Mathmatics

[belwar]

Ok,

So i've been trying to learn about some of the electrical concepts that surround pickups. While I understand that these numbers don't mean very much if you can't wind a good pickup to begin with, I still want to learn them out of facination. I dont have a stong knowledge in electronics so I have to teach myself all the terms as I go.. Everything from the differences between AC & DC, to impedance, and inductance.

I've sifting through some website, books, and articles to try to come up with the formulas for obtaining a few items. I was hoping someone here would look these over and see if they are correct for pickups. I'm a little confused in what units to use (for example if an equation contains "L" should I put the number in Henries, or Micro-Henries?)

So anyways here are two I'm working on

IMPEDANCE:           Z  =  L  x  ƒ₁ x  π  x  2


RESONANCE FREQ:      ƒ₂  =      1
                            ----------
                              2π√(LC)

So just for reference here are the descriptions of the letters:

Z = Impedance
L = Inductance
ƒ₁= Frequency the inductance was measured at
ƒ₂= Resonance Frequency
C = Capacitance measured at the same frequency as L

Anyone here want to take a look at these? am I way off?

[Joe Gwinn]

There is too much to say to attempt explaining it here.

The fastest way home is to read the relevant chapters of any college physics textbook.

The formulas given in current physics books will assume seconds, volts, amps, meters, henrys, and farads. In short, they use the SI system of units, which is essentially equal to the old MKS system.

[madialex]

There is too much to say to attempt explaining it here.

The fastest way home is to read the relevant chapters of any college physics textbook.

The formulas given in current physics books will assume seconds, volts, amps, meters, henrys, and farads. In short, they use the SI system of units, which is essentially equal to the old MKS system.

If Joe said it, then take it to the bank...It's on the money..

[Old Tele man]

...to answer your mathematical questions:

1) the ƒ1-frequency, in your first equation, is the "driving" frequency of a REACTANCE-circuit (not IMPEDANCE). That equation represents an inductors' AC-opposition to changing current flow. For inductance (transformers, coils, chokes, wire, etc.) it's called INDUCTIVE-reactance XL:

XL = 2*PI*F*L

...and, for capacitance (capacitors, transformers, tubes,wire, etc.) it's the opposition to changing voltage and is called CAPACITIVE-reactance XC:

XC = 1/(2*PI*F*C)

2) the ƒ2-frequency, in your second equation, is the "peak or resonance" frequency of oscillatory (resonant) circuit, the point of maximum signal level (and minimum Z) in an excited or oscillatory LC-circuit.

...IMPEDANCE (Z) is the vector-summation of (a) the DC-RESISTANCE (R) and (b) the AC-REACTANCE (comprised of inductive-REACTANCE (XL) minus capacitive-REACTANCE (XC)), here's the correct formula:

Z = SQRT[ R^2 + (XL - XC)^2]

...so, why is the XC substracted from the XL? Because of their opposing current "phase angles"--XL is upward, while XC is downward--when they're both the same (ie: XL = XC), their values "cancel" leaving only R in the circuit.