 Hello, we have discussed various components of an EPR spectrometer. Today, we are going to see how the whole spectrometer is made up. So, for that, let us see a simplest possible EPR spectrometer that is shown here. Microwave power comes from a some source, it could be a Klaistron oscillator or a Gaon oscillator. Sample is kept inside a transmission cavity. Microwave enters through this iris here and comes out and again through a waveguide, it goes to the detector and this sample is kept in the magnetic field. So, by scanning the magnetic field, one can see the spectrum. But this is not a very sensitive spectrometer. As I said earlier, the Q of this transmission cavity is very low. So, even though such spectrometer were used earlier, nowadays this set of spectrometer is never used. So, we almost always use a reflection cavity whose Q is much higher. Now, how is that used? So, we need to have the microwave coming from cavity, microwave from the Klaistron, go to the cavity and when the power is reflected from the cavity, it should not go back to the Klaistron, it should go back to the detector. So, for that we use a special microwave component called a circulator. This is shown here. See, it has got three holes, one here, here and there and they are all connected. If you see that this is real through and through hole there. But the property of this device is such that it is non reciprocating. What do you mean by that? For that, let me draw the schematic diagram of this circulator. Here are three holes and we call them port, port number 1, 2 and 3. The way this circulator behaves is very interesting. Suppose, the microwave power is entering here. Then, even though internally they are all hollow spaces, it cannot appear here, it has to appear here. That is the way power comes out. Similarly, if the microwave power enters here, port number 2, then it will only appear at port 3 as an output. Similarly, if the microwave power entering in port number 3, then it cannot appear here, it can only come here. So, this is the non reciprocating device. That is, property for the radiation to enter go from port 1 to 2 is not same as property for radiation when it enters 2 to 1. In other words, 1 to 2, I may say this gives a low insertion loss, but 2 to 1 gives high attenuation. Same is true for the other pair of ports here. This could be as 0.3 dB, this could be as high as 20 dB. So, using this, we can make a spectrometer, which will allow us to change the microwave, allow us to, for the microwave power to go from the klystone to the cavity in this fashion. Let us see. This is the circulator. Port number 1, 2, and 3 are connected in this fashion and the klystone or the ghan oscillator produces microwave power, which enters port number 1. This enters power, enters from 1 to 2 and from this waveguide, it goes to the cavity and cavity will be reflection type. It reflects the microwave power and goes back here. While going back, it will not go to port number 1, instead it will go to port number 3 and there we keep a detector. So, the key of the cavity is much higher than the transmission cavity. So, it is more sensitive and the spectrometer works on the principle of reflection of microwave from the cavity. Now, we have seen that this reflection cavity forms standing wave and we can adjust the microwave frequency such that it forms a standing wave and reflection from the cavity is minimum. For the standing wave to form here, we have seen in the last lecture that the frequency of this must match the dimension of this thing certain way and that to happen, I must therefore, first see that the microwave frequency from there is same as the characteristic frequency of this. How do I find that out? After that, I start with varying the microwave frequency of the klystron by modulating its reflector voltage, so that this gives out all sorts of frequency. In other words, we try to see the mode of the klystron and we klystron mode, we have seen that as function of frequency power output has this sort of pattern here. So, these are the possible frequencies that the klystron can give as a function of frequency, but this also be written in terms of the reflector voltage because changing the voltage of the reflector changes the frequency. So, what is done here is to continuously change the reflector voltage and see this mode on an oscilloscope. Then keep on changing the frequency such that the power that comes here will show a certain dip something like this kind that is at this frequency the cavity does not reflect. That means that frequency the turning of is formed and to explain that I have made a small animation here. In this slide, let us say this is the frequency tuning norm. If we turn this the frequency of the klystron is going to change, what is shown here is the klystron mode the output of the microwave power coming from the klystron as function of frequency. But since same power is going to the cavity and cavity in general will have different resonance frequency complete power is reflected from the cavity. So, this is the mode of the klystron. Now, let us try to tune the frequency of the klystron and see that we get a pattern of this kind that where the microwave power is not reflected on the cavity here. So, turning the frequency tuning knob and going through and here the dip is seen. So, this frequency therefore corresponds to the frequency of the