DC-DC converters are circuits that convert a DC voltage to another DC voltage level. They use switching elements like transistors and power switches to efficiently step up or step down voltage. The buck converter is a common DC-DC converter topology that can step down voltage. It uses a switch, inductor, diode, and capacitor. By periodically opening and closing the switch, the inductor filters the output to produce a lower average voltage. The output voltage of an ideal buck converter is equal to the input voltage multiplied by the duty cycle of the switch. Real converters have non-ideal components that cause additional voltage ripple. Proper component selection and design considerations are needed to minimize ripple.
These slides provide an elementary description of Power Electronics and its application domains. It also shows the different power devices and converters.
These slides provide an elementary description of Power Electronics and its application domains. It also shows the different power devices and converters.
This presentation describes the per-phase equivalent circuit of induction motor - Power flow diagram - Ratio of air gap power, rotor copper loss and mechanical power developed.
This directional over current relay employs the principle of actuation of the relay....It has a metallic disc free to rotate between the poles of two...
Automatic generation control (AGC) is a system for adjusting the power output of multiple generators at different power plants, in response to changes in the load. Since a power grid requires that generation and load closely balance moment by moment, frequent adjustments to the output of generators are necessary. The balance can be judged by measuring the system frequency; if it is increasing, more power is being generated than used, which causes all the machines in the system to accelerate. If the system frequency is decreasing, more load is on the system than the instantaneous generation can provide, which causes all generators to slow down.
Introduction to reactive power control in electrical powerDr.Raja R
Introduction to reactive power control in electrical power
Reactive power in transmission line :
Reactive power control
Reactive power and its importance
Apparent Power
Reactive Power
Apparent Power
Reactive Power Formula
INTRODUCTION
A chopper is a static device which is used to obtain a variable dc voltage from a
constant dc voltage source. A chopper is also known as dc-to-dc converter. The thyristor converter offers greater efficiency, faster response, lower maintenance, smaller size and smooth control. Choppers are widely used in trolley cars, battery operated vehicles, traction motor control, control of large number of dc motors, etc….. They are also used in regenerative braking of dc motors to return energy back to supply and also as dc voltage regulators.
Choppers are of two types
• Step-down choppers
• Step-up choppers.
In step-down choppers, the output voltage will be less than the input voltage
whereas in step-up choppers output voltage will be more than the input voltage.
Classification of Choppers:
(a) Depending upon the direction of the output current and voltage, the converters can be classified into five classes namely Class A [One-quadrant Operation] Class B [One-quadrant Operation] Class C [Two-quadrant Operation] Class D [Two-quadrant Operation] Class E [Four-quadrant Operation]
(b) Based on the output voltage of the output, the choppers are classified as
(i) Step-Down Chopper In this case the average output voltage is less than the input voltage. It is also known as step down converter
(ii) Step-Up Chopper Here the average output voltage is more than the input voltage. It is also known as step up converter
(iii) Step-Up/Down Chopper This type of converter produces an output voltage that is either lower or higher than the input voltage
(c) Depending upon the power loss occurred during turn ON/OFF of the switching device, the choppers are classified into two categories namely
(i) Hard switched Converter Here the power loss is high during the switching (ON to OFF and OFF to ON) as a result of the non zero voltage and current on the power switches.
(ii) Soft switched or resonant converters In this type of choppers, the power loss is low at the time of switching as a result of zero voltage and/or zero current on the switches.
2
PRINCIPLE OF STEP-DOWN CHOPPER
Figure 2.1 shows a step-down chopper with resistive load. The thyristor in the
circuit acts as a switch. When thyristor is ON, supply voltage appears across the load and
when thyristor is OFF, the voltage across the load will be zero. The output voltage and
current waveforms are as shown in figure 2.2.
Inverter is a device which convert a DC input supply voltage into symmetric AC voltage of desired magnitude and frequency at the output side. It is also know as DC-AC converter.
Ideal and practical inverter have sinusoidal and no-sinusoidal waveforms at output respectively.
If the input dc is a voltage source, the inverter is called a Voltage Source Inverter (VSI). One can similarly think of a Current Source Inverter (CSI), where the input to the circuit is a current source. The VSI circuit has direct control over ‘output (ac) voltage’ whereas the CSI directly controls ‘output (ac) current.
