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Undirectional Paramagnetic Amplifier Design Research ,/f. .ASAC ^ ...-. ,- 1-KC ~ i I ,AA.,iU,ETlL t' .i .. ; .c tic s UNDIRECTIONAL PARAMAGNETIC AMPLIFIER DESIGN M. W. P. STRANDBERG TECHNICAL REPORT 363 JUNE 26, 1959 L·A/t 1_·-l-lmr · : '' -',- I'C RESEARCH LABORATORY OF ELECTRONICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASSACHUSETTS The Research Laboratory of Electronics is an interdepartmental laboratory of the Department of Electrical Engineering and the Department of Physics. The research reported in this document was made possible in part by sup- port extended the Massachusetts Institute of Technology, Research Laboratory of Electronics, jointly by the U.S. Army (Signal Corps), the U.S. Navy (Office of Naval Research), and the U.S. Air Force (Office of Scientific Re- search, Air Research and Development Command), under Signal Corps Con- tract DA36-039-sc-78108, Department of the Army Task 3-99-20-001 and Project 3-99-00-000. Unidirectional Paramagnetic Amplifier Design* M. W. P. STRANDBERGt, FELLOW, IRE Summary-The radio-frequency parameters and the quantum- amplifiers along these lines is apparent. This is difficult mechanical parameters entering into the design of paramagnetic to understand because, for example, the application of quantum-mechanical amplifiers are described and discussed. The physical and electrical limitations on such parameters as gain-band- paramagnetic amplifiers to L-band radioastronomy is width product, gain stability, and nonreciprocity are described ana- hampered by the lack of a lossless L-band circulator. lytically and with design curves. Two realizations of nonreciprocal Furthermore, other methods of obtaining unidirectional amplifiers are described and discussed. In particular, operation of a gain-for example, through the use of a circulator (non- nonreciprocal amplifier at 9 kmc is described. Explanations for the reciprocal) or through the use of a negative-resistance observed properties of previously reported amplifiers are given, and the steps necessary to achieve high gain-bandwidth product and bridge-are incomparably more difficult to engineer for nonreciprocity with paramagnetic amplifiers are described. acceptable performance than is a circular-polarization amplifier. Probably the only other reason for the ab- INTRODUCTION sence of interest in a circular-polarization amplifier arises from the fact that a concrete and detailed design F THE MANY desirable characteristics of a does not exist. This paper offers a simple and easily solid-state amplifier, such as large gain-band- realizable design for a circularly-polarized cavity ampli- width product, low noise figure, and tunability,' fier. The basic idea upon which the amplifier rests is one important quality is a unidirectional and nonre- quite simple. It is that a two-port RF system can be ciprocal amplification characteristic. Although it has made to absorb or to emit, coherently, energy in a uni- been pointed out' that these amplification characteris- directional fashion if the RF fields comprising the sys- tics are achievable by using circularly-polarized electro- tem are resolvable into two orthogonal field systems. magnetic fields and the inherent Faraday effect of para- This system can also have nonreciprocal gain if the mat- magnetic systems, little interest in development of ter in which the fields exist exhibits a Faraday effect and the orthogonal modes are positive and negative cir- * Original manuscript received by the IRE, June 26, 1959; re- cularly-polarized fields. The system need not exhibit a vised manuscript received, January 12, 1960. This work was sup- pure Faraday effect, however, and still have a nonrec- ported in part by the U. S. Army Signal Engineering Laboratories and in part by the U. S. Army (Signal Corps), the U. S. Air Force iprocity of gain which is sufficient to stabilize the am- (Office of Scientific Research, Air Research and Development Com- plifier against gain-fluctuation arising from variation of mand), and the U. S. Navy (Office of Naval Research). t Res. Lab. of Electronics, Mass. Inst. Tech., Cambridge, Mass. the reflection coefficient of the input or output ports. 1 M. W. P. Strandberg, "Quantum-mechanical amplifiers," PROC. IRE, vol. 45, pp. 92-93; January, 1957. As a matter of historical AMPLIFIER STRUCTURE accuracy, it is necessary to point out that many of these ideas were developed in collaboration with H. R. Johnson in the summer of This discussion will be restricted to a regenerative or 1955. Pioneering work on ammonia beam experiments (see H. R. Johnson and M. W. P. Strandberg, "Beam system for reduction of cavity paramagnetic amplifier. This is not a severe re- Doppler broadening of a microwave absorption line," Phys. Rev., striction; ample gain-bandwidth product is available vol. 85, pp. 503-504; February 1, 1952) had indicated the limitations on the use of ammonia beam masers as practical amplifiers. Discus- from