Conventional torches come in all shapes and sizes.
From a single AAA cell to 4, 5 and 6 "D" cells, as well as "lantern" and "fisherman's."
This project uses a white LED to produce  illumination equal to a small torch.

White LEDs have different "characteristic voltages." A 1,000mcd white LED used in this project had a characteristic voltage of 3.5v and a 3,000mcd white LED had a characteristic voltage of 3.2v. Both LEDs were driven at 20mA and the 3candala LED produced a brighter, whiter light while the 1candella LED had a yellowish ring around the edge of the illumination.

A LED torch is one of the simplest projects you can build and it's very interesting as it uses a super-bright white LED.
In the history of LED production, red LEDs were the first to be invented and their output was so dim you could barely see if they were illuminated. You needed a darkened room to see them at all.
Then came green, yellow and orange LEDs.
As time went by, the brightness improved and it came to a point where the output would shine into the surrounding air. These were called Super-bright LEDs.
Then came the blue LED. At first it was dull, but gradually the output increased to a dazzling glare.
With the combination of red, green and blue, manufacturers had the potential of producing a white LED.
This was the dream of all LED manufacturers.
Since the illumination produced by a LED comes from a crystal, it is not possible to produce white light from a single crystal or "chip." The only way is to combine red, green and blue. As soon as the output of blue came up to the quality of the other colors, a white LED was a marketable product.
White LEDs are now with us and their output makes them a viable alternative to the globe.
There is an enormous array of LED torches on the market, from $2.00 "give-aways" to $200 "rip-offs."
Although a LED torch is passable for illuminating an area, it certainly does not have the illuminating capability of a $10 lantern, using a 6v battery.
A LED torch is more of a "fun-thing" to see how far LEDs have come in the past few years and see what can be done with a single cell and an handful of components.
When we first decided to produce a LED torch project, we wanted to fit the circuit into a 2-cell torch but a white LED requires about 3.4v to operate, and two cells produce only 3v. So we had to think of a number of ways around the problem. That's why we have produced a number of circuits.
As you know, a LED will not operate on a voltage below its characteristic voltage. It simply will not operate AT ALL.
This characteristic voltage depends on the type of LED and is about 1.7v for a normal red LED, while a super-bright LED is about 3.1v - 4v.
The exact characteristic voltage varies with the colour, the intensity of the LED, the current flowing and the way it is manufactured. This feature cannot be altered after it is manufactured and the EXACT voltage must be delivered, otherwise the LED will be not work or if the voltage is higher, it will be destroyed. This is the cold, hard fact. The supply voltage must exactly match the characteristic voltage.
This sounds a difficult thing to do, but a simple solution is to add a resistor in series and the voltage across the LED will sit at the exact value required by the LED, while the extra voltage will appear across the resistor. According to Ohm's Law, a current will flow though the resistor and this will also flow though the LED. This applies when the circuit is supplied with a DC voltage.
All we have to do is create a voltage higher than 3.4v and we can drive one of the latest SUPER-HIGH-BRIGHT white LEDs with a single cell, using a step-up-voltage circuit.
This will produce a series of pulses to the LED and the brightness will be slightly higher than if a steady DC voltage is applied. These are the things we will be covering in this project. 

This project explains the operation of a "transformer" in flyback mode. A transformer is one of the most complex items in electronics. Even a simple hand-made "transformer" requires a lot of understanding to see how it works. This project will demystify some of the features.

The first circuit in this discussion is the simplest design.
It consists of a transistor, resistor and transformer, with almost any type of LED. The circuit will drive a red LED, HIGH BRIGHT LED, or white LED.
The circuit produces high voltage pulses of about 40v p-p at a frequency of 200kHz.
Normally you cannot supply a LED with a voltage higher than its characteristic voltage, but if the pulses are very short, the LED will absorb the energy and convert it to light. This is the case with this circuit. The characteristic voltage of the LED we used was very nearly 4v and this means the voltage across it for a very short period of time was 4v. The details of the transformer are shown in the photo. The core was a 2.6mm diameter "slug" 6mm long and the wire was 0.95mm diam. In fact any core could be used and the diameter of the wire is not important. The number of turns are not important however if the secondary winding does not have enough turns, the circuit will not start-up.

