RF coil calculator Calculator

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Impedance of the tuned circuit Z_in:		Ω
Enameled wire
Metal type:
Height of the loop b:		m
Width the PCB trace w:		m
ESR resistance of the used capacitors (one capacitor) R_{C_esr}:		Ω
Q degrading resistor in series with the inductor PCB trace R_{L_dump}:		Ω

Used formulae:

(1.)	1. L = μ_0 * l * ln ( 8 * A / ( l * w ) ) / ( 2 * PI )

(2.)	2. R_L_loss = l * sqrt ( PI * f * μ_0 / σ ) / ( 2 * w ) + R_L_dump

(3.)	3. R_L_radiation = 320 * PI \\\\ 4 * A * A / λ \\\\ 4

(4.)	4. Z = Z_C \|\| Z_L

(5.)	5. Z_C = R_C - j1/(ωC)

(6.)	6. Z_L = R_L + jωL

(7.)	7. R_L = R_L_loss + R_L_radiation

(8.)	8. R_S = R_L + R_C

(9.)	9. R_P = Z(ω_0)

(10.)

10. Im(Z) = 0 <=> -L\\\\2*ω\\\\2*C + L + ω\\\\2*C\\\\2*L*R_C\\\\2 - R_L\\\\2*C = 0

(11.)

11. ω_0 = sqrt ( L - R_L\\\\2*C / ( L\\\\2*C - R_C\\\\2*L*C\\\\2 ) )

(12.)

12. C = ( R_L\\\\2 + ω\\\\2*L\\\\2 +- sqrt ( ( R_L\\\\2 + ω\\\\2*L\\\\2 )\\\\2 - 4*R_C\\\\2*ω\\\\2*L\\\\2 ) ) / ( 2*R_C\\\\2*ω\\\\2*L )

(13.)

13. C_1 = C * sqrt ( R_P / z_in )

(14.)

14. C_2 = C * C_1 / ( C_1 - C )

(15.)

15. Q = ω_0 * L / R_S

3D calculator output:

3D calculator code (editable, help, operator precedence):

Graphical plot: