 Hello, and welcome to this lecture on advanced electric drives. In the last lecture, we are discussing about the hybrid stepper motor. The objective is to get more torque and a small step size. Now, in hybrid stepper motor, the torque is produced by the combination of variable reluctance torque and the permanent magnet torque. And the cross sectional view of a hybrid stepper motor is shown in the following figure. In this case, we have the stator. This is the stator section. We have taken a longitudinal section. We have a stator here. And the stator has got two blocks in this case. And this is also the stator. So, we have the stator here also. So, this is also the stator. And the rotor also has got two blocks. One in the left hand side or the right hand side. And we have the shaft. This is the rotor shaft. And the stator carries winding. In fact, the stator is also having slotted structure. We know that in case of stepper motor, there are teeth and slots. The stator has got also teeth and slots. The rotor also has got teeth and slot. But the stator carries winding. And in this case, the stator carries concentric winding. So, what we have here? This is basically the windings here. So, if we... So, this is the winding we have. This is one winding. And then we have the winding overhangs here. These are the winding overhangs. These are also the winding overhangs. And here also, we have the winding overhangs in this case. And they are called concentric windings. And what we have in case of the rotor? The rotor has got a permanent magnet. And it is an axially polarized rotor. So, we can say here, this is an axially polarized rotor. Axially polarized. How is it polarizing axially? Now, we know that we have two blocks of the rotor. And if we go on putting permanent magnet across the rotor surface, it will be a big task. So, we do not put tiny magnets over the surface of the rotor. What we do instead? We put bar magnets along the rotor shaft. So, that one side is north pole and other side is south pole. So, what we have done here is this, that this is the magnet that we have placed here. And this is actually a magnet along the shaft of the rotor. So, this side is the south pole. And the right side is the north pole. And hence, we can plot the flux lines. The flux line will come out of the north pole and enter the south pole. So, this is the flux lines in this case through the stator yoke. So, this is how the flux lines will pass. Similarly, on the other side, we have the flux lines in the south pole and the north pole. So, we have the flux lines which is coming out of the axially polarized magnet. And here, the north pole is on the right hand side. So, this basically the flux line will come out of the north pole and will enter the south pole. And this enter the south pole like this. Similarly, on the other half, we have the north pole. The flux lines will be coming out of the north pole will be like this. So, these are the flux lines. And they will be entering the rotor block. And this how this enters. As a result, if we see one half of the rotor is a south pole and other half is a north pole. Because, when the flux is entering the rotor, it is a south pole. When the flux is coming out of the rotor, it is a north pole. So, we have not placed tiny magnets across the surface of the rotor. We have put the bar magnets. And as a result, the entire rotor block in the left side is south pole. And in the right side, it is north pole. We can see here, this is the south pole. We have a south pole in the left side, because the flux is entering the rotor. And on the right hand side, we have the north pole. The flux is coming out of the rotor. Now, how is the torque produced? Now, let us assume that in this case, the stator has got 4 poles. If the stator has got 4 poles, we can show the pole structure and show the windings. And the pole structure is shown as follows. So, we have the pole structures, which we can show here. That if we show a structure of the stator, this is the stator surface in the left side. So, we have 4 poles here. So, and this is the rotor. So, 4 pole means we have 4 projection in this case. And the projections could be like this. This is one pole, second pole, the third pole and the fourth pole. So, this is the rotor inner surface as the stator inner surface. And this is the stator outer surface. What about the rotor? The rotor carries slots. And the rotor in fact, carries slots and teeth. And the slots and teeth are so arranged that sometimes, we have a slot. Sometimes, we have a tooth and so on. And in this particular situation, we can show, for example, here we have the structure like this. This is the tooth and this is the slot. We show the slot like this and tooth like this. And the stator, we have the 4 poles and this carry windings. And this carry physical concentric windings. And similarly, this also carries winding. And these windings are all connected. So, it is connected. So, this is phase