The transformer is configured as a BLOCKING OSCILLATOR and the cycle starts by the transistor turning on via the 2k7 base resistor.
This causes current to flow in the 60-turn main winding. The other winding is called the feedback winding and is connected so that it produces a voltage to turn the transistor on MORE during this part of the cycle.
This winding should really be called a "feed-forward" winding as the signal it supplies to the transistor is a positive signal to increase the operation of the circuit. This is discussed in more detail in Circuit Tricks.
This voltage allows a higher current to flow in the transistor and it keeps turning on until it is saturated.
At this point the magnetic flux produced by the main winding is a maximum but it is not expanding flux and thus it ceases to produce a voltage in the feedback winding. This causes less current to flow into the base of the transistor and the transistor turns off slightly.
The flux produced by the main winding is now called collapsing flux and it produces a voltage in the feedback winding of opposite polarity. This causes the transistor to turn off and this action occurs until it is completely off.
The magnetic flux continues to collapse and cuts the turns of the main winding to produce a very high voltage of opposite polarity.
However this voltage is prevented from rising to a high value by the presence of the LED and thus the energy produced by the collapsing magnetic flux is converted to light by the LED. 
The circuit operates at approx 200kHz, depending on the value of the base resistor and physical dimensions of the transformer.
The circuit draws 85mA from the 1.5v cell and the brightness of the LED was equivalent to it being powered from a DC supply delivering 10 - 15mA.
Before we go any further, there are a number of interesting circuits on the web.
The following two circuits need explaining. The first circuit is identical to our "Circuit A" except the design engineer did not do his homework. He only added 8 turns to the 100uH inductor and found the circuit did not start-up. His solution was to add another transistor and tie the base to the collector. What a waste of a transistor!
The second circuit is a very inefficient design. The second transistor is being turned on via a 1k resistor on the collector of the first transistor and when this "turn-on" current is not required, it is being shunted to "deck."
Our circuit uses the "oomph" of the secondary winding to saturate the transistor and this produces the highest efficiency.
Here is a circuit from one of the major chip manufacturers:
Apart from the circuit being enormously complex and expensive, 62mA is too high for many white LEDs. The maximum current must be kept to 20 - 25mA.
The first "poor design" got me thinking. Maybe the signal at the transformer end of the 220R needs to be stabilised to improve the performance of the circuit. I tried a transistor and it did not work.
But I actually thought of placing a small capacitor at the join and taking the other end to the 0v rail. This will allow rail voltage to enter the feedback winding of the transformer but prevent the signal generated by the winding being lost through the 2k7 resistor.
The following circuit is the result:
The brightness of the LED did not alter but the current changed from 85mA to 28mA.
The circuit instantly became 300% more efficient.
I could not believe it.
When I put the CRO across the LED, I realised why. The frequency of the circuit changed from 200kHz to 500kHz. The LED was getting more than twice the number of pulses per second.
That's why you cannot trust anything or anyone. This improvement has never been presented in any circuit on the web. Obviously no-one has done any experimenting at all. 
If the brightness of the LED is equal to a DC voltage of 4v and a current of 10mA, the circuit we have produced is slightly more efficient than delivering a DC voltage to the LED, even though there are some losses in the transformer and transistor.
This proves the fact that LEDs driven with a pulse, are more efficient than being driven by a DC supply.
With this we turn to a surface-mount chip that has been designed to carry out the exact same task as circuit B. The chip is called PR4401. The following is the promotion advert for the chip:
I could not find any sales literature on the internet, but the manufacturer requires 9,000 pieces to be bought at a cost of 36 cents per piece. This comes to $3,240 if you want to incorporate it into your project.
I have described the pro's and con's of this chip in another article "Circuit Tricks" and you should read the features and work out what they really mean.
When you build circuit "B," you will realise the specifications given in the .pdf for the chip, could be improved. We have achieved a supply current of 18mA for an equivalent brightness of 10mA. The chip requires 25mA. So, all the technology in the world has not surpassed a hand-made circuit.
The advantage of our design is the ready availability of components and you can change them to suit your own application.
If you want to increase the brightness, the 2k7 can be reduced to 1k5.
If you want to drive 2 LEDs, they can be added in series:
Adding a 100u across the battery will increase the current by 4mA and the brightness will increase slightly.
When 2 LEDs are placed in series, the current drops from 28mA to 23mA and the brightness from each LED is slightly less. This circuit is operating at about the maximum capability of the transformer. The actual limiting factor is the size of the "core." It can only "hold" a certain amount of magnetic flux and return it to the windings during the collapsing part of the cycle. A larger core will allow three or more LEDs to be illuminated.
The "high efficiency" of this circuit is due to the "pulsing of the LED." When a LED is pulsed with a high current for a short period of time, the brightness is equivalent to a lower, steady, current. That's why a current of 23mA from the battery will illuminate 2 LEDs with an equivalent brightness of about 8mA of steady current. It is very difficult to compare the brightness of one LED against another and these results are the best you can make by visual inspection. We are not driving the LEDs to their maximum but the output is very impressive.

