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New in Mathematica 9 › Advanced Hybrid and Differential Algebraic EquationsMathematica 9 extends the broad language of modeling with differential equations to include advanced algorithms for solving differential-algebraic equations and hybrid systems with a mix of continuous- and discrete-time behavior. DC to DC converter is very much needed nowadays as many industrial applications are dependent upon DC voltage source.
The output voltage and current waveform of step down chopper with resistive load is shown below. Step up chopper or boost converter is used to increase the input voltage level of its output side. With the help of Buck-Boost converter we can increase or decrease the input voltage level at its output side as per our requirement. So VL = VSWhen chopper is OFF inductor L reverses its polarity and discharges through load and diode, So.By evaluating (v) and (vi) we get,Taking magnitude we get,D can be varied from 0 to one.
Hence, in the interval 0 a‰¤ D a‰¤ 0.5, output voltage varies in the range 0 a‰¤ VO a‰¤ VS and we get step down or Buck operation. Whereas, in the interval 0.5 a‰¤ D a‰¤ 1, output voltage varies in the range VS a‰¤ VO a‰¤ a?z and we get step up or Boost operation.
If output voltage (VO) and output current (IO) follows the direction as marked in figures then the chopper operation will be restricted in the first quadrant of VO a€“ IO plane.
It may also happen that both output voltage and current is opposite to the marked direction in figure a€“ 1. It is a single quadrant chopper whose operation is restricted in first quadrant of VO a€“ IO plane.

It is interesting to note that load must have a dc voltage source E for this kind of operation.
This is a two quadrant chopper whose operation is bounded between first and second quadrant of VO - IO plane. When CH2 is ON, output voltage VO will be zero but output current IO will flow in opposite direction of current shown in the figure and inductor will be charged up. We can conclude that the operation of type-c chopper is the combined operation of type-A and type-B chopper.
It is nothing but a high speed switch which connects and disconnects the load from source at a high rate to get variable or chopped voltage at the output. Hence output voltage VO can be varied from 0 to VS.So, we can conclude that output voltage is always less than the input voltage and hence the name step down chopper is justified. So, we will get summation of both source voltage VS and inductor Voltage VL as output voltage, i.e.
But arranging the devices in proper way we can get output voltage as well as output current from chopper in our required direction. 1 but current flows in the opposite direction then VO is taken positive but IO as negative. So, both are taken as positive hence load power is positive which means power is delivered from source to land.
This is also called step down chopper as average value of VO is less than the input voltage.

So, power flows from load to source and operation of type-B chopper is restricted in second quadrant of VO a€“ IO plane.
This type of chopper obtained by connecting type-A and type-B chopper in parallel as shown in the figure. It is clear that output voltage is always greater than the input voltage and hence it boost up or increase the voltage level. When CH1 is OFF, induction will discharge through D1 and current IO will flow through same direction with zero output voltage. Examples of such applications are subway cars, trolley buses, battery operated vehicles etc.
It is also possible that a chopper operates in all the quadrants, which are known as 4-quadrant chopper.
So, we can see the operation of CH1 is nothing but the operation of type-A chopper by which we can operate a chopper in the first quadrant.
We can see operation of CH2 is nothing but operation of type-B chopper by which we can operate the chopper in the second quadrant.

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