. :._,___;_____::____9:_:.__:__:_:___ __ mmm ‘9; , .r.., (xxx “$wa llJIIIIIIIl|lll|1il|lllllllflll1lWllflllflfllfllllll ‘ LIBRARY [Mlchlgan State University This is to certify that the thesis entitled Theory of the Use of the Super-Regenerative Receiver for the Detection of the Nuclear Resonance presented by Salah I. Tahsin has been accepted towards fulfillment of the requirements for fili— degree in__P_hXSi S Majorirofessor Date PLACE IN RETURN Box to remove this chedtout from your record. TO AVOID FINES remm on or before date due. MAY BE RECALLED with earlier due date if requested. THE THEORY OF THE USE OF THE SUPERAREGENERATIVE RECEIVER FOR THE DETECTION OF THE NUCLEAR MAGNETIC RESONANCE by Salah Izzat Tahsin A Thesis Submitted to the Graduate School of Michigan State College of Agriculture and Applied Science in partial fulfilment of the requirements for the degree of MASTER OF SCIENCE Department of Physics 1951 ACKNOWLEDGEMENT I wish to express my sincere thanks to Dr. R. D. Spence for the unlimited help he was ever ready to give during this work, and for his unequaled patience in clearing up many intricate aspects of the subject. 5’ij ‘ . " p‘ (‘31 )3 l'hif } {I I. II. III. V. CONTENTS Introduction Theory of nuclear magnetic resonance The principle of resonance Relaxation.time Nuclear susceptibility Radio frequency signal at resonance Use of super-regenerative receivers in detecting nuclear resonance absorption The principle of super-regeneration Separately quenched super-regenerative receivers Self quenched super-regenerative receivers Types of circuits Types of signals observed Summary Bibliography Page SOO‘PW 13 15 22 25 30 31 I. INTRODUCTION In l92h, W} Pauli1 suggested that the hyperfine structure of atomic spectra could be explained by the association of a magnetic moment to the nucleus. Uhlenbeck and Goudsmit introduced the electro- nic spin (1925) to explain the fine structure in spectral lines. The success with which the electronic Spin explained these details en- couraged physicists to associate mechanical spin with the nuclear magnets. At present the evidence for the existence of nuclear spin and nuclear magnetic moment is numerous and both are considered as characteristic of the nucleus. The nuclear spin system can be made to absorb energy under certain conditions which will be discussed later. A knowledge of this energy provides a large amount of information about the nucleus itself and may also lead to a further knowledge of the constituents of the media in which the nucleus is imbedded. Many methods have been used to detect this energy. Gorter2 in 1936 made an unsuccessful attempt to detect heating of the crystal- line lattice as a consequence of the energy absorbed by the spin system from.the radio-frequency field and transferred to the lattice by the relaxation mechanism. 1. N. Bloembergen. "Nuclear magnetic relaxation" p. 9, The Hague Martinus Nijhoff, from.W. Pauli, Naturwissenshafters 12, 7m, (1921.) 2. c. J. Garter. Physics 3, 995 (1935) The first successful method was devised and used by Purcell, Torrey and Pound in l9h63. This method consisted of measuring the losses arrising from.nuclear absorption from a sample placed in a resonant cavity. The poor sensitivity of the method for increased power levels led Bloembergen, Purcell and Poundh to the use of a radio- frequency bridge. The principles involved in these two methods will be made clear when we discuss the experimental details. ‘ In l9h7, Roberts5 suggested the use of the super-regenera- tive receiver for the detection of nuclear radio-frequency resonance absorption. The full description and the theory of this method is the subject of this thesis. In Part I, a brief review of the theory of nuclear magnetic resonance is presented. In Part II, the main subject is discussed. .3. E. M. Purcell, H. C. Torrey and R. V. Pound, Phys. Rev. 69, 37 (l9h6) A. N. Bloembergen, E. M. Purcell and.R. V. Pound, Phys. Rev. 73,679 (19u8) 5. A. Roberts, Rev. Se. inst. 18,8A5 (191.7) PART I THEORY OF NUCLEAR MAGNETIC RESONANCE 1. Nuclear spins and magnetic;moments Seeking an explanation of the hyperfine structure in line spectra and the intensity alteration in band spectra, it was necessary to assume that the atomic nucleus as well as the electron possess an intrinsic