# DC Wave Questions

NSM wrote:

I like Jack's terminology. The wave itself isn't DC, but I think "fully DC" is an acceptable way of describing its location.
AC generators and transformers are usually designed to produce sine waves with no DC, but sine waves were known long before those inventions.
A wave is a succession of curves. A sine wave is a wave whose displacement follows the form of a sine. A pure acoustic tone is a sine wave regardless of ambient pressure. A ripple on a pond is a sine wave regardless of the water level.
As not all voltage variations are curves, our generic term was "waveforms". If the plate voltage of an amplifier tube varied from 998 to 1000 volts in the form of a sawtooth, we'd call that two-volt variation a sawtooth waveform. If it was sinusoidal we'd call it a sine wave.
To call a waveform an AC sine wave implies that there is no DC, but this thread is the first time I've read the claim that all sine waves are AC sine waves.
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FWIW, most waveforms can be created as the sum of sine waves. I wrote an interesting computer demo once that showed how a sine and it's harmonics could be added graphically to form a better and better approximation of a square wave, running through what looked like Butterworth etc. responses.
N
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NSM wrote:

With high frequency and amplitude, a sine wave could be very steep at 0 and 180 degrees. It could also turn sharply at 90 and 270, like the corner of a square wave. You would need low frequency and amplitude for a sine wave to approximate the flat peaks of a square wave.
That part is simple enough for me, but I don't understand harmonics. If you overdrive an amplifier with a sine wave, the output will resemble a square wave. I know the output can be broken down into the input frequency and its odd multiples. I'll have to accept it on faith.
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Choreboy wrote:

You might want to look into the basis of Fourier analysis. It all falls out of a very simple mathematical property of the sine wave.
If you take any periodic waveform, and multiply its value at every point in time with the value of any frequency of sine wave at the same points in time, over all time and add up (integrate) all the products and divide by the total time (an infinite amount of time), only sine waves that fit an integral number of cycles within the period of the waveform will produce nonzero results (infinite integral divided by infinite time). In fact, it can be shown that you get the same quotient for harmonics if you use any integral number of periods of the waveform, including one period. Testing an infinite number of waves is only necessary to show that non harmonics always produce a zero contribution. For instance, if you test a sine wave that fits 1.000001 cycles into a cycle of the waveform, you don't reach the first zero result till you include a million periods of the waveform (and you get more zeros at every integer multiple of a million cycles, with a smaller and smaller cycle of results between those millions as the number of cycles increases because you are dividing by larger and larger times).
Harmonics (sine waves that fit an integral number of cycles within the waveform) will produce a finite result representing that frequencies contribution to the waveform. (Actually you have to test both the sine and cosine against the waveform to cover all possible phase shifted versions of the sine. Any phase shifted sine can be broken sown into sine and cosine components. Another nice property of sine waves.) Since only harmonics contribute to the total wave shape, you can skip all the other frequencies, and just evaluate the part each harmonic contributes to making the total waveform.
That is Fourier analysis.
The rest is about making the math more efficient.
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John Popelish wrote:

That's easy for you to say!
I think you've shown me something. When I hear "sine wave" I imagine one cycle. I guess that's wrong, and a wave is a train of cycles.
Musical harmony is in a sustained interaction between trains of cycles. The interaction won't be simple enough to hear unless the quotient between the frequencies is a small integer.
When they talk about harmonics in an electrical wave, I guess they're talking about the potential for energy transfer. In that case, only odd multiples of the fundamental will stay in phase to tap the energy from the distortion. Where a wave is flattened it may resemble part of a sine curve with a longer period than the fundamental, but that doesn't count because you can't tap energy from the flat part.
If there's any truth in what I've said, I'll forget in a flash. In 1975 I was working in a repair facility. We'd use Bird Wattmeters to see forward and reflected power in antenna feeds. We knew the jargon and how to use the meters, but one day it struck me that none of us understood why they worked. I had a flash of insight and everybody stopped work to listen to me explain. Their faces lit up with comprehension. I felt pretty smart. The next day I couldn't remember whatever it was I'd figured out.
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Choreboy wrote:

(snip)
True mathematical sine waves extend from infinite negative time to infinite positive time. Practical sine waves last long enough for things to respond to their frequency. How long that is, depends o what is reacting to it. A frequency counter operating in period mode needs only a single cycle to make its measurement. An ear needs several cycles to several dozen cycles, depending on exactly what part of the audible spectrum being detected (this property of ears is part o the MP3 music encoding scheme). A quartz lattice filter may need thousands of cycles to of a pure frequency before it develops a nearly steady state output.