A. We can call this to be A 1 and A 2. And similarly, in this case, we have the windings here. This is B 1. And it is wound like this. This is B 2. So, the stator carries concentric winding that we have already shown here. And these windings are shown in the following fashion. So, this is A 1 and A 2, B 1 and B 2. And then, when we talk about the rotor slots and teeth, when we excite phase A 1 and A 2, we can excite in the following sequence. We can excite A 1, A 2, B 1, B 2, A 2, A 1 and B 2, B 1. So, in this following way, we can excite. So, we can excite like this. First of all, we can excite A 1, A 2. And then, B 1, B 2. And then, A 2, A 1 and then, B 2, B 1. And then, it repeats. So, we can start again with A 1, A 2. When we see the tooth and the slot arrangement, we see that this is the phase A is facing a tooth. So, this is a tooth. And phase A 2 is facing a slot. And when we excite that particular phase, we create a north pole. In fact, this entire block is actually south pole. So, we can say that this is the south pole, the left side of the rotor as we have seen here that the left side is entirely south pole. So, we are in fact, plotting the cross section of the left side of the rotor. So, the left side is entirely a south pole. So, we have shown the south pole. And in the south pole, when we excite phase A 1 and A 2, we create a north pole under A 1. So, what we have here is that we have north pole here. And then, we have a south pole here. When we excite A 1, A 2, we create a north pole under A 1 and south pole under A 2. And A 1 is facing a tooth and A 2 is facing a slot. What about B 1 and B 2? B 1 is neither facing a tooth nor facing a slot. So, we have a situation like this that in this case, the tooth is here. And the slot in this case is like this. So, if we see the phase B 1 and B 2, B 1 is neither facing a slot nor facing a tooth. And B 2 is also neither facing a slot nor facing a tooth. Now, right now, when we change from A 1, A 2 to B 1, B 2, what happens? Earlier, A 1 was north pole. And now, when we sit from A 1, A 2 to B 1, B 2, B 1, the phase under B 1 will become a north pole. So, when B 1 becomes a north pole, the rotor will try to move. And try to move by what angle? So, that the B 1 phase will see a tooth. So, in this case, we can see here, when it moves towards the, I mean in the anticlockwise direction like this, when we excite B 1 and B 2, we will have a north pole here. So, if we have a north pole here, this north pole will attract the south pole tooth. So, this will be moving in the anticlockwise direction. And finally, this tooth will be coming fully under B 1. And hence, the movement of the rotor will be by one quarter of tooth pitch. By tooth pitch, we mean, we have in fact, we have a tooth like this and a slot like this. Basically, these are the tooth and slot structure. We have so many teeth and so many slots. So, when we excite phase B 1, B 2, the movement will be by one quarter of the tooth pitch. So, this is basically one quarter of tooth pitch. What is the tooth pitch? The tooth pitch will have one full tooth and one full slot. So, this is one tooth pitch. This is one tooth pitch. One tooth pitch is made of one full tooth and one full slot. And when the movement is by one quarter, this is one quarter of tooth pitch. So, this is how the rotor will move. And when it moves in the anticlockwise direction, when we excite phase B 1 and B 2, a tooth will be under phase B 1. And then, after that, we will be exciting A 2 and A 1 because we have to go in a sequence. We have started with A 1, A 2, then B 1, B 2. Then, we have to again go back to A 2, A 1 so that A 2 will become a north pole and A 1 will become a south pole. Now, north pole will always attract a south pole tooth. So, if we excite A 2, A 1 after B 1, B 2 will be exciting A 2, A 1. What happens? It means when we excite A 2, A 1, this is A 2 and this is A 1. So, we have A 2 phases here. A 1 is here. When we excite A 2, A 1, this is already moved by one quarter. So, in fact, A 2 is now facing, when B 1 is excited, A 2 is basically facing neither a tooth nor a slot. It is at the age of a tooth. Again, when we excite A 2, A 1, the tooth will come in and again, the movement will be by one quarter of tooth pitch. So, here the step size is basically one quarter of tooth pitch. So, when we excite, say for example, when we started with A 1, A 2, the angle was 0. When we have excited B 1, B 2, it moves by one quarter tooth pitch and then we have excited A 2, A 1, it further moves in anticlockwise direction by one quarter. So, one quarter of tooth pitch and then we again excite B 2, B 1, it moves by one quarter of tooth pitch and then again by A 2, A 1, it completes one quarter of tooth pitch. So, here what is the step size? The step size is, in fact, one quarter of a tooth pitch. Say for example, in the rotor, we have let us say 60 teeth. So, if we have 60 teeth in the rotor, what is the step size? 360 by 60 by 4. So, say