## 1 Introduction  
Conductivity, as a parameter of ferromagnetic materials, can serve as an index to sort different materials, and evaluate heat treatment condition or measure the stress of mechanical parts [1; 2; 3]. Due to the advances in electromagnetic nondestructive evaluation, pulsed eddy current (PEC) testing has become a feasible and preferred technique for measuring conductivity of materials in recent years [4; 5]. However, for ferromagnetic samples, the measurement of conductivity is affected by the inhomogeneity of tested samples and the confounding cross-sensitivity to conductivity and permeability, which is undesirable in precision PEC testing [6; 7]. Especially, the influence of permeability is complex and irregular. On the other hand, correspondingly, the permeability of ferromagnetic material will change when the environmental magnetic field changes. Therefore, reducing the permeability effect or the influence of environmental magnetic field in the measurement of electrical conductivity of ferromagnetic samples is an important problem to be solved in PEC testing. It is important and meaningful to improve the detection accuracy of conductivity of ferromagnetic samples. In PEC testing, the measurements of conductivity and permeability have been studied by many scholars in recent years. [PERSON] et al. [8] decoupled the influence of permeability and conductivity in PEC measurements and the contributions of the electromagnetic properties (permeability and conductivity) were analyzed with a view to isolate the influence of these two properties. It was found that the conductivity effects are prominent in the rising edge of the transient response and the permeability effects are prominent in the stable phase of the transient response. [PERSON] et al. [4] studied the electrical conductivity measurement of ferromagnetic metallic materials using the PEC technique. In the measurement of conductivity, an inverse problem method based on a PEC analytical model was proposed to determine the conductivity and permeability of ferromagnetic plates. [PERSON] et al. [9] described the method of determining the equivalent parameters of the coil, a scaling method for a conductivity meter based on the elimination of liftoff on conductivity results, and a proposition for an effective method to measure the conductivity of rough elements. [PERSON] et al. [1,10] found a conductivity lift-off invariance phenomenon and proposed an inverse problem method to determinate the conductivity and permeability of ferrite metallic plates. [PERSON] et al. [2] proposed an eddy current measurement method to determinate electrical conductivity of samples, which indicated that the logarithm of phase signature of impedance change basically varies linearly with electrical conductivity. [PERSON] et al. [11] observed a conductivity invariance phenomenon of eddy current non-destructive testing (NDT), and used it to estimate the magnetic permeability of metals without the influence of its conductivity. [PERSON] et al. [12] proposed a novel approach based on decay time (DT) using PEC and a highly sensitive magnetoresistive (MR) sensor in conductivity measurement of materials. The results indicate that the DT parameter is linearly correlated with material conductivity allowing it to be used for estimating the conductivity from the PEC measurement. According to the above studies, it is found that the conductivity measurements of ferromagnetic samples with a permeability effect are rarely studied by using PEC testing when permeability changes. These works also revealed that the change of PEC signals caused by conductivity and permeability is indistinguishable in the measurement of ferromagnetic samples. In other words, when the conductivity is measured, the influence of permeability can not be reduced or eliminated in PEC signals. Thus, it is important and significant to reduce the influence of permeability on PEC signals, and accurately measure the conductivity of ferromagnetic samples when permeability changes.