Design and simulate three DC-DC converter topologies in MATLAB Simulink

To design and develop the Simulink model of three topologies of DC-DC converter listed below;

Table 1- Topology of Selected DC-DC Converter

Abstract:

In today’s world, we are surrounded by electronics such as Phones, laptops, and various electronic accessories like smartwatches, Headphones, Chargers, Smart ACs, and so on. And we know that each electronic appliance needs efficient Power conversion. Power conversion is done by various means according to the application requirement, we convert the power in four stages;

Figure 1- Different Stages of Power Conversion

For effective power conversion we use modern power converters. In this project we focus only on DC-DC power converter. We explain three topologies as mentioned in table above.

Topology-01:

Buck Converter or Step-down Converter in CCM:

• A buck converter is a type of DC-DC power converter that is used to step down a DC voltage from a higher level to a lower level. It is also known as a step-down converter.
• In this converter, Inductor placed at the output side and switch(MOSFET, IGBT and BJT, etc.) is placed at the Input side of the converter, we can see in the following figure-02;

Figure 2- Conventional Buck Converter

• Output Capacitor is used for to reduce the ripple in output voltage and make it constant at steady-state.
• Diode is used to freewheel the energy of converter Inductor when the switch is OFF.

Working Principle:

Since, a Buck converter contain non-linear devices such as one Switch and one uncontrolled Diode, hence the circuit operates in two mode as given below;

ON-Mode of Operation:

• ON mode means the Switch is “ON” and the Diode is “OFF”. When we apply this the change in circuit as following;

Figure 3- Buck converter during 'ON' Mode

• During “ON” mode, DC voltage source delivers the energy to the inductor and inductor is linearly charged till the switch is in “ON” condition.

OFF-Mode of Operation:

• OFF mode means the Switch is “OFF” and the Diode is “ON”. When we apply this the change in circuit as follows;

Figure 4- Buck converter during 'OFF' Mode

• During “OFF” mode, freewheeling diode is activated and Inductor discharge energy through this path where this freewheeling diode is present.
• Thus, we see that Converter inductor is charged during “ON” and discharge during “OFF” condition, so we observe that the waveform of the Inductor current is periodic, and we know very well that “If we passing periodic current through the Inductor than, the average Voltage across the Inductor should be zero”

Specs of Buck Converter in CCM:

Given,

Vin = (40-50)V,

Vout = 30V,

Power = 500W,

Let, fs = 50KHz,

So, the output load Resistance come out to be as,

Where,

Designing of Buck converter in CCM:

Duty Ratio:

We know that,

We know that voltage converter ratio for a Non-Isolated Buck Converter,

For Vin = 40V,

For Vin = 50V,

So, the duty ratio range of Buck converter,

Designing Of Inductor:

In Continuous Conduction Mode(CCM),

For Inductor current to be continuous, in worst case scenario,

 

Figure 5- Waveforms of Buck Converter

From waveform we see that,

 

 

From this, we get the minimum value of inductor such that inductor current will be continuous, 

 

In the worst-case scenario, the input voltage should be minimum, Therefore, the inductor value can be calculated as follows: 

For D= 0.6,

For D= 0.75,

 

 

So, in worst case scenario, we choose the higher value of inductor that is:

Assume 40% ripple, then Inductor is,

To design an Inductor for a specific % of current ripple we use this formula;

Where,

Selection of Inductor:

• For selection of an Inductor we are using a quite popular website named “Coilcraft” one can choose Digikey, Mouser and Magnetics as well.

Figure 6- Website of 'Coilcraft' for selection of Converter Inductor

• Go to site and fill the details of this topology and it gives you a suitable list of Inductors based on the ripple % and switching frequency, you can play with the filters to get your desire inductor.
• We clearly see that coil craft suggesting inductor of 33uH and 44% ripple. So we chose any one inductor.
• We choose TH Shielded High Current Power Inductors–AGP4233 Series

Figure 7- TH Shielded High Current Power Inductors – AGP4233 Series

• Shielded Through-hole(TH) mount power inductors from the Coilcraft AGP4233 Series have excellent current handling in a wide range of inductance values and low DC resistance, making them an affordable choice for a number of general-purpose applications.
• Selected Inductor is L=33μH, for this topology.

 

Designing of output Capacitor:

Assume that we want output voltage ripple is less than 10%;

We know the output Capacitor formula,

Where,

Now,

For D= 0.6,

 

For D= 0.75,

 

So we choose maximum value of capacitor that is 6.06μF, but for the safety reason we choose 20% higher than of it;

Final choice of output capacitor is,

Selection of Capacitor:

• For Capacitor selection we using website name “Digikey”. It’s quite popular worldwide.
• It has a simple GUI with lots of filter to choose a suitable electronic components according to the specification.
• We here looking for the ≥7.272μF capacitor with less ESR(Equivalent series Resistance) and ESL(Equivalent series Inductance).

Figure 8- Website of 'Digikey' for selection of Capacitor

• We get the ceramic based surface mount capacitance of value 10μF and withstand voltage capacity of 50V, which is definitely a right choice for this topology.

Figure 9- 10μF ±20PV Multi-Layer Ceramic Capacitor (MLCC)

• Selected Capacitor is C=10μF, for this topology.

Designing of MOSFET:

First we focus on the suitable selection of MOSFET, one can chose IGBT as well.

We required,

Blocking Voltage:

According to given topology specs, during turn “OFF”, the MOSFET maximum blocking voltage comes out to be 50V, but for the safety reason we choose the MOSFET whose value is 50% higher than the maximum blocking voltage, so we have;

From this we observe that the drain to source voltage of MOSFET should be as,

 

Peak current in MOSFET:

• According to the circuit of the Buck Converter, we can easily find the MOSFET peak current that could flow during “ON” condition.
• In this case we observe that the peak current of converter inductor should be same as the peak current of the MOSFET, that is;

Where,

Selection of MOSFET:

After getting some essential data for the MOSFET we looking for the searching of MOSFET and we choose the website Infineon, one can choose “Mouser” or “Digikey” as well,

Suitable MOSFET that we chosen as,

Figure 10- OptiMOSTM3 Power-MOSFET, 80V

Features of MOSFET BSZ340N08NS3-G:

• Optimized technology for DC/DC converters.
• Superior thermal resistance.
• Dual sided cooling,
• Low parasitic inductance.

From datasheet of BSZ340N08NS3-G MOSFET, some the following parameters are observed:

 

Table 2- Key Performance Parameters

From the above table V_GS, R_G, C_iss, C_oss and C_rss and some other parameters are help to find the suitable Gate Driver for this topology.

Designing of Gate Driver:

Gate driver designing is totally based on the selection of MOSFET, we already select the MOSFET ‘BSF450NE7NH3 G’. Before choosing the Gate driver first we see some interesting features of an ideal Gate Driver:

Ideal Gate Driver features:

• It should have a capability of Level shifting.
• Meet the voltage and current requirements of the gate emitter/source region.
• It should have a capability to deal with floating supply.
• High Input Impedance.
• High CMTI(Common-mode Transient Immunity).