Inverter is a device which convert a DC input supply voltage into symmetric AC voltage of desired magnitude and frequency at the output side. It is also know as DC-AC converter.
Ideal and practical inverter have sinusoidal and no-sinusoidal waveforms at output respectively.
If the input dc is a voltage source, the inverter is called a Voltage Source Inverter (VSI). One can similarly think of a Current Source Inverter (CSI), where the input to the circuit is a current source. The VSI circuit has direct control over ‘output (ac) voltage’ whereas the CSI directly controls ‘output (ac) current.
It’s a power electronics project. It is able to give output voltage(DC) more and less than input voltage as per requirement.
We can generate variable DC voltage which is less than input, but, the special things about this converter is, it has capability to produce variable DC voltage as high as twice the input voltage.
We have specially designed and manufactured inductor for this project.
This presentation describes the per-phase equivalent circuit of induction motor - Power flow diagram - Ratio of air gap power, rotor copper loss and mechanical power developed.
This directional over current relay employs the principle of actuation of the relay....It has a metallic disc free to rotate between the poles of two...
Automatic generation control (AGC) is a system for adjusting the power output of multiple generators at different power plants, in response to changes in the load. Since a power grid requires that generation and load closely balance moment by moment, frequent adjustments to the output of generators are necessary. The balance can be judged by measuring the system frequency; if it is increasing, more power is being generated than used, which causes all the machines in the system to accelerate. If the system frequency is decreasing, more load is on the system than the instantaneous generation can provide, which causes all generators to slow down.
Introduction to reactive power control in electrical powerDr.Raja R
Introduction to reactive power control in electrical power
Reactive power in transmission line :
Reactive power control
Reactive power and its importance
Apparent Power
Reactive Power
Apparent Power
Reactive Power Formula
INTRODUCTION
A chopper is a static device which is used to obtain a variable dc voltage from a
constant dc voltage source. A chopper is also known as dc-to-dc converter. The thyristor converter offers greater efficiency, faster response, lower maintenance, smaller size and smooth control. Choppers are widely used in trolley cars, battery operated vehicles, traction motor control, control of large number of dc motors, etc….. They are also used in regenerative braking of dc motors to return energy back to supply and also as dc voltage regulators.
Choppers are of two types
• Step-down choppers
• Step-up choppers.
In step-down choppers, the output voltage will be less than the input voltage
whereas in step-up choppers output voltage will be more than the input voltage.
Classification of Choppers:
(a) Depending upon the direction of the output current and voltage, the converters can be classified into five classes namely Class A [One-quadrant Operation] Class B [One-quadrant Operation] Class C [Two-quadrant Operation] Class D [Two-quadrant Operation] Class E [Four-quadrant Operation]
(b) Based on the output voltage of the output, the choppers are classified as
(i) Step-Down Chopper In this case the average output voltage is less than the input voltage. It is also known as step down converter
(ii) Step-Up Chopper Here the average output voltage is more than the input voltage. It is also known as step up converter
(iii) Step-Up/Down Chopper This type of converter produces an output voltage that is either lower or higher than the input voltage
(c) Depending upon the power loss occurred during turn ON/OFF of the switching device, the choppers are classified into two categories namely
(i) Hard switched Converter Here the power loss is high during the switching (ON to OFF and OFF to ON) as a result of the non zero voltage and current on the power switches.
(ii) Soft switched or resonant converters In this type of choppers, the power loss is low at the time of switching as a result of zero voltage and/or zero current on the switches.
2
PRINCIPLE OF STEP-DOWN CHOPPER
Figure 2.1 shows a step-down chopper with resistive load. The thyristor in the
circuit acts as a switch. When thyristor is ON, supply voltage appears across the load and
when thyristor is OFF, the voltage across the load will be zero. The output voltage and
current waveforms are as shown in figure 2.2.
Inverter is a device which convert a DC input supply voltage into symmetric AC voltage of desired magnitude and frequency at the output side. It is also know as DC-AC converter.
Ideal and practical inverter have sinusoidal and no-sinusoidal waveforms at output respectively.
