Among the core performance parameters of inductors, magnetic permeability, magnetic induction intensity B (magnetic flux density), magnetic field intensity H, and saturation magnetic flux density Bs are the four core indicators that characterize the magnetic characteristics of inductors, directly determining their energy storage capacity, loss level, operating limit, and adaptability to application scenarios. Whether in the fields of power management, high-frequency communication, industrial control, intelligent devices, etc., the selection, design, and performance optimization of inductors cannot be separated from a profound understanding of these four parameters. Many engineers tend to confuse the definition and correlation of the four major parameters in practical operations, resulting in selection mismatch, circuit failure, or performance redundancy. This article will start from the essence of physics, break down the definitions, core correlations, and influencing factors of the four major parameters layer by layer, analyze their application logic in combination with engineering practical scenarios, and balance professional depth and practicality to help you thoroughly grasp the core logic of inductance magnetic parameters.

1、 Core definitions of the four major magnetic parameters

2、 The intrinsic logic of the four major parameters

• The formula for calculating inductance value is L=μ × N ² × A/Le, where L is the inductance value (unit: H), μ is the magnetic permeability of the magnetic core, N is the number of coil turns, A is the effective cross-sectional area of the magnetic core, and Le is the effective magnetic circuit length of the magnetic core. This formula clarifies the decisive role of μ in the inductance value - under the same coil structure (N, A, Le are the same), the larger the μ, the larger the inductance value L; On the contrary, the smaller the μ, the smaller the L. This is also why high-frequency inductors often use high μ magnetic cores (such as ferrites), which can achieve larger inductance values in smaller volumes.
• The formula for calculating magnetic flux density is B=μ × H=μ × NI/Le, which connects four major parameters in series and intuitively reflects the mutual influence of each parameter: ① Under the same magnetic core (μ, Le, A fixed), the larger N and I (H), the larger B; ② Under the same excitation conditions (fixed N and I), the larger the μ, the larger the B; ③ When B reaches Bs, even if N or I continues to increase (increasing H), B no longer increases. At this point, μ sharply decreases and L decays significantly. In addition, by combining the relationship between magnetic flux and B, the correlation between inductance value and magnetic flux can be derived as L=N Φ/I, further reflecting the linkage between magnetic parameters and core performance of inductance.

• B-H curve (magnetization curve): This is the core curve that describes the relationship between B and H, and is also the key to understanding the correlation between the four major parameters. The curve is divided into three stages: ① Linear segment: When H is small, B increases linearly with H, and μ remains basically constant, which is the normal operating range of the inductor; ② Saturation stage: When H increases to a certain extent, the growth rate of B slows down until it tends to stabilize, at which point it reaches Bs, and μ sharply decreases; ③ Demagnetization section: When H decreases to 0, B will not decrease to 0, and the residual B value is remanent Br. Reverse H (coercive force Hc) needs to be applied to reduce B to 0, forming a hysteresis loop. The area enclosed by the hysteresis loop is proportional to the hysteresis loss within one magnetization cycle.
• The dynamic variation of μ: μ first increases with the increase of H (reaching a maximum value of μ m), and then gradually decreases. When H is large enough and the magnetic core reaches saturation, μ approaches μ ₀. Meanwhile, μ also decreases with the increase of operating frequency - at high frequencies, the hysteresis loss and eddy current loss of the magnetic core increase, the magnetization ability decreases, and μ decreases; Temperature can also affect μ. Usually, as the temperature increases, μ first increases slightly and then sharply decreases after reaching a certain peak. After exceeding the Curie temperature Tc, the magnetic core loses its ferromagnetism, and μ ≈ μ ₀. Bs also decreases with increasing temperature, which is one of the core reasons for the degradation of inductance performance in high-temperature environments.

3、 The influencing factors of the four major parameters (from materials to working conditions)

