Single Phase Converter

Summary

This lecture delves into single-phase converters, crucial for converting AC to DC, especially with the shift from DC to AC supply. It covers rectification principles, types of rectifiers, and their applications, including household DC fans. The lecture discusses waveform analysis, harmonic content, and the impact on AC networks. It explores rectifier characteristics like form factor, ripple factor, and power factor, focusing on uncontrolled, half-controlled, and full-controlled rectifiers. The importance of understanding the rectifier's effect on power quality and network equipment is highlighted, with a look ahead to further discussions on AC to DC conversion.

Takeaways

• 🔌 The single phase converter is crucial for converting AC to DC, especially in applications where DC supply was previously used, such as older households in Calcutta.
• 📈 The process of conversion from AC to DC is known as rectification, which is a key topic in power electronic converters where power flows from the AC side to the DC side.
• 🔍 Analysis of rectifiers involves examining waveforms during AC to DC conversion, focusing on average values, RMS values, and how these are affected by different types of loads (e.g., RL, RLE).
• 🌊 Non-linear conversion from AC to DC leads to harmonic contamination in the input, which is an important consideration in the design and analysis of rectifiers.
• 🔑 Voltage and current ratings of power electronic devices used in rectifiers are critical for ensuring the proper operation and safety of the system.
• 🛠 Controlled rectifiers are generally achieved using thyristors, which allow for more sophisticated control over the rectification process.
• 📊 The script introduces several key terms and concepts for analyzing rectifiers, such as peak value, average DC value, RMS effective value, form factor, ripple factor, and fundamental component.
• 🔢 Fourier series is used to analyze the harmonic content in the input side of rectifiers, helping to understand the impact of different harmonics on the system.
• 💡 The displacement power factor (DPF) and power factor of the rectifier are important parameters that describe the relationship between the voltage and current waveforms and their impact on the overall system performance.
• 🔄 Commutation in rectifiers is the process of transferring current from one device to another, and understanding this process is essential for designing efficient and reliable rectifiers.
• 🔩 The script also covers various configurations of rectifiers, including single phase and three phase, uncontrolled, half-controlled, and full-controlled rectifiers, along with their respective topologies and characteristics.

Q & A

What is the primary function of a single phase converter?

The primary function of a single phase converter is to convert AC voltage and current to DC voltage and current, a process referred to as rectification.

Why was rectification necessary in older households in Calcutta?

In older households in Calcutta, rectification was necessary because they initially had a DC supply, and they needed to convert it to power DC loads such as fans.

What are the main points of interest when analyzing a rectifier?

The main points of interest when analyzing a rectifier include the waveform of the AC to DC conversion, the DC value after rectification, the influence of the load on the rectified voltage and current, and the harmonic content in the input.

How does the type of load affect the waveform of the rectified voltage and current?

Different types of loads, such as RL or RLE, will give rise to different waveforms of the rectified voltage and current. The load characteristics influence the shape of the waveforms and the amount of ripple present.

What is the significance of harmonic content in the input when converting AC to DC?

Harmonic content in the input is significant because the non-linear conversion from AC to DC leads to harmonic contamination in the source side, which can affect the power quality and the performance of other electrical devices on the network.

What are the different types of rectifiers mentioned in the script?

The script mentions uncontrolled rectifiers, half-controlled rectifiers, and full-controlled rectifiers. These can be further classified based on the type of supply, such as single phase or three phase, and the configuration like half wave or full wave.

What is the role of thyristors in controlled rectifiers?

Thyristors play a crucial role in controlled rectifiers by allowing the control of the conduction angle, which in turn controls the amount of voltage and current being rectified, providing a means for regulation.

What are the simplifying assumptions made in the analysis of rectifiers?

The simplifying assumptions include considering the internal impedance of the AC source as zero and treating power electronic devices used in rectification as ideal switches.

What is the peak inverse voltage across the diode in a single phase uncontrolled converter?

The peak inverse voltage across the diode in a single phase uncontrolled converter is equal to the peak value of the AC supply voltage, Vm.

How does a freewheeling diode affect the average DC value in an RL load?

A freewheeling diode prevents the negative voltage from appearing across the load, which increases the average DC value available to the load, thus improving the efficiency of the rectifier.

What is the significance of the extinction angle in a controlled rectifier?

