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When I plot phase shift on paper, I get inevitable distortion. I know the waveform looks reduced and undisturbed on the oscilloscope, as it should. Is there "less" to phase shift than what is normally described? Anybody reading about phase shift, who did not know otherwise, would say the waveform is definitely distorted through the RC.

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I think phase shift occurs on upswing and the downswing, not at the point the voltage changes direction. This is why there is no distortion. I have plotted this scenario with real numbers several times. If the input to an RC is 14vpp, and the resistance and reactance are equal, then each element can only have 7Vpp across it. Plug the numbers in, and it appears that the source, resistor, and capacitor voltages are in phase at the peak of the input. And the same holds true for the trough.

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Could it be that the noise found at the home outlet contains all sorts of things. They talk about all types of nonlinear loads putting harmonics into the power distribution system, but they only mention the 60Hz harmonics. I don't how I would go about creating harmonics from a "pure" 60Hz sinewave if I wanted to create them.

Why don't they just say the 60Hz has all sorts of noise.

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A high current rectified and filtered power supply creates "pits" or "flat tops" in the mains sine-wave waveform when the rectifiers conduct.
A light dimmer creates spikes on the mains waveform.
Anything electric that turns on or off creates a blip on the mains waveform.

If you want lots of distortion and harmonics then make a fuzz circuit for a guitar.

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Why don't they just say the 60Hz has all sorts of noise.



Hey Kevin,

I am not 100% sure that I am getting your question. As far as this quote is concerned maybe I can help a bit. When you are talking about the power grid in North America, the fundamental frequency of the power is 60hz. If you have a non-linear load (i.e. a rectifier) harmonics are created. Depending on the nature of the load, you will get different harmonics.


Here is an example:

If you have a fundamental frequency of 60hz feeding a 3 phase 6pulse rectifier. You will have 5th and 7th harmonics present, they will have frequencies of 300 and 420 Hz respectively.

If you try to tune a filter to 480 Hz, you will get rid of the 7th harmonic, however the waveform will still be distorted due to the 5th. If you could filter out all harmonics (which is very difficult and costly) you would see a pure sine wave at 60hz.



If you are passing a purely fundamental wave through an inductor or capacitor, ELI the ICE man has all of your answers.

When a circuit is inductive:
Voltage leads current.

When the circuit is capacitive:
Current leads voltage

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Hey Kevin,

If you have a non-linear load (i.e. a rectifier) harmonics are created.


Harmonics are created by tuned ampflication. You may be tuned to let's say 350Hz, but you will have to change the outlet current quite a lot to see it materialize in the outlet waveform. My question is, where are the 60Hz hamonics coming from? They are not coming from my high current circuits tuned to 350Hz. If I had bicycle to produce 60Hz electricity for my lightbulb, there wouldn't be any harmonics, it would be a pure sinewave. If I made a 60Hz tuned amplfier powered by my pure sinewave bicycle, the harmonics would be very very low, because the magnitude of the 60Hz is so much more than the noise level.
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An incandescent lightbulb is a varying resistance. When the sine-wave is at its peak voltage then the lightbulb's filament is getting hotter so its resistance increases, but with a delay. So if the lightbulb uses the max available current from the sine-wave generator then some parts of the sine-wave are more heavily loaded than others which produces distortion which makes harmonics.

A fluorescent light conducts for only part of the cycle so it also produces distortion and harmonics.

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I have never seen a crystal produce a fundamental audio frequency. They are for high frequencies.

Any waveform can be converted to a perfect sine-wave is you use a good lowpass filter to remove all the harmonics.

My very low distortion sine-wave generator starts with a square-wave, then it is converted to a stepped sine-wave with 10 steps, then it is filtered with an 8th-order switched-capacitor Butterworth lowpass filter so its distortion is so low it is almost unmeasurable.

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I'm thinking crystals are the main ingredient for generating harmonics. Producing perfect multiples of a fundamental does not sound easy at all without a crystal.


You are missing the point. Harmonics are created in any load that is non-linear. There is no magic crystal. Just non-linear loads.

I promise
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Okay, now I'm reminded. The power line harmonics come from the alternators used by the electric company. I can't believe an alternator spinning out 60Hz can produce such strong odd harmonics. Maybe the higher harmonics are what we  really want, but we run 60Hz so that the alternators don't have to spin as fast.

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The third harmonic from the electrical outlet is about 50% magnitude of the fundamental, the fifth is quite high too. If these harmonics were filterd out as soon as they are generated, then the amplitude at your outlet would be lower. Filtering out the harmonics once it comes from the outlet is fine, because your load is relatively high impedance to the outlet.

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What are you talking about?
The electrical waveform is a sine-wave. Its distortion is low so its 3rd harmonic is only about 1% of the amplitude of the fundamental. Its 5th harmonic is only about 0.75%.

The most amount of harmonics are from a square-wave. Its harmonics have levels much lower than you say the sine-wave has.

If you add the power of all the harmonics of a square-wave then their total is exactly the same power as the fundamental sine-wave.
Therefore the fundamental has exactly 50% of the total power of a square-wave.

post-1706-14279143274309_thumb.png

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Kevin,
Your article says and shows that the total harmonic distortion of the electrical voltage into homes is only 3.5%. The 3rd and 5th harmonics are only 1%.

They have a graph on page 2 with the 3rd and 5th harmonics at more than 50%, but the voltage scale is in decibels (100dB full scale) so they are at only 1%.

post-1706-14279143274578_thumb.png

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Filtering out large magnitudes not only affects the waveforms appearance, it affects the amplitude. I see it very good when I apply superposition theorem.


You need to step back about 50 yards, harmonics are not just added to the fundamental.


PT=(PF + P 3rd harmonic2 + P 5th Harmonic 2 + P 7th Harmonic 2.........)1/2

I really don't mean to be rude but I think you are completely missing the point here, harmonics do not affect the value of the fundamental portion of a signal, they are additive but in a bad way. They are adding "distortion" to the signal.

The fundamental frequency is the only part of the signal that you want to use. The harmonics are undesirable side effects created by non-linear loads.

Here is a bad analogy:

I have a rock, the rock grows moss due to the environmental conditions surrounding it, I scrape the moss off.

Rock = fundamental
moss = harmonics
environment = type of load/power grid
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