• Magnetic permeability μ: The μ r of ferrites (MnZn, NiZn) can reach 1000-10000, suitable for high-frequency and low current scenarios; The μ r of nanocrystalline and amorphous alloys can reach tens of thousands to hundreds of thousands, combining high μ and high Bs, suitable for high-precision and low loss scenarios; The μ r of silicon steel sheet is about 500-8000, with high Bs (1.5-2.0T), suitable for low-frequency and high current scenarios; The air core's μ ≈ μ ₀ (μ r ≈ 1) is suitable for high-frequency and high stability scenarios (such as RF inductors). In addition, the purity and grain size of magnetic core materials also affect μ. The higher the purity and the more uniform the grains, the more stable μ.
• The saturation magnetic flux density Bs: Bs is determined by the atomic magnetic moment density and Curie temperature of the material, and is the upper limit of the intrinsic magnetic properties of the material. The Bs of metal magnetic cores (silicon steel sheets, pure iron, nanocrystals) are much higher than those of ferrites, for example, the Bs of silicon steel sheets are ≈ 1.5-2.0T, the Bs of nanocrystals are ≈ 1.2-1.5T, while the Bs of ferrites are only 0.3-0.5T. Therefore, metal magnetic cores are preferred for high current and high energy storage scenarios (such as power inductors), and ferrites can be used for high-frequency and low current scenarios (such as RF inductors). At the same time, material composition can also affect Bs, for example, different ratios of Mn and Zn in ferrites can result in differences in Bs.
• The correlation between H and B: Under the same excitation conditions, the higher the μ of the magnetic core material, the greater the B produced by the same H; The higher the Bs of the material, the higher the saturation limit of B and the greater the H it can withstand.

• The impact on μ: As the frequency increases, the hysteresis and eddy current losses of the magnetic core increase, and the response speed of the magnetic moment cannot keep up with the changes in the magnetic field, resulting in a decrease in μ. The higher the frequency, the more significant the decrease in μ. For example, when MnZn ferrite is below 1MHz, μ is stable, and when it exceeds 10MHz, μ sharply decreases. Therefore, high-frequency scenarios (such as radio frequency) require the use of high-frequency specialized ferrites (such as NiZn ferrite), whose μ changes more smoothly with frequency. This is also why the μ of high-frequency inductors is usually lower than that of low-frequency inductors, but the high-frequency losses are lower.
• The impact on B and Bs: As the frequency increases, the eddy current loss of the magnetic core increases, causing the core to heat up and the temperature to rise, resulting in a slight decrease in Bs; At the same time, the rate of change of H accelerates at high frequencies, and the magnetization response of the magnetic medium lags behind. The B generated by the same H is slightly lower than that in low frequency scenarios. Therefore, the actual working B value of high-frequency inductors needs to be further reduced to avoid saturation.

• The impact on μ: Within the temperature range of -40 ° C to 85 ° C, μ slightly increases with increasing temperature, reaches its peak (usually around 85 ° C), and then sharply decreases as the temperature continues to rise; After exceeding the Curie temperature Tc, the magnetic core loses its ferromagnetism, and the inductance value almost disappears. The Curie temperature of different materials varies, with ferrite Tc ≈ 200-450 ℃, nanocrystalline Tc ≈ 400-500 ℃, and silicon steel sheet Tc ≈ 700-800 ℃. Therefore, high Tc materials should be selected for high-temperature scenarios. In addition, temperature changes can also cause fluctuations in μ, affecting the stability of inductance values. The temperature coefficient α μ can be used to characterize this change, and the smaller the α μ, the better the temperature stability.
• The impact on Bs: Bs decreases linearly with increasing temperature, with a decrease of approximately 1% -2% for every 10 ℃ increase in temperature. For example, the Bs of a certain ferrite is 0.4T at 25 ℃ and may decrease to 0.35T at 100 ℃. Therefore, in high-temperature scenarios, more Bs margin should be reserved (usually 60% -70% of Bs) to avoid magnetic core saturation. Its temperature dependence can be described by Weiss molecular field theory: M ₛ (T)=M ₛ (0) (1 − T/T ꜀) ᵝ, where β is the critical exponent and M ₛ is the saturation magnetization, directly related to Bs.

4. Coil structure: indirectly affects parameter performance

• The more turns N: N, the greater the H and B at the same current, making it easier to reach Bs; at the same time, the more N, the greater the inductance value L (L is proportional to N ²). But too much N will increase the coil resistance, resulting in increased losses, and it is necessary to balance the number of turns and losses.
• The longer the magnetic circuit length Le, the smaller H and B under the same NI, making it more difficult to reach Bs; the shorter Le, the larger H and B, and the larger the inductance value L (L is inversely proportional to Le).
• The larger the cross-sectional area A, the greater the magnetic flux Φ and inductance value L (L is proportional to A) for the same B; Meanwhile, the larger A, the larger the heat dissipation area of the magnetic core, and the greater the current it can withstand, making it less likely for Bs to decrease due to heating. In addition, the geometric shape of the magnetic core also affects the effective magnetic circuit length and effective cross-sectional area, indirectly affecting the distribution of H and B.