The extinction angle in a controlled rectifier refers to the time interval from when the current through the outgoing thyristors becomes zero to when a positive voltage is applied, which is important for understanding the commutation process and device selection.

Outlines

00:00

🔌 Introduction to Single Phase Converters

The paragraph introduces the topic of single phase converters, their historical context, and their applications. It explains the transition from DC to AC supply and the need for rectifiers to convert AC to DC for DC loads such as motors. The process of rectification is defined, and the importance of analyzing the waveform during AC to DC conversion is emphasized. The influence of load types on the rectified voltage and current waveforms is discussed, highlighting the non-linear nature of the conversion process and its impact on harmonic content in the input. The paragraph also touches on the analysis of voltage and current ratings for power electronic devices used in rectifiers and the effects of rectifiers on AC networks, including reactive power, power factor, and harmonics. The discussion sets the stage for a deeper analysis of rectifiers, including controlled rectifiers using thyristors, and introduces simplifying assumptions for analysis.

05:01

📊 Understanding Rectifier Waveforms and Parameters

This paragraph delves into the technical aspects of analyzing rectifier waveforms, focusing on various parameters such as peak value, average DC value, RMS effective value, form factor, ripple factor, and fundamental component. It explains how these parameters are calculated and their significance in understanding the performance of rectifiers. The concept of Fourier series is introduced to analyze the harmonic content in the waveforms, with detailed explanations on how to calculate the fundamental and Kth harmonic components. Additionally, the paragraph discusses the crest factor, distortion factor, and total harmonic distortion (THD), which are critical for assessing the quality of the rectified output. These parameters are essential for analyzing both single-phase and three-phase converters.

10:04

🔗 Displacement Power Factor and Rectifier Analysis

The paragraph discusses the displacement power factor (DPF) of rectifiers, which is defined as the cosine of the phase angle between the fundamental components of voltage and current. It explains the concept using an example of thyristors being triggered at a delay angle, causing a phase shift. The paragraph also covers the power factor of rectifiers, which is the ratio of real power to apparent power, and how it can be affected by the harmonic distortion. The relationship between power factor, displacement factor, and THD is explored. Additionally, the concept of pulse number in rectifiers is introduced, which is crucial for understanding the output characteristics of different rectifier topologies. The paragraph concludes with a brief mention of commutation in rectifiers, which is the process of transferring current from one device to another, and the potential issue of commutation failure.

15:05

🔄 Commutation, Firing, and Extinction Angles in Rectifiers

This paragraph focuses on the commutation process in rectifiers, detailing the roles of outgoing and incoming devices during current transfer. It explains the concept of commutation failure, which occurs when the outgoing device fails to turn off, leading to potentially dangerous short circuits. The paragraph introduces the firing angle (alpha) of a rectifier, which is the angle by which the conduction of thyristors is delayed, and its significance in controlled rectifiers. It also discusses the extinction angle and the overlapping angle (mu), which are crucial for understanding the commutation process in practical rectifiers. The relationship between these angles and the total half cycle of the rectifier's operation is highlighted. The paragraph concludes with a transition to the simplest circuit configuration of a single-phase uncontrolled converter with a resistive load.

20:13

🌊 Single Phase Uncontrolled Converter with Resistive Load

The paragraph discusses the behavior of a single-phase uncontrolled converter, specifically a half-wave diode rectifier, when connected to a resistive load. It explains the need for the diode to block the peak reverse voltage and calculates the average output voltage, RMS value, and peak inverse voltage across the diode. The efficiency of the rectifier and the effective RMS value of the AC component are also analyzed. The paragraph further explores the impact of the load on the input current waveform and the total harmonic distortion (THD) of the input current. It concludes with a discussion on the effect of a freewheeling diode in an RL load configuration, which helps to increase the average DC value available to the load and improve the overall performance of the rectifier.

25:14

🔌 Single Phase Uncontrolled Converter with RL Load and Freewheeling Diode

This paragraph continues the discussion on single-phase uncontrolled converters, focusing on the case where the load is inductive (RL load) and a freewheeling diode is included in the circuit. It explains how the freewheeling diode prevents negative voltage from appearing across the load, which would otherwise increase the ripple. The paragraph details the commutation process involving the diode and the freewheeling diode, and how it affects the average output voltage and current. The inclusion of the freewheeling diode is shown to increase the average DC value delivered to the load, which is beneficial for AC to DC conversion applications. The paragraph concludes with a summary of the benefits of using a freewheeling diode and a teaser for the next class, which will continue the discussion on AC to DC conversion.