The secret of this circuit is the transformer.
We normally think of a transformer as a device with an input and output, with the voltage on the input and output being connected by a term called "turns ratio."
If the output has more turns than the input, the output voltage will be higher.  This is called a step-up transformer. If the output has less turns than the input, the output voltage will be lower.
This applies to "normal" transformers where the voltage is rising and falling at a regular rate, commonly called a "sinewave."
But the transformer in this circuit is different.
The voltage applied to it is not rising and falling smoothly, and thus it does not work in normal "transformer mode."
The voltage is being applied and then turned off. When the voltage is applied, the primary winding (the 60 turn winding) produces magnetic flux. When the voltage is turned off, the magnetic flux collapses and produces a VERY HIGH voltage (in the REVERSE DIRECTION), in all the windings.
Our transformer is really a coil in flyback mode with a feedback winding.
The feedback winding delivers a voltage to the transistor to turn it on HARDER. If the winding is connected around the wrong way, the circuit will not work.
The other important factor about the transformer is the core material. There are many different types of ferrite. Ferrite is a type of iron which is powdered very finely so that the magnetic lines that pass through the particles do not create eddy-currents. These eddy currents absorb the magnetic flux. The material we have used is F29 and this is suitable for high frequency applications.
The circuit also employs a term called RE-GENERATION. This is the effect where a circuit is turned on slightly by a component (the 2k7 base resistor in this example) and then the transistor turns itself on more and more until it is fully turned on. The feedback winding is configured so that the voltage it produces (actually the current it produces) is fed into the base to turn the transistor on.
Thus the feedback winding is very clever. It produces energy and is delivered in a particular direction - in other words it can be a positive or negative energy. In this case it produces positive energy, to turn the transistor on harder.
This is called POSITIVE FEEDBACK as it turns the transistor ON during the active part of the cycle.
Now we come to the MAIN, PRIMARY or FLYBACK winding.
This winding produces a high voltage during part of the cycle (the FLYBACK part of the cycle) and this is passed to the LED.
If the LED is removed, the transformer produces a high voltage with a low current, but when the LED is inserted, an amazing thing happens. The energy from the transformer is converted to a lower voltage with a higher current.
What actually happens is the LED absorbs the energy and turns it to light as soon as the voltage rises to 3.6v.
We could achieve the achieve the same low-voltage, high current requirement, with less turns, but the number of turns has actually been determined so the core does not saturate.
The voltage for the LED is produced when the transistor is switched off and the magnetic flux in the ferrite core collapses.
The speed of the collapse produces a very high voltage in the OPPOSITE DIRECTION and that's why a positive voltage emerges from the end connected to the LED. These two facts are important to remember.
The other important fact is called "transformer action." This is the action of magnetic flux.
When a voltage is applied to a winding of a transformer or a coil of wire, a current will flow and this will produce magnetic flux. If another winding is present, the magnetic flux will cut the turns of this extra coil and produce a voltage in it.
However, there is a very important point to remember. The magnetic flux can be: EXPANDING, STATIONARY or CONTRACTING.
When the magnetic flux is expanding, a voltage will appear in the second winding mentioned above.
When the magnetic flux is stationary, NO VOLTAGE will appear in the second winding.
When the magnetic flux is contracting a voltage will appear in the second winding with REVERSE POLARITY.
The size (the amplitude or "value") of the reverse voltage will depend on the speed of the collapsing magnetic flux. If the flux collapses quickly, the amplitude will be very high.
That's how the transistor turns itself on and on until it is fully turned on. At this point the current flowing through the circuit is a maximum but the flux is not expanding so the base of the transistor does not see the high "turn-on" energy and thus the transistor suddenly turns off.
The magnetic flux collapses and the transistor sees a reverse voltage on the base to keep it turned off until the flux is fully collapsed. The current through the 2k7 enters the base to start the cycle again.
From this you will be able to see how the transistor and transformer work.