angular momentum.or nuclear spin designated by (I). When one computes the magnetic moment due to a spinning sphere of mass (m) and a uniformly distributed surface charge (e), one finds: i c arse P (1) where (P) is the angular momentum of the spinning shell and (c) is a constant numerically equal to the velocity of light. The nucleus does not conform to this model or any other pr0posed model. In fact, the resonance absorption phenomena provides one of the experimental methods for finding the relation between the nuclear magnetic moment and the vector P. A variety of experiments have shown that — z __e:._ '73 /‘ f 2 MC (2) Uhere (g) is a constant of the nucleus called the "gyromagnetic ratio", a number characteristic of a given nucleus in a given nuclear energy state. (M) is the proton mass and (e) is the proton charge. If (I) is the nuclear spin quantum number, the angular momentum of the nucleus (P) due to its'spin is -— f /P/= 127;- where (h) is Planck's constant. The expression for the magxetic moment becomes: //“/=i1#fl€/‘}I:c (3) Whenever a magnetic moment (/1) is subjected to a magnetic field or whenever interaction between the field and the magnetic moment exists, a precession of (/2 ) takes place at a certain angular velocity about the direction of the external magnetic field, similar to the pre- cession of a mechanical top in the gravitational field. This precession is called the "Larmor precession" and the frequency of precession is the "Lamar frequency". Classical electrodynamics give the Larmor frequency as 44%..5/7’ (1.) Where (H) is the applied external field. Substituting for 3,757; from (3) into (1.) we get 2/. = :31 Thus a determination of the Larmor frequency for a certain field intensity leads to a determination of the nuclear magietic moment. 2. The principle of nuclear resonance 0n quantum mechanical basis, the components of the magnetic moment in the direction of the field can take only certain assigied values. A magnetic quantum number (m) is associated with these components, which may take any one of the values (i m ) where (m) is related to (I), the nuclear spin quantum number, by me I’l-I,I'£, """ I“! Thus there are (11+!) possible components in the field direction or, in other words, there are (21+I) permitted orientations of spin relative to the direction of the field. When a magnet is placed in a magnetic field, its tendency is to orient itself in the direction of the field where it possesses minimmm potential energy. The same is true of the nuclear magnets, the smaller the angle they make with the direction of H, the smaller is their potential energy and vice versa. Thus, when the field is applied, the nuclear magnets will be distributed on (21*!) energy levels. To effect a transition from one energy level to a higher one an amount of energy 611 4—57»; H) is required, the method of inducing such a transition is the main object of nuclear magnetic resonance experiments. Gorter (2) remarked that, just as in Na-vapor an anomalous electric dispersion occurs at the position of the yellow resonance line, there must be an anomaly in the nuclear paramagnetic susceptibility in the radio-frequency range, if the substance is placed in a large magnetic field H, the anomalous dispersion will be accompanied by absorption at the "Larmor frequency“. If one subjects a sample containing nuclear magnets in a magnetic field to radiation at the Larmor frequency, a nucleus in a lower energy level may absorb a quantum.of energy and jump to a higher energy level. The allowed transitions are only those with Amethhich is the selection rule for this phenomenon. Consider the magietic moment (it ) in the constant field (*7; ), Fig. (l), which is precessing about (17, ) as explained before. A small rotating magnetic field is somehow imposed at right angles to ( H: ), this small field will exert a torque E =/‘: Xi], which is also rotating with the same frequency as (H, ). If the angular velocity of ( l1"; ) is not the same as the Larmor angular velocity of precession 0’: ( f: ), the field (IL-I: ) and ( f: ) will fall in and out of phase ( W'WL) times a second, where (W ) is the angular velocity of ( I27. ), and consequently the torque ( l: ) will tend to increase the angle ( 9 ) when in phase and decrease it when out of phase, thus the time average of the torque action on ( i. ) will be zero. 0n the other hand, if «Jaw; , the torque will keep its tendency to either increase ( 9 ) over the whole period or decrease it over the whole period, re- sulting in our absorption of energy in the first case and emission in the second case. This is what is called the resonance phenomenon. 