for example, we can, we can take an example here. Rotor number of teeth is equal, let us say, we can say it is 60. So, if 60 is the number of teeth in the rotor, what is the step size? The step size will be basically one fourth of the tooth pitch and tooth pitch here, one revolution is 360 degree. So, 360 by 60 is 6 degrees and one fourth of that is 1.5 degrees. So, step size here is 360 is the complete revolution, one circle by 60 is the number of teeth in the rotor. This is the tooth pitch, 1 upon 4 is the quarter of a tooth pitch and that is equal to 6 degrees by 4 and that is equal to 1.5 degrees. Now, it is so interesting that without increasing the number of poles, we have only 4 poles in the stator. We are not increasing the number of poles in the stator, we have only 2 phases A 1 phase A and phase B, A 1 A 2 and B 1 B 2. But what we have done? We have placed a magnet in such a way that one half of the south rotor is the south pole and other half is the north pole. And by doing that and by increasing the number of teeth and slot, we are able to have a reduced step size. In fact, the step size can be further be reduced if we increase the number of teeth. So, here we have the step size is equal to 1.5 degrees. Now, we have seen actually one half of the rotor, what happens to the other half? So, we have two side, one side is in the left hand side and other side is the right hand side. So, in fact, what we can see here that if we see the structure of the stator and structure of the stator here, they are something very similar. What about the rotor structure? This is the rotor and here also we have the rotor and we have four poles here, one pole, the second pole, the third pole and the fourth pole. And similarly here also we have four pole structure, one and three and four and these will carry windings. This all will be carrying windings here, this also will be carrying the windings. So, in this case, how does this two place with respect to each other? Now, we have a left side and we have a right side because we understand that in this case, the rotor has got two blocks. The left block is entirely south pole and the right block is entirely north pole and the stators are also connected like this. The stators will be excited in a similar fashion. In fact, when we say a 1, a 2, all the stators are excited at the same time and when we say b 1 and b 2, the stators, the left side and the right side are excited at the same time. So, this stator is a 1, this is a 2, this is also a 1 and this is a 2 have been similar windings. We have b 1 here and b 2 here, this is also b 1 and this is also b 2. The difference comes in the rotor. The rotor left side is entirely south pole. So, what we have here is that this is entirely south block and then the right side rotor is north pole, this block is entirely north pole. So, this is called a homopolar structure. It means the whole of the rotor in the left side is south pole, the whole of the rotor in the right side is a north pole. Now, when we excite a 1, a 2, a north pole is created under the stator also. So, the stator is north pole here. Now, this is the north pole. In this case, when we excite a 1, this becomes a north pole, this also becomes a north pole and a 2 becomes a south pole, this also becomes a south pole. Now, when we talk about the rotor teeth, the rotor teeth in the left side here we have a teeth, we have a tooth here and we have a slot here and this is neither facing a tooth nor facing a slot, something like this. What about the right side? Right side again, this is a north block. So, this would be a slot and this would be a tooth. So, if we see the right side rotor block and the left side rotor block and try to compare this, the tooth and slot structure, they will be offset of each other. In fact, the slot of the left side is aligned along a tooth of the right side. The tooth pitch of the left side and the right side are the same, but they are offset by half a tooth pitch. It means the slot of the left side is coinciding with the right of the right side, tooth of the right side. So, in fact, they are offset by half a tooth pitch. So, if we are to show the entire structure like this, rotor structure, if this is a tooth and this is a slot like this, in the left side, in the right side what we have is the following, right side we will have the structure here, we have exactly a slot here and we have a tooth here. So, it means a tooth is matching with a slot of the right side. A slot of the left side is exactly coinciding with the tooth of the right side and this is entirely a south pole block, this entirely a north pole block. So, if we see the right side once again, we see that when we excite phase A and A 2, north pole is under A 1 and south pole is under A 2. So, the tooth of this is attracted by the south pole structure here. So, that also is conducive for the torque production. So, in this case, the two blocks are offset by half a tooth pitch. Now, this