According to my knowledge, a practical inductor is composed of an ideal inductance in serires with the effective resistance of that inductor.
Skin effect increases effective resistance with the increase in operating frequency.
For receiver ckt, the selectivity is calculated by 2*pi*f L/r, which means the selectivity depends on frequency as well as effective resistance and inductance. So the design of an inductor depends on the required selectivity and frequency as well as consideration of effective resistance.
For a SMPS inductor design, I learned that the inductance for forward converter is calculated by (Vin-Vo) Ton max/ I min.
I need to understand more about this.
How come the inductance depends on the input and output voltage difference, the maximum on time and the minimum current drawn.
Are the equations I know right or wrong?
Where can I find these practical equations for calculations as well as descriptions on how they are derived from the fundamental theories of Electricity and Electronics?
That's a decent 1st order model; there are fancier ones available if you need the extra accuracy.
It also increases the effective inductance until you hit self-resonance.
Yes, although in many cases you try to have the inductor's resistance be small relative to, e.g., load resistance.
I suppose you could say that, but keep in mind that how the core behaves (specifically its loses, which go up superlinearly with frequency, and sizing it to avoid saturation) plays a large part in the overall inductor design as well.
For a "standard" buck converter operating in non-continuous mode, yes.
Well... first, you might want to mentally separate "RF inductor design" from "SMPS inductor design." In the former, at least for "signal" levels, frequency response and self-resonance tend to be the driving factors in making a design work. In the later, the power you need to deliver and the switching frequency drive current through the inductor, and this drives the wire size and the core size (to avoid saturation). Unless you're building switchers above, say, a MHz, you usually don't have to worry much about self-resonance and frequency response.
Umm... err... rather than write half a page here, could you get a copy of, e.g., Abraham Pressman's "Switching Power Supply Design" or similar? (Check Amazon to find similar tomes.) It goes through the derivation, which isn't difficult (just algebra), but it helps to have some pictures to look at. Someone like Eeyore (if he took his meds today :-) ) can probably quote you the derivation irectly. If you can't get ahold of a book, look for application notes on switch-mode power supplies on, e.g., Linear's web site.
They're "correct" but I get the impression you're not aware of a lot of the context that they're to be used within.
University lectures? Books? Application notes on web pages?
If you tell us what you'd like to design, we can probably point you towards a reasonably specific resource.
A really useful thing to know, assuming you're not put off by a little derivative notation, is
v(t) = L* di/dt
That is, the voltage across a pure inductance is proportional to the inductance and also to the rate of change of current. So if you put, say, 5 volts across an ideal inductor that's 20 microhenries, then current will increase at the rate of 1/4 amp per microsecond. If you want the current to build to 3 amps, leave the voltage applied for 12 microseconds: 12usec*0.25A/usec = 3A. To more accurately account for what happens, you need to include effects like the resistance (note that current through the resistance lowers the voltage applied to the ideal inductance), the stray capacitance among the turns, saturation of the core material that effectively makes the inductance a function of current (and therefore of time), and some other things like that. But to a first order, with inductors that are properly applied, the v = L * di/dt will go a long ways in aiding basic understanding. Can you, for example, now see where that SMPS formula you posted comes from?
Of course there's lots more to know, but see where that takes you. (Transformers are coupled inductors, and the above can be extended to cover them, also to a first approximation, pretty easily.)
Yes and no. It's a bit misleading. The apparent inductance raise with frequency below resonance because of shunt capacitance. But it'll also raise *without* this parasitics, between 2 asymptotic values (one DC value and one HF value) thanks to skin effect that changes the current distribution and thus the total stored energy. (look for internal inductance).
As Joel wrote, start by studying either a good book or app notes. When I learned this stuff in the 80s/90s I found that Unitrode's app notes were excellent. Still are, except now you find them on the web site of TI because they acquired Unitrode.
With SMPS you need to start thinking about inductors as energy storage devices. IOW what goes in must come out in discontinuous conduction mode (DCM), or partially come out in continuous conduction mode (CCM) but there you must pay attention that the balance remains at healthy levels. Especially in the latter case great care needs to be taken to avoid inductor current "ratcheting" which will result in profound destruction if unchecked. When the voltage on a cap increases the cap will eventually break down. When the current of an inductor increases it will simply go into saturation and the device feeding it will typically be destroyed, usually in a rather spectacular manner.
Also, study diodes (especially their storage time effects), gate control of FETs, ringdown etc.
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