Something like that. Each frequency component in the signal has to last long enough for the time response of that frequency of the ear's sorting system to respond to it. If two frequencies fall within a single reception band, they are not heard as two tones, but as a beat addition and cancellation) as a single tone at about the average of the two frequencies and an AM modulation at the difference of the two frequencies. Obviously, if the beat is very long period, you have to hear the two beating tomes for a cycle or two of the beat period to detect that effect. Harmonically related tones just produce a repeating pattern at some integer multiples of each of the component frequencies. This can produce a very pleasing effect. You hear sound from one musical source as a fundamental and several harmonically related frequencies. If a second musical source (a harmonizing voice, for example) has its fundamental at one of the harmonics of the other signal, your brain recognizes this simple multiple relationship as a pleasing musical harmony. For some ratios. This page shows some of the approximate ratios between notes that sound interesting together: http://www.jimloy.com/physics/scale.htm

Not really. since linear circuit components react to many frequencies by the addition if the effect of each frequency, it is a very powerful analytical procedure to break a signal down into its harmonics and evaluate the response of a circuit to each of those harmonics, and add all the effects together to get the total response.

Symmetrical distortion of a sine wave (shape of positive half cycle is a mirror image of that on the negative half cycle) can be shown to be made up of only the fundamental and odd harmonics (3 times. 5 times, etc.). If the distortion peaks up one half cycle and flattens the other or shifts the zero crossing so that one half cycle lasts longer than the other, there are even harmonics in the wave shape. There may also be odd ones, too. Got to do that Fourier analysis to quantify that.

You can with a resistor. From a Fourier perspective, that flat part just represents a time when the curve of some frequencies is nearly canceled by the curve from other frequencies. You need an infinite number of harmonics to make a truly flat square wave with perfectly square corners.

I hate it when that happens.
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http://www.elektroda.net/cir/index/Detector%20Circuits/NEGATIVE%20PEAK%20DETECTOR.htmgative
Impedance varies with frequency if there are reactive components, L's and C's. Since you haven't told us whether this is a series or parallel circuit of L's, R's and C's, We don't know what the impedance is at DC, zero frequency or any other frequency for that matter. If it's a parallel circuit the DC impedance is zero unless there is resistance in series with the L as is the usual case. In that case, the impedance is R at DC. If it is a series circuit, the DC impedance is infinite. SO, you have three choices, Zero ohms, Infinite ohms or R ohms depending on the connection.
A peak detector will have to work on the range of voltages expected on it's input. I can't get to the URL, sorry. Bob
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Bob Eldred wrote:

That is not always true.
Take 1) A resistor of resistance R in series with a capacitor of capacitance C.
2) Another identical resistor of resistance R, but in series with an inductor L.
Make R=sqrt(L/C)
and put 1 and 2 in parallel and measure the impedance across that combination. The impedance is always R, and is independent of frequency.
A useless fact I would admit!!
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Not exactly useless, you just described a Zobel network.
It is used as crossover to feed two loudspeaker on HI range and LOW range presenting a constant resistive load to the Amp.
It is used to compensate a shunt at higher freq. The transfer function is perfectly flat even with two reactances in the circuit.
It is used to terminate a DC distribution line R+L with a R+C to avoid resonances, the line is perfectly damped, when the load current steps there are no oscillatory transients.
MG
MG
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O.K. here's the combinatrics:
Combo 1: DC Sine Wave + (R+L in series with C parallel)
Combo 2: DC Sine Wave + (R+C in series with L parallel)
Combo 3: DC Sine Wave + (L+C in series with R parallel)
Combo 4: DC Sine Wave + (R, L, and C all in parallel with each other)
Combo 5: DC Sine Wave + (R, L and C all in series)

O.K., so can I correctly infer from your response that a negative peak detector will yield a value of +5V for a sine wave which varies from +5V to +15V?
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snipped-for-privacy@yahoo.com wrote:

There is no such thing as a "DC sine wave." I suspect you mean what would more correctly be described as a 10 volt peak-to-peak sine wave with a +10 volt DC offset.

The principle of superposition applies: the currents and voltages in the circuit will be the sum of those that would result if the DC voltage and the AC sine wave were applied to it seperately.

http://www.elektroda.net/cir/index/Detector%20Circuits/NEGATIVE%20PEAK%20DETECTOR.htm
That circuit (I've fixed the link) exploits the fact that the LM139 comparator has an open-collector output. It runs off a negative rail, and cannot produce a positive output voltage.
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Not that it's that important, but I don't see why a "DC sine wave" is an impossible concept, considering the definition of DC as a current which flows in one direction:
http://www.answers.com/topic/direct-current
A "DC Sine wave" doesn't say that current reverses direction, only that the current flow wanes and waxes.....like a river is still a river even though its flow varies with rainfall...

