Small loop antennas are the most suitable and popular approach for mobile and handheld appliances [Myron Loewen, Microchip Technology Inc., 2003]. The small loop antenna consists of a simple loop of conductor (wire or PCB trace) that is tuned using capacitor at the working frequency of the radio transmitter/receiver/transceiver. This small loop antenna calculator helps in calculating the small loop antenna parameters such as impedance matching, loop dimensions, capacitor values, etc. This calculator also presents visually the various characteristics of the small loop antenna you are trying to design such as filtering of higher harmonics, etc. Small loop antennas tend to have very high Q (search for Halo antennas on the Internet). The Q should be reduced to widen the frequency band of the small loop antenna and make the manufacturing easier. A Q under 20 is desired. To degrade the Q use a resistor R_Ldump in series with the antenna inductor. The current small loop antenna calculator has been successfully used to design a transceiver with MAX7032 [MAX7032 datasheet].

Impedance of the tuned circuit Zin:	Ω   mΩ
Working frequency f:	MHz   KHz   Hz
Width of the loop a:	m   cm   mm   in   feet   yards
Height of the loop b:	m   cm   mm   in   feet   yards
Width the PCB trace w:	m   cm   mm   in   feet   yards
ESR resistance of the used capacitors (one capacitor) RCesr:	Ω   mΩ
Q degrading resistor in series with the inductor PCB trace RLdump:	Ω   mΩ

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 - j*1/(ω*C)

(6.)	6. Z_L = R_L + j*ω*L

(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