 2002 Microchip Technology Inc.

DS00232A-page 3

AN232

EQUATION 2:

FIGURE 2:

CALCULATING

MAGNETIC FIELD

STRENGTH

The field strength is therefore proportional to the:

• Number of turns (N)

• Current (I)

As one moves away from the source with r>>a the sim-

attenuation. For practical reasons, the designer may

the field strength using Equation 3.

EQUATION 3:

From Equation 3 with a given coil voltage at some dis-

tance from the coil, one now finds that B is inversely

proportional to N. This is due to the fact that the current

Only the case of an air-coiled inductor has been

described, but one can use a ferrite-cored inductor as

well. Adding a core has the effect of increasing the

effective surface area, enabling one to reduce the

physical size of the coil.

Serial Resonance

A typical serial resonant tank circuit is shown in

Figure 3.

FIGURE 3:

SERIAL RESONANT TANK

CIRCUIT

The formulas for calculating serial resonant tank values

are shown in Equation 4.

EQUATION 4:

Note that R represents all losses such as resistive,

magnetic, etc. A short description of each equation

given above is as follows:

(a) Used to calculate the resonant frequency of the

tank.

(b) Gives the maximum serial current as a function of

applied voltage (note this is not the same as inductor or

capacitor current) and effective serial resistance.

(c) Shows that the inductor and capacitor voltage is

equal to Q times the source voltage at resonance.

(d) Shows all the various ways to calculate the Quality

Factor (Q) of the tank circuit.

(e) Used to calculate the 3 dB bandwidth.

Figure 4 shows the frequency response curve for a

typical serial resonant tank circuit.

B

p

ω

2

2 a

2

r

2

+

()

32

⁄

--------------------------------

ω

2

2r

3

() m

⁄

[]

≈

=

where

I = Current [A]

N = Number of turns

a = radius of coil [m]

r = distance from coil [m]

P

Z

X

Y

r

a

coil

current

flow

Note:

For r >> a, the field strength falls of with

B

V

2

ω

-----------------

1

r

3

----





≈

with L

for r>>a

L

C

R

+

-

L

R

CR

R

L

Q

Vs

Q

V

V

R

Vs

I

LC

F

C

L

/

1

/

1

2

1

2

0

0

0

max

max

max

0

0

=

−

=

=

=

=

⋅

=

=

=

=

=

⋅

ω

ω

β

ω

ω

β

ω

ω

π

(a)

(b)

(c)

(d)

(e)