Keywords

💡Rectification

Rectification refers to the process of converting alternating current (AC) voltage and current to direct current (DC). In the context of the video, this is a fundamental concept as it describes the primary function of a rectifier. The video discusses how single-phase converters are used for rectification, especially in older systems where DC supply was common, and how the process involves converting AC to DC for applications like powering DC fans.

💡Power electronic converter

A power electronic converter is a device that changes the form of electrical power, often from AC to DC or vice versa. The video emphasizes the role of power electronic converters in rectification, highlighting that power flows from the AC side to the DC side in a non-generative way, typically involving DC motors as loads.

💡Waveform

A waveform represents the shape and form of a signal, such as voltage or current, over time. The video discusses the importance of analyzing the waveform during AC to DC conversion, as it helps in understanding the characteristics of the rectified output, including the average and RMS values of the rectified voltage and current.

💡Ripple

Ripple refers to the fluctuation or oscillation in the output voltage of a rectifier, which is not a constant DC. The video explains that due to rectification, the output voltage has a ripple, which is characterized by the RMS value of the AC component superimposed on the DC value. This ripple is an important factor in determining the quality of the rectified output.

💡Harmonics

Harmonics are multiples of the fundamental frequency of the waveform, which can be introduced into the electrical supply due to non-linear loads. The video mentions that the AC to DC conversion process, being non-linear, leads to harmonic contamination in the source side, which is a significant consideration in the analysis of rectifiers.

💡Thyristor

A thyristor, also known as a silicon-controlled rectifier (SCR), is a four-layer, three-terminal semiconductor device used for controlling the rectification process. The video discusses how thyristors are used in controlled rectifiers to achieve specific control over the power flow from AC to DC.

💡Form Factor

The form factor of a waveform is the ratio of the RMS value to the average value. In the video, the form factor is used to describe the shape of the rectified voltage waveform, indicating how much of the waveform is due to AC components versus DC components. A higher form factor implies a more sinusoidal waveform, while a lower form factor indicates a more rectangular waveform.

💡Ripple Factor

The ripple factor is a measure of the AC content in the rectified DC output and is defined as the ratio of the effective value of the AC component to the DC component. The video explains that the ripple factor is calculated as the square root of one minus the square of the form factor, which helps in understanding the quality of the DC output.

💡Total Harmonic Distortion (THD)

THD is a measure of the distortion in a waveform, quantifying the amount of harmonic content relative to the fundamental component. The video discusses THD as an important parameter for assessing the power quality of the input current in a rectifier, indicating the level of distortion introduced by the rectification process.

💡Displacement Power Factor (DPF)

DPF is a measure of the phase difference between the fundamental components of the voltage and current in a circuit. The video defines DPF in the context of rectifiers, where the phase shift between the input voltage and current waveforms is crucial for understanding the performance of the rectifier and its impact on the power supply.

💡Pulse Number

The pulse number of a rectifier refers to the number of output voltage or current pulses in a single time period of the input AC supply. The video explains that this is an important parameter for classifying rectifiers, particularly in three-phase systems, where different configurations can result in different pulse numbers, affecting the performance and harmonic content of the rectifier.

Highlights

Introduction to single phase converter and its historical use in Calcutta.

Explanation of rectification as the conversion from AC to DC.

Importance of analyzing the waveform during AC to DC conversion.

Impact of load type (RL, RLE) on the waveform of rectified voltage and current.

Discussion on harmonic content in the input due to non-linear conversions.

Analysis of voltage and current ratings for power electronic devices in rectifiers.

Introduction to controlled rectifiers using thyristors.

Simplifying assumptions made in the analysis of rectifiers.

Types of rectifiers: single phase, 3 phase, uncontrolled, half controlled, and full controlled.

Definition and calculation of peak, average, RMS, form factor, and ripple factor.

Explanation of Fourier series coefficients and harmonic components.

Definition of Crest factor and its calculation.

Introduction to Total Harmonic Distortion (THD) and its significance.

Discussion on displacement power factor (DPF) and its calculation.

Analysis of power factor in rectifiers and its calculation.