cavity. Now, depending upon the voltage this can be anywhere in the profile of the klystron mode for example, here this frequency of the cavity will does not change. What is changing is the condition of oscillations of the klystron. As I change the reflector voltage the position of the frequency here appears to change. But keep in mind that cavity frequency does not change it is the klystron that giving out that voltage that is here that voltage is changing. So, we could in principle work anywhere in this profile here, but what is done is that we try to get the maximum microwave power out from the klystron. So, we try to work at the top of the mode how to do this let us say it is gone all the way down there. So, we have to go back and then try to bring the this cavity dip as it is called to the peak of this somewhere here where the maximum output comes here. So, this is the place I must keep the klystron frequency note here that though much of the microwave power is absorbed by the cavity reflection is small nevertheless this is not completely 0 here this bottom of this thing is not touching 0. That means, even at that frequency some microwave power is getting reflected from the cavity. We can improve on this. So, that the matching is such that very little power is reflected for that what we do is the cavity has a iris tuner the cavity has a tuner screw in front of this iris hole. By adjusting the position of the screw one can match the microwave that is coming from the klystron entering the cavity and that is reflected from the cavity that can be matched. So, that reflection is minimum to see that I have again got another animation here. So, let us say the tuner screw is quite far and cavity is not matched properly this is the tuner screw shown in red. Now, I try to insert the screw slowly inside and this is small dip that you see here is the place where the cavity is trying to retain the microwave power inside it all around this one. So, here the cavity tuning screw is gently inserted and see the how the deep is increasing. Deep is increasing means less and less power is getting reflected from the cavity here. So, almost this is the 0 level where reflection will be almost 0. So, here it almost touches 0. Now, if we go beyond that this will further start reflecting microwave power. So, this position where it goes to the bottom most is called the critically matched cavity or critically coupled cavity. The cavity is critically coupled to the waveguide that allows the microwave to come in it will do it once more. So, if you go beyond the critically coupled condition microwave power will be further reflected start from here. So, I am try to tune it by adjusting the depth of the screw slowly going down and down. So, here it is trying to go to 0 this is 0. So, this is called the critically coupled cavity. So, we try to work almost here if it is under coupled then the cavity dip let us say this is the critical coupled condition. So, it just about to touch this bottom most position is called the slightly under coupled cavity and if it is it goes beyond that and again comes out that is called over coupled cavity. In either case the reflected power will be slightly finite that is it is not going to be exactly 0 it will be exactly 0 if it is critically coupled. So, this again going beyond critically coupled. So, it has become over coupled power is getting reflected ok. So, this is the spectrometer now where let us say we have achieved the critical coupled or very nearly critical coupled condition. So, the very little micro power is getting reflected and appearing in the detector. Now, this is fine, but not good enough because the detector diode has very little power that falls on it. We saw in the last lecture that the characteristic of the detector depends on the power that falls on it in this fashion current which looks something like this. So, when it is very small it is very insensitive somewhere here it is more sensitive that we saw in our last lecture. So, we want to have a sensitive spectrometer. So, there is small change in microwave because of the EPR absorption can be detected much more conveniently. This should be as high as possible for a small change of micro power that is here versus here more detector voltage is possible. So, here we can bias the detector diode such that instead of working here we like to work somewhere here. Now, one way to do is to instead of working at critical coupled condition or very nearly critical coupled condition we deliberately mismatch it. So, that always some micro power comes from here and falls on the detector that is possible, but there though it is possible and sometimes it is done it is not the very desirable arrangement because we are deliberately losing the sensitivity by spoiling the matching here. So, instead what is done here is that we take micro problem in the klystone directly and to another path we try to bring it here and call it a bias power that is done in the so only the next slide. So, you see here in the blue line some part of the microwave is taken here and it is passed through a phase shifter this 5 transfer phase shifter and this comes here and then it falls in the detector we call this bias power. So, that is by design we can bias the detector to work at a place wherever you want in this fashion. So, this taking a micro power from the waveguide is done through a type of