If the input dc is a voltage source, the inverter is called a Voltage Source Inverter (VSI). One can similarly think of a Current Source Inverter (CSI), where the input to the circuit is a current source. The VSI circuit has direct control over ‘output (ac) voltage’ whereas the CSI directly controls ‘output (ac) current.
Inverter is a device which convert a DC input supply voltage into symmetric AC voltage of desired magnitude and frequency at the output side. It is also know as DC-AC converter.
Ideal and practical inverter have sinusoidal and no-sinusoidal waveforms at output respectively.
If the input dc is a voltage source, the inverter is called a Voltage Source Inverter (VSI). One can similarly think of a Current Source Inverter (CSI), where the input to the circuit is a current source. The VSI circuit has direct control over ‘output (ac) voltage’ whereas the CSI directly controls ‘output (ac) current.
It’s a power electronics project. It is able to give output voltage(DC) more and less than input voltage as per requirement.
We can generate variable DC voltage which is less than input, but, the special things about this converter is, it has capability to produce variable DC voltage as high as twice the input voltage.
We have specially designed and manufactured inductor for this project.
A novel single switch resonant power converterSameer Kasba
This deals with the novel single-switch resonant power converter for renewable energy generation applications. This circuit topology integrates a novel single switch resonant inverter with zero-voltage-switching (ZVS) with an energyblocking diode with zero-current-switching (ZCS).
A detailed step-by-step procedure for the design of a buck converter. Different active and passive components are selected as per the requirement specified in the design problem.
Seminor on resonant and soft switching converterAnup Kumar
Soft Switching Techniques Are Highly Recommended To Reduce Switching Losses And Conduction Losses, During Each Turning On & Turning Off of Power Electronics Devices.
Evaluation reports of various DC-DC converter products that are available in Japan. DC-DC converter is used to provide a stable output DC voltage to its load such as rechargeable battery. We have tested 5 types DC-DC converter samples which can be available in amazon.co.jp. As of 2016/12.
For more information, please visit the following site.
www.wireless-square.com
Bipolar Junction Transistor (BJT) DC and AC AnalysisJess Rangcasajo
BJT AC and DC Analysis
This slide condenses the two ways analysis of BJT (AC and DC).
At the end of the slide, it has review question answer with answer key as providing.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
2. DC-DC Converters
DC-DC converters are power electronic circuits that convert a DC
voltage to a different DC voltage level, often providing a regulated
output.
A BASIC SWITCHING CONVERTER
An efficient alternative to the linear regulator
Uses Power electronics switches like BJT,MOSFET IGBT…
Also known as DC Chopper
3. DC-DC Converters
Figure: (a) A basic DC-DC switching converter; (b) Switching
equivalent; ( c) Output voltage.
Assuming the switch is ideal
• The output is the same as the
input when the switch ON
• And the output is zero when the
switch OFF
Periodic opening and closing of the
switch gives the pulsed output
waveform.
The average or DC component of the
output voltage is
𝑉𝑜 =
1
𝑇
0
𝑇
𝑣 𝑜 𝑡 𝑑𝑡 =
1
𝑇
0
𝐷𝑇
𝑉𝑠 𝑑𝑡 = 𝑉𝑠 𝐷
4. DC-DC Converters
𝐷 ≡
𝑡 𝑜𝑛
𝑡 𝑜𝑛 + 𝑡 𝑜𝑓𝑓
The DC component of the output voltage will be less than or equal to
the input voltage for this circuit.
ideal switch Zero loss Zero voltage across when ON Zero
current through it when OFF
But real switch has some power loss Considerable because it
creates heat on the switch.
5. THE BUCK (STEP-DOWN)
CONVERTERApplication Example: Controlling the speed of DC Motor
Low-pass filter will be placed at the output
• The diode provides a path for the inductor
current when the switch is opened and is
reverse-biased when the switch is closed.
6. THE BUCK (STEP-DOWN)
CONVERTERVOLTAGE AND CURRENT RELATIONSHIPS:
𝑣 𝑥 in Fig. above, is 𝑉𝑠
when the switch is closed and is zero when the
switch is open, provided that the inductor current remains positive,
keeping the diode on.