3. W Any method of achieving nuclear resonance cannot be re- stricted to absorption alone or emission alone as is evident from the discussion of the previous section. At resonance two types of trans- ition are equally probable, those magnetic moments in a high energ state may emit energy and go to the next lower state and those in a low energy state may absorb energy and go to the next higher energ level. To simplify the argument consider the proton with 1:7,:— , then Ms+1,-~ZL , l Figure 1 thus two energy states are available for the proton, if the popu- lation of the two states is the same, no net absorption or emission takes place, but fortunately at thermal equilibrium.a Boltzmann dis- tribution of energy levels exists. Pake6 calculated from.the Boltzmann factor the excess number of protons in the lower state at room temperature in a field of about 20000 gauss and found that for every million nuclei in the upper energy state there are a million and fourteen nuclei in the lower energy state, it is these fourteen nuclei in each two million which are reaponsible for the net nuclear magnetization of the sample and for the absorption of energy at resonance. Lowering the temperature of the sample increases the population of the lower energy states and thus more energy is absorbed at resonance. Rabi? computed the transition probability for an isolated magietic moment with In}: in a constant strong magnetic field and a weak precessing field and came to the conclusion that there is an equal probability of transition in one direction as in the other. Therefore, if a net absorption is to occur there must be, at all times, an excess number of nuclear magnets in the lower state. This calls for a relaxation mechanism to bring the excited nuclear magnets to the 6. G. E. Pake. "Fundamentals of nuclear magnetic resonance absorption" Typewritten notes at Hashington University, Saint Louis, Mo. p. 9. 7. I. I. Rabi. Phys. Rev. 51,652 (1937) lower state. The time required for all but l/e of the equilibrium excess number to reach the lower energy state is called the "relaxa- tion time". The equal probability of transition found by Rabi does not apply completely to practical cases. Rabi considered an isolated magnetic moment while in practice we deal with a very large number of such moments very close to each other. The interaction of these moments is responsible for the relaxation process. The important interactions are, the spianattice and the spin-spin interactions. In the first, the spin system gives up its energy to the vibrating atoms in the lattice and thus "cool down" to a lower energy state. The second interaction considers the additional field set up at the position of a magnet by a neighboring nuclear magnet. If the two magnets are anti-parallel, the "local" field set by one at the position of the other has two unique effects. The component of the local field along the external field will change the Larmor frequency, thus causes a dispersion in the resonance frequency and increases the width of the resonance line. The component perpendicular to the external field will be precessing with the frequency of precession of the source magnet. If the nuclear magnets are identical, their frequency of precession will be the same and nuclear resonance will occur flipping over both nuclei resulting with their exchanging orientations. This "spin- spin collision” phenomenon does not change the population of the levels but it shortens the half life of a certain level thus accelerating the relaxation process. The relaxation:mechanism.was the subject of extensive research 5 have studied re- by many pioneers, Bloembergen, Purcell and Pound laxation in fluids and found that Brownian motion at the Larmor fre- quency provides the relaxation mechanism. Spin-Lattice relaxation times thus far measured range from 10 -h seconds or less in certain solutions containing paramagnetioigfito several hours for very