Gate drivers are broadly classified in two types:

• Non- Isolated Gate Driver.
• Isolated Gate Driver

We always prefer an isolated gate driver over non-isolated gate driver if there is no economic constrain. Because isolated gate driver has a capability to isolate the converter from the microcontroller and it has a long life cycle as compare to non-isolated gate driver.

Selection of Gate Driver:

Gate driver choice is depends on the parameters of MOSFET like Input capacitance, output capacitance, reverse transfer capacitance , gate to source threshold voltage, gate resistance, delay time, rise time and net charge etc. These parameters are already given in the datasheet of the MOSFET as discussed above.

For making Buck converter or step-down converter we select single-channel high-speed low-side Gate Driver that is UCC27511A.

Figure 11- Gate Driver UCC27511A

Reasons for choosing Gate Driver UCC27511A:

• From the datasheet of this gate driver we analyse the following below points;
• According to given topology, we required a power supply to activate this IC and we choose 15V power supply, one can use the Bootstrap method to given the power supply from the existing power supply.
• Other parameters are given in the datasheet of this driver;

Figure 12- Gate Driver parameters

• UCC27511A device is an automotive-grade single-channel low-side, high-speed gate driver rated for MOSFETs, IGBTs, and emerging wide-bandgap power devices such as GaN.
• The device features fast Glitch-Free Operation at Power Up and Power rise times, fall times, and propagation delays, making device suitable for high-speed applications.
• The split output configuration enables easy and independent adjustment of rise and fall times using only two resistors and eliminating the need for an external diode.

Pin Configuration:

Figure 13- DBV package 6-pin Gate driver

Pin Function:

1. V_DD: This is the power supply voltage input pin for the device. The voltage range for V_DD is between 4.5V and 18V.
2. IN+: Non-Inverting Input
3. IN-: Inverting Input
4. OUTH: Sourcing current output of driver. Connect a resistor between the OUTH pin and the gate of the power switching device to adjust turn on speed.
5. OUTL: Sinking current output of driver. Connect a resistor between the OUTL pin and the gate of the power switching device to adjust turn off speed.
6. GND: Ground.

Typical Application Diagrams:

   Figure 14- Gate driver schematic for non-inverting Input

Figure 15- Gate driver schematic for inverting Input

Closed-loop Buck Converter Analysis using PI Controller:

In order to get the stability of a Buck converter or any type of system, it’s always good to do transient and steady-state analysis, this will tell you the overall behaviour of a system. Although there are various type of close loop techniques available in the real world, but the basic structure is common in all of the close loop technique that is;

Figure 16- Block diagram of Closed-loop System

Procedure:

Step-01: Find the Transfer function(Gv(s)) of the Buck Converter;

Figure 17- Conventional Buck Converter

ON-MODE ;

Figure 18- Buck Converter during 'ON' Mode

State variable ,

From Inductor,

Form Capacitor

OFF-MODE ;

Figure 19- Buck Converter during 'OFF' Mode

From Inductor,

From Capacitor,

State-space Equation during ON-Mode;

State-space Equation during OFF-Mode;

Averaging of State Space Model:

So, above we get two State Space equation from ‘ON’ and ‘OFF’ mode of operation of a Buck converter, which represents the Large Signal Model of the buck converter.We need to combine both large signal Model into one, for this we use Averaging method as;

              

 Where,

For small signal Analysis, if the system, operating point deviate from its equilibrium position, then from the transfer curve between input and output,

So,

So, for the buck converter, Average signal model Equations are,

We analyze that,

Similarly,

For small signal Analysis, following assumptions are made;

So,

In steady state,

So, we simplified equation (4) & split the steady state part from the small signal part;

So, from the Small signal Model we obtained transfer function of plant/converter, hence,

Similarly.

Step-02: After finding Transfer function we have to find PID Controller Transfer function as;

Step-03: Now, we have to find controller Gain parameters(). In order to find that, we here, using MATLAB Autotune option which is belong under the window of PID controller block.

We have,

D = (0.6+0.75)/2 = 0.675

R = 1.8 Ω

L = 33μH

C = 10μF

Figure 20- Testing, Response of a signal through step signal

Figure 21- System Response after testing

Step-04: The output of a PID controller given to the PWM DC-DC Generator block which generate required PWM pulses for given duty ratio. And this PWM is given to Gate driver and Gate driver output is produce gate pulses for the Gate terminal of the MOSFET.

 Schematic of closed loop Non-Isolated Buck Converter:

Used Blocks and Parameters value:

• MOSFET:

• Diode:

• Inductor:

• Capacitor:

• Load Resistance:

• PID Controller:

• PWM Generator (DC-DC):

• Input Voltage:

Simulation Result:

We run this Simulation for 1ms and we got the desire result as following:

Case-01:

For Vin = 40V,

Zoom-OUT:

 Zoom-IN:

Output Voltage and Output Current:

• In this topology, we clearly see that the output voltage waveform during transient have not any peak overshoot or oscillation. It catches the steady state smoothely.
• In steady state, the output voltage is approximately 30V, and ripples are also less than 5%.

• Since the load here is resistive therefore, the output current waveform nature is same as the output voltage waveform and the observed average output current is around 16.67A, which is similar as we calculated above in theory part.

Inductor Voltage and Inductor Current:

• At steady state, the average inductor current is approximately equal to the average output current that is 16.67A.

           
         
           

• Inductor ripple current is approximate 28% which is less than the 40% of the ripple.

• In the below plot we seen that the inductor voltage is 10.3V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -31.5V. But in theoretically during turn ON voltage came 10V and turn OFF voltage came out to 30V.

MOSFET Voltage and MOSFET Current:

 

• In theoretically, MOSFET peak current came out to 20A, but due to presence of non-ideality in this converter we see that in above plot the peak MOSFET current is around 19A.

• In the above plot of MOSFET voltage, we clearly see that the peak MOSFET voltage is 40.8V and in theory voltage came out to 40V.
• So we observe that our choosen MOSFET and their ratings are appropriate for this topology.

Diode Voltage and Diode Current:

• In the below plot we observe that the Diode and MOSFET wave shape are similar in nature except MOSFET operates, during Turn ON and Diode Operates during Turn OFF.
• Diode peak current is same as MOSFET peak Current which is around 19A.

• In the below plot of Diode voltage is similar to plot of MOSFET voltage with same magnitude but opposite in nature.

• Diode peak inverse voltage is 40V.

Capacitor Current and Capacitor Voltage:

• In the below plot of capacitor current we observe that the ripple is less than 10% and wave shape is triangular in nature that shows the charging and discharging of charge during each cycle.
• 
  
  

• Capacitor voltage plot is similar to the plot of output voltage as discussed above because Load resistance and capacitor are connected parallel to each other.

PWM and Duty Ratio:

• PWM is generated by PWM Generator(DC-DC) block where input of this block is controlled duty cycle, produced by the PI controller block.
• In the below plot we see that PWM is generated with a switching frequency of 50KHz in the range of (0-1)V.