If the switch is closed periodically at a duty ratio D, the average
voltage at the filter input is 𝑉𝑠
𝐷
An inductor current that remains positive throughout the switching
period is known as continuous current.
Conversely, discontinuous current is characterized by the inductor
current’s returning to zero during each period.
7. THE BUCK (STEP-DOWN)
CONVERTERBuck converters and DC-DC converters in general, have the following properties when
operating in the steady state
1. The inductor current is periodic.
𝒊 𝑳 𝒕 + 𝑻 = 𝒊 𝑳 𝒕
2. The average inductor voltage is zero
𝑽 𝑳 =
𝟏
𝑻
𝒕
𝒕+𝑻
𝒗 𝑳 𝝀 𝒅𝝀 = 𝟎
3. The average capacitor current is zero
𝑰 𝑪 =
𝟏
𝑻
𝒕
𝒕+𝑻
𝒊 𝑪 𝝀 𝒅𝝀 = 𝟎
4. The power supplied by the source is the same as the power delivered to the load. For
non-ideal components, the source also supplies the losses.
𝑷 𝒔 = 𝑷 𝒐 𝒊𝒅𝒆𝒂𝒍
𝑷 𝒔= 𝑷 𝒐 + 𝒍𝒐𝒔𝒔𝒆𝒔 𝒏𝒐𝒏𝒊𝒅𝒆𝒂𝒍
8. THE BUCK (STEP-DOWN)
CONVERTERAssumptions for Analysis of Buck converter:
• The circuit is operating in the steady state.
• The inductor current is continuous (always positive)
• The capacitor is very large, and the output voltage is held constant
at voltage Vo. This restriction will be relaxed later to show the
effects of finite capacitance.
• The switching period is 𝑇; the switch is closed for time 𝐷𝑇 and
open for time (1 − 𝐷)𝑇.
• The components are ideal.
The key to the analysis for determining the output 𝑉𝑜 is to
examine the inductor current and inductor voltage first for
the switch closed and then for the switch open.
9. THE BUCK (STEP-DOWN)
CONVERTERANALYSIS FOR THE SWITCH CLOSED:
• The voltage across the inductor is
• 𝑣 𝐿 = 𝑉𝑆 − 𝑉𝑜 = 𝐿
𝑑𝑖 𝐿
𝑑𝑡
• Rearranging,
•
𝑑𝑖 𝐿
𝑑𝑡
=
𝑉 𝑆−𝑉𝑜
𝐿
𝑠𝑤𝑖𝑡𝑐ℎ 𝑐𝑙𝑜𝑠𝑒𝑑
•
𝑑𝑖 𝐿
𝑑𝑡
=
∆𝑖 𝐿
∆𝑡
=
∆𝑖 𝐿
𝐷𝑇
=
𝑉 𝑆−𝑉𝑜
𝐿
• ∆𝑖 𝐿 𝑐𝑙𝑜𝑠𝑒𝑑 =
𝑉 𝑆−𝑉𝑜
𝐿
𝐷𝑇
10. THE BUCK (STEP-DOWN)
CONVERTERANALYSIS FOR THE SWITCH OPEN:
• When the switch is open, the diode becomes forward-biased to carry the inductor
current
• The voltage across the inductor when the switch is open is
𝑣 𝐿 = −𝑉𝑜 = 𝐿
𝑑𝑖 𝐿
𝑑𝑡
• Rearranging,
𝑑𝑖 𝐿
𝑑𝑡
=
−𝑉𝑜
𝐿
𝑠𝑤𝑖𝑡𝑐ℎ 𝑜𝑝𝑒𝑛
• The derivative of current in the inductor is a negative constant, and the current
decreases linearly
• The change in inductor current when the switch is open is
∆𝑖 𝐿
∆𝑡
=
∆𝑖 𝐿
1−𝐷 𝑇
=
−𝑉𝑜
𝐿
∆𝑖 𝐿 𝑜𝑝𝑒𝑛 = −
𝑉𝑜
𝐿
(1 − 𝐷)𝑇
11. THE BUCK (STEP-DOWN)
CONVERTERAt steady state
∆𝑖 𝐿 𝑐𝑙𝑜𝑠𝑒𝑑 + ∆𝑖 𝐿 𝑜𝑝𝑒𝑛 = 0
𝑉 𝑆−𝑉𝑜
𝐿
𝐷𝑇 −
𝑉𝑜
𝐿
1 − 𝐷 = 0
• Solving for 𝑉𝑜,
𝑉𝑜 = 𝑉𝑠 𝐷
• Therefore, the buck converter produces an output voltage that is less than or
equal to the input.
