See waveform comparison below. The analysis is the same to the diode, only that the integration limit is different. The derivation is easier if the current waveform is breakdown into 2 parts. First part is A1 and A2 for the second part. A1 is triangular while A2 is a pulse. In the above equation, there is a presence of Imax.
Imax is the peak level of the waveform. The peak level is common to all the current waveforms diode, inductor and switch. It is easier to deal with few variables only. Imax is can be substituted by an expression involving di. During the design stage, this can be defined as design given. Basically, all the things done in RMS current derivation are all applicable to the DC current derivation. However, this time the working equation in deriving the A1 and A2 are different.
Follow below analysis to learn how the DC value is derived. The working of the boost converter is to boost the input voltage while buck converter is used for reducing the input voltage level. Isolated DC-DC converters consist of three main parts that are inverter , transformer and rectifier. The inverter for converting DC input voltage into AC, Transformer for stepping-up or stepping-down the AC voltage and finally the rectifier for converting back into required DC voltage. In contrast, the input and output of non-isolated DC converter are not isolated by AC part.
The main agent responsible for converting DC-DC conversion in non-isolated converter is a controlled switch. When the switch is ON; the input voltage appears across the load while the voltage appearing across the switch is zero.
The switch turns ON and turns off periodically which results in pulsating output. The output is then passed through filter which will extract the DC average value of the pulsating output. The DC average value is then controlled by the turn-on and turn-off time of the switch known as Duty cycle. Ideally the power loss is zero because the input power is equal to output power.
DC current source and voltage source with no ripples and no AC components. The same requirement is also for the output of DC-DC converter.
The output is required to be perfectly converted by converter with zero ripples and no AC components. Practically the input of DC-DC converters has current ripples while their outputs have voltage ripples. Therefore, filters are required at both input and output ends. The filter at output is must for removing ripples and extracting average voltage.
A buck converter steps down the applied DC input voltage level directly. By directly means that buck converter is non-isolated DC converter. Non-isolated converters are ideal for all board level circuits where local conversion is required.
Fax machines, scanners, Cellphones, PDAs, computers, copiers are all examples of board level circuits where conversion may require at any level inside the circuit. Hence, a buck converter converts the DC level of input voltage into other required levels. Buck converter is having a wide range of use in low voltage low power applications.
Multiphase version of buck converters can provide high current with low voltage. Therefore, it can be used for low voltage high power applications. This article will discuss both low voltage low power converter and low voltage high power converter.
The efficiency of the converter can be improved using synchronous version and resonant derivatives. The other method of improving efficiency is to use Multiphase version of buck converters. The improvement of efficiency with multiphase inverter is discussed at the end of the article. The basic buck converter consists of a controlled switch, a diode, capacitor and controlled driving circuitry.
The time for which the switch is ON during the whole period is known as Duty cycle. The value of duty cycle D ranges between 0 and 1. The basic circuit diagram of buck converter can be seen below. The average output voltage of Buck converter is controlled using two different ways i. But PWM is preferred most of the time for operation of buck converter. A buck converter operates in two types of conduction modes i. The inductor current I L never become zero through the switching period.
In contrast, the inductor current in DCM D iscontinues C onduction M ode become zero for some time in switching period. Waveforms for both continuous and continuous conduction modes are shown in the figure below. All the discussion in this article is for CCM buck converter which is required for most of applications. As we have discussed in the previous topic that there are two modes of operation in buck converter i. The converter is said to be operating continuous conduction mode if the load current never become zero during the complete cycle.
If the inductance value is reduced, then the ripple will increase. Further reducing the inductance value will increase the ripples such that ripples will become more than load current. At that time, the operation of converter will change from CCM to DCM because the load current will become zero for some instant. Increasing the load resistance will reduce the load current.
The above graph will become as shown below. The current become zero just for zero interval of time and then start increasing. Further increasing the load resistance will reduce the load current further which will change the operation of buck converter from CCM to DCM.
The operation mode immediately changes when load current reduces more than ripples. The following graph shows the DCM mode. The load current now prematurely drops to zero. By prematurely means that the current goes to zero before the switch is turned on. Properties of CCM. Some of the properties of CCM are given as. More technically speaking, the DCM occurs due to switching ripples in inductor current.