is how we have the combination of both permanent magnet torque, also the variable reluctance torque. Now, to further enhance the torque, the stator structure we have shown in terms of very smooth poles, the stator structure although we have only 4 poles here, the poles shoes are corrugated, poles shoes are not smooth as we have shown here, they are also corrugated to match with the corrugation of the rotor. So, in fact, if we draw the structure of the stator pole, it will be something of this sort. We can draw a stator pole structure, it is having slot and tooth, here we have a tooth and slot again, tooth and slot, tooth and slot, tooth and slot, tooth and slot like this and this is how a pole looks like. And these are so planned that the rotor will be exactly under this, we are drawing the rotor structure and hence there is a perfect locking. This is the rotor surface and here we have the stator pole and we have the windings in this case, the stator actually carry the windings, but the stator pole is not a smooth pole, it is basically corrugated having slots and teeth in such a way that tooth of the rotor is facing the tooth of the stator and slot is facing the slot and hence there is perfect locking and thus we can have a high detent torque. Not only that, when we excite the stator, the torque production is basically due to the permanent magnet torque, also due to the variable reluctance torque and hence we call this to be hybrid motor, hybrid stepper motor. The hybrid stepper motors are very popular because of low stepping size, step size is very very low, also the torque is also enhanced. One drawback of variable reluctance stepper motor is that there is no detent torque, by detent torque we mean when we excite the stator, there is a torque production, there is a locking mechanism, but when we do not excite the torque is 0 and this torque is 0 for a variable reluctance type of stepper motor, but this torque is not 0 for a hybrid stepper motor. In hybrid stepper motor, the torque is still present because of the permanent magnet in the rotor and hence we have a detent torque. Now, these are the various type of stepper motor we have studied, primarily there are three types of stepper motor to summarize. We have variable reluctance type stepper motor, we can increase the step size by increasing the number of stack, we can have a single stack or a multi stack motor. Then we can also have a permanent magnet stepper motor, where we have the torque produced only by the permanent magnet and finally, we have a hybrid stepper motor, where the torque is produced by the combination of permanent magnet and variable reluctance type of torque. Now, having discussed about the structure and the type of stepper motors, we will discuss about the behavior of stepper motor. Now, let us have a look at the stepping rate, now the stepping rate we define as the number of steps per second. So, that is the definition of stepping rate and if we increase the stepping rate, the speed increases and beyond certain stepping rate, the stepper motor does not stay in synchronism. Stepper motor is a very beautiful motor for position control, we do not have to have any position feedback. What we give here is a few pulses and the rotor faithfully obeys this pulses and hence the position control is achieved without any closed loop feedback. Stepper motor control is primarily an open loop control and hence it is much more attractive compared to a servo motor. In servo motor, we have to have a closed position feedback. In stepper motor, we do not have to have a position feedback. We apply the pulses and the rotor follows the number of steps, but if the stepping rate is increased, the motor falls out of synchronism. It does not faithfully obeys the stepping command and we have to confine the operation within a acceptable stepping rate and that is how we can determine the operating range of the motor. Now we can draw a graph which will give us the load torque versus the stepping rate in second. So, this is pulses per second and the load torque could be a Newton meter and we have two types of characteristic and this is basically what you are trying to draw here is torque versus stepping rate characteristic and here what we have here is that we can have two types of graphs here. One is like this, other is like this. So, this is the origin we have and suppose we apply a load torque and the load torque here is T L 1. Now the first curve we can show this by 1 and this is the second curve we can show this by 2. So, this is the first curve and this is the second curve. So, we have two curves here, curve 1 and curve 2 and if we have a load torque and the load torque let us say T L 1, we will have two stepping rates corresponding to 1 and corresponding to 2. What does it mean? Here we have two stepping rates here. This will give us S 1 and this will give us S 2. Now this S 1 is the stepping rate for which the motor should be starting. When the