Now we come to the problem of flashing a white LED, using a 1.5v supply.
The following circuit performs this task:
The oscillator charges the 100u via the 1N 4148 diode and when the voltage reaches about 10v, the BC 547 transistors "zeners" (breaks down) and conducts. Energy in the 100u is then dumped into the LED to make it illuminate. This causes the voltage across the 100u to drop and the transistor comes out of conduction. The oscillator then continues to charge the 100u to repeat the cycle.
The zener voltage of the transistor is not 10v as approx 4v is dropped across the LED. This conforms with an article on the web that said the emitter-collector junction is equal to a 6v2 zener.
The 330R charging resistor produces a fast flash and the 1k produces a slow flash.
The current for the circuit is approx 22mA and any type of LED can be fitted.
Measuring the current-consumption of a circuit is a very difficult thing to do.  When you insert a a meter into the positive line (or negative line) of a circuit, you introduce extra resistance and the operation of the circuit will alter. You may think the low resistance of an ammeter will not affect the performance, but quite often the "ammeter " is really a "milli-amp meter" and the "shunt resistance" on the 200mA scale can be 4 - 7 ohms. This is quite considerable when a circuit is operating on 1.5v and drawing 30mA. This can be a loss of 100mV to 200mV and the current taken by the circuit will alter considerably.
That's why the best approach is to place a 1 ohm resistor in line with the positive of the battery and measure the millivolt drop across the resistor. Each millivolt drop will correspond to 1mA flow and this will change the circuit conditions as little as possible. The following circuit shows how this is done:
A 100u electrolytic across the circuit will reduce the impedance of the supply and keep the circuit working as normal as possible.
As a point to note: The White LED Flasher circuit did not start-up on a flat AAA cell.
Solution: take two flat cells and connect them in series and see how long the LED will flash. You will be very surprised. The circuit will draw about 30mA and the LED will flash very quickly.
The circuit will continue to work on two very flat cells until the flash rate drops to one flash per second.  
This type of circuit puts a very heavy "strain" or "noise" on the power supply. In other words it puts a heavy demand on the battery for a short period of time.
This is not a problem if the only item connected to the battery is the flasher circuit. But if the battery is also driving a circuit such as an mp3 player or microcontroller, the high-frequency noise may upset the operation of the electronics.

