Just to illustrate, here's an estimate of likely flux density changes arising in MM/MI and MC cartridge cores which shows it in both cases to be very small in the context of being unaffected by the large scale non-linearities arising in B-H curves of highly permeable alloys.
Apols it's a bit mathy, but hopefully if the terms used in the JC extracts make sense to you, so should this !
The aim is to estimate the size of flux changes in typical MM/MI and MC cartridges, and relate this to published B-H curves for typical core materials and geometries:Definitions :Coil self inductance L [H]
Number of turns in coil N []
Current in coil I [A]
Induced voltage across coil V [V]
Induced voltage per turn in coil Vt [V] = V/N
Total flux linking coil Ø [Wb]
Flux Density in coil core B [Wb/m²]
Time t [s]
Angular frequency w [rads/s] = 2*pi*frequency
Coil core area A [m²]
Relations :dØ/dt = dI/dt * (L/N)as an inductor, rate of change of flux is proportional to rate of change of current, the constant is inductance per turn.
V = L * dI/dt Vt = (L/N) * dI/dt voltage per turn is proportional to rate of change of current, the constant is inductance per turn
Then
Vt = dØ/dt ; ie coil volts per turn is exactly rate of change of core flux.
Calculations :For an MM/MI N = 1000 , number of turns in the coil is about 1000 ref this thread :
viewtopic.php?p=273610For an MC, N = 50, number of turns in MC coil is about 50, same reference above.
Assume an output of 5mV (MM), or 0.5mV (MC), which is near full scale output ref 0dB@1kHz sine wave. We wish to find Ø, the peak amplitude of total flux in the core, and H the peak flux density in the core.
dØ/dt = Vt = 5mV/1000 = 5E-6 V
Because the stimulus is a sinewave, the peak value of Ø = Vt / w
Then for MM peak Ø = c 8E-10 [Wb]
and for MC peak Ø = c 1.6E-9 [Wb]For MM core section area A might be 5mm², for MC A might be 3mm²
Then peak core flux density B for MM/MI is estimated to be Ø/A = 0.00016 Wb/m²
And peak core flux density B for MC is estimated to be 0.00053 Wb/m²
And the amplitude of flux density changes in coil cores associated with full scale output of the cartridge at 5cm/s@1kHz is estimated to be circa
0.00016Wb/m² for MM, and 0.00053 Wb/m²DiscussionA datasheet for what seems a fairly ubiquitous permalloy core material is listed here :
http://cartech.ides.com/datasheet.aspx? ... &c=TechArt B-H curves are listed, which show the onset of saturation being at flux densities c 1 Wb/m².
Then the working range of flux density changes within coil cores for MM and MC cartridges is estimated to be 0.016% and 0.053% of the working range of that permalloy material. Associated with cartridge outputs representative of 5cm/s@1kHz, 5mV and 0.5mV outputs respectively.
Therefore, it appears that flux density changes represent a very small part of the working range of the core material, and therefore approximate a linear B-H transfer function. Even allowing for normal peak programme level overloads, there appears to be several orders of magnitude margin. Sufficient to support the notion that non-linearities in the B-H transfer curve aren't significant at any level or frequency.
Interesting ? I'd welcome this being checked over, but i think it's right. Comments and questions welcome, as always.