 Hello there, we have seen how a direct detection EPR spectrometer works, let us recapitulate that once again. In the slide this shows the direct detection EPR spectrometer, microwave comes from a source goes through isolator then main power comes through this observing path and intensity is adjusted by the attenuator enters the circulator port 1 appears in port 2 and goes to the cavity gets reflected enters port 2 and appears in port 3 and goes to detector to bias the detector some amount of microwave power is taken through this blue path again it is amplitude is adjusted phase is adjusted and then it is allowed to follow the detector. You balance the micro bridge such a way that very little reflection takes place from here and you work adjust little under couple condition. The reflected micro power is detected by the detector and amplified by the preamplifier its output gives the EPR signal. Now this spectrometer of course does not have very high sensitivity, so how to improve the sensitivity we are going to discuss that in this lecture. Then the sensitivity of the EPR spectrometer, now sensitivity is a measure of how small signal one can detect, of course it depends on the amount of sample that is present there. So the smallest amount of sample that a spectrometer can detect is its sensitivity, so the signal that we see let us say some absorption spectrum this kind. Now it may have electrical noise of this kind let us say, so the quality of the spectrum depends on how much this noise present here and how much signal that is present here. So is defined to be with this number called signal to noise ratio S by N, S is the signal voltage which is usually measured from let us say middle of this patch to this here. This is the signal voltage and N is the noise voltage which is measured by this width of this patch this is the noise voltage. So naturally a good signal is the one for which the signal voltage is high noise voltage is low. So let us say another one which has got this sort of thing here little less noise of this kind. So for both of this the signal voltage is about the same but noise being smaller here, signal to noise ratio for this signal is more than this one, this is a better quality spectrum. So we want to see now how we can improve the sensitivity of the EPR spectrometer, in other words the signal that it collects will have as little noise as possible without sacrificing the signal voltage. For direct detection spectrometer which is used for capturing fast events like transient radicals or measuring relaxation time using pulse techniques we have to use the way it is. So here to improve the signal noise ratio what one does is to do the experiment repetitively again and again and again and use this simple technique called signal averaging and this is possible for repetitive signal. So repetitive signal suppose you got a signal of this kind what about may be the source of that one if I keep on adding this again and again and again then what happens S is my signal voltage and N is the noise voltage for one experiment which is of this kind. So if I add N such signal then the signal due to N let us say addition will be N times S because all the signals should look the same they are adding coherently. How about noise the noise this appears here a random nature so every time I get a signal of this kind the signal voltage will remain the same but the noise will look similar but not quite the same actual fluctuations will be quite random. So if this is the noise voltage that you see here after adding N such thing noise after N addition will add in coherently and from the statistical nature of the random numbers this will be square root of N times the noise voltage which is this one. So signal noise ratio after N addition will be N times signal voltage divided by root N times noise voltage. So this is the signal noise ratio that initially we had here this becomes square root of N times signal noise ratio of the single experiment. So you see here therefore that if I keep on adding this signal I can improve the signal noise ratio by this factor here square root of N. So if I do for example experiment 100 times then the signal noise ratio of the added signal will be 10 times bigger than the signal noise ratio that initially we had for one signal. So this synchronous addition of repetitive signal therefore can improve the signal noise ratio of direct detection spectrometer here you do not sacrifice the speed of the spectrometer we only have to have repetitive signal and then we can improve the signal noise ratio by the signal averaging technique. This is not very common for most stable radical where we work on a steady state mode in other words radicals stay there forever. Here a technique that is used to improve the signal noise ratio is called locking detection or also called phase sensitive detection. Let us try to understand what it is the principle of this is explained in this slide. Here let us say microwave comes from this place and falls on the sample and microwave is absorbed by the sample and is producing a signal which comes out here in the form of signal voltage. Suppose there is an oscillator which gives certain frequency and it modulates the absorbing property of the sample what we mean by that whatever signal that is coming here because the absorption of microwave