• In the below plot of Duty Ratio(D), we observe that for the input voltage of 40V the average duty ratio is approximately equal to 0.75, which is same as when we find duty ratio theoretically.

Case-02:

For Vin = 50V,

Zoom-OUT:

Zoom-IN:

Output Voltage and Output Current:

• In this topology, we clearly see that the output voltage waveform during transient have not any peak overshoot or oscillation. It catches the steady state smoothely.
• In steady state, the output voltage is approximately 30V, and ripples are also less than 5%.

• Since the load here is resistive therefore, the output current waveform nature is same as the output voltage waveform and the observed average output current is around 16.7A, which is similar as we calculated above in theory part.

Inductor Voltage and Inductor Current:

• At steady state, the average inductor current is approximately equal to the average output current that is 16.7A.
• 
  
  
• Inductor ripple current is approximate 44% which is slightly above than the 40% of the ripple.

• In the below plot we seen that the inductor voltage is 20.7V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -31.8V. But in theoretically during turn ON voltage came 20V and turn OFF voltage came out to 30V.

MOSFET Voltage and MOSFET Current:

 

• In theoretically, MOSFET peak current came out to 20A, but due to presence of non-ideality in this converter we see that in above plot the peak MOSFET current is around 20.5A.

• In the above plot of MOSFET voltage, we clearly see that the peak MOSFET voltage is 50.8V and in theory voltage came out to 50V.
• So we observe that our choosen MOSFET and their ratings are appropriate for this topology.

Diode Voltage and Diode Current:

• In the below plot we observe that the Diode and MOSFET wave shape are similar in nature except MOSFET operates, during Turn ON and Diode Operates during Turn OFF.
• Diode peak current is same as MOSFET peak Current which is around 20A.

• In the below plot of Diode voltage is similar to plot of MOSFET voltage with same magnitude but opposite in nature.

• Diode peak inverse voltage is 50V.

Capacitor Current and Capacitor Voltage:

• In the below plot of capacitor current we observe that the ripple is less than 10% and wave shape is triangular in nature that shows the charging and discharging of charge during each cycle.
• 
  
  

• Capacitor voltage plot is similar to the plot of output voltage as discussed above because Load resistance and capacitor are connected parallel to each other.

PWM and Duty Ratio:

• PWM is generated by PWM Generator(DC-DC) block where input of this block is controlled duty cycle, produced by the PI controller block.
• In the below plot we see that PWM is generated with a switching frequency of 50KHz in the range of (0-1)V.

• In the below plot of Duty Ratio(D), we observe that for the input voltage of 50V the average duty ratio is approximately equal to 0.61, which is same as when we find duty ratio theoretically.

Conclusion:

From this topology (Buck CCM), we understand deeply how a closed loop Buck Converter in current continuous mode operates, how to design various components like Inductor, Capacitor Diode and MOSFET and their selection from the practical world. We also create the simulation model of this closed loop converter and observe various plots of it. All theoretical and practical results are approximately matching to each other, hence the analysis of the closed loop Buck Converter in CCM is completed.

Topology-02:

Boost Converter or Step-up Converter in CCM:

• A boost converter is a type of DC-DC power converter that is used to step up a DC voltage from a lower level to a higher level. It is also known as a step-up converter.
• In this converter, Inductor placed at the input side and switch(MOSFET, IGBT and BJT, etc.) is placed at the mid-side of the converter, we can see in the following figure-02;

Figure 1- Conventional Boost Converter

• Output Capacitor is used for to reduce the ripple in output voltage and make it constant at steady-state.
• Diode is used to freewheel the energy of converter Inductor when the switch is OFF.

Working Principle:

Since, a Boost converter contain non-linear devices such as one Switch and one uncontrolled Diode, hence the circuit operates in two mode as given below;

ON-Mode of Operation:

• ON mode means the Switch is “ON” and the Diode is “OFF”. When we apply this the change in circuit as following;

Figure 2- Boost converter during 'ON' Mode

• During “ON” mode, DC voltage source deliver the energy to the inductor and inductor is linearly charged till the switch is in “ON” condition.

OFF-Mode of Operation:

• OFF mode means the Switch is “OFF” and the Diode is “ON”. When we apply this the change in circuit as following;

Figure 3- Boost converter during 'OFF' Mode

• During “OFF” mode, freewheeling diode is activated and Inductor discharge energy through this path where this freewheeling diode is present.
• Thus, we see that Converter inductor is charged during “ON” and discharge during “OFF” condition, so we observe that the waveform of the Inductor current is periodic, and we know very well that “If we passing periodic current through the Inductor than, the average Voltage across the Inductor should be zero”

Specs of Boost Converter in CCM:

Given,

Vin = (200-300)V,

Vout = 400V,

Power = 4KW,

Let, fs = 50KHz,

So, the output load Resistance come out to be as,

Where,

Designing of Buck converter in CCM:

Duty Ratio:

We know that,

We know that voltage converter ratio for a Non-Isolated Buck Converter,

For Vin = 200V,

For Vin = 300V,

So, the duty ratio range of Boost converter,

Designing Of Inductor:

In Continuous Conduction Mode(CCM),

For Inductor current to be continuous, in worst case scenario,

 

Figure 4- Waveforms of Boost converter

From waveform we see that,

 

 

From this, we get the minimum value of inductor such that inductor current will be continuous, 

 

In the worst-case scenario, the input voltage should be minimum, therefore, the inductor value can be calculated as follows:

For D= 0.25,

For D= 0.5,

     

So, in worst case scenario, we choose the higher value of inductor that is:

Assume 40% ripple, then Inductor is,

Maximum possible average current in inductor,

We observe that in case of Boost Converter,

 To design an Inductor for a specific % of current ripple we use this formula;

Where,

Selection of Inductor:

• For selection of an Inductor we are using a quite popular website named “Digikey” one can choose Coilcraft, Mouser and Magnetics as well.

Figure 5- Digikey website for selection of Inductor

• Go to site and fill the details of this topology and it gives you a suitable list of Inductors based on the ripple % and switching frequency, you can play with the filters to get your desire inductor.
• We clearly see that ‘Digikey’ suggesting inductor of 200uH. So we chose this inductor.
• We choose Power Inductors– IHV-20-200.
• Selected Inductor is L=200μH, for this topology.

 

Designing of output Capacitor:

Assume that we want output voltage ripple is less than 10%;

We know the output Capacitor formula,

Where,

Now,

For D= 0.25,

 

For D= 0.5,

 

So we choose maximum value of capacitor that is 2.5μF, but for the safety reason we choose 20% higher than of it;

Final choice of output capacitor is,

Selection of Capacitor:

• For Capacitor selection we using website name “Digikey”. It’s quite popular worldwide.
• It has a simple GUI with lots of filter to choose a suitable electronic components according to the specification.
• We here looking for the ≥3μF capacitor with less ESR(Equivalent series Resistance) and ESL(Equivalent series Inductance).