motor is on the standstill condition we can maximum give a given a stepping rate that is equal to S 1 to start the motor and when the motor starts you can increase the stepping rate to S 2. So, the starting stepping rate should be below S 1 and when the motor starts up you can increase the stepping rate to S 2 and hence we can call this graph 1 to be the start graph or the starting graph and the graph 2 should be the running. So, we can say that the starting stepping rate, starting stepping rate should be lesser equal to S 1, the running stepping rate should be lesser equal to S 2. So, this is for a load torque for a given load torque, for a given load torque what is the load torque here? Load torque is T L 1. So, for a given load torque T L 1 to start the motor the stepping rate should be less than S 1. What happens if you apply more than S 1? Say for example, S 1 is 3000 pulses per second. If I apply 350 pulses per second what happens? The motor will not respond, motor will refuse to start. So, for starting of the motor the stepping rate should be less than S 1. The motor understands the condition it is having some inertia. So, to start the motor the stepping rates should be low 1 and when the motor starts you can apply a higher stepping rate that is up to S 2. So, we can call this to be this to be the slew range. So, this green colored region we can call this to be the slew range. And the region which is left of 1 which we can show by let us say this blue graph this is called the start range. It means if you want to start the motor the stepping rate should be in the start range. So, after the motor successfully started you can increase the stepping rate to the slew range. And it should be under no situation should be in the right side of second characteristic. If we go beyond this suppose we have we have the stepping rate which is here and for this stepping rate motor falls out of synchronism motor does not stay in step and the position control is lost. So, we have to be very careful that for starting of the motor the stepping rate should be in the start range and when the motor runs we can operate the stepping rate can be increase to the slew range. So, this is how the stepping rate is determined for a given load torque. Now, when we have a stepper motor drive stepper motor we need a we require a drive for that we want to have a converter which can inject current into the various windings. So, we can have a simple structure in which we can inject the current on to the various phases unless we excite the various phases motor would not start. So, we have to have a converter to inject the current on to the windings of various phases. So, that the motor starts and hence we can have a variety of converters which can be used with a stepper motor. So, let us see one type of converter. So, we will have the drive circuit for stepper motor a very simple drive circuit. What we can have here is the following we have we have a DC supply and then we have a switch and then we have the phase of the stepper motor the winding of course, we have to have a freewheeling diode. So, this is this is the voltage that we have V D and we have the phase and we can have the current in the phase that is I phase and this is the freewheeling diode we have that is D F. So, this is this is the simple circuit for a stepper motor drive we have a DC voltage we have a switch here we have we have the winding and then we have a freewheeling diode. Now, what is our ideal characteristic when we excite a stepper motor the current should rise very sharply and raise the maximum value because current determine the flux determine the M M F hence the current should be essentially a rectangular current. So, what we have here is the following that this is our ideal characteristic we want our characteristic to be ideal. So, this is the time axis and this is the axis of I phase. So, this should be the ideal characteristic. So, this is the ideal current. So, the actual current however does not follow the ideal behavior. So, the actual current rises like this and it is the maximum value and then when we close the switch the current rises reaches the maximum value and it stays there. And then when when you want the current to be equal to 0 we switch off this switch we have a switch here this is turned off and when we turn off this switch the current freewheels through the diode D F and this decreases in the freewheeling process the current decreases. So, what we have here is that the current falls like this. So, this is how the current in a winding changes, but we want the ideal behavior. So, we can improve upon this particular circuit to achieve a ideal characteristic and that will be seen subsequently. We are discussing about the drive circuit of the stepper motor and we know that we want an ideal behavior of the current. Wherever we close the switch current should rise to the finite value when we open the switch current should come back to 0, but it