Electronic – 9 V to 360 V via boost converter

Your boost is operating in discontinuous conduction mode or DCM (inductor current goes to zero each switching cycle). The duty cycle becomes a function of load as well as the duty cycle. If you increase the load, the inductor value, or switching frequency, you'll reach a point where you'll see your regulation where you expect it - this is called CCM, or continuous conduction mode. The inductor current doesn't fall to zero, but continuously flows. Your duty cycle formula will be valid here.

20 kHz is very slow for a boost converter. 14A peak inductor current is also unrealistic. Most PFC boost converters operate from 70 to 100 kHz. Lower frequency converters generally need larger inductors. If you want to achieve CCM at 20kHz, you'll need a much larger boost inductance value. Try 470uH in your simulation and you'll see the voltage closer to 12V. (If you had a controller in your model, it would automatically adjust the duty cycle to achieve 12V regardless of CCM or DCM operation).

Because your converter is so heavily into DCM, the switching node voltage resembles the output voltage. If you get closer to CCM, you'll see a clearer picture.

For this simulation, the capacitor is sized such that the switch on-time voltage sag (caused by the load) isn't excessive. In real life, there are other parameters that matter (overall loop stability, ripple current and life rating) that you must consider, along with proper MOSFET choice, reverse recovery and softness of the boost diode...

My objective is to create a device that will generate a constant current to a load that varies in resistance from approximately 1Kohm-40Kohm

OK, so far so good.

For the sake of this question, the current I am trying to generate is 5mA.

5 mA through a 1 kohm load means the circuit has to supply 5 volts to the load. 5 mA through 40 kohm means 200 volts applied to the load.

I've done a bit of reading over the last few days and the concept of a boost converter in its simplest form is rather straightforward.

Here's where the first hurdle is arising because a boost converter can only produce an output voltage that is greater than the input supply voltage (you specified 12 volts). If your supply is 12 volts and you want a current of 5 mA through a load that can vary between 1 kohm and 40 kohm then you need a buck-boost converter; a booster won't do what you want.

You could use a buck regulator to set a voltage at (say) 4 volts then use a booster to deliver 5 volts to 200 volts but that is pushing technology too far. I would strongly consider generating (say) 210 volts using a "booster" then using some form of linear regulation to deliver the required voltage for the correct current to the load.

Any advice or tips would be greatly appreciated. I am looking for similar ways to achieve a constant current given different loads.

The type of "booster" I would use would be a step-up flyback converter like either of these two: -

So, you get a high voltage regulated DC supply and use a linear current regulator to control the current to the load. If you generate 210 volts and you need to supply 5 mA the worst case power dissipation is going to be just over 1 watt into a short circuit so you will need a small heatsink.

If you can allow your load to be floating then a fairly simple constant current sink will do what you want providing you choose an output transistor that is rated at overs 210 volts (300 volts recommended): -

Applications in which a microprocessor can be used are helpful because I can choose different output currents with ease (say, 6mA instead of 5mA)

If you want it microprocessor controlled then you could generate a PWM output and use a low pass filter to create an analogue voltage that feeds Vset.