Figure 6- Digikey website for selection of Capacitor

• We get the ceramic based surface mount capacitance of value 3μF and withstand voltage capacity of 500V, which is definitely a right choice for this topology.

Figure 7- 3μF ±20@0V Fast Switching Capacitor-Flex Assembly (FA) series

• Selected Capacitor is C=3μF, for this topology.

Designing of MOSFET:

First we focus on the suitable selection of MOSFET, one can chose IGBT as well.

We required,

Blocking Voltage:

According to given topology specs, during turn “OFF”, the MOSFET maximum blocking voltage comes out to be 400V, but for the safety reason we choose the MOSFET whose value is 50% higher than the maximum blocking voltage, so we have;

From this we observe that the drain to source voltage of MOSFET should be as,

Peak current in MOSFET:

• According to the circuit of the Boost Converter, we can easily find the MOSFET peak current that could flow during “ON” condition.
• In this case we observe that the peak current of converter inductor should be same as the peak current of the MOSFET, that is;

Where,

Selection of MOSFET:

After getting some essential data for the MOSFET, we looking for the searching of MOSFET and we choose the website “Infineon”, one can choose “Mouser” or “Digikey” as well,

Suitable MOSFET that we chosen as

Figure 8- High voltage CoolMOS™ superjunction MOSFET, 600V

 

Features of MOSFET IPW60R037CSFD:

• Ultra-fast body diode
• Best-in-class reverse recovery charge (Qrr)
• Low parasitic inductance.

From datasheet of IPW60R037CSFD MOSFET, some the following parameters are observed:

Table 1- Key Performance Parameters

From the above table V_GS, R_G, C_iss, C_oss and C_rss and some other parameters are help to find the suitable Gate Driver for this topology.

Designing of Gate Driver:

Gate driver designing is totally based on the selection of MOSFET, we already select the MOSFET ‘BSF450NE7NH3 G’. Before choosing the Gate driver first we see some interesting features of an ideal Gate Driver:

Ideal Gate Driver features:

• It should have a capability of Level shifting.
• Meet the voltage and current requirements of the gate emitter/source region.
• It should have a capability to deal with floating supply.
• High Input Impedance.
• High CMTI(Common-Mode Transient Immunity).

Gate drivers are broadly classified in two types:

• Non- Isolated Gate Driver.
• Isolated Gate Driver

We always prefer an isolated gate driver over non-isolated gate driver if there is no economic constrain. Because isolated gate driver has a capability to isolate the converter from the microcontroller and it has a long life cycle as compare to non-isolated gate driver.

Selection of Gate Driver:

Gate driver choice is depends on the parameters of MOSFET like Input capacitance, output capacitance, reverse transfer capacitance , gate to source threshold voltage, gate resistance, delay time, rise time and net charge etc. These parameters are already given in the datasheet of the MOSFET as discussed above.

For making Boost converter or step-up converter we select single-channel high-speed low-side Gate Driver that is UCC27511A.

Figure 9- Gate Driver UCC27511A

Reasons for choosing Gate Driver UCC27511A:

From the datasheet of this gate driver we analyse the following below points;

• According to given topology, we required a power supply to activate this IC and we choose 15V power supply, one can use the Bootstrap method to given the power supply from the existing power supply.
• Other parameters are given in the datasheet of this driver;

Figure 10- Gate Driver parameters

• UCC27511A device is an automotive-grade single-channel low-side, high-speed gate driver rated for MOSFETs, IGBTs, and emerging wide-bandgap power devices such as GaN.
• The device features fast Glitch-Free Operation at Power Up and Power rise times, fall times, and propagation delays, making device suitable for high-speed applications.
• The split output configuration enables easy and independent adjustment of rise and fall times using only two resistors and eliminating the need for an external diode.

 

Pin Configuration:

                                                                                                                            
                                                                                                                                   Figure 11- DBV package 6-pin Gate driver

Pin Function:

1. V_DD: This is the power supply voltage input pin for the device. The voltage range for V_DD is between 4.5V and 18V.
2. IN+: Non-Inverting Input
3. IN-: Inverting Input
4. OUTH: Sourcing current output of driver. Connect a resistor between the OUTH pin and the gate of the power switching device to adjust turn on speed.
5. OUTL: Sinking current output of driver. Connect a resistor between the OUTL pin and the gate of the power switching device to adjust turn off speed.
6. GND: Ground.

Typical Application Diagrams:

Figure 12- Gate driver schematic for non-inverting Input

Figure 13- Gate driver schematic for inverting Input

Closed-loop Boost Converter Analysis using PI Controller:

In order to get the stability of a Boost converter or any type of system, it’s always good to do transient and steady-state analysis, this will tell you the overall behaviour of a system. Although there are various type of close loop techniques available in the real world, but the basic structure is common in all of the close loop technique that is;

Figure 14- Block diagram of Closed-loop System

Procedure:

Step-01: Find the Transfer function(Gv(s)) of the Boost Converter;

Figure 15- Conventional Boost Converter

 

ON-MODE ;

Figure 16- Boost Converter during 'ON' Mode

State variable ,

From Inductor,

Form Capacitor,

  

OFF-MODE ;

Figure 17- Boost Converter during 'OFF' Mode

From Inductor,

From Capacitor,

State-space Equation during ON-Mode;

State-space Equation during OFF-Mode;

 Averaging of State Space Model:

So, above we get two State Space equation from ‘ON’ and ‘OFF’ mode of operation of a Boost converter, which represents the Large Signal Model of the boost converter.
We need to combine both large signal Model into one, for this we use Averaging method as;

Where,

So, for the boost converter, Average signal model Equations are,

We analyze that,

Similarly,

For small signal Analysis, following assumptions are made;

So,

We know that, in steady state,

So, we simplified equation (4) & split the steady state part from the small signal part;

So, from the Small signal Model we obtained transfer function of plant/converter, hence,

So, from the Small signal Model we obtained transfer function of plant/converter, hence,

 Similarly,

Step-02: After finding Transfer function we have to find PI Controller Transfer function as;

Step-03: Now, we have to find controller Gain parameters(). In order to find that, we here, using MATLAB Autotune option which is belong under the window of PID controller block.

Hence we know all the parameters values such as;

Vc = Vout = 400; IL = 20A; R = 40Ω; L = 200μH; C = 3μF;

D = (0.5 + 0.25)/2 = 0.375

Figure 18- Testing, Response of a signal through step signal

Figure 19- System Response after testing

Step-04: The output of a PID controller given to the PWM DC-DC Generator block which generate required PWM pulses for given duty ratio. And this PWM is given to Gate driver and Gate driver output is produce gate pulses for the Gate terminal of the MOSFET.

Schematic of closed loop Non-Isolated Boost Converter:

 Used Blocks and Parameters value:

• MOSFET:

• Diode:

• Inductor:

• Capacitor:

• Load Resistance:

• PID Controller:

• PWM Generator (DC-DC):

• Input Voltage:

Simulation Result:

We run this Simulation for 10ms and we got the desire result as following:

Case-01:

For Vin = 200V,

Zoom-OUT:

Zoom-IN:

Output Voltage and Output Current:

• In this topology, we clearly see that the output voltage waveform during transient have not any peak overshoot. It catches the steady state smoothely.

