[sdiy] 90-degree phase displacement network calculations
Ian Fritz
ijfritz at comcast.net
Wed Jan 13 23:34:16 CET 2021
Well, I can’t get the Orchard paper, so I can’t tell. The Johannesson variant looks like it converges very rapidly, though, at least for his example. So it, too, can give perfect accuracy, in the current sense.
> On Jan 13, 2021, at 2:30 PM, David G Dixon <dixon at mail.ubc.ca> wrote:
>
> Interesting. However, the Landen transformation approach is actually easier
> to implement in code, and gives perfect accuracy, whereas Johannesson's
> approach is approximate.
>
> In 1950, the repeating algorithm would have been very tedious indeed, but
> today it is trivial.
>
> The Weaver method is a similar approximation, which gives less optimal but
> still useful results, but again, Orchard's approach is actually easier to
> implement in code.
>
>
> -----Original Message-----
> From: Ian Fritz [mailto:ijfritz at comcast.net]
> Sent: Wednesday, January 13, 2021 12:24 PM
> To: David G Dixon; 'Bernard Arthur Hutchins, Jr'; synth-diy at synth-diy.org
> Subject: Re: [sdiy] 90-degree phase displacement network calculations
>
> [CAUTION: Non-UBC Email]
>
> In a note re the Orchard paper, Johannesson presented a modification that
> does not require the "repeated Landen transformations". It uses just a few
> terms from expansions. He says his numerical results for the Orchard
> example agree with the original.
>
> https://worldradiohistory.com/UK/Experimental-Wireless/50s/Wireless-Engineer
> -1950-08-09.pdf
>
> Thanks to Bernie for including this reference in his early article.
>
> Ian
>
>
>> On 1/12/2021 8:28 PM, David G Dixon wrote:
>> -- I understand what you did and for the third time state that there
>> is nothing wrong with what you did.
>>
>> I already knew that, Bernie. I wasn't seeking your approval. I was
>> just presenting a technique for everyone to use as they wish.
>>
>> -- But you have avoided my repeated questions about what the error
>> plot looks like if you do fewer iterations. [ Neither have you
>> commented your program or (despite saying there were several errors
>> along the way) provided a full corrected copy. ]
>>
>> OK, I'll say it one more time: There are no iterations. If one does
>> not take the necessary number of steps to complete the Landen
>> transformation, then one gets inaccurate numbers for the elliptic sine
>> and cosine. I see no purpose to calculating anything if the elliptic
>> functions are not accurately calculated. Once the necessary elliptic
>> functions are calculated, then the pole values are calculated simply
>> from those.
>>
>> To do what you request would be like calculating a trigonometric
>> function with sines and cosines, but instead of actually using those
>> functions, using series expansions truncated at the third step. Why
>> would anyone do that?
>>
>> Orchard presents an equation to calculate the maximum error in the
>> phase angle directly. However, it does not seem to give the correct
> answer.
>> For phase angle, I am calculating it directly from the RC factors of
>> the filter, and summing up the total phase angle for all stages in
>> each chain, then subtracting one phase angle from the other. I have
>> benchmarked my results against the QuadNet program, and the two
>> results are identical. The equation in Orchard dramatically
>> underestimates the maximum error. For example, a 16-stage PDN with a
>> bandwidth of 4 decades will generate a maximum phase error of 0.133
>> degrees. The Orchard equation gives 0.066 degrees. With a bandwidth
>> of 5 decades the maximum error increases to about 0.5 degrees. The
>> Orchard equation gives 0.116 degrees. So, that's a fail. It bears
>> noting that the equation given in Darlington for this purpose is
>> different, so the old guard were not all on the same page, evidently.
>>
>
> --
> ijfritz.byethost4.com
>
>
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