Toroidal Choke Choke

Their catalog doesn't seem to identify the material, so it's hard to guess, but maybe you can tell from the actual package. You need to get all the dimensions and the material saturation flux. Then, are you talking ac current or dc current? If it's ac, it's the voltage that you worry about (OK, I know voltage and current are related) and you check that with Faraday's law

B_max = (V_rms x 10⁸)/(4.44 f A N)

B is the flux density in gauss, V is the rms voltage across the choke, f is the frequency in Hz, A is the cross-sectional area in cm², and N is the number of turns. This will tell you whether you're driving the ferrite into saturation. If you do, you'll get a different AL value (that value may also be frequency dependent, so check that).

Now, if you're running dc current, that's not nice. You need to calculate the dc magnetizing force

H = (0.4 π N I)/L where L is the mean magnetic path length in cm, and H is in Oersteds. Then you need a family of curves relating H to effective permeability. That effective permeability then will tell you what AL really is in this case.

So, if you want to calculate it, you need a bunch of data sheets. Do you have any idea what you have? Perhaps I can help you find it.

Is the effective permeability is same as amplitude permeability ?

I think they're close. I'm an OF when it comes to magnetics and I tend to know and use terminology that's sometimes out of date. So, I don't use μ_a but I think it's what I mean.

I have another question regarding permeability:

Is the initial permeability is the minimum permeability the core can offer ?

No, the magnetic permeability μo is considered to be for free space. This has a value of 4π*10^-7 with a unit of Newtons/Amperes². For most materials there is an additional dimensionless relative permeability value μ_r. For most materials μ_r=1 but some material is diamagnetic and thus μ_r<1. Some material μ_r>1 and is considered paramagnetic. In all of these cases does μ_r not vary much from 1. Then there's the nonlinear ferromagnetic materials. In these material μ_r can be greater than 100. But ferromagnetic materials can saturate if the flux density B exceeds a certain threshold. Likely you have a ferromagnetic material so that your initial permeability will be several hundred times that of free space. But when you exceed this flux density, your permeability drops back to the free space permeability.

So to to answer your question, the initial permeability of your core is the maximum permeability of the core.

Initial Permeability is defined to be the permeability of the core at near-to-zero current. I think you are asking whether the supplier is giving you a typical value or a minimum one. If it is for use as a common mode blocking choke it ought to be the minimum - but I would not personally rely on this. In any case, the high-permeability cores used in blocking chokes can be very sensitive to temperature (inductance increasing with increasing temperature), and it's most likely that Radio Shack have given the value at some nominal temperature. (If you want an accurate value of inductance, you should use a gapped core...)

The short answer to your question is that you cannot use this core for any current to give you the inductance you wish. So your intuition about saturation is a real possible concern.

I don't know where you got your equation though. The inductance for a toroid has the form of L=μ*N²*h*(2π)^-1*ln(b/a) (equation 1.98 page 493) with N being the number of turns of the inductor. All of the other variables in the equation involve either the dimensions of the toroid or the permeability of the core material. Radio Shack does not give enough information to permit translation into a suitable equation but you will notice that the inductance is proportional to the square of the number of turns. Now that I've bothered to do the proportional calculation myself, I see you already know this because you will need 82.5 turns to obtain the inductance you desire. (I guess you meant 175 mh @ 1000 turns.) But without knowing the magnetic material being used, one cannot identify at what flux density this core is likely to saturate.

Strictly speaking (or is it typing) the above equation will still be valid when in saturation, but μ will become free space permeability, μ_o. You will also have potentially further changes at high frequencies but now I'm wandering way past your question.

This http://www.mag-inc.com/design/software/ct_design_software & this http://www.smps.us/magnetics.html of great help for you.

You can only make full turns on this toroid.
I note also that it is intended for use as a blocking filter; this would imply that the material has been selected for good blocking capability rather than for low loss, so it is possible that the electrical conductivity of the core could be relatively high. In addition, I wouldn't expect that a blocking core would have tight permeability tolerance. If it was intended mainly for balanced lines, and therefore to block unbalanced signals it will almost certainly saturate at quite low currents; if on the other hand it was intended for single-ended use it would have been required to pass signal and supply currents without saturation. Given the illustration provided by radio shack, I suspect the former - but you can't rely on this.

If you want something that is properly specified, try using a manufacturers' distributor; you will then be able to check the characteristics against the manufacturer's data sheet.