O.K. - now we're getting somewhere......you're saying the current and voltage (and the implied impedance Z = V/I) of the "DC sine wave" is the sum of the respective current and voltage of a +10V DC signal and a -5V/+5V AC signal going into the same load.
Example: DC +10V into load produces 1 Amp, therefore implied resistance = 10 ohm. and AC -5V/+5V (and given frequency) into load produces 0.5 amps, therefore implied impedance = 20 ohms,
then what would the superposition prinicple predict as the resulting combined current and impednace?
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snipped-for-privacy@yahoo.com wrote:

The current is simply the sum of the AC and DC components e.g. 0.5 amps peak-to-peak AC with a 1 amp DC offset Max. instantaneous current = 1.25 amps Min. instantaneous current = 0.75 amps
Impedance can be represented as a complex number: real part = reisitance = R = 10 ohms imaginary part = reactance = X
Total impedance Z = R + jX
To work out the imaginary part, you have to do a vector addition because current and voltage in a reactance are 90 degrees out of phase:
Ipk = Vpk / sqrt(X*X + R*R)
0.25 = 5 / sqrt(X*X + 10*10)
X = sqrt(300) = 17.3
i.e. Z = 10 + j*17.3
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Maybe you shouldn't believe everything you read. DC has: 1. Constant amplitude (that's not to say you can't change it. 2. Frequency of 0 Hz. Also, a non 0 frequency does not imply polarity changes.
Tam
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If the low peak of the sine wave (and the rest of the the sine wave for that matter) is "fully" above the "zero" reference point, then isn't it true that the current DOES NOT alternate? That is to say, that current only flows in one direction....i.e. "direct current"? Isn't it also true that if the low peak of the sine wave is -0.00001V then the sine wave results in current flowing in both direction (albeit for a nanosecond)....i.e. "alternating current".....I'm not arguing that my use of nomenclature is "pure" or conventional....but I don't see how it is fundamentally wrong, without merit, or lacking a reasonable basis.....
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snipped-for-privacy@yahoo.com wrote:

You seem very attached to the word, "alternating" that is abbreviated in the term AC. Once people get involved in analyzing circuits and waveforms, they start to think in terms of frequencies. All kinds of signals can be described in terms of the frequencies they contain. Signals with zero frequency are analyzed and described as DC, while everything else is some frequency other than zero. And there are two distinct kinds of frequency. One is based on number of sinusoidal cycles in a given period of time and the other is based on exponential decay or growth rate (number of decay or growth time constants per time period).
I am sure that many who have not learned the math of Laplace transforms have a hard time thinking of a decaying, unidirectional pulse as a kind of frequency, since it never alternates, but there are such powerful analytical reasons to take this view that anyone who understands this power has little difficulty with this rather non literal extension of the AC frequency concept.
So only those with a very primitive view of frequency and are bothered by describing a non alternating but time varying signal as a kind of frequency (and informally called AC). The simple minded terms, AC and DC are just not up to the job of describing many waveforms, unless you are willing to be quite flexible in the usage.
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I will absolutely buy what you said, but understand the import of what you're saying....you're saying that the language of "AC" and "DC" has essentially been somewhat bastardized from its original meanings to also mean zero-frequency and non-zero-frequency signals. Therefore, to describe a 10Vpp signal with a 10VDC offset as an "AC" signal is actually contrary to the original connation of "alternating current" since it (net) results in a signal which yields only a mono-directional (i.e. direct) current flow (albeit time variant). So in a sense, you could say I am holding "pure" to the original (circa 1890's) definition of AC/DC while its use has been "officially" corrupted to cover the concepts of "zero frequency" and "non-zero-freuency".
Agree?
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snipped-for-privacy@yahoo.com wrote:

Now you are cooking with gas. Old words take on new meanings as our needs change. Those words were coined when our understanding and use of electricity was pretty primitive.

What you say about current applies only to a resistor connected across that voltage. Connect a capacitor across it and the DC part is ignored and AC (alternating current) passes through the capacitor as if the wave were perfectly centered on zero volts.

I prefer "expanded", "enhanced", "extended" or "refined".

Sure. The important thing is that the speaker and listener are using similar definitions of the words in use, or there is bound to be a misunderstanding.
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On 6/10/05 10:53 PM, in article snipped-for-privacy@g47g2000cwa.googlegroups.com,

No.
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It's like saying you've got copper pipes and water flowing through them, but you want to know how much, and how pure the Water pressure is flowing into your home. One could argue what the hell does the copper pipes have to do with water pressure and purity.
* Forget the term Sine Wave in this Case: It has been converted to Pulsating DC and a DC Waveform has no Sine or Cosine values that matter to the LCR Network it supplies., as in a wall wart= 120VAC input 10VDC output ~ now the length of that pulse is important and can be referenced from the supply voltage of the rectifier circuit or measured with a scope before the filters which refine the output to a near solid unwavering DC Signal.
Other than that; I have to concurr with the others that the term "DC SineWave" is obnoxious & irrelevant and used to chagrin the entire ojective of the query posted. Think: The more mathematical pointer is the term "SIne" which is irrelevant in DC but is widely applicable to AC calcs, DC can only mimic an AC Wave at best and it's common known forms are Saw Tooth and Square and the refined Pulsating Wave Form that can actually operate at AC Values but are not Sine Waves but fixed DC values pulsing on and off at a Similar Frequency., (or Pulse).
Roy
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