device which is shown here this is called directional coupler. So, here you see that one waveguide is through and through hole here and other one has got a hole here, but it is blocked at this end and also it has got arrow of this kind let me draw this is blocked here and arrow has this sort of element. So, essentially it has got 3 ports let us call it 1 2 3. The way it works is that micro power that entering here will appear port number 3, but a part of that will be coupled to this side and how much of this will coupled depend on the construction. On the other hand the power that is entering here will of course come here, but part of that will get coupled to this part, but here is blocked and also we have inside that we have put a material which absorbs the microwave. So, this does not reflect. So, this type of coupler which couples microwave in a directed way that is power enters here and only in this direction it gets coupled here is called a directional coupler. So, this is the directional coupler say power entering here will get coupled here and if the entering here it will come here and get absorbed. So, this is the directional coupler which is shown here. So, with this we can adjust the bias, but here you see that the detector sees micro power coming from 2 sources one is from the bias path and other from the cavity. So, if they do not have the same phase then they will try to interfere in a destructive fashion. So, we must have some way to both the some way to have that this 2 radiation have the same phase that is done by changing the phase of the reference power or the bias power that comes through the bias arm. Also where you want to work here how much power we want to use to bias it. So, that is also important because any arbitrary amount of power may not be the optimum value because noise also increases as the this bias power increases. So, for that we need to have a few more micro element in the spectrometer here now. So, let us go through once again the micro power comes from the klystron or ghan oscillator and it goes to this main path called observing power and I have got an attenuator here which can be adjusted to enable me to have any desire amount of micro power to come to the sample. So, this path this is a directional coupler again attenuator is put there. So, that I can decide how much of bias power is necessary and that phase of the bias power is changed by the phase shifter here and then this is for allowed to come to the detector. We have also put a isolator here and its job is to make sure that microwave radiation goes only along this direction any reflection from this direction or here is blocked by this one. So, that this radiation does not reach the microwave source and was interference and this of course the cavity is kept in the magnetic field and this completes the spectrometer and that is the way a modern EPR spectrometer looks like. Now, what happens during EPR transition the property of the cavity changes the matching get disturbed what is the matching is what matching means that we have seen that reflection from the microwave cavity is very very small that matching get disturbed. So, little bit of micro power is reflected. So, you see this is bit of a funny situation that when the sample absorbs micro power then the detector actually sees that more power is falling on it unlike a conventional absorption spectrometer detector will see less power when the sample absorbs. But here the way we set up the spectrometer is that when the sample absorbs micro the detector sees more power we understand why because it is based on this matching of the cavity to the microwave frequency such that well little power is the steady state condition where no absorption takes place. Another important thing is that the coupling decides the phase of the power that is reflected from the microwave cavity. So, let us say this is the reference power or the bias power and this is the signal from the cavity. So, when you go from here very nearly critical couple condition to over coupled condition the phase of the micro power that goes from the cavity actually the opposite. So, it becomes this type of thing. So, what is usually done is that we do not work at all under in the over coupled condition always optimum coupling is done. So, that goes very near to the critical coupling but not quite over coupled condition. So, that the actual phase is decided once and for all. Now why does it happen that phase changes and analogy is probably useful here let us see the Wheatstone bridge. Here this 4 resistances R A R B and R 1 R 2 are arranged in this fashion and connected to a battery here. Now here if the ratio R A and R B this R A by R B is equal to R 1 by R 2 and voltage V 1 is exactly equal to V 2. So, there is no current going through this and we say that this bridge has reached null condition. Now let us say special type of Wheatstone bridge where this R 2 here also R 2 here that is resistance value for these 2 are same. In that case the bridge is balanced when R A will be equal to R 1 then again the current flowing through this will be 0 and we say the bridge is balanced and null is condition is achieved. Now if R A is less than R 1 the current will flow from left to right and if R A is greater than R 1 the current flows from right to left. So, the direction of current is exactly opposite depending upon whether this is