Could you please explain to me the tcr number? Higher means that coil is more sensitive to the change of resistance?
If you were to make a chart for your coil that plots temperature (in Celsius) on the horizontal axis versus resistance on the vertical axis, then TCR would be the slope of the resulting curve at a given point. In other words, it tells you the rate of change in resistance of the coil for a given change in temperature. The larger the TCR, the steeper the slope of the curve, and therefore the more sensitive the resistance of the coil to changes in temperature. All other things being equal, larger TCR's generally allow for more accurate temp control, but it is entirely dependent on the chemistry of the materials used.
It is worth noting that the curve is not entirely linear. So the slope of the curve changes depending on where you are on that curve. It is steeper in some spots and shallower in others. But TCR is a measure of the slope at a single point on that curve. For that reason, in theory at least, the further away the actual temperature of your coil is from the temperature that correlates with the point at which the TCR was derived, the less accurate the temperature estimate will be. So, to minimize this error, TCR's that are most commonly used for our purposes tend to be calculated/measured at temps that are close to those temps that we actually vape at. Interestingly, from what I can tell steam-engine.org measures TCR at 300 degrees Celsius (572 Fahrenheit), which is quite a bit hotter than I tend to vape at. But I think Daniel at djlsbvapes.com measures TCR at lower temps (around 210 Celsius or so), which is closer to my vaping range. But frankly, these differences are trivial for most of the commonly used materials.
If you're interested in the math to calculate TCR, it looks like this:
TCR = ((Rhot / Rcold) - 1 ) / (Thot - Tcold)
where:
Rhot = Resistance at operating temp
Rcold = Resistance at resting temp
Thot = Operating temperature (in Celsius)
Tcold = Resting Temperature (in Celsius)