--- title: "Magnetization characteristic of iron core with AC excitation" subject: "Electrical Machines I" chapter: 1 key: "semester_4/electrical_machines_i:magnetization-characteristic-ac" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/magnetization-characteristic-ac site: BCT Engineering --- # Magnetization characteristic of iron core with AC excitation Electrical Machines I · Chapter 1: Magnetic Circuits and Induction - Asked in: 2071 Magh, 8 marks - Video: [Magnetic Circuits - Sinusoidal Excitation](https://www.youtube.com/watch?v=bV5L4dEZiq8) — Energy Conversion Academy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/magnetization-characteristic-ac - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-1 ## Question Explain the magnetization characteristic of an iron core with AC excitation. ## Short answer The ac magnetization characteristic is the curve joining the tips (Bₘ, Hₘ) of hysteresis loops at different excitation levels. It shows a linear region with high permeability, a knee, and saturation. Under ac, hysteresis and eddy currents cause loss; the non-linear B-H relationship makes magnetizing current non-sinusoidal. ## Answer When an iron core is excited from an ac source, B and H vary cyclically. The **ac magnetisation characteristic** is the curve of peak flux density $B_m$ against peak magnetising force $H_m$ (or $\phi_m$ against $I_m$), obtained by joining the tips of the hysteresis loops traced at different excitation levels. It shows how the core magnetises under ac and gives its permeability and saturation. #### Obtaining the characteristic ```text B | ___ saturation | _.-' | / (tips of loops) | /: | / : <- knee | / : | / linear region | / |/ --+------------------- H | ``` 1. A coil on the core is fed from a variable ac voltage at fixed frequency. 2. For a given voltage, the core goes round a hysteresis loop between $\pm B_m$ and $\pm H_m$. Since $V \approx 4.44 f N \phi_m$, $B_m$ is fixed by the voltage. 3. The voltage is raised step by step; each time a bigger loop is traced. 4. The curve through the tips $(H_m, B_m)$ of all the loops is the ac (normal) magnetisation curve. #### Regions of the curve - **Initial region:** at very low H the slope is small (domains move reversibly). - **Linear region:** B rises almost in proportion to H; permeability is high and nearly constant. Machines and transformers are designed to work just below the knee. - **Knee:** the slope falls as domains approach full alignment. - **Saturation region:** further H gives very little increase in B; $\mu_r$ falls towards 1. #### Features under ac excitation - **Hysteresis:** each cycle traces a loop of area $\oint H\,dB$, giving loss $P_h = \eta B_m^{1.6}fV$. - **Eddy currents** widen the dynamic loop further, and total core loss $P_c = P_h + P_e$ appears as the core-loss component of exciting current. - **Non-sinusoidal current:** if the voltage (and so flux) is sinusoidal, the non-linear curve makes the magnetising current peaky with strong 3rd harmonic, especially near saturation. - **Apparent (ac) permeability** $\mu = B_m/H_m$ varies with excitation level, being highest near the knee. #### Use The curve is used to choose the working flux density (about 1.2–1.7 T for silicon steel), to find the magnetising current for a given voltage, and to judge how much over-voltage a transformer can take before saturating. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the ac magnetisation characteristic of an iron core obtained? A. By plotting B against H for a dc current raised slowly from zero B. By joining the tips (Hm, Bm) of hysteresis loops traced at different excitation levels C. By plotting the area of the hysteresis loop against frequency D. By joining the points where each loop crosses the B axis Answer: B. The curve through the tips of loops of increasing size is the ac (normal) magnetisation curve. (Key point: Definition of ac curve) 2. In the test, why does raising the ac voltage at fixed frequency give a bigger loop? A. Because a higher voltage increases the frequency of the flux B. Because V ≈ 4.44 f N φm, so a higher voltage means a higher peak flux and Bm C. Because a higher voltage lowers the core's permeability D. Because it reduces the number of turns that link the flux Answer: B. With f and N fixed, φm (and Bm) is proportional to V, so each voltage step traces a larger loop. (Key point: Why voltage fixes Bm) 3. In which region of the curve are machines and transformers designed to work? A. Deep in saturation, where B is largest B. In the initial region, where the slope is small C. Just below the knee, where permeability is high and nearly constant D. Beyond saturation, where μr falls towards 1 Answer: C. Working just below the knee gives high B with little magnetising current; in saturation more H gives almost no extra B. (Key point: Working region) 4. If the voltage and flux are sinusoidal, what does the non-linear curve do to the magnetising current? A. It makes it a perfect sinusoid in phase with the voltage B. It makes it a square wave with only even harmonics C. It makes it zero because the core is ideal D. It makes it peaky and non-sinusoidal with a strong 3rd harmonic, especially near saturation Answer: D. Because B is not proportional to H, a sinusoidal flux needs a distorted current rich in 3rd harmonic. 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