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Dave, I found your webpage while searching for a formula for determing the number of turns for a given inductance of a spider web coil. The formula on your page is fine but isn't too practical if you want to build a coil to a specific inductance. Well, I used your formula to derive a formula for determing the number of turns required. After some math manipulations I was able to get what I wanted. The formula was checked for accuracy throughout the range of 1uH to 2000uH. The results agreed with the original formula. At first glance, the formula looks overwhelming since it is a quartic equation ( a 4th degree polynomial), but with the "Quartic Equation Solver" available for use at www.akiti.ca/Quad4Deg.html, it is a piece of cake to solve.

The formula for determining the number of turns required for a given inductance of a spider web coil is: w^2x^4 + 4rwx^3 + 4r^2x^2 - 60Lwx - 32Lr = 0

Where x = number of turns to be determined

w = diameter of wire (inches)

r = inner radius of coi (inches)

L = desired inductance of coil (uH)

Enter the values for w, r, and L in the above formula; do the indicated multiplications and the formula will then appear as: Ax^4 + Bx^3 + Cx^2 - Dx - E = 0

A, B, C, D, E represent the results of the multiplications. Now take these values (don't forget that D and E are negative) and plug them into the similarly labeled boxes in the quartic equation solver. Press the "calculate solutions" button and it will spew out the results. Since this is a quartic equation, there will be 4 answers displayed. The correct answer will be obvious since it is a positive number, the other 3 will be either negative or complex.

George Miller, W4DNW (ex DL4ADP)

Spider Coil Examples

Here are some actual measurements of some coils that I have made. I will add to this table as I make more coils. These inductances are a little larger than you usually see. This is because I build the coils a little larger so I can take a little wire off if needed to trim the coil to the circuit. The lengths are in inches and feet

A little note about my Q numbers: These numbers were reached using my unverified HP 4342A Q meter. Since I made the measurements on the same machine using the same methods, I will stand by the numbers inasmuch as they relate to one another. I do not make any claims of these being actual Q values. I have measured a limited number of coils using the old manual method that I used to use before getting the Q meter. They do fall in line with what I have measured on the HP. I do, however find that my numbers are in the ball park with others that have measured the Q of similar coils. So please take them on your own beliefs.

L µH Thickness I.D. O.D. Litz Size Turns Length Q-1Mhz Cself

154 .125 2.25 3.50 40/44 40 32ft 330 4.7pF

248 .125 2.25 3.50 40/44 46 40

225 .125 1.75 3.50 40/44 56 38ft 340 3.5pF

248 .125 1.75 3.50 40/44 58 40ft 375 3.7pF

149 .125 2.25 4.75 100/45 39 33ft 540 6.3pF

238 .125 1.75 4.25 100/45 55 42ft 620 5.4pF

241 .125 2.25 4.75 100/45 49 42ft 620 5.4pF

146 .125 1.88 4.25 165/46 42 34ft

200 .125 1.88 4.25 165/46 48 38ft

220 .125 1.88 4.25 165/46 51 42ft

232 .125 1.75 4.75 165/46 55 44ft 750 4.0pF

250 .125 1.88 4.25 165/46 54 45ft

250 .125 2.25 4.75 165/46 49 45ft

155 .125 1.88 6 630/46 40 43ft

244 .125 1.88 7 630/46 49 62ft

150 .125 1.88 6 660/46 39 42ft 1000+ 4.7pF

241 .125 1.88 7 660/46 48 60ft 1000++ 3.0pF