pure ice crystals at liquid nitrOgen temperature6. h. Nuclear Susceptibility The magnetic flux.density or magnetic induction in a magnetic substance is given as jE-= ii:# #iT'iT where E is the magnetic moment per unit volume of the sample. In isotropic substances Elie proportional to the magnetic field H.. The prOportionality factor (3( ) is defined as -él‘i x‘eH and at ordinary room temperature it is usually written out (CK ) is called the magnetic susceptibility, its relation to the absolute temperature is called the "Curie susceptibility" and is given as V = 3%32/‘5 ““9 where (N) is the number of nuclei per unit volume, (8) is the gyro- magnstic ratio (/M.) is the nuclear magneton and (I) is the nuclear spin quantum number. 10 The magnetic susceptibility (7C ) is important in this treatment since it is the source of the nuclear energy absorption. It is con- sidered a complex quantity :x = "Wu/'1” F. Bloch8 in seeking a description of the nuclear induction effect set up and solved the equations of motion involving the nuclear magnet- ization E and the total magnetic field. From these equations he obtained theoretical expressions for ( X ). The expressions for (SCI) and (OCH) as found by Block are called the ”Block susceptibilities" and are "I: (tat-w) . ’___I_ w T x -2 (X0 9 l ’+-T;1(wo-u)i and "X wT~ I '2‘ ° ° 1+7;’(w.-U)‘ (6) II ()4. Where (£41.) is the resonance frequency,w(é) is the Larmor frequency and (T2) is the time required for the components of the magnetic moments to die out to ’/e of their initial value. 96' versus time is plotted in figure 2(a),’X”versus time is plotted in figure 2(b). 5. Radio—frequency siggal at resonance In nearly all the methods used in measuring nuclear sigials the sample is inserted in an inductance coil. The energy absorbed at resonance may be considered as due to the introduction of a dissipative 8. F. Bloch. Phys. Rev. 70.1.60 (191.6) ll resistance H6) in series with the inductance. We find first the potential drop at resonance and then ta). At resonance, the p.d. across the coil is ~_ a/f: ' (4} L. f V- /"- L- W J /“' where L. is the inductance of the air filled coil and I is the com- plex current flowing through the coil. Blit /’t=/+6‘7r'X= /+#F,X/_J-#”-fxll therefore 17=JLJL0 f(/+#IT’X’-J H” 9‘”) or E =%.juL,(/+qrrrx’)+47rwz.,o¢” where i is the impedence of the coil. We are interested in the dis- sipative or real part of this impedance, 0,1.8. 1?. {2%}: r(é)= inmates” In terms of the circuit Q - factor “3R1“, this becomes r(£) .- znr QR’x’TtJ where R is the series ohmic resistance of the circuit. Since the only time variable in the expression for r(£) is ’X’W), the plot for rU'Iis the same as that for I’Mshown in figure 2(b) with a simple change of scale. e____ Iperiod I Figure 2 Kry”’"’rfi \,/” ( a) X” ~« -~ Ipedod m-u~J I (b) PART II USE OF SUPER—REGENERATIVE RECEIVERS IN DETECTING NUCLEAR RESONANCE ABSORPTION Although our main concern is the theory of super-regenerative receivers as used in nuclear resonance experiments, an account of the bridge method seems to be of a great help in pointing out the advantages of the super-regenerative receiver. Furthermore, both methods have the same basic arrangement for producing nuclear resonance absorption. The essential features of the bridge method is the balancing of a signal flactuations. In figure (3), the important parts of the circuit arrangement is shown. The signal is fed to the two branches of the bridge. Two identical oscillating circuits are connected to each branch of the bridge. One of the oscillatory circuits has the sample as the core of its coil. The branches are so arranged that when the signal components from the two branches meet at point (A), they are 180 degrees out of phase. Their amplitudes cancel giving a null effect to the detector. The sample coil is put at right angles to the direction of a strong uniform.magnetic field. The field is modulated by a 60 cycle current carrying coils. The Operation starts by the application of the signal. This sets the oscillatory circuits on the branches oscillating. The fre- quency of oscillation is determined by other experiments and is kept constant during Operation. Next, the magnetic field is turned on and increased gradually until equation (3) is satisfied. This means that .1. E