• In steady state, the output voltage is approximately 400V, and ripples are also less than 10%.

• Since the load here is resistive therefore, the output current waveform nature is same as the output voltage waveform and the observed average output current is around 10A, which is similar as we calculated above in theory part.

Inductor Voltage and Inductor Current:

• At steady state, the average inductor current is approximately equal to the average input current that is 20A.
• 
  
  
• Inductor ripple current is approximate 39% which is less than the 40% of the ripple.

• In the below plot we seen that the inductor voltage is 200V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -217.2V. But in theoretically during turn ON voltage came 200V and turn OFF voltage came out to -200V.

MOSFET Voltage and MOSFET Current:

• In theoretically, MOSFET peak current came out to 24A, but due to presence of non-ideality in this converter we see that in above plot the peak MOSFET current is around 24.7A.

• In the above plot of MOSFET voltage, we clearly see that the peak MOSFET voltage is 417.2V and in theory voltage came out to 400V.
• So we observe that our choosen MOSFET and their ratings are appropriate for this topology.

Diode Voltage and Diode Current:

• In the below plot we observe that the Diode and MOSFET wave shape are similar in nature except MOSFET operates, during Turn ON and Diode Operates during Turn OFF.
• Diode peak current is same as MOSFET peak Current which is around 23.9A.

• In the below plot of Diode voltage is similar to plot of MOSFET voltage with same magnitude but opposite in nature.

• Diode peak inverse voltage is around 416.3V.

Capacitor Current and Capacitor Voltage:

• In the below plot of capacitor current we observe that the peak current is less than 15A and wave shape is trapezoidal in nature that shows the charging and discharging of charge during each cycle.
• 
  
  

• Capacitor voltage plot is similar to the plot of output voltage as discussed above because load resistance and capacitor are connected parallel to each other.

PWM and Duty Ratio:

• PWM is generated by PWM Generator(DC-DC) block where input of this block is controlled duty cycle, produced by the PI controller block.
• In the below plot we see that PWM is generated with a switching frequency of 50KHz in the range of (0-1)V.

• In the below plot of Duty Ratio(D), we observe that for the input voltage of 200V the average duty ratio is approximately equal to 0.5025, which is approximately same as when we find duty ratio theoretically.

Case-02:

For Vin = 300V,

Zoom-OUT:

Zoom-IN:

Output Voltage and Output Current:

• In this case, we clearly see that the output voltage waveform during transient have maximum peak overshoot of voltage 541.1V. After some oscilation output voltage waveform approaches steady state voltage that is 400V.
• In the above plot we also see that during transient the output current peak value is approximately 13.5A

• In steady state, the output voltage is approximately 398.2V, and ripples are also less than 10%.

• Since the load here is resistive therefore, the output current waveform nature is same as the output voltage waveform and the observed average output current is around 9.95A, which is similar as we calculated above in theory part.

Inductor Voltage and Inductor Current:

• At steady state, the average inductor current is approximately equal to the average input current that is 20A.
• 
  
  
• Inductor ripple current is approximate 44% which is due to non-idealities of the switches.

• In the below plot we seen that the inductor voltage is 300V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -107.8V. But in theoretically during turn ON voltage came 300V and turn OFF voltage came out to -100V.

MOSFET Voltage and MOSFET Current:

• In theoretically, MOSFET peak current is equivalent to inductor peak current but due to presence of non-ideality in this converter we see that in above plot the peak MOSFET current is around 17.1A but in case of inductor peak current, it comes around 16.5V

• In the above plot of MOSFET voltage, we clearly see that the peak MOSFET voltage is 407.9V and in theory voltage came out to 400V.
• So we observe that our choosen MOSFET and their ratings are appropriate for this topology.

Diode Voltage and Diode Current:

• In the below plot we observe that the Diode and MOSFET wave shape are similar in nature except MOSFET operates, during Turn ON and Diode Operates during Turn OFF.
• Diode peak current is same as Inductor peak Current which is around 16.3A.

• In the below plot of Diode voltage is similar to plot of MOSFET voltage with same magnitude but opposite in nature.

• Diode peak inverse voltage is around 407V.

Capacitor Current and Capacitor Voltage:

• In the below plot of capacitor current we observe that the peak current is less than 15A and wave shape is trapezoidal in nature that shows the charging and discharging of charge during each cycle.
• 
  
  

• Capacitor voltage plot is similar to the plot of output voltage as discussed above because load resistance and capacitor are connected parallel to each other.

PWM and Duty Ratio:

• PWM is generated by PWM Generator(DC-DC) block where input of this block is controlled duty cycle, produced by the PI controller block.
• In the below plot we see that PWM is generated with a switching frequency of 50KHz in the range of (0-1)V.

• In the below plot of Duty Ratio(D), we observe that for the input voltage of 200V the average duty ratio is approximately equal to 0.2527, which is approximately same as when we find duty ratio theoretically.

Conclusion:

From this topology (Boost CCM), we understand deeply how a closed loop Boost Converter in current continuous mode operates, how to design various components like Inductor, Capacitor Diode and MOSFET and their selection from the practical world. We also create the simulation model of this closed loop converter and observe various plots of it. All theoretical and practical results are approximately matching to each other, hence the analysis of the closed loop Boost Converter in CCM is completed.

Topology-03:

SEPIC(Single-Ended Primary-Inductor Converter) Converter in CCM:

• SEPIC converter is a type of DC-DC power converter that is used to either step up or step down the DC voltage. It is widely used because it has a power to overcome the limitations of a conventional Buck-Boost converter like reverse output voltage, discontinuity at input and output current and high voltage stress on an active elements.
• In this converter, one Inductor is place at the input side and the other inductor is place at the mid of the converter in such a way so that both the inductor contributed current in the diode whose position is actually responsible for the no change in polarity of the output voltage. We can see in the following figure-1;

Figure 1- Conventional SEPIC Converter

• Output Capacitor is used for to reduce the ripple in output voltage and make it constant at steady-state.
• Diode is used to freewheel the energy of converter Inductor when the switch is OFF.

Working Principle:

Since, a SEPIC converter contain non-linear devices such as one Switch and one uncontrolled Diode, hence the circuit operates in two mode as given below;

ON-Mode of Operation:

• ON mode means the Switch is “ON” and the Diode is “OFF”. When we apply this the change in circuit as following;

Figure 2- SEPIC Converter when Switch is 'ON'

• During “ON” mode, DC voltage source deliver the energy to the inductor L1 and inductor is linearly charged till the switch is in “ON” condition and the intermediate capacitance C1 discharges their energy linearly through inductor L2.
• The output capacitance C2 discharges their energy to load during “ON” mode of operation.

