J
Jon Kirwan
Guest
On Sat, 25 Jul 2009 11:22:23 +1200, greg <greg@cosc.canterbury.ac.nz>
wrote:
N = t_on / t_off
Total period is,
t_total = t_on + t_off
The charging duty cycle occurs during t_off, so,
duty = t_off / t_total
= t_off / (t_on + t_off)
= t_off / (t_off * N + t_off)
= t_off / [t_off * (N + 1)]
= [t_off / t_off] / (N + 1)
= 1 / (N + 1)
or voltage, as they are two facets of an underlying whole.)
Assume for a moment that the capacitor is 'large' and that there is no
change in voltage during operation (in other words, as current is
drawn the voltage doesn't change except by a very tiny amount.)
For one cycle of the period, t_total, we have:
W_out = (V_out * I_out * t_total)
Assume the diode is perfect (has no voltage across it) and that
everything is in an equilibrium state, the collector winding's energy
at Ic_peak must be:
W_in = (1/2) * L * I^2
But by definition, it's in equilibrium, so,
W_out = W_in
Therefore,
V_out * I_out * t_total = (1/2) * L * Ic_peak^2
or,
Ic_peak = SQRT(2 * V_out * I_out * t_total / L)
or,
Ic_peak = SQRT(2 * V_out * I_out / [frequency * L])
This isn't what you came up with.
Now assume for a moment that the capacitor is 'somewhat smaller' and
that there is some change in voltage during operation (in other words,
as current is drawn the voltage does change by some small, but
measurable amount.)
Assuming the voltage drop is linear vs time and goes from V_max down
to V_min for one cycle of the period, t_total, we have:
W_out = [(V_min+V_max)/2] * I_out * t_total
Again, assume the diode is perfect (has no voltage across it) and that
everything is in an equilibrium state, the collector winding's energy
at Ic_peak must be:
W_in = (1/2) * L * I^2
Therefore,
[(V_min+V_max)/2] * I_out * t_total = (1/2) * L * Ic_peak^2
[V_min+V_max] * I_out * t_total = L * Ic_peak^2
or,
Ic_peak = SQRT( [V_min+V_max] * I_out * t_total / L)
Again, not much different, really.
It's about accounting for energy, not accounting for current. When
the capacitor is charged up to its equilibrium voltage, it doesn't
take much current at that voltage to add substantial energy.
Of course, I'm a hobbyist. So... that's only how I see it.
Jon
wrote:
Set up variable N as being the ratio,In a fit of temporary insanity, I wrote:
However, the transistor will be on for only
1/N of the time, so the *peak* transistor current
will be N *squared* times 20mA.
Scrub that, it's completely wrong.
The on period of the transistor is N times the off
period,
N = t_on / t_off
Total period is,
t_total = t_on + t_off
Yup. To encourage more to follow the logic...so the charging period of the capacitor is
1/(N+1) of the whole cycle,
The charging duty cycle occurs during t_off, so,
duty = t_off / t_total
= t_off / (t_on + t_off)
= t_off / (t_off * N + t_off)
= t_off / [t_off * (N + 1)]
= [t_off / t_off] / (N + 1)
= 1 / (N + 1)
Energy in equals energy out (I prefer to not look so much at currentand the average current charging the capacitor during that time must be
(N+1) * 20mA.
Since the current is a linear ramp during both
periods, the peak output current, and therefore
also the peak collector current, will be twice
that, or 2 * (N+1) * 20mA.
I hope I got it right this time!
or voltage, as they are two facets of an underlying whole.)
Assume for a moment that the capacitor is 'large' and that there is no
change in voltage during operation (in other words, as current is
drawn the voltage doesn't change except by a very tiny amount.)
For one cycle of the period, t_total, we have:
W_out = (V_out * I_out * t_total)
Assume the diode is perfect (has no voltage across it) and that
everything is in an equilibrium state, the collector winding's energy
at Ic_peak must be:
W_in = (1/2) * L * I^2
But by definition, it's in equilibrium, so,
W_out = W_in
Therefore,
V_out * I_out * t_total = (1/2) * L * Ic_peak^2
or,
Ic_peak = SQRT(2 * V_out * I_out * t_total / L)
or,
Ic_peak = SQRT(2 * V_out * I_out / [frequency * L])
This isn't what you came up with.
Now assume for a moment that the capacitor is 'somewhat smaller' and
that there is some change in voltage during operation (in other words,
as current is drawn the voltage does change by some small, but
measurable amount.)
Assuming the voltage drop is linear vs time and goes from V_max down
to V_min for one cycle of the period, t_total, we have:
W_out = [(V_min+V_max)/2] * I_out * t_total
Again, assume the diode is perfect (has no voltage across it) and that
everything is in an equilibrium state, the collector winding's energy
at Ic_peak must be:
W_in = (1/2) * L * I^2
Therefore,
[(V_min+V_max)/2] * I_out * t_total = (1/2) * L * Ic_peak^2
[V_min+V_max] * I_out * t_total = L * Ic_peak^2
or,
Ic_peak = SQRT( [V_min+V_max] * I_out * t_total / L)
Again, not much different, really.
It's about accounting for energy, not accounting for current. When
the capacitor is charged up to its equilibrium voltage, it doesn't
take much current at that voltage to add substantial energy.
Of course, I'm a hobbyist. So... that's only how I see it.
Jon