such structures, and they can be cascaded by any sions, which were held in Cambridge, Massachusetts, and in Culver number of means to form an amplifying structure with City, California, established a firm scientific basis for confidence in the ultimate and tremendous usefulness of solid-state amplifiers. Sim- over-all gain and bandwidth characteristics equal to ple though it sounds, the novel idea at that time was that paramag- those envisaged by present slow-wave structures. netic materials presented the means by which one could make a prac- tical quantum-mechanical amplifier with large gain-bandwidth Whether one calls such a structure a cascade of low- product, low noise figure, tnability, and large dynamic range. In loaded Q resonant systems or a slow-wave structure is a 1955, the state of development of quantum-mechanical amplifiers showed a lack of ability to achieve all of these qualities rather than lack of matter of semantics rather than of engineering. The re- confidence in being able to build amplifiers, since all of the methods lationship between the Q of the structure, the gain in for obtaining negative resistance in gases and solids that are known today had been disclosed (and some demonstrated) at that time. Gen- decibels per free-space wavelength G', and the wave- eral design problems were given further consideration by the writer slowing factor s, the ratio of the group velocity vg, of and were discussed with various people. Some of these ideas were presented at a Physics Department Colloquium at M.I.T., in May, the structure to the velocity of light c is, 1956. These discussions inspired interest in many quarters in most of the elements of paramagnetic-amplifier design and use, the outstand- 20rs log (e) ing exception being the realization of a circular-polarization cavity Q= I (1) amplifier. A proper understanding of the noise figure of quantum- G mechanical amplifiers was certainly not available before the analysis made by the writer and others in 1956 and, furthermore, the proper The type of structure to be used is obviously dictated application of this theory in terms of observed circuit parameters was by the gain not well understood even after that. The actual translation of theory and bandwidth requirements for any par- into application to actual devices is always difficult; this paper is ticular application. For example, in the hydrogen-line merely intended, again, as a translation of theory into a concrete radioastronomy studies at 1420 mc, a bandwidth of 300 device. Cf. M. W. P. Strandberg, "Inherent noise of quantum-mechani- cal amplifiers," Phys. Rev., vol. 106, pp. 617-620; May 15, 1957. mc with a gain of 20 db would be sufficient; but for ther- 1308 PROCEEDINGS OF THE IRE July mal-source studies one would like to have a bandwidth = of the order of the operating frequency and a gain of Qz Qo(1 + i2(f J )) (4rn)-1 (6) 20 db. For radar or communications applications, one would possibly have requirements for modest band- If a cavity containing this complex susceptibility width of the order of a few tens of megacycles with gains terminates a transmission line having an admittance Y0, of the order of 30 db. In some work there is also a re- it represents a load admittance, Y=g+ib, which is con- quirement for high stability of gain of the device with ventionally described in terms of the cavity unloaded changes in operating conditions. For example, in broad- Q, Qo, the magnetic Q, Q, the coupling Q, Qe, and the band radioastronomy, the thermal radiation is inte- frequency as: grated in time in order to improve the sensitivity of the g Qe Qe (7) device. Here the requirement for the gain stability is Yo Q. Q0 high and has a high priority. b (f-fo) 2f The traveling-wave amplifier has an exponential in- -=2Qe- - (8) crease of gain with length as follows: Yo fo Be Then the reflection coefficient (or voltage gain) is: Pout = elPin = GPin (2) Yo - Y where r + Y Y0+ Y 8w2fr = _- Im (). (3) Qe Qe _ 2J ( 2A Qxo (1 - - i- )( 1 + i-J - (9) Here f is the wave frequency, rqis the filling factor, and a Qe single resonant term in the complex susceptibility is2 Qo Be B, + Qo Q0 -B, ) (I B, Qz0 f (4) The bandwidth, B, of a single-tuned stage is defined as the frequency width between the points at which the (f - fo) + i - 2 magnitude of the reflection coefficient squared is re- duced to half of itsvalue at resonance. 16Af4 + 4Af2[Be2(1 Qe) + B2 - 2 BeB] + Be2B2 (1 Q-- 2 16f4 +4A2 [B 2(1 +) + 2 -2 Qe BeB Q Q0 (10) 4 2 2 B 2 2 q 16Af - Af B o 1 q- - 2 Q- BeBx Be2Bx 1 Q., Q,, Q0 QXO Q0 QQo) with B. the paramagnetic resonant linewidth. The gain Therefore, thus exponentially follows the frequency variation of B [1 (e2 Qe the susceptibility of the paramagnetic material both B2 = [- 1 Be2 +Bz2 _- 2-BeB through the imaginary part of the susceptibility direct- 2 Qo/_ Qo ly and through the real part of the susceptibility in its influence on the group velocity.
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