this modulating voltage impressed upon the sample is such that this absorption is changed according to this modulating voltage. So that signal voltage is coming here which is getting modulated at this modulating voltage here. Now there is a some electronic circuit let us say we called a multiplier circuit it takes two inputs one is this signal that is coming out from the sample and falling here other one is a reference voltage which comes from the same oscillator and coming here and these two signals are multiplied. See Vm is the modulating voltage and Vs is the signal voltage and Vr is the reference voltage the output of the multiplier is product of Vs and Vr which is this. Now this is now passed through a electronic filter which removes the high frequency component and allows on the low frequency to pass through and that is the output signal. Now this is supposed to be the phase sensitive detection principle. Now in this diagram nothing will make sense. So to understand what is happening let us make use of the mathematical part of what is going on here. Let us say Vm is the modulating voltage which is let us say Vm0 cos omega p is the frequency of modulation. Vr is the reference voltage that goes to the multiplier let us call it Vr0 cos omega t plus phi r and the signal that the sample gives Vs similarly Vs0 is a cos omega t plus phi of signal. It is easy to understand that why this frequency has to be same because it is the same oscillator which is given the reference signal to the multiplier coming from here and same signal goes to the sample to cause the change in the absorption at this particular frequency. What is possible on the other hand that phase of this and this need not be the same this phi r is the phase difference between the modulating voltage and the reference voltage. The phase of this signal need not be same as this one and this is the phase difference between this what the multiplier does is to multiply this and this. So Vr times Vs this is the product of two cosine function. So this can be written in terms of the property of cosine times plus cosine. Now here this frequency is quite high two times omega t. So in this diagram see the low pass filter job is to remove the high frequency component out of this product of the voltage that comes from the multiplier. So what comes out of this low pass filter is nothing but this term which is V out is V0r V0s times 2 times cosine phi s minus phi r. So here you see that maximum voltage output will come when this is 0 or in other words phi s is equal to phi r. When this content is satisfied the maximum output will come out of this low pass filter and that is the appear signal. How does it help improving the signal to the noise ratio? How does it selectively throw away the noise component? For that suppose some noise comes whose voltage let us say V noise could be written as V0n cosine omega of n t plus phi of n noise comes in all possible frequencies. It has in general no relation to the frequency of the modulation that is used here. So let us say one particular noise component has frequency Wn and its phase is phi n. Now let us go through the same type of argument now and see what happens. The multiplier will act in the similar fashion so output will be let us say output will give the noise Vr which will be something like this here again the low pass filter will remove this frequency to give rise to this sort of output. Now see what can happen in general these are different so if this is much higher much different from this one let us say higher or lower then this will oscillate so rapidly that on the average this will give 0 contribution. So the output will have contribution only when the noise frequency is very nearly equal to the frequency of the modulation. So in that time this term which is appearing here the phase difference between the noise and the reference also will decide how much output comes from the noise component. If the phase of the noise is randomly changing and has no relation to the reference phase then again on the average this cosine term will be giving average value of nearly 0 and this will be very small. So it is therefore very important to realize that only those type of noise components which has exactly same frequency of the modulation and same phase as the reference can presumably give some contribution as a noise so everything else is getting to be removed by this technique. So this is a very tremendous improvement that one can expect from this sort of detection technique and this that we call a phase sensitive detection because detection is done with respect to certain reference phase or the reference phase and reference frequency decides the selective removal of noise. Also it is called lock-in detection because this detector signal is sort of locked into certain reference frequency either term is used in this terminology. So phase sensitive detection removes all the noise that is outside its bandwidth of detection and also those not in phase with the detection frequency and one can get a vast improvement in the signal to noise ratio of the order of 1000. Now what is done in DPR spectrometer which uses this idea what is done is shown here that we modulate the magnetic field that is Z1 magnetic field that is here by using a pair of Helmholtz coil which is mounted usually on the cavity