Importance of pulse number in rectifiers and its calculation.

Explanation of commutation in rectifiers and its significance.

Discussion on commutation failure and its implications.

Introduction to firing angle and its role in rectifiers.

Explanation of extinction angle and overlapping angle in rectifiers.

Analysis of a single phase uncontrolled converter with a resistive load.

Calculation of average output voltage, current, RMS value, and efficiency for a single phase uncontrolled converter.

Introduction to single phase uncontrolled rectifier with RL load and freewheeling diode.

Effect of freewheel diode on the average DC value available to the load.

Conclusion and预告 of the next class on AC to DC conversion.

Transcripts

Welcome to the advanced power electronic and control courses.

We shall discuss today single phase converter.

Single phase converter finds its applications, wide application because previously we had

a DC supply and thus we had a DC loads.

Once the supply has been changed to the AC, then we require genuine purpose to rectify

this.

For example, actually in older household in Calcutta, we already had a DC supply.

We required to rectify it to put it to the actually DC fans in other applications.

So now we refer to the process of conversion to the AC to DC as rectifications.

So rectification refer to the process of converting an AC voltage and current to the DC voltage

and current.

And rectifications specially refer to the power electronic converter where the power

flows from AC side to the DC side and not in a generative way.

Mostly load is, mostly AC will be the source and load will be the DC and mostly these are

DC motors.

Now point of interest of the analysis of the rectifier will be actually we require to analysis

the waveform of the, while AC to DC conversion, so while various things.

Where the inputs side, when you talk about the waveforms and characteristics values,

when you talk about DC value after rectification, we will have an average value.

And when the RMS value becomes my ripple DC, not a constant DC with the rectified voltage

have the current.

Then due to rectification, there the influence of the load and the rectified voltage and

the current will change according to the type of load, whether it is RL, RLE, different

kind of load will give rise to a different kind of waveform.

Harmonic content in the input.

So you are feeding AC, so since it is a non-linear conversions, AC to DC conversion, then leads

to the harmonic contamination in the source side.

So you will see that what is the problem or what is all of the arising the harmonics in

the input.

Voltage and current ratings of the power electronic device used for the rectifier operation, that

also will be analyzed.

So what should be the proper rating for the particular wattage of the load.

Reactions of the rectifier circuit upon the AC networks reactive power equipments and

the power factor harmonics, these will be the actually characteristics of this actually

the rectifications and rectifier controlled aspects for controlled rectifier, generally

it has been achieved by the thyristors.

Now in the analysis following simplifying assumptions will be made.

Internal impedance of the AC source is 0 if otherwise not mentioned or taken into the

consideration.

Power electronic device used in rectifications are the ideal switches.

So types of the rectifies.

We have a single phase and the 3 phase.

Today, we shall consider a single phase.

And definitely, we have uncontrolled fitted by the diode rectifier.

You have a half controlled fitted by the combinations of the thyristors and the diode.

That of full controlled, it is fed through actually the thyristors.

Then we may have a half wave where we require to buck down a voltage a lot.

Then we have a full wave where you require to have a total cycle.

Then we have a different kind of supply, whether you have a, actually the midpoint of the transformer

is available or not, that is also a matter of questions.

If it is available, then we will go for the split supply.

And otherwise, we have a bridge kind of configurations.

And same way, in 3 phase also we have uncontrolled fitted by a diode with rectifier.

We have a half controlled and the full controlled.

If uncontrolled, we have a half wave as well as a full bridge.

And same way, you have a full control, we have a half wave and full bridge.

So all those topology will be discussed.

First we will take out actually the single phase.

So let f be the instantaneous value of any voltage and current associated with the rectifier

circuit.

Then following terms, characterizing the property of f can be defined.

The peak value of f.

As the name suggests f= mod f max for all the time.

Similarly, average DC value, that is Fav, assume f to be periodic over the time period

T. And Fav will be actually you have 1/T 0 to T f of dt.

And if it is RMS effective, then f will be periodic over the same thing and the expression

of the RMS will be under root 2 1/T 0 to T f square dt.

Similarly.

we will define the term form factor as f defined by f of F FRMS/Fav.

Similarly, we will define the ripple factor that is basically; form factor is a ratio

of basically, the RMS is associated with the AC and average is associated with the DC since

in any periodic functions, if it is bipolar in nature, average value comes out to be 0.

