Ⅰ. Low frequency band (50Hz-10kHz) 

1. Relatively low loss: 

At low frequencies, the hysteresis and eddy current losses of amorphous nanocrystalline materials are relatively small, and the residual loss is also at a low level. Because at low frequencies, the internal magnetic domain flips and magnetic flux changes in the material are relatively slow, and the additional losses caused by magnetostriction are not obvious. For example, in a 50Hz power system, the residual loss of the amorphous nanocrystalline transformer core is greatly reduced compared to the traditional silicon steel sheet core, which can effectively improve the efficiency of the transformer. 

2. Hysteresis loss accounts for a relatively high proportion: 

Although the overall loss is low, the proportion of hysteresis loss in the total loss is higher than that in other high-frequency bands. This is because the domain flips relatively easily at low frequencies, while eddy current losses and other high frequencies-related loss mechanisms have not yet fully played out. 

Ⅱ. Medium frequency band (10kHz-50kHz) 

1. Residual loss begins to rise: 

As the frequency increases, the magnetic domain flip speed accelerates, and the eddy current effect gradually increases, resulting in the residual loss begins to rise. However, due to the high resistivity of amorphous nanocrystalline materials, they suppress the rapid growth of eddy current loss to a certain extent, so the increase in residual loss is relatively gentle. 

2. The impact of magnetostrictive effect is prominent: 

In the medium frequency band, the proportion of energy loss caused by magnetostrictive effect in the residual loss gradually increases. Magnetostriction causes stress changes inside the material, which in turn causes additional energy loss, and this loss is frequency-related and increases as the frequency increases.

Ⅲ. High frequency band (50kHz-100kHz and above) 

1. Residual loss growth accelerates: 

When the frequency further increases to above 50kHz, the residual loss will increase rapidly with the increase of frequency. This is because the eddy current loss and magnetostrictive loss are significantly increased at high frequency. At the same time, the movement of the magnetic domain wall inside the material is more complicated, and the vibration, bending and fracture of the magnetic domain wall are intensified, resulting in a significant increase in additional energy losses.  

2. Sensitivity to material characteristics and process:

In the high frequency band, the residual loss of amorphous nanocrystalline materials is very sensitive to factors such as the composition, microstructure and preparation process of the material. For example, the impurity content, grain size distribution, heat treatment process, etc. in the material will have an important impact on the magnetic properties and residual losses at high frequencies. By optimizing material composition and preparation process, the residual loss at high frequency can be reduced to a certain extent, but overall, the control of residual loss at high frequency is more difficult. 

To sum up, the residual loss of amorphous nanocrystalline materials is lower at low frequencies, and gradually increases with the increase of frequency, and grows rapidly in the high frequency band and is affected by various factors. In practical applications, it is necessary to select appropriate amorphous nanocrystalline materials and processes according to the specific operating frequency range to reduce residual losses and improve the performance and efficiency of the equipment.