OFF-Mode of Operation:

• OFF mode means the Switch is “OFF” and the Diode is “ON”. When we apply this the change in circuit as following;

Figure 3- SEPIC Converter when Switch is 'OFF'

• During “OFF” mode, freewheeling diode is activated and both Inductor discharge energy through this path where this freewheeling diode is present.
• Thus, we see that Converter inductor is charged during “ON” and discharge during “OFF” condition, so we observe that the waveform of the Inductor current is periodic, and we know very well that “If we passing periodic current through the Inductor than, the average Voltage across the Inductor should be zero”

Specs of SEPIC Converter in CCM:

Given,

Vin = (300-600)V,

Vout = 450V,

Power = 6KW,

Let, fs = 500KHz,

So, the output load Resistance come out to be as,

Where,

  

Designing of SEPIC converter in CCM:

Case 01: SEPIC as a Boost Converter.

Vin = 300V; Vout = 450V

Duty Ratio:

We know that voltage converter ratio for a Conventional SEPIC Converter,

Designing Of Inductor:

In Continuous Conduction Mode(CCM),

For Inductor current to be continuous, in worst case scenario,

 

Figure 4- Figure 7. Voltages and current of each component of the SEPIC in CCM.

From waveform we see that,

 

 

Assume 10% ripple, then Inductor is,

Maximum possible average current in inductor,

We observe that in case of SEPIC Converter,

To design an Inductor for a specific % of current ripple we use this formula;

But we take 10% higher the value of inductors because of safety reasons and we get the suitable value for both the inductor that is,

Where,

Designing of Capacitors:

Intermediate Capacitor(C1):

From the KVL we observe that,

And we know that the average voltage of inductor is zero.

So,

Assume that we want output voltage ripple is less than 10%;

Thus;

We know the Intermediate Capacitor formula,

Output Capacitor(C2):

We know the output Capacitor formula,

But we take 10% higher the value of output capacitor because of safety reasons and we get the suitable value for both the capacitor that is,

Where,

 

Case 02: SEPIC as a Buck Converter.

Vin = 600V; Vout = 450V

Duty Ratio:

We know that voltage converter ratio for a Conventional SEPIC Converter,

Designing Of Inductor:

In Continuous Conduction Mode(CCM),

Assume 10% ripple, then Inductor is,

Maximum possible average current in inductor,

We observe that in case of SEPIC Converter,

To design an Inductor for a specific % of current ripple we use this formula;

But we take 10% higher the value of inductors because of safety reasons and we get the suitable value for both the inductor that is,

Where,

Designing of Capacitors:

Intermediate Capacitor(C1):

From the KVL we observe that,

And we know that the average voltage of inductor is zero.

So,

Assume that we want output voltage ripple is less than 10%;

Thus;

We know the Intermediate Capacitor formula,

Output Capacitor(C2):

We know the output Capacitor formula,

But we take 10% higher the value of output capacitor because of safety reasons and we get the suitable value for both the capacitor that is,

Where,

From above two cases, we select the inductors and capacitor whose value is higher and we observe that case-02 parameters are suitable for this topology.

Selection of Inductor:

• For selection of an Inductor we are using a quite popular website named “Mouser” one can choose Coilcraft, Digikey and Magnetics as well.

Figure 5- Mouser website for selection of Inductors L1, L2

• Go to site and fill the details of this topology and it gives you a suitable list of Inductors based on the ripple % and switching frequency, you can play with the filters to get your desire inductor.
• We clearly see that we select inductor of 560uH and 420uH. So we choose these inductors for this topology.

Figure 6- Specs of Inductor L1 for SEPIC converter

Figure 7- Specs of Inductor L2 for SEPIC converter

• Selected Inductor is L1=560μH & L2=420μH for this topology.

 

Selection of Capacitor:

• For Capacitor selection we using website name “Digikey”. It’s quite popular worldwide.
• It has a simple GUI with lots of filter to choose a suitable electronic components according to the specification.
• We here looking for the ≥0.191μF intermediate capacitor C1 with less ESR(Equivalent series Resistance) and ESL(Equivalent series Inductance) with >600V rated voltage capability.
• We here also looking for the 3μF output capacitor C2 with less ESR(Equivalent series Resistance) and ESL(Equivalent series Inductance) with >450V rated voltage capability.

Figure 8- Selection of Intermediate Capacitor C1&C2 through ‘Digikey’

• We get the ceramic based surface mount intermediate capacitance of value 0.2μF and withstand voltage capacity of 630V, which is definitely a right choice for this topology.
• We also get the output capacitance of 3.9µF ±10P0V Ceramic Capacitor.
• Selected intermediate Capacitor is C1=0.2μF & output capacitor C2=3.9µF for this topology.

Designing of MOSFET:

First we focus on the suitable selection of MOSFET, one can chose IGBT as well.

We required,

Blocking Voltage:

According to given topology specs, during turn “OFF”, the MOSFET maximum blocking voltage comes out to be 1050V, but for the safety reason we choose the MOSFET whose value is 20% higher than the maximum blocking voltage, so we have;

From this we observe that the drain to source voltage of MOSFET should be as,

Peak current in MOSFET:

• According to the circuit of the SEPIC Converter, we can easily find the MOSFET peak current that could flow during “ON” condition.
• In this case we observe that the peak current of converter inductor L1 and the peak current of intermediate capacitance C1 would be same as the peak current of the MOSFET, that is;

Where,

Peak current of Converter inductor L1 is maximum when input voltage is 300V, so the MOSFET peak current should must be >22A

Selection of MOSFET:

After getting some essential data for the MOSFET, we looking for the searching of MOSFET and we choose the website “Infineon”, one can choose “Mouser” or “Digikey” as well,

Suitable MOSFET that we chosen as

Figure 9- 950 V CoolMOS™ PFD7 superjunction MOSFET in TO-220-3 package

Features of MOSFET IPWS65R075CFD7A:

• Optimized for higher battery voltages upto 475V thanks to further improved robustness.
• Lower switching losses enabling higher switching frequencies.
• High quality and reliability
• Increase defficiency in light load and full load conditions.

From datasheet of IPWS65R075CFD7A MOSFET, some the following parameters are observed:

  

Table 1: Key Performance Parameters

From the above table V_GS, R_G, C_iss, C_oss and C_rss and some other parameters are help to find the suitable Gate Driver for this topology.

Designing of Gate Driver:

Gate driver designing is totally based on the selection of MOSFET, we already select the MOSFET ‘BSF450NE7NH3 G’. Before choosing the Gate driver first we see some interesting features of an ideal Gate Driver:

Ideal Gate Driver features:

• It should have a capability of Level shifting.
• Meet the voltage and current requirements of the gate emitter/source region.
• It should have a capability to deal with floating supply.
• High Input Impedance.
• High CMTI(Common-Mode Transient Immunity).

Gate drivers are broadly classified in two types:

• Non- Isolated Gate Driver.
• Isolated Gate Driver

We always prefer an isolated gate driver over non-isolated gate driver if there is no economic constrain. Because isolated gate driver has a capability to isolate the converter from the microcontroller and it has a long life cycle as compare to non-isolated gate driver.

