how non linear device can generate harmonics

Discussion in 'Homework Help' started by cdennis414, Dec 19, 2012.

  1. cdennis414

    Thread Starter New Member

    Dec 19, 2012
    14
    1
    Hi i need some help please
    One of the question on my assignment is
    Describe how a non liner devise can generate harmonics? and I need to describe two devices.
    My first choice is a diode.
    I know what the harmonics are
    I can build the circuit in Multisim
    I know that they are produce because voltage is disproportional to current....
    But i don't know HOW ARE THEY PRODUCED
    And i don't know what to chose as second device
    Any help would be much appreciated..
    Thaks...
     
  2. Brownout

    Well-Known Member

    Jan 10, 2012
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    Harmonics are frequecies that are integer multiples of the frequency of the original signal. If you have a sine wave of, say 1KHz, you can have harmonics of 2KHz, 3KHz, 4Khz, etc. Nonlinear circuits generate harmonics when fed a signal. For example, a BJT amplifier produces harmonics due to its exponential forward transfer characteristics. A MOSFET produces harmonics due to its "square" transfer characteristics. Basically, the output slope is multiplied by the nonlinear function, producing the harmonics. As an experiment, draw the slope of a sine wave form, say -∏/2 to +∏/2. Then draw an expontial curve which would be output from a transistor amplifier, using the sine wave as the input. Using the graphing functions of Excel is helpful here ( or any graphing program or graphing calculator ) Notice the faster rise of the exponential vs the sine wave. That's the harmonics.
     
  3. crutschow

    Expert

    Mar 14, 2008
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    It's related to the frequencies in a particular waveform as defined in its Fourier transform. Any waveform, other than a pure sinewave, is composed of harmonics. For example, a square wave-wave contains many harmonics of its fundamental frequency. So any time you distort a sinewave with a non-linear circuit you will generate harmonics of that fundamental frequency.
     
  4. Papabravo

    Expert

    Feb 24, 2006
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    It is non-linear operations on a pair of input signals that produce frequencies, including harmonics, that are not found in the original signals. For a mild brain bender study the trigonometric identity where two cosine waves of different frequencies are multiplied together and the output contains components at brand new frequencies.
     
  5. Brownout

    Well-Known Member

    Jan 10, 2012
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    Pairs of signals aren't needed for harmonics to be produced by a nonlinear operation. Harmonics are procuded on a single input signal ( see frequency doubler, tripler ) To see this is so, do a Taylor series expansion on a nonlinear function, say an exponential. Then subsitute a time-periodic signal for the variable, and apply trig identities for the higher order terms.
     
  6. Papabravo

    Expert

    Feb 24, 2006
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    So how much of the output is at the fundamental and how much is at the 2nd harmonic. In the case of a mixer, two input frequencies in, give four frequencies out. Does a doubler behave the same way, or is the fundamental attenuated by some significant amount amount?
     
  7. Brownout

    Well-Known Member

    Jan 10, 2012
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    It totally depends on the kind of circuit being used. A doubler would be designed to maximize the harmonics, and an amplifier would be designed to minimize them. In either case, the calculations would be the same. The output would be a fraction of the fundamental, at least down to 1/4 in the 2nd harmonic, by virtue of the 1/2 factor in the taylor series expansion ( in the case of the exponential ) and the 1/2 factor that comes from the cos^2 identity.
     
  8. BillO

    Well-Known Member

    Nov 24, 2008
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    You might find some answers here: LINK
     
  9. cdennis414

    Thread Starter New Member

    Dec 19, 2012
    14
    1
    Thank you all very much for your replies, it's cleared things up a bit, but I am still not quite sure I understand it completely.....So far how I understand it : The input voltage creates distorted output current because non liner relation but what happened to output voltage does it get distorted according to Ohm,s Law ? are there any equations for it?
    Thanks..
     
    KL7AJ likes this.
  10. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
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    A diode DOES follow Ohm's Law, but you have two variables, one being the resistance itself, which is somewhat inversely proportional to the applied voltage. This is why (over a small region) the "output" of a diode voltage foillows the square law.

    Eric
     
  11. Brownout

    Well-Known Member

    Jan 10, 2012
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    It has nothing to do with Ohm's law. It's due soley to the non-linear relationship between input votage or current and output voltage or current. If the output current is distorted, then so will be the voltage.

    You can caluculate the harmonics, usually by using a Taylor series.
     
  12. BillO

    Well-Known Member

    Nov 24, 2008
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    Fourier analysis might be a better approach. You would apply a Fourier transform to find the constituants of the waveform in the frequency domain.
     
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