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**Instructor: Po-Yu Kuo (郭柏佑) 國立雲林科技大學 電子工程系**

降壓式轉換器 Buck Converter Instructor: Po-Yu Kuo (郭柏佑) 國立雲林科技大學 電子工程系

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Switching Converter In a switching converter circuit, different from the linear regulator, the transistor operates as an electronic switch by being completely ON or completely OFF. This circuit is also known as a dc chopper. Different researchers use different names for this converter topology, some of them are: switched mode power converters, switch mode power supplies and switching regulators. In this course, we use switch mode power converters (SMPCs). In order to improve the efficiency, converter with only lossless components should be used. These include inductors, capacitors, and switches.

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**Ideal Switching Converter**

For an ideal switch, power consumption is zero, in both the ON (switch closed) and OFF (switch open) stages PowerON = VSW · ISW = 0(ISW) = 0 PowerOFF = VSW · ISW = VSW(0) = 0 Recall: average absorbed power by inductor and capacitor for steady-state periodic operation is 0 Theoretically ideal switching converter is a lossless system

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**Ideal Switching Converter**

Fig. 2 shows a basic switching converter with an ideal switch. The output is the same as the input when the switch is closed, and the output is zero when the switch is open. Periodic opening and closing of the switch results in the pulse output and the average or dc component of the output is The dc component of the output is then controlled by the duty cycle D, which is the fraction of the period that the switch is closed:

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Buck Converter By adjusting the duty cycle D, the load will have an average output voltage VsD. However, most of electronic loads require a continuous and steady output voltage as shown in Fig. 3(a). However, problem occurs when the switch is OFF. The inductor current cannot change instantaneously and a very high voltage spike will generate across the switch and will cause a spark across the switch. So, a second switch as shown in Fig. 3(b) is needed to make a functional switching converter.

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**Buck Converter The operation of the converter is as follows:**

State 1: S1 is ON and S2 is OFF vL = Vs – Vo → iL ramps up State 2: S2 is ON and S1 is OFF vL = 0 – Vo → iL ramps down S1, S2 , L and C are all lossless elements → no energy loss (theoretically) → η = 1 can be achieved Since the switching converter consists of 2 reactive elements, the inductor L and the capacitor C, it is known as a second order converter.

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Steady State Analysis

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Steady State Analysis The buck converter has the following properties in steady state : The inductor current is periodic: iL(t+T) = iL(t) The average inductor voltage is zero The average capacitor current is zero The power supplied by the source = the power delivered to the load. For ideal components: Ps = Po and for non-ideal components: Ps = Po + losses Following assumptions should be made before analyzing the buck converter: The circuit is operating in steady state. i.e. steady-state analysis The inductor current is continuous and always positive. i.e. CCM operation The capacitor is very large and output voltage is held constant at Vo. Io=Vo/R The component is ideal. i.e. Ps = Po

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Steady State Analysis When the switch is closed, the diode is reverse biased & the voltage across the inductor is The derivative of the inductor current is positive → the current increases linearly When the switch is open, the diode becomes forward biased and the voltage across the inductor is The derivative of the inductor current is negative → the current decreases linearly

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Steady State Analysis In steady state, the net inductor current = 0. i.e. or Solving for Vo gives Vo = VsD which is expected. As D < 1, the buck converter can only produce an output which is less than or equal to the input Output voltage only depends on the input voltage. If the input voltage fluctuates, the output voltage can be regulated by adjusting the duty ratio appropriately An alternative derivation using volt-second balance equation (conservation of flux in inductor): average inductor voltage is zero for periodic operation. i.e.

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Inductor Value Since the average current of the capacitor is zero, the average current of the inductor is the same as the average current of the load. i.e. IL=IR=Vo/R. Now the change of inductor current or inductor ripple: The maximum & minimum inductor current can be computed as

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Inductor Current Since the inductor current is always positive (CCM). To satisfy ILmin must be greater than 0 The minimum inductance value required for CCM operation is

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**Buck Converter: Output Voltage Ripple**

In the preceding analysis, we assume the capacitor is very large to keep the output voltage to a constant value. However, in practice, the output voltage cannot be kept perfectly constant with a finite capacitor value. The variation of the output voltage vr (known as ripple voltage) can be computed from the voltage-current relationship of the capacitor The capacitor current: iC = iL – iR (positive current → capacitor is charging) Ripple voltage is calculated as follows:

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**Buck Converter: Waveforms**

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**Buck Converter: Waveforms**

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**The tradeoff of high fs is the increased power loss in the switches**

Buck Converter: Design Considerations When fs increases, both Lmin for producing CCM operation and C for limiting the output ripple decrease. Therefore, higher switching frequency is desirable to reduce L and C values. The tradeoff of high fs is the increased power loss in the switches The inductor wire must be rated at the rms current and the core should not saturate for peak inductor current. The capacitor must be selected to withstand peak output voltage and to carry the required rms current

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