Inductance of loop area

Further to my post about the IR2110 gate driver, does anyone have a nice simple equation for calculating the inductance of a given loop on a pcb ?

Yes I know..... we looked at it when I was about 17 / 18. Never needed it since then until now.

Cheers, Graham

Lol @ Radio Engineer's Handbook. That was one area I never planned to get involved in !

Cheers, Graham

Hmmmm..... so for wire diameter I presumably substitute pcb track cross sectional area ? I hadn't imagined that to be a factor, just expected the 'cut area' to influence.

Graham

Oh my God !

Kind of thinks " why did I ask " !

I think I prefer John's equation for simple rule of thumb !

All this 'high frequency' stuff is quite new to me. I can make analogue and digital stuff work ok though !

For small variations in d where d is fairly small to begin with does it really make much difference to the result ? E.g. where the cut area is a few square inches, does a 40 thou ( mil ) track have significantly less inductance than a

Graham

buy a copy of Terman's Radio Engineers Handbook, then use pp47-72 for to solve for the geometry present. This was one of my first "old" books, and I have used it for this purpose for a decade or so now. Grover is pretty good too, but Terman suffices for most PCB-type problems.

Cheers Terry

Laugh ye not:

rectangle of round wire, sides s1 & s2, diagonal g, wire diameter d L=0.02339[(s1+s2)*log(4*s1*s2/d)-s1*log(s1+g)-s2*log(s2+g)] + 0.01016*[u*delta*(s1+s2) + 2(g+d/2) - 2(s1+s2)]

rectangle of rectangular wire, thickness b, width c (into plane of loop) L=0.02339[(s1+s2)*log(2*s1*s2/(b+c))-s1*log(s1+g)-s2*log(s2+g)] + 0.01016*[2*g - 0.5*(s1+s2) + 0.447*(b+c)]

all dimensions inches, L in uH. u is permeability (1.25e-6), delta is skin depth

Cheers Terry

it is little more than an LRC circuit. the trick is recognising L, R & C.

he gives a simple loop formula:

L = 0.00508*p*[2.303*log(4*p/d)-theta], uH

L = 0.00508*p*[ln(4*p/d)-theta], uH

p = perimeter of loop, d = diameter of wire in inches (convert rectangle area into circular area)

theta = shape factor = 2.451, circle = 2.561, regular octagon = 2.636, regular hexagon = 2.712, regular pentagon = 2.853, square = 3.197, equilateral triangle = 3.332, isoscoles right-anlge triangle

Terman claims 0.5% accuracy. clearly theta=2.65 is a pretty good compromise.

Cheers Terry