So form factor is basically says that the ratio of actually AC versus DC.

And another aspect is the ripple factor.

Ripple factor is given by fRF.

So if I put I, then it is for the current ripple.

If I put voltage, if it is a voltage ripple, that is FRMS square-Fav square/Fav.

So ultimately it comes out to be basically the form factor square-1.

And fundamental component F1, since it is contaminated with the harmonics, the inputs

side we wanted to know what is the fundamental value of the fundamental component.

And in our case, what will be the 50 Hz component of it.

Its RMS value of the sinusoidal component in a Fourier series expressions of f will

be frequency 1/T because you have a sine and cos component.

So it will be fA1 square+fB square.

Similarly, we can calculate the term fA1 and fB1.

These are basically the Fourier components.

So in the same we have find it out the Fourier series coefficients, same way we can do it.

So it is 2/T 0 to T ft cos 2pi/Tdt.

And similarly for fB1, we will have instead of cos, we have a sin term.

Now for Kth harmonic, if I wish to know because there is a symmetric generally different kind

of harmonics are present for the different kind of system.

Sometime actually triplet harmonic is absent.

Sometime actually we have harmonic content with a 6n+-1 and is fast, 5th and 7th, there

after 11, 13 and so on.

So if we wish to calculate the Kth harmonic component of this Fk, it is the RMS value

of the sinusoidal component of the Fourier series expressions of f with frequency K/T.

So Fk=under root of 1/2fAK square+1/2BK square.

So from there, we can calculate the result fAK=2/T 0 to T ft cos 2 piKt/Tdt.

Similarly, you can have the sin term that is basically 2/T 0 to T ft sin term.

SO there will be a definition called Crest factor.

Crest factor is by definition is ((star)) (09:00) f/FRMS that is the peak value/RMS.

Similarly, we will have a distortion factor.

Distortion factor is given by basically by definition, it will be F1, that is the fundamental

component, /RMS will give you the distortion factor.

And another term is actually total harmonic distortion.

This is a very important classifier.

We want that actually now I quickly practices says THD of the input current or anything

equal to be a specified limit.

The amount of the distortion in the waveform, f is quantified by means of the index total

harmonic distortion is given by THD=under root of actually K=0 to infinity Fk/F1 square

and from there, actually we can derive, students are requested to refer to the any standard

book and the derivations will be there.

So we can find it out the THD=under root of 1-DF square/DF.

So these are few terms we can use very frequently while analyzing the single phase and the 3

phase converter.

Another is the displacement power factor of the rectifier, that is DPF.

Let us say if vi in a phase, an amount of the voltage and current of the rectifier are

actually phase shifted, then the displacement power factor or rectifier is defined as that

is cos phi 1/phi 1 as the phase angle between the fundamental components and current and

the voltages.

Let us understand what does it mean by this?

So let us consider that you know actually this is the sinusoidal voltage and you know

you were triggering thyristors.

So it will be delayed by an angle alpha.

So current will start conducting from here.

So then there will be delay.

So this delay corresponds to alpha and that if you say that is phi, then let us go back

and understand this definition.

If vi and ii are the phase input voltages and current of a rectifier respectively or

converter, then displacement factor of the rectifier/converter is defined as DPF=cos

phi i, is the phase angle between the fundamental component of the vi and ii.

So we assume that voltage only have fundamental and it has lot of harmonics.

So if you actually whatever its fundamental phase difference with the fundamental voltage,

that will be actually defined as DPF.

Power factor of the rectifier, so as for any equipment, the definition of the power factor

of a rectifier is the actual power factor of the rectifier upon the apparent input of

the rectifier.

That mean if the phase input voltage and current of the rectifier vi and ii respectively, then

actually power factor will be given by Vi1 of fundamental ii1, that is the fundamental,

*cos phi of i of the input power factor angle between the fundamental of voltage and current,

which we have calculated here, /Irms and the Vrms.

So this will be the power factor in the rectification.

These terms will be used and values will be, when assignment will be given to calculate

those terms.

If the rectifier is supplied from an ideal sinusoidal voltage source, then as I have

drawn little bit ago, that is Vi1 and V fundamentals become same.

That is the PF, power factor will be Ii1/Irms*cos phi i, that is basically DF1*DPF.