• An alternative derivation of the output voltage is based on the inductor voltage.
• Since the average inductor voltage is zero for periodic operation
𝑉𝐿 = 𝑉𝑆 − 𝑉𝑂 𝐷𝑇 + −𝑉𝑂 1 − 𝐷 𝑇 = 0
• Solving for 𝑉𝑂
𝑉𝑂= 𝑉𝑆 𝐷.
12. THE BUCK (STEP-DOWN)
CONVERTERThe average inductor current must be the same as the average current in
the load resistor, since the average capacitor current must be zero for
steady-state operation.
𝐼𝐿 = 𝐼 𝑅 =
𝑉𝑂
𝑅
The maximum and minimum values of the inductor current are computed
as
∆𝑖 𝐿 𝑐𝑙𝑜𝑠𝑒𝑑 =
𝑉𝑆 − 𝑉𝑜
𝐿
𝐷𝑇
∆𝑖 𝐿 𝑜𝑝𝑒𝑛 = −
𝑉𝑜
𝐿
(1 − 𝐷)𝑇
𝐼 𝑚𝑎𝑥= 𝐼𝐿 +
∆𝑖 𝐿
2
=
𝑉𝑂
+
1 𝑉𝑂
1 − 𝐷 𝑇 = 𝑉𝑂
1
+
1 − 𝐷
13. THE BUCK (STEP-DOWN)
CONVERTER
𝐼 𝑚𝑖𝑛 = 𝐼𝐿 −
∆𝑖 𝐿
2
=
𝑉𝑂
𝑅
−
1
2
𝑉𝑂
𝐿
1 − 𝐷 𝑇 = 𝑉𝑂
1
𝑅
−
1 − 𝐷
2𝐿𝑓
where 𝑓 = 1/𝑇 is the switching frequency.
• The above Eq. can be used to determine the combination of L and f
that will result in continuous current. Since 𝐼 𝑚𝑖𝑛 = 0 is the boundary
between continuous and discontinuous current,
𝐼 𝑚𝑖𝑛 = 0 = 𝑉𝑂
1
𝑅
−
1 − 𝐷
2𝐿𝑓
(𝐿𝑓) 𝑚𝑖𝑛=
(1 − 𝐷)𝑅
2
14. THE BUCK (STEP-DOWN)
CONVERTER• If the desired switching frequency is established,
𝐿 𝑚𝑖𝑛 =
(1 − 𝐷)𝑅
2𝑓
𝑓𝑜𝑟 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
where 𝐿 𝑚𝑖𝑛 is the minimum inductance required for continuous current.
• In practice inductance is chosen greater than 𝐿 𝑚𝑖𝑛
• The peak-to-peak variation in the inductor current is often used as a design
criterion in buck converter.
• to determine the value of inductance for a specified peak-to-peak inductor
current for continuous-current operation:
∆𝑖 𝐿 =
𝑉𝑠 − 𝑉𝑜
𝐿
𝐷𝑇 =
𝑉𝑠 − 𝑉𝑜
𝐿𝑓
𝐷 =
𝑉𝑂 1 − 𝐷
𝐿𝑓
𝑜𝑟 𝐿 =
𝑉𝑠 − 𝑉𝑜
∆𝑖 𝐿 𝑓
𝐷 =
𝑉𝑂 1 − 𝐷
∆𝑖 𝐿 𝑓
15. THE BUCK (STEP-DOWN)
CONVERTER• Since the converter components are assumed to be ideal,
the power supplied by the source must be the same as the
power absorbed by the load resistor.