this modulating current is passed through this coil typically at 100 kHz. So the main magnetic field which is the Z1 magnetic field that is modulated at this frequency what happens then. Now to understand now what happens let us say this is the absorption profile of a EPR signal and the Z1 field is slowly scanned from left to right this is the Z1 field here and every instant of time the Z1 field is modulated by this red oscillatory magnetic field. So as the field is being swept very quickly it is going left and right left and right. So here let us say at this instant if this is the EPR signal where the magnetic field goes down this voltage signal goes down when this goes up again it goes up. So I get EPR signal which will have oscillatory component of this kind when the same amplitude of modulation is present all the time but the Z1 field is now brought somewhere here again this is modulating magnetic field and see here when it goes from this to this the voltage changes in this direction I get a similarly oscillatory EPR signal but its magnitude has now become bigger than what was here. If you keep going in the same direction and somewhere here now in the other side of the absorption graph magnetic field is modulated in the same fashion now here the difference is the modulation of the magnetic field goes down here it goes up the signal goes up. So the same oscillatory EPR signal is seen here but the phase of this is exactly opposite to this side now if you continue to move the magnetic field further away from resonance here again I get oscillatory signal but of smaller amplitude now let us animate this one and see what way it looks like. So a magnetic field modulation is shown in red and output signal is shown in the blue color at different places of the Z1 magnetic field. You notice here the phase of this magnetic field modulation is same but the output is changing its phase when you go from left side to right side so the amplitude of this signal depends on the slope of this absorption profile so long as this amplitude of modulation are very large and also the phase of the depends on the whether it is left side or right side. So if you do now a phase sensitive direction now we have described here we will get a signal which will be a measure of this oscillatory voltage and also the sign of this one. Notice here that if it is exactly at the peak of the absorption profile then what happens? Here if we modulate the field in this fashion here it goes down here but then so in one cycle it actually completes one here this half cycle is here another half cycle it goes here. So this will have this sort of behavior where this frequency is actually two times the frequency of this one. So if this is 100 kHz this will be 200 kHz so there will not be 100 kHz component here so the signal will therefore look like this. So this black curve shows the direct detection appear signal absorption profile and the first wave signal will be having this sort of profile here goes up and then goes to 0 and in opposite direction comes here because the sign of the 100 kHz modulated signal that comes from the cavity changes from left to right and exactly 0 here. So this lock in detection or phase sensitive direction gives rise to a very impressive improvement in signal and noise ratio. What will be the ultimate appearance of the EPR spectrum? I said the phase changes through the peak of this thing so the absorption profile could be either this way first it goes up comes down and goes up or comes down or it could be first goes down and then comes up or goes down or comes up what does it depend on? Of course depends on the reference phase first here for example the output signal depends on the phase difference between the signal and the reference if this is 0 then it gives maximum signal but also if it is phase of the signal is actually phase reference plus 180 degree then this will change sign. So by changing the phase of the reference power the EPR signal can be converted from this to this but I have also seen earlier the absorption profile this itself can change to this if the bias power phase changes that will also change the derivative signal from this to this and finally the cavity coupling whether it is under coupled or over coupled changes the phase of the micropower by 180 degree that will also change the appearance of the absorption profile either from here to there or which in turn can change the derivative signal from this to this. So all this thing will decide the final appearance of the derivative signal. So one has to decide what way the spectrometer is operating and one for all agree the acceptable representation of the derivative signal. So conventionally this is the form that is taken to be the right profile though there is no reason but that is the way it has been taken to be the conventionally right that is first the signal goes up and then comes down goes up and comes down. This is easy to understand that if you have the absorption profile which looks like this that if you agree that our derivative spectrum meter gives absorption in this fashion then naturally the derivative signal should look like this way first positive and negative. Some appear spectrometer is said to detect the second derivative mode instead of detecting at the same frequency as the modulation frequency it detects