A
Anonymous
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This is a comparison between two hypothetical pulse induction designs, one conventional resistance current limited, and one with jump-start. I have used my jumpstart topology as the basis, but the results would come out the same using JC's topology.
THE BASIS DESIGN
Coil circuit: 500 microhenries, 2 ohms, 500 pF parallel capacitance. Damping resistor presumed to be 680 ohms, although we'll ignore it in the calculations.
Flyback voltage: 100 volts.
Peak coil current just before flyback: 2 amperes.
Transmit on-time (including jumpstart): 90 microseconds.
Pulse rep rate: 2 kHz (500 microseconds)
Storage capacitor: for the purpose of analysis, it is presumed that this is a storage capacitor, not a half-cycle resonant capacitor. A half-cycle resonant capacitor would be 12 microfarads, so a storage cap would be much larger than that. Of course you'd want a fairly low ESR unit. Note: the design could be half-cycle resonant, but the numbers would come out a little different.
COMMENTS ON THE SPECTRUM: The flyback will have a lot of energy at 50 kHz and will go downhill beyond that. The period of current flow will have a lot of energy at 5 kHz, and the energy will extend down to the fundamental frequency of 2 kHz. The jumpstart version will have quite a bit more low frequency energy, improving its response on high-conductivity targets, but that's not my emphasis in this comparison.
BEFORE: CONVENTIONAL RESISTANCE CURRENT-LIMITED DESIGN
We'll do 2 time-constants. That's not a lot of current limiting, but it's enough that the waveform wouldn't look like a triangle on the 'scope.
The total resistance equals the inductance divided by the (45 us) time-constant, which comes to 11.1 ohms. We've already got 2 ohms in the coil, so our extra current-limiting resistance will be 9.1 ohms.
Let the power supply be +27 volts. Hey, we're generous here! Allow a loss of 1 volt in the transistor and rectifier, and we can deliver 26 volts to the coil circuit.
When the transistor is first turned on, the current is zero, and it rises at the rate of 52 milliamperes per microsecond. Without resistance, it'd hit 2.34 amperes in 45 us, but because that's one time-constant, it'll only hit 63% of that, or 1.47 amperes. During the second time-constant we'll add 37% of that, or .54 amperes. That totals 2.01 amps at the beginning of flyback.
The mean current is approx. 1.33 amperes over the 90 us transmit time. Averaged over the full rep interval of 500 microseconds, that's 239 milliamperes. Power consumption from a 27 volt power supply is 6.46 watts. Ouch.
AFTER: JUMP-STARTED DESIGN
Let the power supply be +5 volts, and assume a loss of 1 volt in the rectifier and transistor, as before. We can deliver 4 volts to the coil.
Let the jumpstart time be 10 microseconds. With 100 volts applied to the coil, the current rises to 2 amperes. 4 volts is being dropped across the resistance of the coil.
Now turn the main transmit transistor on. We continue to deliver 4 volts to the coil. The sustaining current is 2 amperes, dropped across the resistance of the coil, and no voltage is dropped across the inductance because the current isn't changing. This continues for another 80 microseconds.
The current drain during those 80 microseconds was 2 amperes the whole time. Averaged over the 500 us rep interval, that's 320 milliamperes. Power consumption from a 5 volt supply is 1.6 watts.
So did we cheat? only a little. The flyback is 10 microseconds, and the jumpstart is 10 microseconds, and they're both 100 volts, but... those are only approximations. There are resistive losses during flyback and jumpstart, although they're small in proportion to the losses during the transmit-on time. The easiest way to make up the difference is to have the jumpstart time slightly shorter than flyback, which means that jumpstart won't get it all the way up to 2 amps, maybe 1.6 amps. This leaves a voltage difference between the coil resistance and the driver transistor so the current can ramp up to 2 amps.
The extra circuitry in the jumpstart system will require power to switch it, so that's another loss that was ignored. However, one would expect this power to be much less than the power dissipated in the loop.
--A REALITY CHECK------
The jumpstart system is supposed to have efficiency somewhere in the same ballpark as an otherwise comparable VLF unit. 1.6 watts transmit power for a VLF unit is stompin' pretty loud. So, how do the numbers add up?
Of the energy being dissipated in the PI, most of it is in the ballpark of 5 kHz. We're hitting it with about 2 amperes at an 18% duty cycle. On an RMS basis, that's equivalent to about 800 milliamperes. Math a little sloppy, we're just doing a reality check.
The searchcoil has a reactance of 16 ohms at 5 kHz. If it were driven with a 32 volt P-P sinusoid, the RMS current would be 700 mA. Dissipated in 2 ohms resistance, that's an I-squared-R of 1 watt. Looks like we're not too far wrong here.
As far as I know, nobody in the industry drives VLF's this hard, not even close. At 5 kHz with a 500 uH 2 ohm loop, you might expect to see on the order of 14 volts P-P, dissipating 200 milliwatts in loop resistance, in a high end power hog.
-----CONCLUSIONS---------
In this example we got a 6.46:1.6 = 4.04:1 estimated reduction in power consumption. We cheated a little on the jumpstart system, but it has a better waveform, so for equal sensitivity to high conductivity targets the 4:1 improvement figure is reasonable.