𝑃𝑆 = 𝑃𝑂
𝑉𝑠 𝐼𝑠 = 𝑉𝑜 𝐼 𝑜 𝑜𝑟
𝑉𝑜
𝑉𝑠
=
𝐼𝑠
𝐼 𝑜
• Basically from this expression we can say that DC-DC
converter is DC transformer.
16. THE BUCK (STEP-DOWN)
CONVERTER• OUTPUT VOLTAGE RIPPLE
• In the preceding analysis, the capacitor was assumed to be very
large to keep the output voltage constant.
• The variation in output voltage is computed from the voltage-
current relationship of the capacitor.
• The current in the capacitor is
𝑖 𝐶 = 𝑖 𝐿 − 𝑖 𝑅
• While the capacitor current is positive, the capacitor is charging.
From the definition of capacitance,
𝑄 = 𝐶𝑉𝑜
∆𝑄 = 𝐶∆𝑉𝑜
∆𝑉𝑜 =
∆𝑄
𝐶
17. THE BUCK (STEP-DOWN)
CONVERTER• The change in charge ∆𝑄 is
the area of the triangle
above the time axis
∆𝑄 =
1
2
𝑇
2
∆𝑖 𝐿
2
=
𝑇∆𝑖 𝐿
8
• resulting in
∆𝑉𝑜 =
𝑇∆𝑖 𝐿
8𝐶
18. THE BUCK (STEP-DOWN)
CONVERTER
• Using ∆𝑖 𝐿 𝑜𝑝𝑒𝑛 = −
𝑉𝑜
𝐿
(1 − 𝐷)𝑇 = ∆𝑖𝐿
∆𝑉𝑜 =
𝑇𝑉𝑜
8𝐶𝐿
1 − 𝐷 𝑇 =
𝑉𝑜(1 − 𝐷)
8𝐿𝐶𝑓2
• It is also useful to express the ripple as a fraction of the
output voltage
∆𝑉𝑜
𝑉𝑜
=
1 − 𝐷
8𝐿𝐶𝑓2
• 𝐶 =
1−𝐷
8𝐿(∆𝑉𝑜/𝑉𝑜)𝑓2
19. THE BUCK (STEP-DOWN)
CONVERTER
• Using ∆𝑖 𝐿 𝑜𝑝𝑒𝑛 = −
𝑉𝑜
𝐿
(1 − 𝐷)𝑇 for ∆𝑖𝐿
∆𝑉𝑜 =
𝑇𝑉𝑜
8𝐶𝐿
1 − 𝐷 𝑇 =
𝑉𝑜(1 − 𝐷)
8𝐿𝐶𝑓2
• It is also useful to express the ripple as a fraction of the
output voltage
∆𝑉𝑜
𝑉𝑜
=
1 − 𝐷
8𝐿𝐶𝑓2
• 𝐶 =
1−𝐷
8𝐿(∆𝑉𝑜/𝑉𝑜)𝑓2
20. CAPACITOR RESISTANCE—THE
EFFECT ON RIPPLE VOLTAGE
The ESR may have a significant effect on the output voltage rippleA
real capacitor can be modelled as a capacitance with an equivalent
series resistance (ESR) and an equivalent series inductance (ESL).
ESR, often producing a ripple voltage greater than that of the ideal
capacitance.
The inductance in the capacitor is usually not a significant factor at
typical switching frequencies.
The ripple due to ESR can be approximated by first determining the
ripple current assuming the capacitor ideal
∆𝑉𝑜,𝐸𝑆𝑅 = ∆𝑖 𝐶 𝑟𝐶 = ∆𝑖 𝐿 𝑟𝐶
∆𝑉𝑜 < ∆𝑉𝑜,𝐶 + ∆𝑉𝑜,𝐸𝑆𝑅
21. CAPACITOR RESISTANCE—THE
EFFECT ON RIPPLE VOLTAGE
• The ripple voltage due to the ESR can be much larger than the ripple
due to the pure capacitance.
• In that case, the output capacitor is chosen on the basis of the
equivalent series resistance rather than capacitance only.