Selection of Gate Driver:

Gate driver choice is depends on the parameters of MOSFET like Input capacitance, output capacitance, reverse transfer capacitance , gate to source threshold voltage, gate resistance, delay time, rise time and net charge etc. These parameters are already given in the datasheet of the MOSFET as discussed above.

For making Boost converter or step-up converter we select single-channel high-speed low-side Gate Driver that is UCC27511A.

Figure 10- Gate Driver UCC27511A

Reasons for choosing Gate Driver UCC27511A:

From the datasheet of this gate driver we analyse the following below points;

• According to given topology, we required a power supply to activate this IC and we choose 15V power supply, one can use the Bootstrap method to given the power supply from the existing power supply.
• Other parameters are given in the datasheet of this driver;

Figure 11- Specs of Gate Driver

• UCC27511A device is an automotive-grade single-channel low-side, high-speed gate driver rated for MOSFETs, IGBTs, and emerging wide-bandgap power devices such as GaN.
• The device features fast Glitch-Free Operation at Power Up and Power rise times, fall times, and propagation delays, making device suitable for high-speed applications.
• The split output configuration enables easy and independent adjustment of rise and fall times using only two resistors and eliminating the need for an external diode.

Pin Configuration:

Figure 12- DBV 6 pin Gate Driver

 

Pin Function:

1. V_DD: This is the power supply voltage input pin for the device. The voltage range for V_DD is between 4.5V and 18V.
2. IN+: Non-Inverting Input
3. IN-: Inverting Input
4. OUTH: Sourcing current output of driver. Connect a resistor between the OUTH pin and the gate of the power switching device to adjust turn on speed.
5. OUTL: Sinking current output of driver. Connect a resistor between the OUTL pin and the gate of the power switching device to adjust turn off speed.
6. GND: Ground.

Typical Application Diagrams:

Figure 13- Gate driver schematic for non-inverting Input

Figure 14- Gate driver schematic for inverting Input

Closed-loop Boost Converter Analysis using PI Controller:

In order to get the stability of a Boost converter or any type of system, it’s always good to do transient and steady-state analysis, this will tell you the overall behaviour of a system. Although there are various type of close loop techniques available in the real world, but the basic structure is common in all of the close loop technique that is;

Figure 15- Block diagram based PI Controller of a Closed-loop System

Procedure:

Step-01: Find the Transfer function(Gv(s)) of an Ideal SEPIC Converter;

Figure 16- Ideal SEPIC Converter

ON-MODE ;

Figure 17- SEPIC Converter when Switch is 'ON'

State variable;

By Equation (1), (2), (3) & (4);

State-space Equation during ON-Mode;

OFF-MODE ;

Figure 18- SEPIC Converter when Switch is 'OFF'

By Equation (5), (6), (7) & (8);

 State-space Equation during OFF-Mode;

Averaging of State Space Model:

So, above we get two State Space equation from ‘ON’ and ‘OFF’ mode of operation of a Boost converter, which represents the Large Signal Model of the boost converter.
We need to combine both large signal Model into one, for this we use Averaging method as;

Where,

So, for the boost converter, Average signal model Equations are,

We analyse that,

So, for Averaging,

Similarly,

Now, Average Signal Model of an Ideal SEPIC Converter is;

 For small signal Analysis, following assumptions are made;

So,

We know that, in steady state,

So, we simplified above equations & split the steady state part from the small signal part and put steady state part equal to zero;

So, from the Small signal Model we obtained transfer function of plant/converter, hence,

Similarly.

Where,

We already calculated all the parameters, so we have;

L1 = 560μH, L2 = 420μH

C1 = 0.2μF, C2 = 3.9μF

Vc1 = Vin = 600V, Vc2 = Vout = 450V

IL1 = Iin = 10A, IL2 = Iout = 13.33A

R = 33.75 Ω, D = 0.429

So,

Now, final output to duty ratio transfer function as;

Step-02: After finding Transfer function Gd(s), we have to find PI Controller Transfer function as;

ve ek Current which is around 20
Step-03: Now, we have to find controller Gain parameters(). In order to find that, we here, using MATLAB Autotune option which is belong under the window of PID controller block.

Figure 19- Testing Response of an ideal SEPIC converter through Step Input

Figure 20- Step Reference Tracking through PID Tuner App

Step-04: The output of a PID controller given to the PWM DC-DC Generator block which generate required PWM pulses for given duty ratio. And this PWM is given to Gate driver and Gate driver output is produce gate pulses for the Gate terminal of the MOSFET.

Table 2: Ideal SEPIC Converter Parameters

Schematic of closed loop Non-Isolated Buck Converter:

 Used Blocks and Parameters value:

• MOSFET:

• Diode:

• Inductor:

• Capacitor:

• Load Resistance:

• PID Controller:

• PWM Generator (DC-DC):

• Input Voltage:

Simulation Result:

We run this Simulation for 10ms and we got the desire result as following:

Case-01:

For Vin = 300V,

Zoom-OUT:

Zoom-IN:

Output Voltage and Output Current:

• In the above output voltage waveform of a SEPIC converter we clearly see that during transient oscilations are smooth and the maximum peak overshoot is always be less than steady state value.

• In steady state, the output voltage is approximately 450V, and ripples are also less than 10%, which indicates that the converter design is suitable for this topology.

• In the above plot of output current, we observe that the average output current is around 13.33A, which is similar as we calculated above in theory part. Since the load here is resistive therefore, the output current waveform nature is same as the output voltage waveform. In steady state,
• 
  
  

Inductor Voltage(VL1) and Inductor Current(IL1):

• At steady state, the average inductor current IL1 is approximately equal to the average input current that is 20A.
• 
  
  
  
• Inductor ripple current is approximate 3.06% which is less than the 10% of the ripple.

• In the below plot we seen that the inductor voltage VL1 is 300V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -493.6V. But in theoretically during turn ON voltage came 300V and turn OFF voltage came out to –Vout, that is -450V.
• We clearly see that in this plot during turn ‘OFF’ the average inductor voltage of VL1 is approximately -450V.

Inductor Voltage(VL2) and Inductor Current(IL2):

• At steady state, the average inductor current IL2 is approximately equal to the average output current that is 13.33A.
• 
  
  
  
• Inductor ripple current is approximate 6.4% which is less than the 10% of the ripple.

• In the below plot we seen that the average inductor voltage VL2 is around 299.7V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -449.85.V. But in theoretically during turn ON voltage came 300V and turn OFF voltage came out to –Vout, that is -450V.

MOSFET Voltage and MOSFET Current:

• In theoretically, MOSFET average current came out to 33.33A, but due to presence of non-ideality in this converter we see that in above plot the average MOSFET current is around 34.75A.