A , l——-T->to detector from signal A generator 5 t-T—l Irw-J or 1 - _._ / \ l W W l-- LLJ z o <[ 2 r) to 30-cycle magnetic field modulator Figure 3 13 nuclear resonance is taking place. The modulating coils serve to swing the magnetic field back and forth through resonance 120 times a second so that the signal may be easily detected and amplified. The energy absorbed at resonance in the tank circuit is taken out of the energy flowing through the branch of the bridge to which it is connected. This destroys the null effect at point A since the component of the signal flowing through the other branch is still the same. The slight difference in energy is sent to a detector and observed on the oscilloscOpe screen. It is to be noticed that at least three parts of this arrangement should be designed very care- fully and present many parameters to be taken care of. These are, the signal generator, the oscillatory circuit and the detector arrange- ment. It will be shown next that all of these parts are taken care of in one simple super-regenerative circuit. The principle of super-regeneration The main feature of the super-regenerative receiver is the periodic building up and decay of free oscillations. Regeneration An easy approach to the principle of super-regeneration is through a discussion of the regenerative receiver. Figure (4) represents a simple regenerative receiver circuit. The regenerative receiver consists of two distinct circuits, a diode detector circuit (the tank circuit) with the cathode and the grid forming the diode and a suitable grid leak combination for de- 1A tection. The detected current is fed to a one stage amplification circuit (the plate circuit) which uses all three electrodes as its tube. When the circuit is connected to the power supply a direct current flows through the plate circuit, the coupling between the plate circuit and the tank circuit is so arranged that the energy fed to the tank circuit is not enough to set up free oscillations. When a signal is received, a varying voltage is impressed on the detector circuit and is amplified in the plate circuit. A part of the energy from the tickler coil (L2) is fed back to the tank circuit through the coupling between L. and L; . The energy fed back adds further amplification to the signal. This process of amplification proceeds until the signal amplitude reaches an equilibrium.value. Two important points must be emphasized. a) The energy fed back should always be kept under a certain critical value at which free oscillations are started in the tank circuit. These free oscillations, if started, block the reception of any signal. b) The simplicity of the circuit, its combined detection and amplification is very desirable. ‘figper-regenergtigg Keeping the same elements in the regenerative receiver, we can turn it into a super-regenerative receiver as follows: 15 a) The coupling between the tickler and the tank coils is increased until free oscillations are set up in the tank circuit. b) The voltage supplied to the plate of the tube is periodically turned on and off. This results in a periodic build up and decay of oscillations. The frequency of these bursts of oscilla- tions is the same as the frequency with which the plate supply voltage is turned on and off. Making the circuit alternately oscillatory and non-oscillatory is called the "quenching action". Our circuit now is a super-regenerative receiver in a rather primitive sense. In the coming sections we will discuss the two types of quench and the different modes of Operation. 1. ‘§gpg5§te quench super-regenerative receiver; In separately quenched super-regenerative receivers, the quenching voltage.from a separate oscillator is applied to one of the electrodes of the tube. The point of application of the quench voltage is customarily the plate of the tube. To understand the basic principles of the Operation of the separately quenched super-regenerative receiver, we shall take the previous circuit as a prototype of all separately quenched receivers and analyze its Operation in detail. For the sake of definiteness, we shall assume that the quenching action is accomplished by a plate. supply voltage whose wave form is rectangular as shown in figure (5). During the interval (‘t’) the supply voltage rises to the value Ebb which is sufficient to allow self-sustained oscillations to E(t) r(t) R (a) Figure 6 Cl E __l l 3&9 0* RI .. B+ Figure 4 ul—‘t—pa———‘[’——H-t T'-———» T —_'T Ebb __f_;.. Figure 5 R'tt) ””1 ’P C 7‘99 3 (b) 1"sz 16 build uplin the tank circuit. The interval.