∆𝑉𝑜 ≈ ∆𝑉𝑜,𝐸𝑆𝑅 = ∆𝑖 𝐶 𝑟𝐶
22. SYNCHRONOUS RECTIFICATION FOR
THE BUCK CONVERTER
Figure: A synchronous buck converter. The MOSFET S2 carries the inductor current
when S1 is off to provide a lower voltage drop than a diode.
23. THE BOOST CONVERTER
Assumptions
1. Steady-state conditions exist.
2. The switching period is 𝑇, and the
switch is closed for time 𝐷𝑇 and open
for (1 − 𝐷)𝑇.
3. The inductor current is continuous
(always positive).
4. The capacitor is very large, and the
output voltage is held constant at
voltage 𝑉𝑜.
5. The components are ideal.
24. THE BOOST CONVERTER
• ANALYSIS FOR THE SWITCH CLOSED:
𝑣 𝐿 = 𝑉𝑆 = 𝐿
𝑑𝑖 𝐿
𝑑𝑡
𝑜𝑟
𝑑𝑖 𝐿
𝑑𝑡
=
𝑉𝑆
𝐿
∆𝑖 𝐿
∆𝑡
=
∆𝑖 𝐿
𝐷𝑇
=
𝑉𝑆
𝐿
• Solving for ∆𝑖 𝐿 for the switch closed,
∆𝑖 𝐿 𝑐𝑙𝑜𝑠𝑒𝑑 =
𝑉𝑆 𝐷𝑇
𝐿
28. THE BOOST CONVERTER
A condition necessary for continuous inductor current is for 𝐼 𝑚𝑖𝑛 to be
positive.
Therefore, the boundary between continuous and discontinuous inductor
current is determined from
𝐼 𝑚𝑖𝑛 = 0 =
𝑉𝑠
1 − 𝐷 2 𝑅
−
𝑉𝑠 𝐷𝑇
2𝐿
𝑜𝑟
𝑉𝑠
1 − 𝐷 2 𝑅
=
𝑉𝑠 𝐷𝑇
2𝐿
=
𝑉𝑠 𝐷
2𝐿𝑓
𝐿𝑓 𝑚𝑖𝑛 =
𝐷 1−𝐷 2 𝑅
2
𝑜𝑟 𝐿 𝑚𝑖𝑛 =
𝐷 1−𝐷 2 𝑅
2𝑓
From a design perspective, it is useful to express 𝐿 in terms of a desired ∆𝑖 𝐿,
𝐿 =
𝑉𝑠 𝐷𝑇
∆𝑖 𝐿
=
𝑉𝑠 𝐷
∆𝑖 𝐿 𝑓
29. THE BOOST CONVERTER
The peak-to-peak output voltage ripple can be calculated from the
capacitor current waveform.
The change in capacitor charge can be calculated from
∆𝑄 =
𝑉𝑜
𝑅
𝐷𝑇 = 𝐶∆𝑉𝑜
An expression for ripple voltage is then
∆𝑉𝑜=
𝑉𝑜 𝐷𝑇
𝑅𝐶
=
𝑉𝑜 𝐷
𝑅𝐶𝑓
𝑜𝑟
∆𝑉𝑜
𝑉𝑜
=
𝐷
𝑅𝐶𝑓
where 𝑓 is the switching frequency.
𝐶 =
𝐷
𝑅(∆𝑉𝑜/𝑉𝑜)𝑓
30. THE BOOST CONVERTER
As Buck Converter the voltage ripple due to the ESR is
∆𝑉𝑜,𝐸𝑆𝑅= ∆𝑖 𝐶 𝑟𝐶 = 𝐼𝐿,𝑚𝑎𝑥 𝑟𝐶
Effects of Inductor Resistance
• Inductors should be designed to have small resistance to minimize power loss and
maximize efficiency.
• Inductor resistance affects performance of the boost converter, especially at high duty
ratios.
• For the boost converter, recall that the output voltage for the ideal case is
𝑉𝑜 =
𝑉𝑠
1 − 𝐷
• The power supplied by the source must be the same as the power absorbed by the
load and the inductor resistance, neglecting other losses.
𝑃𝑠= 𝑃𝑜 + 𝑃𝑟𝐿
𝑉𝑠 𝐼𝐿 = 𝑉𝑜 𝐼 𝐷 + 𝐼𝐿
2
𝑟𝐿
where 𝑟𝐿 is the series resistance of the inductor.
