Question E6D08:
Which of the following materials has the highest temperature stability of its magnetic characteristics?  

Choices:  
A: Brass  
B: Powdered iron  
C: Ferrite  
D: Aluminum    

Correct Answer is  B: Powdered iron  

Correct answer: Powdered iron

Why it’s correct
- Powdered iron cores have a distributed air gap. This makes the effective permeability $\,\mu_e\,$ much less sensitive to temperature changes in the core material’s intrinsic permeability $\,\mu_r$.
- Result: inductance and Q remain more stable over temperature than with ferrites, which have higher $\,\mu_r\,$ but a larger temperature coefficient.

Useful relationships
- Inductance with a magnetic core: $$L = A_L N^2$$ where $A_L \propto \mu_e$.
- For a gapped core (powdered iron behaves like a “distributed gap”):
  $$\mu_e \approx \frac{\mu_r}{1 + \mu_r \, \frac{\ell_g}{\ell_c}}$$
  Let $k = \ell_g/\ell_c$. Then:
  $$\mu_e = \frac{\mu_r}{1 + k\mu_r}$$
  Sensitivity of $\mu_e$ to changes in $\mu_r$:
  $$\frac{d\mu_e/\mu_e}{d\mu_r/\mu_r} = \frac{1}{1 + k\mu_r}$$
  If $k\mu_r \gg 1$ (gap dominates), temperature-driven changes in $\mu_r$ have little effect on $\mu_e$ and thus on $L$.

Why the other choices are incorrect
- Ferrite (C): Higher permeability, but its magnetic properties (permeability, loss, Q) vary significantly with temperature and approach the Curie temperature more critically. This causes larger inductance drift than powdered iron.
- Brass (A) and Aluminum (D): Essentially non-magnetic ($\mu_r \approx 1$; diamagnetic/paramagnetic). They are not suitable magnetic core materials and provide no useful, stable magnetic permeability for inductors; their high conductivity can also introduce eddy-current losses, not temperature stability.

Rule of thumb
- Use powdered iron mixes for temperature-stable inductors in RF oscillators and filters.
- Use ferrites when high permeability or broadband transformer action is needed, understanding their greater temperature dependence.