(‘t') is followed by the interval (17'), which may or may not be equal to ('F') in length and during which the plate voltage falls to zero. During the interval (‘tJ) the amplitude of the oscillations in the tank circuit decays because of energy losses in the tank circuit. To understand the process of build up and decay of oscilla- tions in the tank circuit, we introduce the equivalent circuit shown in figure 6(a). The L~C combination is that of the tank circuit. The constant resistance R is responsible for the ohmic and radiation losses of the tank circuit. f(hlrepresents the time dependent resistance which is added to the circuit by inserting the sample in the inductance coil. we have previously shown that r(l) = #ITG’R’X’W) The time dependent negative resistance R'(l‘)al_lows oscillations to build up in the circuit during the period 1?. We may form an estimate of the factors which determinelrwby the following analysis. The current (i) in the tank circuit is given as l =J‘0C '5} : where (ch) is the capacitive susceptance and (Q3 ) is the grid voltage. The plate voltage is epggfieg 9 where (/k ) is the amplification factor of the tube. From.the equivalent plate circuit of figure 6(b), it is clear -=__Af:-__ that the pLate current is ‘P F +JWL‘ P 17 The emf. induced in L1 due to the voltage drOp in L is #632 VP +J ML,- 2 9:JWM(}= —JWM A1 6 C '"p +JWLz We may simplify this term by assuming that J'wlz << rp and replacing M by its absolute value so that ' I‘ Ml' =IM'L.___= l (gm 8 C r? ) where (3", ) is the transconductance of the tube and is defined as 3n2='%%; 7 which is the lepe of the tube characteristic curve. Since .2 = R16)! we get the expression for '3’“) by dividing the last expression for (e) by (i) m - M 'R (Haiti; (7) For the last relation to hold, the slope of the character- istic curve should be a constant, at least at the Operating part of the curve because we assumed linearity when we used the relation 8P z —- f1- 8} We now return to the equivalent circuit of figure 6(a). The differential equation for the current is alt' - _I_ ' .. L 12...,- R(t)¢+C/m’l‘—0 where 7?“) : R-R'(U+rm (8) Differentiating and collecting terms we get dgf'thilfrrffri—‘dfimliw (9) 18 The differential equation as it stands has variable co- efficients which arise from the time dependence ofrU.) and'R—(f). It is of the Hill type since r(t) and RYHare periodic in time. Its exact solution is rather complicated. However, we may make some approxi- mations based on the fact that NH and R- (H vary very slowly compared to the natural frequency of the circuit. Let us put the differential equation (9) in the simpler form I ”m + F(£)I'(H+3(HI(U .- o .. R H l VhOI'O F(e)-——1£_— ama/ 5(f)aZ-E-+L%Ew assume now a solution —fr(0c/r when substituted in the differential equation we get Mm Jim .. gm)- g-r’al] «rm-=- 0 making the substitution /r’(£) = 9a) - ef‘m— #70 the equation takes the form xu-"(é)+ I‘F‘U’) 'V/f/ = 0 Before we go further in the solution, let us examine the time dependence of our variables. Mdvaries with the natural frequency Of the circuit, which is of the order of 1016-/5e¢.-/f(l)depends onR(é)which in turn depends on r“) and R10 . In normal operation the fundamental frequency of R70 and r“) a are the order of lose/a“, and I0 0/590, respectively. 19 With Mt) a very slowly varying function of time, we may assume an exponential solution 1 :tj/ Ml) d! + I ’U'( H: e " or . t J gun/r rwr) = 48 ° Substituting this solution in the differential equation for/V , we get 00/,” yW -.- F[/r(H] V-Jy’: Ir‘m With gar/a very slow variable of time we can assume g’<< y‘. Therefore to a first approximation r3 = 1* It And to a second approximation y r If If - All -’ngl The corresponding second approximation for (’U' ) becomes l' 4 I :J/kmd; “ff—$0” '4 «:J‘] Irma/r ”U“! = 148 v o :: -——— e o . Wr‘ The general solution for (I) becomes 41 - f -%/F///a/t‘ “f. Irma/f o e I: :48 - V If Giving RH and 30) their values, the complete solution becomes _ 131L611. rjlfi‘(§)‘f I“ 1463 2L ' C ‘1— 7 _ . / 2'2 +52)? where we have drapped a term Egg.) because of its smallness and con- sidered the average value of R ( t ) for the evaluation of the exponents. 