33. BUCK-BOOST CONVERTER
• The output voltage of the buck-boost converter can be either
higher or lower than the input voltage.
• Assumptions :
1. The circuit is operating in the steady state.
2. The inductor current is continuous.
3. The capacitor is large enough to assume a constant
output voltage.
4. The switch is closed for time 𝐷𝑇 and open for (1 − 𝐷)𝑇.
5. The components are ideal.
37. BUCK-BOOST CONVERTER
• For steady-state operation, the net change in inductor current
must be zero over one period.
(∆𝑖 𝐿) 𝑐𝑙𝑜𝑠𝑒𝑑 + (∆𝑖 𝐿) 𝑜𝑝𝑒𝑛= 0
𝑉𝑠 𝐷𝑇
𝐿
+
𝑉𝑜 1 − 𝐷 𝑇
𝐿
= 0
• Solving for 𝑉𝑜,
𝑉𝑜 = −𝑉𝑠
𝐷
1 − 𝐷
• The required duty ratio for specified input and output voltages can be
expressed as
𝐷 =
𝑉𝑜
𝑉𝑠 + 𝑉𝑜
38. BUCK-BOOST CONVERTER
• The average inductor voltage is zero for periodic operation,
resulting in
𝑉𝐿 = 𝑉𝑠 𝐷 + 𝑉𝑜 1 − 𝐷 = 0
• Solving for 𝑉𝑜 yields
𝑉𝑜 = −𝑉𝑠
𝐷
1 − 𝐷
• The output voltage has opposite polarity from the source
voltage.
• If 𝐷 > 0.5, the output voltage is larger than the input; and
if 𝐷 < 0.5, the output is smaller than the input.
39. BUCK-BOOST CONVERTER
• Power absorbed by the load must be the same as that supplied by the source, where
𝑃0 =
𝑉𝑜
2
𝑅
𝑃𝑠 = 𝑉𝑠 𝐼𝑠
𝑉𝑜
2
𝑅
= 𝑉𝑠 𝐼𝑠
• Average source current is related to average inductor current by
𝐼𝑠 = 𝐼𝐿 𝐷
• resulting in
𝑉𝑜
2
𝑅
= 𝑉𝑠 𝐼𝐿 𝐷
• Substituting for 𝑉𝑜 and solving for 𝐼𝐿, we find
𝐼𝐿 =
𝑉𝑜
2
𝑉𝑠 𝑅𝐷
=
𝑃0
𝑉𝑠 𝐷
=
𝑉𝑠 𝐷
𝑅(1 − 𝐷)2
41. BUCK-BOOST CONVERTER
• OUTPUT VOLTAGE RIPPLE
• The output voltage ripple for the buck-boost converter is computed
from the capacitor current .
∆𝑄 =
𝑉𝑜
𝑅
𝐷𝑇 = 𝐶∆𝑉𝑜
• Solving for ∆𝑉𝑜,
∆𝑉𝑜 =
𝑉𝑜 𝐷𝑇
𝑅𝐶
=
𝑉𝑜 𝐷
𝑅𝐶𝑓
𝑜𝑟
∆𝑉𝑜
𝑉𝑜
=
𝐷
𝑅𝐶𝑓
42. BUCK-BOOST CONVERTER
• As is the case with other converters, the equivalent series resistance of
the capacitor can contribute significantly to the output ripple voltage.
The peak-to-peak variation in capacitor current is the same as the
maximum inductor current.
∆𝑉𝑜,𝐸𝑆𝑅= ∆𝑖 𝐶 𝑟𝐶 = 𝐼𝐿,𝑚𝑎𝑥 𝑟𝐶
43. BUCK-BOOST CONVERTER
•As is the case with other converters, the
equivalent series resistance of the capacitor can
contribute significantly to the output ripple
voltage. The peak-to-peak variation in capacitor
current is the same as the maximum inductor
current.
∆𝑉𝑜,𝐸𝑆𝑅= ∆𝑖 𝐶 𝑟𝐶 = 𝐼𝐿,𝑚𝑎𝑥 𝑟𝐶