So we can replace them in terms of the THD.

So power factor will be DPF/under root 1+THD square.

Another important parameters of analyzing the rectifier and the converter is that, pulse

number of a rectifier.

Refer to the number of the output voltage current, whatever parameter you are analyzing,

whether output voltage or current, pulse in a single time period in the input AC supply.

Mathematically, the pulse number of the rectifier is given by the time period of the input voltage

supply/time period of the minimum order harmonic in the output voltage or current.

So that required to be little understood.

So it depends only mainly the 3 phase supply.

So there we can see the different kind of pulses.

How many number of pulses will be generating.

So classification of the rectifier can also be done in terms of the pulse number.

And for this reason, we have a different kind of pulse converter.

In 3 phase, we say that it is 6 pulse converter.

Because what happen you know we will discuss in detail while discussing actually the 3

phase circuit, if it is uncontrolled one pair of thyristors or diode or combination of the

thyristors-diode in case of the semi-controlled, we will convert for the period of 60 degree.

So you have a total actually 360 degree.

So you got a 6 pulses.

So for this reason, classification of the rectifier can also be done in terms of their

pulse number.

Similarly, we can have actually a phase shifted by 30 degree and we can by a transformer and

we can have a 12 pulse.

Similarly, we have a 24 pulse.

Similarly, we may have a 48 pulse.

And we shall see the utility of it while reduction of the harmonic and the other characteristics

that has been required.

Commutation in a rectifier.

Rectifier to process the transfer of current form one device through the another device,

mostly it is diode or thyristors, to the other rectifier.

The device from which current is transferred to the other transfer, is called the outgoing

device.

And the device to which the current is transferred is called the incoming device.

The incoming device turn on at the beginning of the commutation while the outgoing device

turns off at the end of the commutation.

So we have sometime there is an overlap.

We will come across it and we will see that what is the cause of the overlapping also.

Commutation failure.

It refers to the situation where outgoing devices fails to turn off at the end of the

commutations and continues to conduct current and that is dangerous.

Say you have a thyristors ((lags)) (17:13).

So you may actually some thyristors is going out and some thyristors comes in.

Generally, if you have a, it may leads to the shorting of the ((legs)) (17:26).

So that is quite dangerous phenomenon.

Firing angle of a rectifier, that is alpha, we have discussed in detail in the thyristors.

So it is the angle by which the conduction of the thyristors is delayed and it is measured

from the instant when devices become a forward biased with the resistive load.

Therefore, the reference point should be a fixed point.

So for the single phase, it is a forward 0 crossing and it is a for the 3 phase, in the

place where actually this Vc and Va cross, so that place is considered as a firing reference.

We can start calculating firing reference from that point for the 3 phase.

But today, our discussion will be mainly on the single phase.

Extinction angle of the rectifier or converter.

Is also used in connections with a controlled rectifier.

Refers to the time interval from the instant when the current through the outgoing thyristors

becomes 0 and the negative voltage is applied across it to the instant when a positive voltage

is applied.

So within that time actually, that is said to be the extinction angle of the converter

or rectifier, overlapping angle, that is called mu.

it arises though we favour contradictions with our first assumption.

We have assumed that actually source does not have an impedance.

It comes into the picture when source got an inductance.

Commutation process in a practical rectifier is not instantaneous.

During the period of commutation, both incoming and the outgoing devices conduct current simultaneously

for a small period of time.

This period is expressed in radians.

All angles are expressed in radians and is called the overlapping angle of the rectifier

and easily verified that alpha+mu + this actually the extinction angle, that should be equal

to the total half cycle of the period that is pi.

And generally this mu will be larger if there is a huge source inductance.

Now let us come to the first simplest circuit configuration that is single phase uncontrolled

converter, half wave diode rectifier fitting a resistive load.

So what happens here?

Actually diode has to block the peak reverse voltage.

So what happens when it conducts?

So it has to be blocked the peak reverse voltage and this is basically the voltage across the

load.

And this is the voltage across the diode.

Now for a simplest circuit, let us calculate the parameter.

Now we can calculate this parameter that is actually the average value of the voltage

which we have shown there.

So it is 1/pi 0 to pi and so on.

So you get Vm/pi for the half wave for the single phase uncontrolled.

Average output load current, you divide it just it by R, you get this value, Vm/pi R.