a signal at twice the modulation frequency. Now second area of this will look like if you do this mentally try to see the every point it depends on slope of this one then this is going to be appearing in this fashion. But here again conventionally a secondary representation is given as this type of behavior this type of signal. So one simply changes the sign of this to appear make it appear in this fashion. The reason meaning that this is some sort of resemblance to the absorption profile here. So secondary representation is taken to be the correct form when it is displayed in this fashion though not mathematically. So you have seen that magnetic field modulation and phase sensitive detection is very high sensitivity. But there are few problems associated with this technique. One is called modulation side band and this causes the lines to be somewhat broad. What is that? So here we are using some AC modulation of the order of less typically 100 kilohertz. Omega of modulation is let us say 2 pi times 100 kilohertz. So this frequency is causing the magnetic field to be modulated. So here the diode sees a signal that comes out of cavity which is getting modulated to this frequency. So this will be generating some frequency and difference frequency of the microwave. Microwave frequency at that is 9.5 gigahertz. So diode being a non-linear device it somehow that modulated voltage could be generating an addition of this and subtraction of this one. So effectively it will generate let us say omega of microwave plus minus omega of modulation. This is the frequency that is going to see there. So this in turn will be seen as a line which is let us say this is the absorption line here. This will because of this two type sum and difference frequency present there this will appear as some transition which is this and this here. Omega microwave plus omega m or omega microwave minus omega m. Now how far this is going to be? This comes from again from the Larmor frequency. Omega is going to gamma electron times b. So here this is the modulation frequency omega m. So this because of if you call this is the effective magnetic field that is it is going to be seen in the spectrum given by the frequency of modulation. So here if omega m is 2 pi times 100 kilohertz and one can calculate corresponding bm that is to be about 30 milligahertz. So here this is the main peak of the IPR signal. So this will be appearing as 30 milligahertz away from this one. Similarly another one will be 30 milligahertz away from the main peak here. Because 30 milligahertz is a very small amplitude of this separation from the main peak and one usually does not see this in the experiment. What one sees is that if the lines are very narrow one tends to become slightly broader line. So the original line width may not be seen if this original line is comparable to 30 milligahertz. The broader line will have no effect on this one. So this is one problem of this modulation broadening due to the side band. So if someone is interested getting a true line width of a very very narrow line then one of course has to lower the frequency of modulation instead of 100 kilohertz one can go to let us say 10 kilohertz or even 2 kilohertz for the magnetic wave modulation and then this will be corresponding made smaller. But then at the same time one sacrifices the sensitivity of the spectrometer in this fashion. I said in our earlier lectures the diode has its own characteristic noise spectrum. Noise that the diode gives out is not constant in all frequencies. It has this type of spectrum diode noise universal proportional to the frequency. So if you work at a high frequency detection for example 100 kilohertz whatever noise I see here will be 1 by 100 kilohertz. If you work at a lower frequency this will be 1 by let us say 10 kilohertz. So correspondingly the noise from the diode will be more. So if we detect the signal at higher frequency diode contributes less noise to that. So that way we have to compromise on the sensitivity if we are interested in recording very narrow line by working at lower frequency of modulation. And second problem is that the increased response time of the spectrometer that is spectrometer becomes very sluggish. I said the direct direction spectrometer is fastest one where one can get response time of the order of 100 nanosecond but that is not possible here. The reason is very simple that the low pass filter is supposed to remove this high frequency component that is generated because of the multiplication here. So typically let us say 100 kilohertz is the modulation frequency and that has to be removed by the filter. 