Why is permeability measurement result unstable when a low permeability magnetic material or a thin magnetic material is measured with the 16454A?

It is because the impedance of the magnetic material inserted into the 16454A is too low for the impedance analyzer to measure it accurately.
The permeability measurement software of the E4991A option 002 and the permeability measurement sample software of the 4294A calculate the permeability from the impedance measurement result for a toroidal magnetic material inserted into the 16454A. Since the impedance decreases as the frequency lowers, the measurement accuracy and stability are degraded when the impedance at low frequencies is lower than the measurable impedance range of the analyzer. The low frequency limit of the permeability measurement is determined from the lowest measurable impedance of the impedance analyzer as follows:

Theoretically, since the relationship of f x µ0r – 1) x h  ln(c/b) ≥ XLL should be satisfied, the lowest frequency limit is given as:
f ≥ XLL / { µ0r – 1) x h  ln(c/b)}

Where, XLL: Lower limit of the measurable impedance (reactance) range of the impedance analyzer,

f: Measurement frequency
µ0: Permeability of free space (4π x 10-7 H/m)
µr: Relative permeability of magnetic material
h: Height of magnetic material (m)
c: Outer diameter of magnetic material
b: Inner diameter of magnetic material

Note: The above equation applies when Tan δ (dissipation factor) < 0.1 and Short compensation is performed.

The following graph shows the typical lowest frequency limit of permeability measurement for various permeability values and dimensions of the toroidal magnetic material when the 16454A is used with the E4991A. 