• In the above plot of MOSFET voltage, we clearly see that the average MOSFET voltage is 750.2V and in theoretically voltage came out to 750V, that is;

Diode Voltage and Diode Current:

• In the below plot we observe that the Diode and MOSFET wave shape are similar in nature except MOSFET operates, during Turn ON and Diode Operates during Turn OFF.
• Diode average current is close as MOSFET average current which is around 33.2A.

• In the below plot of Diode voltage is similar to plot of MOSFET voltage with same magnitude but opposite in nature.

• Diode peak inverse voltage is around 793.0V.

Intermediate Capacitor Current(Ic1) and Capacitor Voltage(Vc1):

• In the below plot of intermediate capacitor current we observe that the peak current is 21.2A and wave shape is trapezoidal in nature that shows the charging and discharging of charge during each cycle.
• During turn ‘OFF’,
• 
  
  
• During turn ‘ON’,
• 
  
  
• But in theoretically we see that the Intermediate capacitor current during turn ‘ON’ is 13.33A and during turn ‘OFF’ is 20A

• In the below plot, during transient, intermediate capacitor voltage Vc1, have some underdamped oscilation and the maximum peak overshoot is around 659.9V.

• In the below plot, during steady state, average intermediate capacitor voltage is around 300.25V which is very close to the theoretical average intermediate capacitor voltage value that is 300V.

• From the plot,
• 
  
  

 

Output Capacitor Current(Ic2) and Output Capacitor Voltage(Vc2):

• In the below plot of output capacitor current we observe that the peak current is 21.6A and wave shape is trapezoidal in nature that shows the charging and discharging of charge during each cycle.
• During turn ‘OFF’,
• 
  
  
• During turn ‘ON’,
• 
  
  
• But in theoretically we see that the output capacitor current during turn ‘ON’ is 13.33A and during turn ‘OFF’ is 20A

• Capacitor voltage plot is similar to the plot of output voltage as discussed above because load resistance and capacitor are connected parallel to each other.

PWM and Duty Ratio:

• PWM is generated by PWM Generator(DC-DC) block where input of this block is controlled duty cycle, produced by the PI controller block.
• In the below plot we see that PWM is generated with a switching frequency of 500KHz in the range of (0-1)V.

• In the below plot of Duty Ratio(D), we observe that for the input voltage of 300V the average duty ratio is approximately equal to 0.59835, which is similar when we find duty ratio theoretically that is 0.6.

Case-02:

For Vin = 600V,

Zoom-OUT:

Zoom-IN:

Output Voltage and Output Current:

• In the above output voltage waveform of a SEPIC converter we clearly see that during transient oscilations are smooth and the maximum peak overshoot is always be less than steady state value.

• In steady state, the output voltage is approximately 450V, and ripples are also less than 10%, which indicates that the converter design is suitable for this topology.

• In the above plot of output current, we observe that the average output current is around 13.33A, which is similar as we calculated above in theory part. Since the load here is resistive therefore, the output current waveform nature is same as the output voltage waveform. In steady state,
• 
  
  

Inductor Voltage(VL1) and Inductor Current(IL1):

• At steady state, the average inductor current IL1 is approximately equal to the average input current that is 20A.
• 
  
  
  
• Inductor ripple current is approximate 8.36% which is less than the 10% of the ripple.

• In the below plot we seen that the inductor voltage VL1 is 600V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -449.65V. But in theoretically during turn ON voltage came 600V and turn OFF voltage came out to –Vout, that is -450V.
• We clearly see that in this plot during turn ‘OFF’ the average inductor voltage of VL1 is approximately -450V.

Inductor Voltage(VL2) and Inductor Current(IL2):

• At steady state, the average inductor current IL2 is approximately equal to the average output current that is 13.33A.
• 
  
  
  
• Inductor ripple current is approximate 9.2% which is less than the 10% of the ripple.

• In the below plot we seen that the average inductor voltage VL2 is around 599.65V when, MOSFET is “ON” and Diode is “OFF” and when MOSFET is “OFF” and Diode is “ON”, inductor voltage is -450V. But in theoretically during turn ON voltage came 600V and turn OFF voltage came out to –Vout, that is -450V.

MOSFET Voltage and MOSFET Current:

• In theoretically, MOSFET average current came out to 23.33A, but due to presence of non-ideality in this converter we see that in above plot the average MOSFET current is around 25.4A.

• In the above plot of MOSFET voltage, we clearly see that the average MOSFET voltage is 1049.65V and in theoretically voltage came out to 1050V, that is;

 

Diode Voltage and Diode Current:

• In the below plot we observe that the Diode and MOSFET wave shape are similar in nature except MOSFET operates, during Turn ON and Diode Operates during Turn OFF.
• Diode average current is close as MOSFET average current which is around 23.3A.

• In the below plot of Diode voltage is similar to plot of MOSFET voltage with same magnitude but opposite in nature.

• Diode peak inverse voltage is around 1082.3V.

Intermediate Capacitor Current(Ic1) and Capacitor Voltage(Vc1):

• In the below plot of intermediate capacitor current we observe that the peak current is 21.2A and wave shape is trapezoidal in nature that shows the charging and discharging of charge during each cycle.
• During turn ‘OFF’,
• 
  
  
• During turn ‘ON’,
• 
  
  
• But in theoretically we see that the Intermediate capacitor current during turn ‘ON’ is 13.33A and during turn ‘OFF’ is 10A

• In the below plot, during transient, intermediate capacitor voltage Vc1, have some underdamped oscilation and the maximum peak overshoot is around 1320.0V.

• In the below plot, during steady state, average intermediate capacitor voltage is around 599.65V which is very close to the theoretical average intermediate capacitor voltage value that is 600V.

• From the plot,
• 
  
  

 

Output Capacitor Current(Ic2) and Output Capacitor Voltage(Vc2):

• In the below plot of output capacitor current we observe that the peak current is 21.6A and wave shape is trapezoidal in nature that shows the charging and discharging of charge during each cycle.
• During turn ‘OFF’,
• 
  
  
• During turn ‘ON’,
• 
  
  
• But in theoretically we see that the output capacitor current during turn ‘ON’ is -13.33A and during turn ‘OFF’ is 10A

• Capacitor voltage plot is similar to the plot of output voltage as discussed above because load resistance and capacitor are connected parallel to each other.

PWM and Duty Ratio:

• PWM is generated by PWM Generator(DC-DC) block where input of this block is controlled duty cycle, produced by the PI controller block.
• In the below plot we see that PWM is generated with a switching frequency of 500KHz in the range of (0-1)V.

• In the below plot of Duty Ratio(D), we observe that for the input voltage of 600V the average duty ratio is approximately equal to 0.42746, which is similar when we find duty ratio theoretically that is 0.429.

Conclusion:

From this topology (SEPIC CCM), we understand deeply how a closed loop Boost Converter in Continuous Current Mode(CCM) operates, how to design various components like Inductor, Capacitor, Diode and MOSFET and their selection from the practical world. We also create the simulation model of this closed loop converter and observe various plots of it. All theoretical and practical results are approximately matching to each other, hence the analysis of the closed loop SEPIC Converter in CCM is completed.