100 kilohertz gives the time period T is equal to 10 microsecond. So this has to be removed by the electronic filter. So typically one uses the time constant of the filter which is at least 3 times higher than this frequency that I am going to remove. So typically therefore the time constant of the filter will be greater than let us say at least 30 microsecond, presumably 100 microsecond something like this. This at least should be 30 microsecond 3 times of that one but may be more than that. So the signal which is changing in this time region cannot be seen by this technique. So this is the problem of this magnetic field modulation and phase signal detection. It makes the spectrometer slow. So anything slower than that can possibly be recorded by this technique. So first signal which changes in microsecond time range cannot be seen by this spectrometer. Nevertheless this is universally used because almost always this spectrometer is used to detect steady state EPR sample for which time is not an issue. So with this we complete the discussion of the EPR spectrometer and its various functions. But one important part we have still not addressed that is how to maintain the matching of the cavity that you have seen earlier that the cavity micropower goes in and comes out. It maintains a good matching condition so that reflected power only remains very very small that we have not yet discussed. It is very important because if we manually match it it is possible that the frequency of the microwave can change slowly either the power supply is changing its voltage or the cavity itself is changing its properties. Maybe it is becoming slightly warm because sample is kept there, microwave is falling on that. So this matching can change. So unless there is an automatic electronic control that microwave frequency always remain matched to the cavity this experiment cannot be done. That technique is called the automatic frequency control also called AFC. Its job is to ensure that the microwave frequency remains the same as the resonance frequency of the cavity and this has to be done over extended period of time. How is it done? To understand that let us again recall how the cavity responds to change in the frequency of microwave. That is again given by this graph that is the frequency of microwave and this is the reflected power. So this is the let us call it the resonance frequency in the cavity. What is necessary is that microwave power that is going to the cavity must always remain same as this one. It is possible that the user itself may shift because as I said the sample can become warm in course of time because it is absorbing microwave property of the cavity changes that changes this one or the frequency itself can change because of the instability of the source of the radiation. How is it done? Now for a cluster on this frequency can be changed by modulating the reflector voltage. So this could as well be written in terms of the reflector voltage. So what is done here? Now suppose at this reflector voltage I apply a small amplitude AC modulation this fashion. See it is a similarity between this and the magnetic field modulation and phase reduction to generate the derivative signal of DPR signal. Very similar idea is used here. We modulate the reflector voltage in this fashion. What happens now? As it is going this way or that way the power will be reflected from the cavity. We will examine two regions now. Suppose we are here and the modulation is this way. So as we go down and up here the reflector power will have this sort of behavior up down up down here. It goes down means it goes up it goes down means it goes up here. Now here similarly suppose another here again we go down up down up here. So here it goes down it goes down then goes up goes down goes up. Again you see that the phase of this is exactly opposite where it we are in this side or that side with respect to the modulating voltage here. So the phase tells me that whether the actual frequency is lower than the cavity resonance frequency or higher than the resonance frequency and also it depends on the how far you are away we are very close or far away. So the amplitude of this decides the extent of deviation. If the deviation is very small this amplitude will be very small if deviation is large this deviation also will be large this amplitude will also be large. So the modulated output has the phase and amplitude. So this gives me the sense of deviation and this gives me the magnitude of deviation. So again if we do the lock in detection at the same frequency I can get the voltage which is the measure of the deviation from the cavity resonance frequency and that is exactly now the correct information that I need to bring back the micro frequency to the desired value. If that voltage is used to change the voltage of the reflector that is produced in the microwave. So similar technique is used also in Garn oscillator whose frequency is modulated and exactly same technique is used to control the frequency of the oscillator. So we have now seen the application of this phase series detection in two instances and how cleverly the noise can be rejected and signal can be amplified and how it is used to generate the derivative EPR signal also generate the automatic frequency control of the micro frequency. Also you see how cleverly it can distinguish various types of signal. The detector sees the microwave modulated by two modulation frequencies. One is the magnetic field modulated by the EPR signal. The other is the frequency modulation of the frequency at typical frequency of the AFC. Two phase detection detectors set to two different frequencies pick up the correct signal based on their reference frequency. That way it can separate the signal. Typical frequency modulation is sometimes used as 70 kilowatts or sometimes 10 kilowatts and this is kept sufficiently away from the magnetic field modulation which works at typically 100 kilowatts. With this discussion now brings us to the complete idea of an EPR spectrometer.