Or it occurs due to reversing the capacitor voltage polarity such that it violates the assumptions made for realizing the switch. In simple words, the inductor current ripples are more than the load current. So, during off time, the load current starts decreasing till it become zero. Mostly in PWM buck converter it happens when both voltage and current of the circuit become zero for a short interval of time. During this interval, a new shape of the circuit forms which is normally not possible.
This is known as DCM mode which is sometimes intentionally designed intentionally designed. The overall D Ts remain unchanged during DCM because the conduction of the signal is controlled by the control signal D.
And this is independent of circuit operation however, D Ts is divided into two new portions i. D 2 and D 3 as shown in the above figure. D2 and D3 are additional unknown parameters which make the calculation a little bit complex.
Properties of DCM. Some of the properties of the converter changes when converter starts operating in DCM. Some of those properties are given below. The working operation of buck converter can be explained in two modes.
Both modes are explicitly discussed here. By turning ON the switch, the diode will become reverse bias to the applied input. Therefore, all the input current will flow through inductor. Hence the DC input current I dc flowing in the circuit is equal to the inductor current. The inductor will charge during turn ON time. This current further divide into load current Io and capacitor current Ic.
The inductor voltage V Lon during this period is the voltage difference between applied DC voltage V dc and output voltage V o. The average voltage across inductor V L is zero according to volt second balance. Recalling the duty cycle equation, the turn ON time t on is the product of duty cycle D and total time T.
By putting the value of V L we get. The final result shows the current slop of inductor current during on time. The wave form shown given below shows the rippling current that first increase in ON time and then reduces with negative slop. After turning OFF the switch, the mode 1 changes to mode 2. In this mode the polarity of inductor reverses and it start acting as a source. The current in this mode flows due to the stored energy in the inductor.
The DC source is disconnected during this period. Therefore, the current flows in the circuit till the inductor discharges. The voltage appearing across the inductor is equal to the load voltage with negative polarity.
After turning OFF the switch, the polarity of inductor changes which make the diode forward bias. The anode voltage become more positive than cathode during this period and hence starts conducting.
The turn off time t off can be derived from turn on time t on in duty cycle. The turn off time can be written in the final form as. The slop of inductor current can be found once again by voltage current equation of inductor. Therefore, both minimum peak and maximum peak of the current need be found. By putting the values that we have been discussed in previous two modes of operation, the form of equation will become as given.
Further simplifying the above equation, the final form of the minimum inductor current can be achieved as given below. By putting the previously discussed values in the above equation, we will get. Further simplifying the above equation, we will get the final form as given below for maximum inductor current. The buck converter needs to be considered in steady state for finding transfer function.
This consideration will make the calculations easy for finding transfer function. The average voltage across the inductor is zero in steady state according to volt second balance. Further, the inductor will act as a short circuit in steady state to a pure DC. By putting the values of V Lon , t on , V Loff , t off in above equation, the result will become.
Further simplifying will result. The final form of the transfer function is. Therefore it shows that the average output voltage is always less than the applied input voltage. This section will discuss the designing of components used in buck converter with their ratings. This section will describe the important aspect of inductor required for buck converter. This includes two main ideas i. Critical inductance Lc is the minimum value of inductance at which inductor current reaches zero.
Therefore, it is most important condition for operating buck converter in discontinues mode. In other words, the value of inductor is chosen below than critical inductance for operating buck converter in discontinuous mode.
The requirement is set by means of minimum percentage load. For operating buck converter in CCM mode, the inductor value is chosen more than critical inductance. The value of critical inductance can be found directly by simplifying the equation. We get the following result after solving the above equation. This is the most important equation for finding critical inductance which will decide the operation mode of buck converter. Where these quantities are selected as given. The peak current rating of inductor can be found using maximum value of the inductive current I Lmax.
The maximum inductor current occurs at maximum load. The peak current rating of inductor can be found using the equation of maximum inductor current as given as.
