a battery to a resistor then openning the switch.
The Fourier Transform of that waveform says that if I want to duplicate it without using the switch,battery and resistor,
I can do it mathematically or physically using sine wave generators.
My next question is: How (physically ) does a battery make sine waves. Every battery I know about makes direct current.
This is a serious question of mine.
Thanks

 

[VEBill]

The battery and the switch makes square waves.

It's God/Nature that makes the sin waves... ;-)

They're really there as can be demonstrated with an AM broadcast band or shortwave radio.

 

[IRstuff]

Is this a homework problem?

Most engineers have had Fourier analysis and this particular topic is covered in the first quarter of F.A.

TTFN

 

[Comcokid]

You can take a square wave generator, and a receiver (i.e. shortware general-coverage receiver) and actually pick up the fundamental and harmonics at their different frequencies and with different signal strengths.

You have probably also heard the "pop" out of the audio of a receiver or TV as a nearby device has been turned on. Similar situation.

 

[harryr]

Comcokid:Thanks for your reply.
Regarding the square wave generator you mentioned,
does it make square waves out of sine waves?
If it does I agree that the "harmonics" exist.
I believe these "harmonics"
are the sine waves that are used to make the square wave.
My question is-- How does a battery which is connected and
and disconnected from a load (making a square wave )
generate "harmonics".
I believe that a 30MHZ signal (for example ) can
only be radiated by an electric charge (electrons) that are accelerating and de-ccelerating at a 30MHZ rate.

 

[VEBill]

Set your signal generator to 1 MHz sin wave. Your radio will pick up a signal pretty much only at 1 MHz (plus or minus any minor imperfections).

Set the signal generator to square wave output. You radio will now pick up strong signals at not just 1 MHz, but also 3, 5, 7, 9, 11 MHz, etc.

It's not a matter of belief. It's the way it works.

 

[Comcokid]

Not sure exactly what you're after, but I'll give more examples.

Example: You can take a sine wave, run it through a limiter circuit, and create a square wave. A limiter circuit is basically a gain stage where the gain exceeds the amplifying limits of the circuit. You might argue that since this involves additional circuits that the output is not really related to the input.

Another example and one that demonstrates a practical phenomena: Take a sine wave source (transmitter) and apply it to an antenna. The connection to the antenna has some corrosion. Metal corrosion acts like a non-linear junction. This will pass the original signal plus also produce harmonics of the signal. The output will be a periodic waveform that will consist of the fundamental and harmonics in some additive arrangement. This points out one of the reasons why connections to the antenna in high power transmitters are kept clean otherwise they may generate noise that will interfere with radio services at other frequencies.

Both examples are of non-linear functions applied to a sinewave producing harmonics.

Still another example: Two transmitters at different frequencies f1 and f2 have their antennas close together. Within the near field of the antennas, additional frequency products will be produced: f1-f2, and f1+f2. These products may additionally interact to produce even more frequency products. In this case, non-linear elements are not even involved (to the best of my understanding). Such a situation was found as a design flaw with a NOAA satellite that had two antennas several years ago and made signal reception from it more troublesome.

 

[harryr]

VE1BLL-- thanks for your input.
My question is, How does the signal generator make square waves?
If it is synthesized from sine waves and the equipment "leaks"
RF energy, you can measure the different freuuencies.

 

[IRstuff]

No, you are confusing Fourier analysis with physical reality.

A square wave train is a square wave train. PERIOD.

Fourier analysis says that you can mathematically represent such a train as a summation of odd harmonics, and that with the appropriate phasing and amplitude can represent a square wave.

The converse is that if you run a square wave through a filter, you will see outputs that are the sinusoidal components of the square wave.

TTFN

 

[VEBill]

"No, you are confusing Fourier analysis with physical reality. A square wave train is a square wave train. PERIOD."

I, and my shortwave radio, disagree.

Those sin wave harmonics are quite real. If you emit a powerful enough "square wave", then you might even get a visit from your local FCC (or DOC) complaining about some of those other sin wave harmonics that will have been causing problems.

A square wave REALLY IS exactly the same thing as a series of appropriately-arranged sin waves. And vice versa.

It isn't just math. It's also physical reality.

 

[IRstuff]

The OP question was whether you needed to use a series of odd harmonice to "synthesize" a square wave, which you don't, as evidenced by digital logic circuits.

TTFN

 

[debodine]

A perfect square wave (theoretical) is a collection of all odd harmonics of the fundamental frequency, ad infinitum.

Square Wave = Fundamental frequency + 3rd harmonic + 5th harmonic + 7th harmonic ---> Infinity of odd harmonics.

Or so I seem to recall the definition when I learned it many many moons ago.

 

[SolderingGunslinger]

An oscillator, limiter and tank circuit tuned for the required Fo makes a wonderful frequency multiplier. Such circuits were at one time fairly common in old VHF and UHF radios.

Hams used to triple the outputs of their 2-Meter transmiters to operate on 70-CM...back when most VHF equipment was home brew (and mostly hollow state).

I remain,

The Old Soldering Gunslinger

 

[fmradio]

Earlier: Two transmitters at different frequencies f1 and f2 have their antennas close together. Within the near field of the antennas, additional frequency products will be produced: f1-f2, and f1+f2. These products may additionally interact to produce even more frequency products. In this case, non-linear elements are not even involved (to the best of my understanding).
____________

The nonlinearity occurs in the output stage of each of the transmitters. The most common mode is the 2nd harmonic of one tx (say f1) mixing with the antenna-coupled fundamental of the co-sited tx (f2), to produce an RF intermod at 2f1-f2. If this component is not far removed in freq from f1, it can pass through the f1 output network and be radiated by the f1 antenna system. The same scenario could exist for f2, which could generate 2f2-f1.

This is a common situation when broadcast stations are co-located, and must be controlled with custom RF filters. Paper 7 at

http://rfry.org

gives some techniques for FM applications.

 

[harryr]

FMRadio -thanks for your reply.
I feel that I have not defined my question well enough.
Many respondents have reminded me about the Fourier transform and how to use sine waves (odd frequencies and phase shift management ) to "create" a square wave.
I agree with that.
No one has yet explained how a square wave (DC signal connected through a switch to a resistor ) can, by turning the switch on and off, "create" sine waves.

 

[IRstuff]

It doesn't "create" sine waves. It is sine waves, which is why passing such a signal through a low-pass filter works.

This is the nature of the time-frequency duality; different ways of describing the same thing.

TTFN