Note that the way voltages scale is markedly different.
THE BASIS DESIGN
Coil circuit: 500 microhenries, 2 ohms, 500 pF parallel capacitance. Damping resistor presumed to be 680 ohms, although we'll ignore it in the calculations.
Flyback voltage: 100 volts.
Peak coil current just before flyback: 2 amperes.
Transmit on-time (including jumpstart): 90 microseconds.
Pulse rep rate: 2 kHz (500 microseconds)
Storage capacitor: for the purpose of analysis, it is presumed that this is a storage capacitor, not a half-cycle resonant capacitor. A half-cycle resonant capacitor would be 12 microfarads, so a storage cap would be much larger than that. Of course you'd want a fairly low ESR unit. Note: the design could be half-cycle resonant, but the numbers would come out a little different.
COMMENTS ON THE SPECTRUM: The flyback will have a lot of energy at 50 kHz and will go downhill beyond that. The period of current flow will have a lot of energy at 5 kHz, and the energy will extend down to the fundamental frequency of 2 kHz. The jumpstart version will have quite a bit more low frequency energy, improving its response on high-conductivity targets, but that's not my emphasis in this comparison.
BEFORE: CONVENTIONAL RESISTANCE CURRENT-LIMITED DESIGN
We'll do 2 time-constants. That's not a lot of current limiting, but it's enough that the waveform wouldn't look like a triangle on the 'scope.
The total resistance equals the inductance divided by the (45 us) time-constant, which comes to 11.1 ohms. We've already got 2 ohms in the coil, so our extra current-limiting resistance will be 9.1 ohms.
Let the power supply be +27 volts. Hey, we're generous here! Allow a loss of 1 volt in the transistor and rectifier, and we can deliver 26 volts to the coil circuit.
When the transistor is first turned on, the current is zero, and it rises at the rate of 52 milliamperes per microsecond. Without resistance, it'd hit 2.34 amperes in 45 us, but because that's one time-constant, it'll only hit 63% of that, or 1.47 amperes. During the second time-constant we'll add 37% of that, or .54 amperes. That totals 2.01 amps at the beginning of flyback.
The mean current is approx. 1.33 amperes over the 90 us transmit time. Averaged over the full rep interval of 500 microseconds, that's 239 milliamperes. Power consumption from a 27 volt power supply is 6.46 watts. Ouch.
AFTER: JUMP-STARTED DESIGN
Let the power supply be +5 volts, and assume a loss of 1 volt in the rectifier and transistor, as before. We can deliver 4 volts to the coil.
Let the jumpstart time be 10 microseconds. With 100 volts applied to the coil, the current rises to 2 amperes. 4 volts is being dropped across the resistance of the coil.
Now turn the main transmit transistor on. We continue to deliver 4 volts to the coil. The sustaining current is 2 amperes, dropped across the resistance of the coil, and no voltage is dropped across the inductance because the current isn't changing. This continues for another 80 microseconds.
The current drain during those 80 microseconds was 2 amperes the whole time. Averaged over the 500 us rep interval, that's 320 milliamperes. Power consumption from a 5 volt supply is 1.6 watts.
So did we cheat? only a little. The flyback is 10 microseconds, and the jumpstart is 10 microseconds, and they're both 100 volts, but... those are only approximations. There are resistive losses during flyback and jumpstart, although they're small in proportion to the losses during the transmit-on time. The easiest way to make up the difference is to have the jumpstart time slightly shorter than flyback, which means that jumpstart won't get it all the way up to 2 amps, maybe 1.6 amps. This leaves a voltage difference between the coil resistance and the driver transistor so the current can ramp up to 2 amps.
The extra circuitry in the jumpstart system will require power to switch it, so that's another loss that was ignored. However, one would expect this power to be much less than the power dissipated in the loop.
--A REALITY CHECK------
The jumpstart system is supposed to have efficiency somewhere in the same ballpark as an otherwise comparable VLF unit. 1.6 watts transmit power for a VLF unit is stompin' pretty loud. So, how do the numbers add up?
Of the energy being dissipated in the PI, most of it is in the ballpark of 5 kHz. We're hitting it with about 2 amperes at an 18% duty cycle. On an RMS basis, that's equivalent to about 800 milliamperes. Math a little sloppy, we're just doing a reality check.
The searchcoil has a reactance of 16 ohms at 5 kHz. If it were driven with a 32 volt P-P sinusoid, the RMS current would be 700 mA. Dissipated in 2 ohms resistance, that's an I-squared-R of 1 watt. Looks like we're not too far wrong here.
As far as I know, nobody in the industry drives VLF's this hard, not even close. At 5 kHz with a 500 uH 2 ohm loop, you might expect to see on the order of 14 volts P-P, dissipating 200 milliwatts in loop resistance, in a high end power hog.
-----CONCLUSIONS---------
In this example we got a 6.46:1.6 = 4.04:1 estimated reduction in power consumption. We cheated a little on the jumpstart system, but it has a better waveform, so for equal sensitivity to high conductivity targets the 4:1 improvement figure is reasonable.
Note that the way voltages scale is markedly different.