I am almost sure that the exact test (not on a simulator), I am talking about, that uses a scope to measure the 3 parameters Bs, Br and Hc of a non-linear iron core, cannot be found on any book or on the internet. But perhaps I am wrong because I can’t get many scientific books and I can’t access many scientific websites as well.
Anyway, you will know if my impression is right or wrong after reading what I will present on thos post.
The LTspice schematic below is a replica of a test on an inductor (L1) whose core is unknown. On the schematic, the mechanical parameters of L1 are set. The 3 parameters of its BH loop are also set. They were derived earlier, by a real test, from the v(t) and i(t) traces (on and in the inductor of interest) that were displayed on the screen of a digital scope.
After running the simulation, the various ‘.meas’ commands (see param_NL_core_07.txt) which get the needed values from the traces V(LL) and I(L1) (now on the LTspice window), also apply the formulas of Bs, Br and Hc (see below) to give the result’s errors (in percentage format).
Br_err% = -0.203454%
Hc_err% = 0.0533104%
Bs_err%= -1.53767%
Only 4 points on the scope’s screen need to be read (as absolute values):
V_max
V_I0 when i(t)=0
I_max when v(t)=0, the flux B is at its highest value.
I_B0 when v(t)=V_max, the flux B is zero
To simplify the end formulas, constants are defined as follows:
Kh = N/Lm
Kb = 1/N/A
Where:
N = the number of turns
Lm = the Magnetic Length (excl. gap), in meter.
A = the Cross-sectional area of the core, in m2
Also:
wt0 = arcsin(V_I0/V_max)
w = 2*pi*F
Br = Kb * Vmax / w * cos(wt0) [Tesla]
Hc = Kh * I_B0 [A/m]
Two more constants are defined for the Bs formula:
Mh = Kh*I_max + Hc
Mb = Kb*V_max/w-1.25664E-06*Kh*I_max
Bs = (Mh-Hc)/(Mh/Mb-Hc/Br) [Tesla]
There is one more question to discuss.
Which is the ‘practical’ value of I_max that lets the calculated Bs be close to its real value?
I compared I_max with three values of i(t):
Irms,
abs(Iavg) of a half cycle and
I_B0.
I chose the latter one,
I_B0, because its sensitivity to I_max is the smallest.
In general, the practical ratio,
I_max / I_B0, is around 3.5.
Kerim