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Опубликовано в Investment westpac | Октябрь 2, 2012

membership function and other parameters. The accurate non-linear model of the converter based on The transfer function of the Buck-Boost converter. Appropriate control requirements have been defined by analyzing open-loop characteristic of converter transfer function through the small-signal. Ključne reči: noninverting buck-boost converter; voltagemode control; control-to-output transfer function, line-to-output transfer function and the.
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Power Electronics 3 3 1 Analysis of Converter Transfer Functions
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Power Electronics Inverting Buck Boost Converter
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D is the duty cycle. It represents the fraction of the commutation period T during which the switch is On. Therefore D ranges between 0 S is never on and 1 S is always on. During the Off-state, the switch S is open, so the inductor current flows through the load. If we assume zero voltage drop in the diode, and a capacitor large enough for its voltage to remain constant, the evolution of I L is:.

As we consider that the converter operates in steady-state conditions, the amount of energy stored in each of its components has to be the same at the beginning and at the end of a commutation cycle. As the energy in an inductor is given by:. From the above expression it can be seen that the polarity of the output voltage is always negative because the duty cycle goes from 0 to 1 , and that its absolute value increases with D, theoretically up to minus infinity when D approaches 1.

Apart from the polarity, this converter is either step-up a boost converter or step-down a buck converter. Thus it is named a buck—boost converter. In some cases, the amount of energy required by the load is small enough to be transferred in a time smaller than the whole commutation period. In this case, the current through the inductor falls to zero during part of the period.

The only difference in the principle described above is that the inductor is completely discharged at the end of the commutation cycle see waveforms in figure 4. Although slight, the difference has a strong effect on the output voltage equation. It can be calculated as follows:. As can be seen on figure 4, the diode current is equal to the inductor current during the off-state. Therefore, the output current can be written as:. Compared to the expression of the output voltage gain for the continuous mode, this expression is much more complicated.

Furthermore, in discontinuous operation, the output voltage not only depends on the duty cycle, but also on the inductor value, the input voltage and the output current. As told at the beginning of this section, the converter operates in discontinuous mode when low current is drawn by the load, and in continuous mode at higher load current levels.

The limit between discontinuous and continuous modes is reached when the inductor current falls to zero exactly at the end of the commutation cycle. Therefore, using the expression of the output voltage in continuous mode, the previous expression can be written as:. These expressions have been plotted in figure 5. The difference in behavior between the continuous and discontinuous modes can be seen clearly.

The four-switch converter combines the buck and boost converters. It can operate in either the buck or the boost mode. In either mode, only one switch controls the duty cycle, another is for commutation and must be operated inversely to the former one, and the remaining two switches are in a fixed position. A two-switch buck-boost converter can be built with two diodes, but upgrading the diodes to FET transistor switches doesn't cost much extra while due to lower voltage drop the efficiency improves.

In the analysis above, no dissipative elements resistors have been considered. That means that the power is transmitted without losses from the input voltage source to the load. However, parasitic resistances exist in all circuits, due to the resistivity of the materials they are made from.

Therefore, a fraction of the power managed by the converter is dissipated by these parasitic resistances. For the sake of simplicity, we consider here that the inductor is the only non-ideal component, and that it is equivalent to an inductor and a resistor in series.

This assumption is acceptable because an inductor is made of one long wound piece of wire, so it is likely to exhibit a non-negligible parasitic resistance R L. Furthermore, current flows through the inductor both in the on and the off states. If we consider that the converter operates in steady-state, the average current through the inductor is constant.

The average voltage across the inductor is:. Therefore, the average voltage across the switch is:. The output current is the opposite of the inductor current during the off-state. Assuming the output current and voltage have negligible ripple, the load of the converter can be considered purely resistive.

If R is the resistance of the load, the above expression becomes:. If the inductor resistance is zero, the equation above becomes equal to the one of the ideal case. But when R L increases, the voltage gain of the converter decreases compared to the ideal case. The non-inverting topology, also named the 4-switch topology, produces an output voltage that is of the same polarity as the input voltage.

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Which can be a disadvantage. But, this disadvantage is of no importance. If the power supply is isolated from the load circuit because at this condition the power supply and polarity of diode can be upturned or reversed. At the reversed condition, the switch can be on either the supply side or at the ground side. Working of inverting topology An Inverting buck-boost converter is shown in below figure.

It is the schematic of a basic inverting buck-boost converter which is working in continuous conduction mode CCM. Inverting Buck-Boost Converter We can see an output capacitor, in the power stage a metal-oxide semiconductor field-effect transistor MOSFET is present, a diode, and an inductor is present.

Anode of the diode is connected to the load. Anode of the diode is also connected to negative terminal of electrolytic capacitor. This results in storing energy in the inductor L1. While M1 is ON, the output capacitor C1 supplies the entire load current. When the M1 is OFF, the diode D1 is forward-biased and the inductor current ramps down at a rate proportional to output voltage Vout. The non-inverting topology Below figure shows a non-inverting buck-boost converter.