The oscillator transistor needs to sink a very high current for a very short period of time (as mentioned above) and thus it must be a "high-current" type. A "high-current" type improves the efficiency of the circuit. If the transistor cannot sink the transformer to the 0v rail, it effectively becomes a "resistance" in the network. Suppose the supply is 1500mV (1.5v  , 1v5) and the transistor can sink to 500mV, 30% of the voltage is dropped across the transistor and thus the circuit is using only 66% of the incoming energy. If the transistor can only sink to 0.75v, the circuit is using 50% of the incoming energy.
Some transistors can sink to 0.3v and thus the circuit is more efficient.
Now we come to the stability of the circuit. The circuit is very unstable and very unreliable. Touching the components with a finger changes the frequency of the flash-rate and connecting  CRO to the collector of the oscillator transistor inhibits the flashing. The oscillator keeps working but the zener transistor fails to operate.
This circuit is totally unsuitable for a commercial design and it reminds me of some of the original transistor flasher circuits. They required precise values of resistance and did not work when the supply voltage dropped.
Fortunately someone came up with the flip-flop flasher and changed everything. It is totally reliable and operates under all sorts of conditions.

Now we come to the design of a higher output circuit, to satisfy those who want to use a larger cell and drive 2 or 3 LEDs to maximum brightness.

To drive more LEDs, a higher output is needed. We have already mentioned, the limiting factor with the circuits above is the transformer. To achieve a higher output, the size needs to be increased. This is quite easily done by getting a larger core. It is the core that determines the amount of flux that can be stored. When turns are wound on a core, the result is called an inductor and when a second winding is added, the result is called a transformer.
Most of the inductors and transformers we use in the circuits in this article have an open magnetic circuit. This means the flux escapes out one end of the core and in general the result is not very efficient. But it has proved to be satisfactory.
An improved core is called a "pot core" and consists of two halves as shown in the diagram below:

The magnetic lines go around the "magnetic circuit" as shown in the diagram above and pass through an air gap. The air gap is to compensate for the DC across the coil (transformer). If the air gap is closed up, the inductor will saturate before the circuit is fully conducting and this may make the inductor less effective. All this theory is very complex and you really have to try the component to see the effect.
Our circuits use a simple "in line" inductor as shown above or a "bobbin" as shown below in the third item. The photo below shows the "slug" transformer used in circuits A, B, and C and the "bobbin" transformer used in circuit D. The size of each transformer gives some idea of the relative output. The centre inductor is a 10mH choke. This is unwound to get the bobbin for the transformer.
The bobbin is re-wound with 35 turns of 0.5mm wire for the primary and 20 turns for the feedback winding. The two pins connect to the primary and the 20 turn-winding is wound on top, with flying leads. The gauge of the wire is chosen so that the windings completely fill the bobbin. The feedback winding can be a thinner gauge, without any detriment to the operation of the circuit. By the appearance, you could expect up to 5-10 times more output from the bobbin.
But with a higher output, you need to provide some form of energy-limiting circuit to prevent damaging the LED.
The following circuit provides current limiting so that the LED will produce maximum brightness for the voltage range 1.5v to 0.9v.

This gives a choice to suit a variety of torches. The smallest penlight torch will only have enough room to drive a single LED while the larger "C" and "D" cell torches will drive two or three LEDs.
There are some slight differences between each of the circuits and you need to read the article if you want to deviate from any of the layouts we have given.
For instance, the 2SC 3279 transistor is capable of sinking 2 amps and this makes it a better driver for circuit-2 but its collector-emitter voltage is only 10v and it may zener in circuit 3, where the voltage is very near this value.

Circuit-1 drives one LED from a single cell

Circuit-2 drives two LEDs from a single cell

Circuit-3 drives three LEDs from two cells

The circuit includes a feature called "current regulation." You can also call the feature "voltage regulation" as both have the same effect of controlling the brightness of the LED.
It can also be called a "constant brightness" arrangement.
It's a feedback arrangement consisting of a BC 547 connected to the base of the main transistor.
When the voltage across the "detector resistor" rises above 0.7v, the BC 547 turns ON and prevents the main transistor operating.
This allows the LED to produce a constant brightness over a wide supply voltage. The circuit will theoretically work to 0.8v.
Do not remove the current regulating transistor as the circuit will over-drive the LED when the supply is 1.5v. The excess current will instantly destroy the LEDs.

