The following network
analysis gives a simple method of measuring inductance or capacitance. For
persons without an LC Meter, this may be an option.
Only basic test equipment is needed,
such as an RF signal generator and RF Voltmeter or Oscilloscope. By connecting
a resistor in series with an inductor or capacitor, L or C values can be
computed. Effective Impedance Z is the series combination of resistor R and reactance device X, expressed in Ohms. Note that resistor R must be a non-inductive device.
A hand solution of the equations is
possible, but a better option is to program a spreadsheet. As a general example, N^2 means the quantity "N" raised to the exponent "2", or "N" squared. Otherwise N^(1/2) represents the quantity “N” raised to the exponent “1/2”, or squareroot of "N". Solutions of essential network equations are shown below in bold.
Voltages Vs and Vr can be measured in Volts peak-peak (pp) for oscilloscopes or Volts (rms) for RF voltmeters. The solution for X hinges on the ratio of Vs/Vr, consequently the choice of voltage scales doesn't matter. However using both Vpp and Vrms scales won't work properly, so don't mix scale types. Any RF voltmeters must be operated in the unterminated high-impedance mode.
General Setup
I = Vr/R = Vs/Z
Z= [R^2 + X^2]^(1/2) = VsR/Vr
X^2 = (VsR/Vr)^2 - R^2
X = [(VsR/Vr)^2 - R^2]^(1/2)
Inductance Solution
X = 2πFL
L = X/(2πF)
Capacitance Solution
X = 1/(2πFC)
C = 1/(2πFX)
Electrical Units
Voltage V, Volts
Current I, Amps
Resistance R, Ohms
Reactance X, Ohms
Impedance Z, Ohms
Frequency F, Hertz
Inductance L, Henrys
Capacitance C, Farads
π = 3.1416
Frequency and Resistance
Use one of the following Resistance
or Frequency approximation tools. Estimate the L or C rating of the
device to be tested. Make choices of frequency to estimate resistance, or resistance
to estimate frequency. Useful ranges are obtained, however exact values aren’t
critical. The goal is to make resistance about half of the reactance value in
Ohms. These tools take guesswork out of picking a good frequency and resistance
for testing.
Inductors
R = (1/2)X = (1/2)(2πFL)
R = πFL
F = R/(πL)
Capacitors
R = (1/2)X =
(1/2)[1/(2πFC)]
R = 1/(4πFC)
F = 1/(4πCR)
