On 10/21/2011 09:35 PM, George Herold wrote:
> On Oct 21, 9:15 pm, George Herold<gher...@teachspin.com> wrote:
>> On Oct 21, 11:02 am, Bill Sloman<bill.slo...@ieee.org> wrote:
>>
>>
>>
>>
>>
>>> On Oct 21, 11:59 am, Jon Kirwan<j...@infinitefactors.org> wrote:
>>
>>>> On Fri, 21 Oct 2011 00:04:21 -0700 (PDT), Benj
>>
>>>> <bjac...@iwaynet.net> wrote:
>>>>> On Oct 13, 7:54 pm, Jon Kirwan<j...@infinitefactors.org> wrote:
>>>>>> On Thu, 13 Oct 2011 16:08:49 -0700, Jim Thompson
>>
>>>>>> <To-Email-Use-The-Envelope-I...@On-My-Web-Site.com> wrote:
>>>>>>> On Thu, 13 Oct 2011 10:24:17 -0700, Jon Kirwan
>>>>>>> <j...@infinitefactors.org> wrote:
>>
>>>>>>>> On Thu, 13 Oct 2011 10:13:20 -0700 (PDT), George Herold
>>>>>>>> <gher...@teachspin.com> wrote:
>>
>>>>>>>>> On Oct 13, 12:59 pm, Jon Kirwan<j...@infinitefactors.org> wrote:
>>>>>>>>>> On Thu, 13 Oct 2011 09:39:21 -0700 (PDT), George Herold
>>
>>>>>>>>>> <gher...@teachspin.com> wrote:
>>>>>>>>>>> This is a continuation of the 50kHz VCO thread I started last week. I
>>>>>>>>>>> tried the stepped sine wave idea as suggested by James A, and Phil
>>>>>>>>>>> H.
>>>>>>>>>>> The circuit clocks a MC14017 at 10x(F) to make a stepped sine wave at
>>>>>>>>>>> frequency (F). The ten outputs from the 4017 are sent through
>>>>>>>>>>> appropriate resistors and into the summing junction of an opamp.
>>>>>>>>>>> Here s a scope shot of the stepped output overlaid with a sine
>>>>>>>>>>> wave.
>>
>>>>>>>>>>> http://imageshack.us/photo/my-images/560/tek0024.png/
>>
>>>>>>>>>>> The resistor values were chosen to intersect the sine wave at each new
>>>>>>>>>>> phase. (R(n) = 1/sin^2(n*18degrees))
>>
>>>>>>>>>>> Approximate values, R0=open, R1=R9=105k, R2=R8=28.9k, R3=R7=15.3k,
>>>>>>>>>>> R4=R6=11k, R5=10k. all 1% resistors.
>>
>>>>>>>>>>> Here s the spectrum as recorded by an SRS770 spectrum analyzer.
>>
>>>>>>>>>>> http://imageshack.us/photo/my-images/839/stepsin.png/
>>
>>>>>>>>>>> The 2nd harmonic is only down by 50dB. I don t understand why it s so
>>>>>>>>>>> big. Is there some way to do better than this? The 9th and 11th
>>>>>>>>>>> harmonics are big and then the 19th and 21st.
>>
>>>>>>>>>>> Thanks George H.
>>
>>>>>>>>>> George, I don't remember the discussion. Probably didn't
>>>>>>>>>> read it. But if you are using a 4017 (decade counter), then
>>>>>>>>>> I'm guessing that you are enabling one resistor at a time
>>>>>>>>>> while disabling others (they tie to the summing junction from
>>>>>>>>>> each, moving output pin.) This worries me a little, mostly
>>>>>>>>>> because of delay and the fact that you are turning off one
>>>>>>>>>> while turning on another, but don't control that very well. I
>>>>>>>>>> also don't know what you are doing to filter the steps.
>>
>>>>>>>>>> Anyway, I'd have wanted to consider, instead, a Gray-coded
>>>>>>>>>> (actually, the real inventor is Boudot, I think, but Bell
>>>>>>>>>> Labs was patenting everything in a flurry in the mid 1900's
>>>>>>>>>> and who could remember Boudot so long ago?) design where you
>>>>>>>>>> only change one of the outputs at a time. Not two.
>>
>>>>>>>>>> Anyway, I'll let the big hitters who probably did read the
>>>>>>>>>> earlier thread tell you what is more likely. Just something
>>>>>>>>>> that crossed my mind, is all.
>>
>>>>>>>>>> Jon- Hide quoted text -
>>
>>>>>>>>>> - Show quoted text -
>>
>>>>>>>>> Hi Jon, Thanks for that.
>>
>>>>>>>> No problem. In the interim, I did a quick search for summing
>>>>>>>> junctions and Gray codes and came up with this link:
>>
>>>>>>>> http://www.wiseguysynth.com/larry/schematics/walsh/walsh.pdf
>>
>>>>>>> I posted this 8 years ago...
>>
>>>>>>> http://www.analog-innovations.com/SED/SineEqualsSumOfSquares.pdf
>>
>>>>>>> I also have this book...