The actual operation of the circuit can be explained in a little more detail.
When the circuit is turned on, the oscillator transistor produces a high voltage from the inductor and this is rectified by a diode to charge a 100u electrolytic.
When the voltage rises to over the total characteristic voltage of the LED or LEDs, they turn on and current flows though the 39R "detector resistor."
The voltage across the 100u will continue to rise and since the characteristic voltage of the LEDs has been reached, any further voltage rise will appear across the resistor. As soon as this voltage reaches 0.7v, the feedback transistor begins to turn on. The feedback transistor acts like a variable resistor as shown in the diagram below and some of the current from the feedback winding is passed to the 0v rail, through the transistor. The oscillator transistor sees a reduced "turn-on" effect and the output of the stage is reduced.
In this way the brightness of the LEDs can be kept constant throughout the life of the battery.

The circuit is actually being "pulled back" when a fresh cell is connected, by the action of the feedback transistor. As the voltage from the cell reduces, the oscillator circuit will not be able to produce a high output and the action of the feedback section will not be needed. Eventually the voltage of the cell will be so low that the LED will start to dim. This is the end of the life of the cell.
Caution: Do not allow more than 25mA to flow though a white LED (unless it is being pulsed) as it will be instantly DESTROYED. Other LEDs (such as low-brightness red LEDs) are much more tolerant - but white LEDs are easily damaged.
A number of circuits similar to this project have been presented on the internet. One circuit had twice the number of components and used 4 transistors.
The art of designing a circuit is to make it as simple as possible, while providing all the needed features. It is pointless making a circuit complex, as it simply adds to the cost and makes fault-finding more difficult.
But a note near one of the circuits was really annoying. It said the circuit "had not been tested, only a simulation was run."  While these simulation programs work in a number of applications, they certainly cannot take into account the characteristics of an inductor. This is one item that no-one can predict. It's performance depends on so many variables.
If you think you can design a circuit such as this on a simulator, and it will work, you are kidding yourself.
Electronics is not that simple.
Transistors exhibit different characteristics according to the current flowing though them and a circuit such as ours requires the main transistor to pass a very high current for a short period of time.
Fortunately, Japanese transistors are capable of passing a high current while some Philips transistors will fail to pass the test. The gain of a transistor under these stressful conditions cannot be determined from a data-sheet.
Circuits should never be presented in an article unless they have been tried and tested.
A simulation program cannot possibly take into account the effectiveness of an inductor in any particular situation, even though the inductance is known.
There are hundreds of ways to produce a 10uH inductor, or any inductor for that matter.
It can be air-cored or ferrite cored. The windings can be thick or thin wire. The core can be made of several different materials. On top of this it will depend on the frequency of the circuit.
The output voltage of an inductor that has been specially designed for a particular circuit can be 100 times higher than an incorrectly designed item. That's why it takes a considerable amount of "trial-and-error" to produce an ideal inductor or transformer.
The output voltage has a lot to do with the "Q-factor" or quality factor and this is a value that is associated with the way the inductor or transformer has been designed. The "Q value" is basically  the ratio of the supply voltage compared to the output voltage.
No simulation program can "guess" the value of "Q" and since the operation of the circuit is entirely dependent on this value, it has to be constructed.
I would not even attempt to put this type of circuit on a simulator.