The simplified form is given below which will define the rating the rating of inductor current. This section will discuss both current and voltage rating of a switch for buck converter. For ideal diode, the V switch-max is equal to V dcmax while for non-ideal diode; V switch-max is equal to V dcmax plus V F.
The current rating for a switch is calculated based on average current. By drawing the switch current waveform, the average value of the current can be calculated. The average current for the switch is calculated here. Overall inductor current is equal to switch current and diode current using KCL. During the turn ON time, the inductor current is equal to switch current while the inductor current is equal to diode current during turn OFF time.
By putting the values in above equation, the result will become as given below. Further simplifying and putting the previously discussed value. The final form of the equation of current rating for the switch become. Shotkey diodes are preferred for the discharging of buck converters due to fast recovery action. These diodes are known as fast recovery diodes so preferable for high frequency operation i. This section will discuss the current and voltage rating of shotkey diode for buck converter.
It is given in the data sheet of the component. Where, the value of V sw is calculated at maximum load current. The same approach is adopted for calculating current rating for diode as it was adopted for the calculation of switch. The average forward diode current is calculated from the current waveform of the diode. As diode conduct during off time of the switch therefore, t off is considered in the calculation. By putting values in the above equation, the result will become. Simplifying the above equation will result.
By putting previously discussed values and simplifying, the result will become. This will lead to one of most important result that is given below. The following wave form is the diode current wave form. It provides ease in finding average value. This section will discuss the important parameter for a capacitor under which the capacitor can be operated in safe mode. Furthermore, the capacitor is designed such that the required functioned is performed. The capacitor is designed and chosen such that the maximum capacitor voltage must withstand the maximum output voltage.
Ideally the maximum capacitor voltage V cmax is. As given as. The case is a bit different for particle capacitors. This contribution made by ESR can be suppressed by using following methods. The designed capacitor will provide a path for AC ripples of inductor current while pure DC current will flow into the load. That is how the capacitor will act as a filter.
The waveform of the capacitor current will look as shown below. It can be seen form the below given waveform capacitor current w. By putting the values and simplifying the result will become.
The final result for minimum capacitance will be as shown below. The capacitor is designed such that the maximum input voltage will be with stand by capacitor voltage. Ideally both are considered equal i. The ESR factor contributes to capacitor loss. The ESR factor can be reduced for better efficiency by two methods. Either by paralleling capacitors or by choosing capacitor with low ESR. By putting the value of q in this equation, the result will be as given below.
I o is considered as I o max. Therefore, the above equation become. This is the required capacitance value while the RMS current rating equation can be found as.
The following table shows all the important equations required for the designing of Buck converter. To design a buck converter that will convert volt input DC to 2. For such conversion we have some known data and some parameters are required. Proper selection of components is must for successful conversion from 12v to 2.
This example will help to design buck converter for any conversion ratio. The duty cycle D can be found from the output input voltage ratio. Critical inductance can be found from previously found equation.
The critical inductance can be chosen as. The peak current rating can be found according to the equation. I Lmax 1. Forward diode current according to the given equation will be. Maximum switch voltage according to the equation derived above. While maximum switch current.
Minimum capacitance required for the converter according to the equation will be. Near value for this required capacitance can be. Voltage rating of capacitor. Losses for the buck converter must be considered when the efficiency estimation is required for it.
Several major losses that are to be considered are given below and discussed briefly one by one. This on resistance greatly contributes in over losses. The two graphs given below show the exponential increase of on state resistance. The other graph shows the increase of on-state resistance with increase in temperature. Drain current in this case 7. Switching losses are related with the transition time of the switch.
During the transition time, both current and voltage are non-zero. Therefore, the main switching losses are due to overlapping of current and voltage. The given graph show that how losses occurs in transition states. The voltage across the switch approaches to zero with a specific slope while current across it increase. During this time losses occur. The same case is with turning OFF the switch. During this time current approaches to zero with a specific slope while voltage drop across it increases.
This is how transition losses occur during transition time. According to the above discussion the overall power losses P loss is equal to the power losses during turn-on time and turn-off time. We know that losses during turning-on time is. While losses during turn-off time is. By putting both these values in the above equation, we will get the following result. By taking common term, the final form for the overall switching losses will become.
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