>>
>>>>>>> "Sequency Theory, Foundations and Applications"
>>>>>>> Henning F. Harmuth
>>>>>>> Academic Press, 1977
>>>>>>> ISBN: 0-12-014569-3
>>
>>>>>>> which covers Walsh Functions in gruesome detail ;-)
>>
>>>>>> I picke up Walsh's original paper (redone, actually, in Latex
>>>>>> and error corrected as it had a few in the original article)
>>>>>> from the web, today. The paper is "A Closed Set of Normal
>>>>>> Orthogonal Functions." I will be reading it more thoroughly
>>>>>> over the next couple of days. Also, already listed the above
>>>>>> link which is a nice, short overview with two examples in it.
>>>>>> Finally, there are a bevy of books (some of them nearly 1300
>>>>>> pages in length) on the subject regarding making and building
>>>>>> synthesizers. I'll be ordering a few before the end of the
>>>>>> week.
>>
>>>>>> A whole world has opened up on this subject for me and I can
>>>>>> bring over Laplace and Fourier. Actually, it is almost easy
>>>>>> for me to see how to apply this with almost any starting wave
>>>>>> shape, not just sine/cosine or square wave. Which probably
>>>>>> isn't terribly practical, but interesting all the same. (Must
>>>>>> be some mathematician out there has already explored the use
>>>>>> of triangle, sawtooth, and pretty much any arbitrary basic
>>>>>> shape.)
>>
>>>>>> I will read your PDF, as well. :)
>>
>>>>>> Jon
>>
>>>>> I was going to suggest using Walsh functions. They make great
>>>>> sinewaves (or ANY repetitive waveshape, although there is a problem
>>>>> with the "peak" on triangles). The difference between Walsh function
>>>>> generation and typical D-A converters is that Walsh functions
>>>>> distribute the switching over the period and don't need a resistive
>>>>> ladder where some elements need high accuracy.
>>
>>>> My intuition suggested changing only one digital output at a
>>>> time -- which is why I gravitated towards Gray coding.
>>>> Searching on that led me to Walsh, which seemed right on the
>>>> money. But I still haven't had time to read about them. I
>>>> did just receive my beautiful copy of Harmuth's "Sequency
>>>> Theory" book, though. And glad to have it. And it does go
>>>> directly into Gray code ordering of Walsh functions, so I'm
>>>> happy now.
>>
>>>>> Read the pdf. and it should explain how to reproduce any waveform. You
>>>>> just need to get the transform of the waveform that lists coefficient
>>>>> of each Walsh function. The beauty of this method is the often many of
>>>>> them are zero and hence do not need to be implemented.
>>
>>>> On the short PDF, I clearly got this message. (odd and even
>>>> functions, etc.)
>>
>>>>> Typically the
>>>>> spectrum is very low in the lower harmonics rising much higher in high
>>>>> harmonics where the "stairsteps" start to produce spectrum. Obviously
>>>>> the more steps you use the further out is that rise.
>>
>>>> Got it.
>>
>>>>> I didn't see the original thread so I don't know what your application
>>>>> is.
>>
>>>> It's not my application, but George's. He's using a 4017
>>>> (decade decoder thing) right now (or was) and ties in
>>>> resistors on each of the 10 pins to a summing point of an
>>>> opamp in order to make a stepped sine wave. But he didn't
>>>> like the spectrum he got, especially the 2nd harmonic.
>>
>>>> I hadn't done this, but my gut told me that the 4017 was
>>>> changing two resistors nearly at once (but perhaps not
>>>> exactly so) and with ripple carry and all I wasn't
>>>> comfortable and wanted to suggest thinking in terms of a gray
>>>> coded approach.
>>
>>> The 4017 is a twisted ring shift-register-based Johnson counter -
>>> whence no ripple carry within the counter, though it does have a
>>> ripple carry output.
>>
>>> http://www.national.com/ds/CD/CD4017BC.pdf
>>
>>> The second harmonic content was almost certainly due to the tolerances
>>> on his resistors - P-channel on-resistance is higher than N-channel in
>>> most CMOS logic, but in modern parts the channel resistance is too low
>>> to have explained the second harmonic content he saw.
>>
>>> <snip>
>>
>>> --
>>> Bill Sloman, Nijmegen- Hide quoted text -
>>
>>> - Show quoted text -
>>
>> Hi Bill, did you read the rest of the thread? I measrured an output
>> impedance of ~180 omhs (at 15V) for the 1MC4017 I was using. That's
>> about 2% of the smallest resistor (10k ohm). Bigger than the 1%
>> resistor tolerance, and certianly the major cause of the 2nd harmonic
>> distortion in my first circuit.
>>
>> George H.
>> (I hope you can forgive the slight correction, I didn't want the
>> thread to end with a mis-statement)- Hide quoted text -
>>
>> - Show quoted text -
>
> So here's a late Friday night question, (after a few Genny's). If I
> used a bipolar output (switching the sign at zero with an opamp, and
> picking new resistors), would the distortion caused by the output
> impedance move from the 2nd harmonic to the third? Squishing both
> sides equally rather than just pushing the top down.
>
> I find it hard moving from distortion in the time demain to the
> frequency domain.
>
> George H.
If the resulting waveform has inversion symmetry, i.e. if for all t
f(t) + f(t+T/2) = 0,
then it can't have any even harmonics.
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics
160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot net
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