does not happen in practice. In fact, every winding is having some inductance every winding is having some resistance and hence when you close the switch the switch is closed the current is going to take some time to rise. And this rise time can be reduced if we reduce the time constant of the circuit. Similarly, when we switch off the switch the current will fall down to 0 by freewheeling through the diode. So, we have this diode here and the current in fact freewheels when the switch is off the current freewheels like this and because of the freewheeling it takes some time for the current to come down to 0. So, we have the rise of the current is like this then it stays at the maximum value then when you switch off the switch the current comes back to 0. And can this be can this rise time and fall time be reduced? The rise time and the fall time can be reduced by a simple means insert a resistance. Insert a resistance in the winding during the on state of the switch and insert some resistance in the freewheeling diode during the off state of the switch. So, what we do here is the following we insert some resistance here maybe we can call this to be R 1 and we can also insert some resistance here that is R 2. So, by inserting resistance what we are trying to do effectively we are trying to reduce the time constant of the circuit. If the inductance is say for example, the time constant is given by tau is L by R and that is equal to L by the resistance of the phase plus R 1 in the on state and in the off state this is the on state time constant. In the off state we have the time constant equal to L by its freewheeling like this this is R phase plus R 1 plus R 2 plus the diode resistance. So, this is the off state time constant and on state time constant is L by R phase plus R 1. So, by introducing resistance in the respective circuit we can minimize the time constant and hence we can reduce the on time and off time. This is one of the techniques followed to minimize the rise time and fall time of the current in a stepper motor drive very inexpensive, but what is the problem? The problem is that the drive is going to be less efficient because whenever we insert resistance it is going to consume power. The overall efficiency is going to calm down. So, we can of course, we can increase the fastness of the circuit the rise time and the fall time can be reduced definitely, but are the cost of the efficiency. So, by introducing the resistance we can perhaps increase the fastness we can say that the rise time improves and the fall time also reduces, but this will be less efficient. So, the efficiency goes down. Now, what is the solution? The solution is to go for an efficient drive. In an efficient drive we can apply sufficiently high voltage. So, that the current rises to the maximum possible value. Now, in the rise time if we see the rise time is not only function of the time constant, but also function of the applied voltage. So, we can apply little higher voltage. So, that we get a faster rise time and then when we want to make the current equal to 0 instead of freewheeling the current we feed the current back to the source and that means the energy of the inductor is not wasted it is fed back to the source and that is an efficient drive circuit which can be employed for stepper motor. So, we will be discussing about an efficient drive circuit for stepper motor. So, an efficient drive circuit an efficient drive circuit. Now, what we have in this case is applied voltage and then we have 2 switches here. We have the phase in this case we have another switch here, we have the diode here. So, this is S 1, S 2, D 1 and D 2 this is a phase V phase here and this is I phase. Now, this operates in a in an interesting way when we want the current to be established in the winding we switch on S 1 and S 2. So, when S 1 and S 2 is switched on the voltage across this winding will be V dc or the applied voltage. So, this is V D or V dc this is applied voltage. So, suppose we want the current to follow a particular pattern say this is the ideal current it should be something like rectangular structure and this is the time axis and this is I or I phase. So, we switch on S 1 and S 2 the current rises here and then we switch off S 2 one of the switches is turned off. When the switches is turned off the current falls down in this case and then we switch on again S 2 the current rises and then we switch off S 2 and the current goes on changing like this. And finally, when you want to bring the current down to 0 we switch off both S 1 and S 2 and the current falls down to 0 like this. So, this is the nature of the current in the winding or the phase of the stepper motor. So, if we plot the corresponding voltage here the applied voltage in this case. So, when you want to when the current builds up we apply V d we we turn on in fact S 1 2 then we switch off S 2 it freewheels through the freewheeling path is like this S 2 is turned