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Originally posted by Carl-NC
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Yes, better late than never!
Part 5: Real Responses
So far we've looked at different responses and applied piecewise-linear solutions to much of it. That is, the PI turn-off was a linear ramp that induced a step EMF in the target. This is a good first-order approximation and a good way to do quick-n-dirty comparisons, like what happens when you try to get a sharper & sharper turn-off slew rate (Part 4).
In reality, the PI coil is an RL circuit during turn-on and an RLC circuit during turn-off. Equations can be derived that accurately describe what they do. I won't derive them here but rather just toss them out. ITMD3 will have full derivations.
The turn-on equation is simple:
The turn-off equation is non-obvious but here it is:
where
Let's look at a realistic example...
Measured coil parameters:
L = 300uH
Rs = 5 ohms (total series R)
SRF = 500kHz (inc. cable etc)
VTX = 10V
The parasitic C for the coil is
The require damping resistor for critical damping is
Now calculate the taus:
VTX (10V) and Rs (5 ohms) tells us the max flat-top current will be 2A. The TX tau os 60us so we would need a TX pulse width of ~300us to reach the flat-top current. A more normal TX pulse width is 100us which makes the calculated peak current 1.62A at turn-off. This becomes the starting point for the turn-off equation.
Here are both equations plotted in Excel. Note that the turn-on curve spans 100us whereas the turn-off curve spans only 3us.
Also note that in the turn-off side the tau_RX is 318ns. If you are expecting the current to be substantially gone in 5*tau (1.59us) you can see it is not. The 0.67% mark occurs at about 2.25ns which is about 7*tau, about 40% more than the usual RL curve.
But that's not the worst part; let's also look at the flyback voltage. Its equation can also be derived:
We have all the variables from above; the curve looks like this:
This curve is also plotted to only 3us. The peak hits ~560v which can be calculated from the derivative of the above equation. Note that the peak occurs at exactly tau_RX. If you were to assume that any kind of 5*tau settling applies here, then you would take 0.67% of 560v (=3.8v) and see that it occurs at about 2.57us, which is about 8*tau.
But this is the raw coil voltage which is then applied to a preamp with a fairly hefty gain, perhaps 500. It's immediately obvious that 3.8v will seriously overload the preamp. To determine a realistic required settling we need to make an assumption: that the preamp must be, say, within 0.5v of settled for the demods to work well. For a gain of 500, this means the coil voltage must be within 0.5v/500 = 1mv of settled. In the curve above, this happens at about 5.42us, or 17*tau.
You might be thinking that 5.42us is pretty darned good. But this is strictly the coil settling; the diode clamps and the preamp overloading have not been accounted for. And everything above assumes the MOSFET never avalanches.
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thanks
paul
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