There are many ways to go about designing an inductor or transformer.
You can sit down and study the theory of inductance, the effectiveness of ferrite material at different frequencies, the use of different wire gauges and the associated inductance formulae.
If you think you will be able to produce an inductor for this circuit entirely from theory, (with the first prototype working perfectly), you are kidding yourself.
There are a number of parameters you cannot specify in the formulae.
Even if you did come up with an answer, no electronics-designer would be satisfied with the first result. He would need to see the prototype and add or remove turns to see the effect. He would use thicker or thinner wire and note the effect. He would carry out all sorts of experimentation, including monitoring the battery current while noting the current though the LEDs to work out the efficiency of the circuit.
It could take 50 or more prototypes to arrive at the best design.
So, where do you start when designing a transformer or inductor?
No-one really knows where to start.
It all comes from trial-and-error and guessing a starting-point.
The easiest way is to copy an existing design.
But if you don't have something to copy, you can begin with say 10 turns. Note the output voltage and current taken by the circuit.
Increase the winding to 20 turns. Again note all details. From the figures you can work out if you are going in the right direction.
Continue collecting data with both additional turns and reduced turns as, sometimes, an unusual feature suddenly arises.
Keep working until you are satisfied with the results.
Even if you have studied inductor theory, you will still have to carry out the practical side of things.
Nothing takes the place of actually "doing-it."

In our 3 circuits, there are many different combinations of windings that will work.
The reason is the circuit is non-critical.
You have to understand the operation of an inductor in an entirely different way to the theoretical model to see how it operates.
This is called a "loose" circuit and a wide range of primary windings will produce the same result.
For example, a primary winding of 35 turns will produce the same LED brightness as 55 turns and the current from the supply will be the same.
The output of the transformer (on no-load) will be more than 200v and thus the circuit must not be operated on no-load as the voltage may damage the transistor.
If the LEDs are removed, the circuit will charge the capacitor to more than 45v and this is above the operating voltage for a 100u/25v electrolytic.
If you remove the LEDs and turn the circuit on, then re-solder the LEDs, they will be damaged. This is because the electrolytic will have charged to 45v.
Thus it is very difficult to experiment with the circuit to see how the transformer charges the electrolytic.
You will have to follow our explanation:

The electrolytic is charged by pulses from the inductor.
In circuit-3 the voltage across the electrolytic is 10v and it is delivering current to the three LEDs at a constant rate of 17mA.
CRO waveform - output of inductor

In the CRO diagram above, the pulses (or spikes) occupy about 10% of the total time.
The area under the graph (under each spike) is shown in orange and this represents the energy supplied to the electrolytic.
The inductor is capable of producing a very high spike when in flyback and this voltage allows a burst of current to pass though the diode and charge the electrolytic.
When the inductor is operating under no-load, it is capable of producing a spike of more than 200v, but this voltage is not allowed to be produced when the load is connected. The voltage-spike is limited to the characteristic voltage across the LED or LEDs, plus the voltage drop across the diode and minus the battery voltage. The voltage will be about 9v.
If we are drawing 17mA for 100% of the time, we must deliver 10 times 17mA for 10% of the time to keep the electrolytic charged. Thus a current of about 17 x 10 = 170mA is needed to pass through the diode to charge the electrolytic.
The other feature of the diode is it prevents the voltage on the electrolytic being discharged to the 0v rail via the transistor when it is turned on.

The frequency at which the circuit operates is determined by the inductance of the inductor. The cycle start when the power is applied and the transistor turns on to allow current to flow though the main winding. This produces magnetic flux in the feedback winding to turn the transistor on harder. This continues until the transistor is turned on fully and maximum flux is produced.
But the flux is not expanding flux and thus it does not cut the turns of the feedback winding and the transistor does not get the full turn on current into the base.
The transistor is turned off and this causes the magnetic flux to collapse. This flux is in the opposite direction and it produces a reverse voltage in the feedback winding to keep the transistor fully turned off.
The main winding also produces a voltage in the opposite direction and it delivers a pulse of energy to the electrolytic via the high-speed diode.
As soon as the magnetic flux is spent, (converted to electrical energy) the cycle starts again.
The combination of these two operations creates the length of time for one cycle.
In our case the circuit operates at approx 90kHz.