off S 1 is still on. So, this freewheels here the voltage is 0 in this case then again we turn on S 1 S 2 it goes down to 0 again. So, the voltage changes like this. So, this is how the voltage changes. So, here what we do we apply again positive voltage and then when you want to finally bring down the current to 0 a negative voltage is applied. So, in fact the conduction sequence is as follows S 1 S 2 then S 1 d 1 S 1 S 2 S 1 d 1 and so on S 1 S 2 and S 1 d 1 and finally, during this time the conduction is fully by d 1 d 2. So, when we turn off both S 1 and S 2 the current is still in the winding and any inductance will try to maintain the current and when we switch off S 1 and S 2 the current tries to flow through d 1 and d 2 and in that process it is fed back to the supply. So, the current does not freewheel the current in this case is fed back to the supply like this. So, this is how the energy in the inductor is not wasted anywhere it is ultimately fed back to the source. So, this is definitely an efficient drive in some situation as we have already seen in case of say for example, a hybrid stepper motor we need to have a bipolar drive. So, this is an example of a unipolar drive by unipolar drive we mean where primarily applying a positive voltage. So, this is an example of a unipolar drive. So, we have primarily this is a unipolar drive when we go for a hybrid stepper motor that is a need of a bipolar drive. In bipolar drive both current should be reversed we can have a 1 a 2 and then we should be able to have a 2 a 1. So, that can be achieved by having 4 transistor in this case when we have a unipolar drive we have only 2 transistors transistor S 1 and S 2 we have the switches S 1 and S 2. Now, if we want to have a bipolar drive we have to have 4 transistors S 1 S 2 S 3 and S 4 as follows. So, we can have a bipolar drive bipolar stepper motor drive. So, what we have here is the following we have the applied voltage here and we have 4 transistors it could be any transistor may be MOSFET or BJT it is a small drive it is a low power drive. So, we do not have to use very high power devices it could be primary MOSFET although we have shown the symbol of BJT these transistors. And then we have the feedback diodes the diodes are inherently present here they will help us in freewheeling or feeding back the current and we have the windings in this case this is say for example, a 1 a 2 this is the V phase with plus and minus this is I phase. So, we have S 1 S 2 S 3 and S 4 and we also have D 1 and D 2 this is feedback diode. So, we have 4 diodes and 4 transistors here. So, this is applied voltage. So, to apply a positive voltage we switch on S 1 and S 2 positive voltage is applied by turning on S 1 and S 2. So, this is the feedback diode. So, that is V D and we can apply a negative voltage by turning on S 3 S 4 and that is equal to minus V D. So, this is how we can we can apply either a positive voltage we can apply voltage to a 1 a 2 when we switch on S 1 and S 2 and when you want to apply a negative voltage we can we can switch on S 3 and S 4 and we apply minus V D. So, this is how we can excite the windings of a hybrid stepper motor where we need to reverse or we need to apply positive and the negative both. We have already seen that the sequence of the switching is a 1 a 2 b 1 b 2 a 2 a 1 and b 2 b 1. So, we have to go in that particular sequence. So, if we apply positive voltage for a 1 a 2 for a 2 a 1 we have to reverse the voltage and that is achieved by switching the other pair of transistors. Now, this is this is this is how the winding of a hybrid stepper motor can be energized. So, we have seen simple drive circuit for stepper motors. The drive circuits can be unipolar for simple stepper motor and that could be for variable reluctance striped stepper motor. For permanent magnet and hybrid stepper motor where we have the permanent magnet whenever we have a permanent magnet, current direction matters. We cannot be applying only in one direction we have to have a facility for bipolar power supply and hence the bipolar stepper motor drive are suitable for permanent magnet and hybrid stepper motor. So, this completes our discussion on stepper motor. We have seen various type of stepper motor starting from variable reluctance type stepper motor to hybrid stepper motors and each one is having its own advantages So, finally, the base possible stepper motor could be the combination of the two that is and hybrid stepper motor where the stepping size or the step size can be reduced to a very small value without any difficulty. So, in the next lecture we will be taking a new type of drive, the application of induction motor drive and how we can have a utility friendly drive which can be applied for high power application like traction and what is the effect of the drive on the power system, how we can improve the quality of electric power while operating the drive that will be discussing in the next lecture.