Am I doing this correctly?

[LeapFrog]

source: https://br.answers.yahoo.com/question/index?qid=20090525124333AAHrJmB
LC circuit question for crystal receiver.

use this
2πfL = 1/(2πfC)

find an adjustable cap, say 5-15pF, and pick a value in the middle of the range, say 10pF. Then calculate the inductance needed to resonate with that cap.

2πfL = 1/(2πfC)
L = 1/(4π²f²C)

L = 1/(4π²(27e6)²(10e-12))
L = 35e-7 H or 3.5µH

11 Meters example from the yahoo answers response.
F=27MHz
C=10pf
L = 1 / (4π² (27e6)² (10e-12) )

4π² = 39.4784176044
27e6 = 27,000,000.0 squared is = 7.29e+14
7.29e+14 x 10e-12 = 7290
7290 x 39.4784176044 = 287797.664336
L = 1/ 287797.664336
L = 0.00000347466 or 3.47 µH

My attempt for a
20 Meters example.

Solve for L
F = 14MHz
C = 10pF

L = 1 / (4π² (14e6)² (10e-12) )

4π² = 39.4784176044
14e6 = 14,000,000.0 squared is = 1.96e+14
10e-12=0.00000000001
1.96e+14 x 10e-12 = 1960
L= 1 / (39.4784176044 x 1960.00)
39.4784176044 x 1960.00 = 77377.6985046
L = 1 / 77377.6985046
L = 0.00001292362 or 12.92 µH

Do the numbers add up?
I know I need to revisit Scientific notation.
Thank You

 

[nomadradio]

Looks pretty darn close to me.

Since what we do tends to get 'tweaked' to tune, I just use the reactance chart from the ARRL handbook. Resonance is the frequency where the reactance of the capacitor equals the reactance of the inductor. The chart has capacitance value along diagonal lines running down from left to right. Inductance value is along diagonal lines going up from right to left. Finding 13 uH and 10pf, the frequency where the lines cross for those two values lands right around 14 MHz.

Should work, so long as your circuit has a variable element in either the inductor or capacitor to "tweak" it on frequency.

73

 

[LeapFrog]

Looks pretty darn close to me.

Since what we do tends to get 'tweaked' to tune, I just use the reactance chart from the ARRL handbook. Resonance is the frequency where the reactance of the capacitor equals the reactance of the inductor. The chart has capacitance value along diagonal lines running down from left to right. Inductance value is along diagonal lines going down from right to left. Finding 13 uH and 10pf, the frequency where the lines cross for those two values lands right around 14 MHz.

Should work, so long as your circuit has a variable element in either the inductor or capacitor to "tweak" it on frequency.

73

Nomadradio,

Thank You for looking this over; I really appreciate the mention (and checking against) of the ARRL handbook, yet another reason why I need to get a copy!

I will most definitely be using a variable element to tweak the values in-circuit; as I couldn't be bothered trimming the L millimeters at a time or adding minuscule amounts of C to finally get to peak resonance.

I (just) found a reactance chart online (didn't know they made those), here it is just in case anyone needs a copy.

I'm going to go study and read about reactance now, thank you once again Nomad.
Also, I appreciate your explanation of resonance!
73