nice coil calculator

As I understand Q it applies to a tank, so how can the inductor by itself have a Q factor?

Q = wL/R, where R is the equivalent series resistive component of the inductor's impedance at radian frequency w.

At low frequencies, R is the DC copper resistance. At higher frequencies, skin and proximity effect kick in.

A tank would have the same Q if the inductor were resonated with an ideal capacitor.

Capacitors are rated for Q too.

In both cases, Q is a function of frequency.

There's a lot of good stuff on that from the NBS from back in the 1920s. I'll have a look in my bookshelf on Monday.

Cheers

Phil Hobbs

You can elect to define it that way. But reactive "power" integrates to zero energy.

Thanks. I was thinking in terms of parasitic R in a LC, but forgot it applies to parasitic R in the L and C alone.

Q is a matter of definition. The first definition kids usually learn is X/R. Resonators have a Q by the same definition (given a suitable equivalent circuit, like a series RLC), understood to be measured at the resonant frequency (w = 1/sqrt(LC)), unless specified otherwise in which case the first definition is probably used.

You can go further and talk about the Q factor of a resonator in a system; this might be very low, such that a filter with high bandwidth is made. In that case, you want the resonator or component Q to be much higher than the system Q, so as to get good efficiency (low insertion loss).

I've seen (1 + Q^2) terms pop up in equations, frequently enough that it seems worthy of a symbol. In that case, you might take the liberty of using a suitably marked variant, maybe a Q', or K (for koalaty factor, if you're Aussie ;) ) or something.

Or you can take the Q factor of a power system, like with generating or rotating machinery. The Q factor of the power grid is usually very low, 0.1 or thereabouts -- there's not that much stored or reactive power in all the high voltage transmission lines, PFC caps, line reactors and rotating machinery.

The only problem in power, is, well, power: they use S = P + jQ for apparent, real and reactive power, respectively. So you have the potential confusion that Q(quality) = Q(reactive) / P... :-)

Tim

Koalas are among the minority of Australian wildlife that _aren't_ out to kill you. Wombats are OK too, I'm told. ;)

Q**2+1 comes up in L-network impedance transformation networks, for instance. Near resonance, an LC tank with a series resistance Rs behaves very similarly to one with a parallel resistance Rp=Rs(1+Q**2).

Really? I'd think it would take a lot more than 1/10 radian at 60 Hz to make all those generators slow down to 1/sqrt(e) of their normal speed, even if you turned off the steam. 0.1rad / (2 pi*60 Hz) = 265 us. It'd be quite a trick to do that without everything breaking into small pieces.

The various definitions of Q are all the same in the high-Q limit, but for Q values near or below 1.0 they diverge in important ways. For instance, an LC tank's peak frequency changes differently with Rs than Rp.

Cheers

Phil Hobbs

Actually, I think that was calculated based on typical power factor, so let me take that back. Inertia should keep things running for a few cycles, give or take how much voltage and frequency you still consider "running".

Yeah, for Q < 5 or so, you can't get away with approximations, and you get a -1 / (R^2 C^2) error term (under the sqrt) for frequency (for a lossy capacitor, or analogously with L/R).

You also get multiple possible definitions for resonance, say for an L-match with resonant load, where you can take peak output power, or imaginary output, or all real input, or... Which all converge at high Q, but at low Q you don't have that luxury.

Tim

I don't have a tech so I wound a coil myself, #14 magnet wire wrapped around a Sharpie pen, which ended up about the diameter I wanted.

It's sort of surface-mount. The middle turns are spaced off the PCB enough to slip a thermally conductive gap-pad under, to conduct heat to the copper pours on the top of the board.

My overall pulse generator current consumption dropped in half when I replaced the three seriesed flat-winding Coilcrafts with this coil.

Center temp of the Coilcrafts was 90C at 1.5 MHz pulse rate. The solenoid mid-point was 68C without the gap-pad, 42C with. I won't even need exotic high-temp insulation on the wire.

So I've got to get my SolidWorks guy to make a good drawing (which he'll enjoy) and then find someone to wind these for us. Any suggestions?

Silvered wire is mostly electropalted with silver, and electroplated silver has a higher resistance than regular copper.

People stopped using silvered wire when this became well-known, many years ago.

Turns-counting coil winding machies are cheap, if you are prepared to wind a handle. Most of them seem to come from China so getting one that would last might be difficult. They work a whole lot better than hand-winding.

For air-cored coils with the optimum one wire diameter spacing between each turn they are a bit of an over-kill.

Neat.

It's pretty traditional, though tradiitionally the end leads went straight down through the board.

No surprise there.

Radio hams? To do it properly you should have a removable former to wind it onto, or perhaps a plastic coil former, but that would cut down your convective colling.