20 The quantity under the radical is easily recognized as (‘0‘a ), the natural frequency of the circuit, thus —Efl_j‘c g-jw/ I- {7) u __e___._. .. e fEJ' The first term in the solution, namely _ Pfllt x42 21. represents the amplitude of the oscillations. To discuss the building up and decay of the oscillations envelope we write the above expression 8.8 ’R'G‘l- [P+r({)] 1' He 2 L (10) Here we have to consider two time intervals. 1. During the interval ( ‘C‘ ), fig. (5), R'( 6 ) is greater than R-H‘Ulthe oscillations build up. 2. During the interval (1"), R'( t ) is less than R+r( 6 ), the oscillations decay. All super-regenerative receivers can be classified on the basis of expression (10), such a classification proceeds as follows: 1. Separately quenched receivers - R ' ( L‘ ) has a constant repetition period. The receiver Operates in one of two modes. a) The _li_n_e£ mode of Operation - The exponent in expression (10) has a very small value. b) The logarithmic mode of Operation - The exponent has a large value. 2. Self-quenched receivers - R-( t ) has a variable repetition period. 21 Although in these. receivers the amplitude of oscillations normally does not build up to the point where it is limited by the equili- brium value set by the tube characteristics, the amplitude does reach a value sufficiently high that the build up curve is no longer linear. It is, therefore, logarithmic. Now, we proceed to discuss the modes of Operation in detail. a. TheJlinear mode - If the exponent 'RYf) - [FH‘O‘J] T 2L is 811311, the amplitude of the oscillations at the end of the period ( ’C’) may be found by taking the first two terms of the exponential expression (10). The amplitude then becomes 'R'GJ— [R'H‘Ull ,9 [I + [ 2L If] Noting that R' ('6 ) and R are constant during the interval (7“ ), it is clear that the amplitude is linearly prOportional to Mt), i.e. to the resistance introduced by nuclear absorption. Therefore, when the sample is off resonance, all the envelopes will have practically the same amplitude and enclose the same area. At resonance the amplitude is less and consequently the enclosed areas are less. Fig. 7(b) shows two types of envelOpes at and off resonance. b. The logarithmic mode - In this mode the oscillations are allowed to build up to their equilibrium value, determined by the characteristics of the tube, be- fore they are quenched. Going back to expression (10) we see that this 22 happens when the exponent has a large value during (1? ). When the sample is off resonance, all the envelopes enclose practically the same area, except for a slight variation due to the unstability of the noise voltage. At resonance, the oscillations take longer tine to build up and a shorter time to decay. This results with a smaller area under the oscillation envelOpes. Fig. 7(a) shows the change in this area when the sample is at resonance. 2. Selfgguenched super-regenerative receivers As the name indicates, this type of receiver quenches its own oscillations. This is achieved by'a simple alteration in the circuit of figure (A). The values of the components in the grid circuit 0131 are so chosen that the oscillations are interrupted periodically in a manner often known as "squegging". In the separately quenched oscillator Cl‘R1 have such values that Cl partially charges and discharges at the frequency of the oscillator. If the values Of cl and R1 are increased, Cl will not discharge when the polarity changes. It will keep on charging at the positive peaks of oscillations until the grid is driven so negative that it cuts off the plate current. The condenser C will then discharge through the resist- l ance R1 until the grid voltage has the right value for the plate current to flow and for the oscillations to start again. The process is re- peated periodically with a frequency determined by the circuit parameters. The quench frequency is not a constant as is the case with separately N. mem..k IOZMDO n3 mm mococome 8 29:8 9 a e at at a a 8:888 to «RES 9 e e e O : moo: mqmz: .. Iozmao mEmmamm llll AV .Aw at Aw, AV AV 9 95 3:33: Eco? x hm u m3 25> <> 3 23.3 322.68 lo 55:3: xem ".3 ., . i . o . s r