more than this or less than this. In a similar fashion when the bridge is balanced in a slightly over coupled or under coupled the phase of the microwave changes exactly by 180 degree in this fashion here. So, this is what we have got so far is called the direct detection EPR spectrometer. So, detector signal that is generated by the detector now is passed through a broadband preamplifier and we can get the EPR signal. To get the signal scan the magnetic field and record this output as a function of the magnetic field. So, the spectra will look like this. So, let us some hypothetical radical gives 5 line and this sort of pattern there. Now the appearance of this will depend on what? Bias power see if we change the phase of the bias power which is here EPRS power by 180 degree then the detector signal changes sign. So, it can change from maybe this to this. So, you have to adjust a bias power and decide what sort of signal we want to record and display. So, we are often dealing with a signal which comes from a radical which are in thermal equilibrium. So, we get an absorptive signal because in thermal equilibrium the lower level has got slightly more population than the higher level. So, there will be net absorptive signal. So, whether this is called absorptive representation now this is absorptive representation that one has to decide one has to decide for all. But the appearance will depend on the phase of the bias power, but it will also depend on the cavity matching with the under coupling or over coupling. That will also change the phase of the power that comes out from the cavity. So, again the appearance of the signal will be depend on whether cavity is critically coupled under coupled or over coupled. But in practice we never work under over coupled condition we work under just a little bit less than critically coupled condition. So, conventionally for absorptive spectrum this is the shape that we have taken to be the true shape of the spectrum it is just convention. Now, this direct detection EPR spectrometer that just now we have described this does not have very high sensitivity nevertheless this has got very fast response time. So, when one interested in looking at transient radical for example, which does not live for long time then this direct detection spectrometer is used transient radical can be created by let us say pulse laser light which lives for radicals may live for few hundred nanosecond to maybe millisecond those are not easy to capture. Sometimes also experiments involve pulse experiment that determines the spin lattice relaxation time for that the relaxation time of the order of microsecond can be detected if the spectrometer is fast enough again the direct detection technique is used there to look at the signal the way we have described now. So, response time of the spectrometer is decided primarily by the cavity Q and the preamplifier. If the preamplifier has a sufficiently broad bandwidth the response time of the spectrometer is decided by the Q of the cavity. So, Q is defined to be nu 0 by delta nu where in this cavity mode this is the delta nu and this is the nu 0. So, this is the Q this is also defined to be the same as the energy stored in the cavity divided by energy dissipated energy dissipated per cycle. So, the higher is the Q see it is going to store energy with a very little loss. So, higher Q cavity will be reluctant to reduce its energy. So, a Q which is very high the micro power inside the cavity does not change very rapidly. What I am trying to arrive at is that to have a very fast responding spectrometer Q should be low or higher Q makes the spectrometer slower. But how is the relation now? So, if you say that response time of the spectrometer tau r and this relation Q is given by 2 times Q l by omega 0. This Q l is called the loaded Q of the cavity. Now, loaded Q is a term we have not used so far. Here whenever the cavity is connected to a waveguide and matched to a micro source what we measure in this fashion is actually the loaded Q of the cavity. So, that is experimentally measured quantity and the way we measure is just this. The another term that is used here is called unloaded Q. It has got more of a theoretical interpretation and it happens to be that this is 2 times Q l. So, we do not have much interest here just it has got some theoretical significance there why it should be twice of this one. But whatever we see in practice is just the loaded Q that we measure experimentally. So, that is this Q given by this formula this is actually this is same as Q l here. So, let us see an EPS spectrometer let us say of this kind working in the X band as frequency omega 0 2 pi nu which is let us say 9.5 into 9 hertz this is 9.5 gigahertz and Q l is typical let us say 2000. Anywhere 2000 to 3000 is the typical values of an X band rectangular cavity. So, if you put it here and then calculate the tau r comes out to be about 65 nanosecond. So, typically a signal which is changing somewhat slower than 65 nanosecond can be recorded by this spectrometer. So, here the higher the Q then because longer that same as what we have said that cavity Q is high then it sort of resist the change of microwave power inside the cavity with this we have basically given the overall appearance of a direct detection EPS spectrometer. And in the next lecture we will see how we can improve the sensitivity of this.