Q of a Coil
where omega is 2(pi)f, f is in hertz, L in heneries, and (AC) r in ohms. Example: At 1 MHz, a 250 uH coil with 6 ohms of AC resistance has a Q = 2*3.14*1*exp(6)*250*exp(-6)/6 = 261. Q is proportional to coil form diameter and inversely proportional to the AC resistance in the coil. Hence, a 3.5 inch dia coil with Litz wire (low loss multi-strand wire) will have a much higher Q than a coil with hookup wire wound on a 2 inch form. Selectivity of a crystal is inversely proportional to Q; that is, the bandwidth of a parallel tuned circuit at near resonance is it's frequency divided by the effective bandwidth, BW.
Inductive Reactance of a Coil
where f is the frequency in hertz and L is the coil inductance in henrys. X is the AC impedance of the coil. Example: At 1 MHz with L equal to 250 uH, X = 2*3.14*1*exp(6)*250*exp(-6)= 1,570 ohms. exp(6) means 10 to the 6th power, or 1,000,000.
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Diode Current and Dynamic Resistance
where iD is the diode current, Io is the diode saturation current, m is the quality factor [from 1 to 2, use 1.2], and vd is the voltage across the diode. Also, rd is the forward dynamic resistance of the diode at the operating point Q.
Capacitive Reactance of a Capacitor
where f is the frequency in hertz and C is the capacitance in farads. X is the AC impedance of the cap. Example: At 1 MHz with C equal to 105 pf, X = 1/(2*3.14*1*exp(6)*105*exp(-12) = 1,516 ohms.
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Formulas, updated 08/18/16
Resonant Frequency of an LC Circuit
For the AM broadcast band, typical inductance (coil) values range from 250 uH down. Capacitance values vary from tens of pfs to several hundred pfs. 365 pf air variable caps are common.
where f is the frequency in hertz, L inductance in henrys, and C capacitance in farads.
Inductance of a Single-Layer Cylindrical (Coil)
where the inductance L is in uH, N is # of turns, coil length "l" is in inches and coil radius r is in inches. Length, "l" is equal to Np where p is the pitch (distance between turns). Note that the formula, as written, solves for the inductance (L). However, you can solve for r, N, or coil length (l) instead. For example, enter a random value for L and desired value to two of the three remaining variables. Then keep entering your desired final value until L reaches your intended coil inductance.
Press the blue-white download button below to load the spreadsheet calculators for the single-layer coil formula above and for the resonant frequency formula of an LC circuit.