EMRFD Message Archive 102

Message Date From Subject
102 2006-08-23 11:21:01 kilocycles Math Mystery in EMRFD Appendix Article
I've come across something that has been bothering me for some time,
in trying to work through the math. In the EMRFD Appendix article, "A
Progressive Communications Receiver", from the November 1981 QST, a
circuit is presented for finding the additional series capacitance
needed to resonate a VFO, given a selected variable capacitor, by
selecting a series capacitor, C1 in the network. This interests me
greatly, as I have some nice variables with values that don't match up
with published VFO designs. Since I started working on the problem, I
have found an identical network, which appears on Page 4.4 of EMRFD,
with the equations to support the calculation of Cnet (the total
capacitance for resonance with the inductor).

My problem is that in spreadsheeting both the equations in the
"Progressive" article and the EMRFD example, I find what I think is an
inconsistency. In the "Progressive" article, everything works out
perfectly until I try to solve the final equation to determine C3.
With 1/C1 = 2.0E10 and 1/C2 = 7.887E9, their sum to the -1 power is
(2.788717E10)exp-1, or 3.58588E-11, or 35.86 pF. Completing the
solution, Cv - (this value) yields 355pf - 35.86 pF, or 319.14 pF.
The solution in the article for C3 is given as 127.02 pF.

Using the equation on page 4.4 of EMRFD in my spreadsheet, I can solve
for C3 and get the same value, 127 pF as shown in the article, with
the correct Cnet for 3uH, 172.3 pF.

I searched the ARRL site for errata on the original article, but found
none. I believe that their must be a typographical error in the lat
equation, the solution for C3 in the article. I've tried to get some
local support in resolving this, but now that we have the EMRFD group,
this is the perfect forum. By the way, once I get this issue
resolved, I'll be glad to put the Excel spreadsheet in the files.

73 es tnx,
106 2006-08-23 21:21:52 Wes Hayward Re: Math Mystery in EMRFD Appendix Article
Hi Ted, et al,

You are correct. There was an error of some sort in the equations
as presented in QST. I remember one of the copies kicking around
the house had them marked up and I used that in answering questions
in the mail. In the example given on page 21 of the Nov 81 QST,
the 127 pF value for C3 is correct. If you just dump it into the
circuit with the variable set to zero, you do indeed come up with
7.2 MHz. But the equations predict 319 pF, as came out of the
KX4OM spreadsheet.

I'll keep digging and will put something up when I get it straight.
I could not find any related feedback item in the QST listings on
the League web site. I'm not sure that the index is very accurate
in this regard.

Incidentally, one of the DOS programs that is distributed with IRFD
solves just this problem. The program is called PadCap, or
something like that. I checked it out and it seems to give the
correct numbers. You can download the programs from the League
web site, no charge. Search for IRFD Programs.

Sorry about that error. And thanks for keeping me honest, Ted.

73, Wes
108 2006-08-24 14:31:52 Wes Hayward Re: Math Mystery in EMRFD Appendix Article
Hi all,

OK, I found the error. It is in equation 3. The first term on the
right hand side should be CU (subscript "uncle") rather than CV
(subscript "victor".) If anyone wants to see the complete
derivation, drop me a note and I'll send it along. It's routine
algebra, so I don't think I'll post it as a file.

Again, thanks Ted.

73, Wes