RMS value, you will get Vm/2.

RMS of the load current, definitely Vrms/R, you get it.

And the peak inverse voltage across the diode, will be Vm, that is what we have seen in the

previous slide.

And the efficiency of the rectifier is Pdc/Pac, so that will be Vdc*Idc Vrms*Irms and you

can calculate what should be this value.

Similarly, effective rms value of the ac component will be Vac Vrms square-Vdc square.

So Vdc is quite actually small for this is actually, this is a considerable amount of

the ac inside it.

The form factor, it is Vrms/Vdc, that is also high.

And also ripple factor is Vac/Vdc, you can form it, that is form factor square-1, that

will be a ripple factor that also will be quite high.

Now single phase uncontrolled converter.

Total harmonic, the harmonic factor or the total harmonic distortion that is an important

parameter for the current or the power quality.

Measures of the distortion of the waveform of the input current that is THD=Ih/Is1, that

is Is square-Is1 square/Is1.

Ultimately you will be get this value.

Essentially, if it is a very high inductive load, then input current will get this form.

Otherwise, it will be Vm/R. So that will be different.

So this will be applicable when actually R is much less than basically XL.

Generally, if R/XL, this ratio is actually around 0.1, then we can say that you know

load current, current through this load almost constant and the input current will have this

kind of profile.

And there we are coming into the analysis, let us say.

And ultimately this is your fundamental of the input current, Is1.

And this is your input current.

So from there, you can calculate the value of the other parameter that is DF cos phi

and the power factor and other parameter also.

Now let us consider a single phase uncontrolled rectifier RL load with the freewheel.

We have seen that different kind of topologies of the converter in our previous class with

SPST switches.

So you have got a diode and thereafter you got a VL and VR.

So what happens, due to inductive load, the conduction period of the diode, D1, will extend

beyond 180 degree because current will still continue to, after 180 degree, until the current

becomes 0.

So this is the point where actually current becomes 0.

This is the point where diode D1 conducts if this thing is absent.

Now what happens, if it is actually closed or it has been put into the circuit?

Then what will happen?

Then there will be a change in the circuit.

So this is the Vm and ultimately it will conduct till this time.

Thereafter, there will be no negative input is associated with it because you know output

voltage will come like this.

And till actually the angle beta and this is actually the VR.

VR will be basically the voltages across this actually the resistance of the load.

VL is the voltage across the inductor, so you can see that change in the polarity takes

place.

This is basically the VD.

Ultimately when it conducts, so it is we assume that actually forward voltage term of this

device is almost negligible and equal to 0.

Then it is blocking this voltages of maximum Vm and this continues.

So this is actually the RL load.

Now what will be the average value of the output voltage, here?

So we can calculate, you see that how it will change.

So Vdc will be actually Vm/2pi 1-cos pi+theta where theta can be calculated basically that

depends on basically this omega L/R ratio.

And where omega is the supply frequency of the source.

And from there, actually you can calculate the amount of the Vdc will come actually as

the average value.

And average value of the current definitely once you calculate, because the inductance

does not contribute anything.

Once you calculate the Vdc, divide it by R, you will get Idc.

So average value of the output voltage.

And hence the current can be increased by making theta=0 so that this value becomes

basically -1 or -12, so you approaches to the resistive load and is Vm/pi which is possible

adding a freewheel diode Dm across the load.

So what does it do, you know?

This diode with a rectifier, if you put a freewheel diode, will increase your average

DC value available to the load.

So this is the one utility of it.

So for this we prefer to have freewheel action in a AC to DC conversion kind of applications.

So single phase uncontrolled converter with RL load with a freewheeling diode, we are

actually discussing.

The effect of the freewheel diode Dm is to prevent the negative voltage appearing.

Once the negative voltage appearing means actually it makes it more DC or more ripple.

Negative voltage appears across the load and as a result, magnetic energy stored into the

system increases at t=pi/omega, the current D1 transferred to Dm and its process called

commutations of the diode.

So you take an example of it.

So this is basically the Vm and this is basically the VR and this is the point where actually

D1 conducts and this is the point where, actually assuming that very high load current, then

only it happens.

Otherwise we will have a discontinuous mode of conductions.

So thank you for your attention.

We shall continue to discuss AC to DC conversion in our next class.

Thank you.