Here we can see a buck step-down converter is joint with a boost step-up converter. Non-Inverting Buck-Boost Converter The output polarity of this type of converter is same like the polarity of the applied input. But the output level may vary i. We can see in the figure that there is only one inductor is used even there is buck mode and boost mode is combined. This single inductor controlled by switches instead of diodes. At a time only one switch is in ON condition.

If it uses many inductors with only one switch same like seen in Cuk or SEPIC topologies, then it is called as "four-switch buck-boost converter". All these above mentioned buck boost topologies generate positive output but these topologies have extra power components and less efficiency as compared to a basic inverting buck-boost converter. Working of non-inverting topology We can see in figure of non-inverting buck-boost conductor; two high frequency switching MOSFETS are used along with the two diodes and these diodes have a low forward junction voltage when it conducts.

Operation of buck converter We can understand the operation of buck-boost inductor on the basis of inductor's "reluctance", which allows quick change in current current across inductor. Initially current through the inductor is zero. When the MOSFET switch is first closed, the blocking diode stops current from flowing through it as it is reversed biased, so the current passes through the inductor.

Initially the Inductor will keep the current low by dropping most of the source voltage, as the inductor doesn't like fast current change. With the time the inductor allows the current to increase slowly with the decrease in voltage drop. By this inductor will store energy i.

This current charges L1, capacitor C1 and supply further to the connected load. The diode D1 is turned off because of the positive voltage on its cathode i. Below figure shows the mode of operation of buck converter i.

Now the inductor L1 is fully charged and now it is the only source of the current. This polarity change turns on the diode D1 and current flows through the diode D2 and further to the connected load. This gives an advantage of less ripple at the output.

This current charges or creates magnetic field around inductor L1. Also in this step the diode D2 not conducts i. Now for this ON period, the charge developed by previous oscillating cycles on the capacitor C1 acts as a supply for the load. The slow discharge of capacitor C1 throughout the ON period and its immediate recharging creates high frequency ripple on the output voltage.

This high frequency ripple is at a potential of approx. As the inductor L1 charged it generates a back E. The value of this E. This inductance is hold by the coil inductor. As the energy in an inductor is given by:. From the above expression it can be seen that the polarity of the output voltage is always negative because the duty cycle goes from 0 to 1 , and that its absolute value increases with D, theoretically up to minus infinity when D approaches 1.

Apart from the polarity, this converter is either step-up a boost converter or step-down a buck converter. Thus it is named a buck—boost converter. In some cases, the amount of energy required by the load is small enough to be transferred in a time smaller than the whole commutation period. In this case, the current through the inductor falls to zero during part of the period. The only difference in the principle described above is that the inductor is completely discharged at the end of the commutation cycle see waveforms in figure 4.

Although slight, the difference has a strong effect on the output voltage equation. It can be calculated as follows:. As can be seen on figure 4, the diode current is equal to the inductor current during the off-state. Therefore, the output current can be written as:.

Compared to the expression of the output voltage gain for the continuous mode, this expression is much more complicated. Furthermore, in discontinuous operation, the output voltage not only depends on the duty cycle, but also on the inductor value, the input voltage and the output current.

As told at the beginning of this section, the converter operates in discontinuous mode when low current is drawn by the load, and in continuous mode at higher load current levels. The limit between discontinuous and continuous modes is reached when the inductor current falls to zero exactly at the end of the commutation cycle. Therefore, using the expression of the output voltage in continuous mode, the previous expression can be written as:. These expressions have been plotted in figure 5.

The difference in behavior between the continuous and discontinuous modes can be seen clearly. The four-switch converter combines the buck and boost converters. It can operate in either the buck or the boost mode. In either mode, only one switch controls the duty cycle, another is for commutation and must be operated inversely to the former one, and the remaining two switches are in a fixed position.

A two-switch buck-boost converter can be built with two diodes, but upgrading the diodes to FET transistor switches doesn't cost much extra while due to lower voltage drop the efficiency improves. In the analysis above, no dissipative elements resistors have been considered. That means that the power is transmitted without losses from the input voltage source to the load. However, parasitic resistances exist in all circuits, due to the resistivity of the materials they are made from.

Therefore, a fraction of the power managed by the converter is dissipated by these parasitic resistances. For the sake of simplicity, we consider here that the inductor is the only non-ideal component, and that it is equivalent to an inductor and a resistor in series. This assumption is acceptable because an inductor is made of one long wound piece of wire, so it is likely to exhibit a non-negligible parasitic resistance R L.

Furthermore, current flows through the inductor both in the on and the off states. If we consider that the converter operates in steady-state, the average current through the inductor is constant. The average voltage across the inductor is:.

Therefore, the average voltage across the switch is:. The output current is the opposite of the inductor current during the off-state. Assuming the output current and voltage have negligible ripple, the load of the converter can be considered purely resistive. If R is the resistance of the load, the above expression becomes:. If the inductor resistance is zero, the equation above becomes equal to the one of the ideal case.

But when R L increases, the voltage gain of the converter decreases compared to the ideal case. Furthermore, the influence of R L increases with the duty cycle. This is summarized in figure 6. From Wikipedia, the free encyclopedia. Type of DC-to-DC converter. This article is about the type of switched-mode power supply. For the autotransformer, see buck—boost transformer.