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A Noise Investigation of Tunnel-Diode Microwave Amplifiers* A

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A Noise Investigation of Tunnel-Diode Microwave Amplifiers* A 1961 PROCEEDINGS OF THE IRE 739 A Noise Investigation of Tunnel-Diode Microwave Amplifiers* A. YARIVt, MEMBER, IRE, AND J. S. COOKt, MEMBER, IRE Summary-An analysis and derivation of the noise figure of a must consider the shot noise accompaniying the tunniel- tunnel-diode microwave amplifier are presented. The agreement be- ing process.7 There are two separate and independenit tween the measured noise figure and the theoretical results is an in- direct check on the existence of full shot noise in germanium tunnel tunineling currents, one consisting of electrons tunnelinlg diodes at microwave frequencies. The limiting noise temperature of from the N to the P side of the junction, which we de- the amplifier is elIR/2k, and can be approached by using diodes with inote by ii, and a second curreit, i2, made up of electrons small (RC) products in which the extreme overcoupling (load mis- crossing the junctioni in the opposite directioni. The niet match) and high gain can be achieved simultaneously. measurable dc current is Io-= ii -| i2 . Since the cur- INTRODUCTION renits ii and i2 are uncorrelated, the total shot noisel is represented by a current generator of mean-square A MPLIFIERS utilizing tunniel diodes were first re- amplitude, ported by Chang' at frequencies up to 80 Mc. He also suggested that the noise conitribution of the diode was due to the shot noise accompanying the j2 = 2e( 1iI + i2 I )B, (1) tunneling process. This suggestion was con1firmed by Lee and MAIonitgomery,2 who showed by measurements where e is the electronic charge and B is the bandwidth at 5 Mc that full shot noise was inideed genierated by the in cycles per seconid in which the noise is conisidered. tunnel diode. Tiemaini3 has reported results similar to When the diode is biased so as to operate in the niegative those of Lee and Mllontgomery, obtained from noise resistance region (see Fig. 1), the currenit i2 is negligibly measurements at 500 kc on germaniium diodes. small and the approximation Approximate noise analyses of tunniel-diode ampli- fiers were given by Somnmlers, et al.,4 Tiemann, and Io I ill + I i Hines and Anderson.5 The simiplified equivalent circuits nmay be used. used were sufficient to derive the limiting nioise behavior for very high gain and extremle overcoupling. Yariv, et al.,6 reported the operationi of a tunnel-diode amplifier at microwave frequencies anid measured its noise figure. In this paper, the details are giveni of the noise analy- sis which led to the noise temperature formula stated by Yariv, et al.6 This anialysis is based on an "exact" equiva- lent circuit, and its results are useful in the intermediate range of small or medium gain as well as in the limiting case described above. The theoretical results are com- pared with the nioise measuremiieints. I. THE PHYSICAL SOURCES OF NOISE Fig. 1-A typical voltage-current characteristic In additioni to the omnipresent noise generated by the curve of an Esaki diode. ohmic losses in the spreading and contact resistance of the diode and the surrouniding mlicrowave structure, we II. THE EQUIVALENT CIRCUIT The amplifier constructed for the noise experiment * Received by the IRE, October 3, 1960. t Bell Telephone Labs., Inc., Murray Hill, N. J. consists of a germanium diode mounited in a sinigle port I K. K. N. Chang, "Low-noise tunnel-diode amplifier," PROC. cavity which is coupled to the load anid the source a IRE (Correspondence), vol. 47, pp. 1268-1269; July, 1959. by 2 C. A. Lee and H. C. Monitgomlery, "Determination of forward low-loss circulator as shown in Fig. 2, the coupling being and reverse tunneling cuirrents in Esaki diodes by shot noise measure- conitinuously variable. The equivalent circuit of this ments," Bull. Amn. Phys. Soc., vol. 3, p. 160; March 21, 1960. 3 J. J. Tieman, "Shot noise in tulnnlel diode amplifiers," PROC. IRE, anmplifier is shown in Fig. 3. The diode is represented by vol. 48, pp. 1418-1423; Augtust, 1960. a negative resistance -R, shunted by a capacitance C, 4 H. S. Sommners, Jr., et al., "Tuinnel diodes for low noise amplifi- cation," 1959 IRE WESCON CONVENTION RECORD, pt. 3, pp. 3-8. " M. E. Hines and W. W. Anderson, "Noise performance theory of Esaki (tunnel) diode amplifiers," PROC. IRE (Correspondence), 7 L. Esaki, "New phenomenon in narrow germanian p-n junc- vol. 48, p. 789; April, 1960. tions," Phys. Rev., vol. 109, pp. 602-603; June, 1958. 6 A. Yariv, et al., "Operation of an Esaki diode microwave ampli- 8 See, for instance, J. R. Pierce, "Physical sources of noise," fier," PROC. IRE (Correspondence), vol. 48, p. 1155; June, 1960. PROC. IRE, vol. 44, pp. 601-608; May, 1956. 740 PROCEEDINGS OF TIHE IREJ . I pril f - 4500MC SOURCE CAVITY - Fig. 2-A schematic view of the Esaki diode amplifier. Fig. 4-The series equivalent circuit of the Esaki diode amplifier. )VN2:=4K TCRCB Series resonance occurs at >RL ,>RC 1 Wres -OIo/1 - -- W02R2C2 (2) where wo2= 1/LC. For resonianice to occur at real fre- 2eR,,s queincies, we must fulfill the condition cooRC > I (3) R~ ~~~~~c for w02R2C2>>A, wres Woo. A necessary aind sufficienit conditioni for positive gain Fig. 3-The equivalent circuit of the Esaki diode amplifier. is that the real part of the total series resistanice, seeni lookinig back into the amplifier terminals, be negative; or from Fig. 4, which accounts for the barrier capacitance. The spread- inig and contact resistance of the diode are lumped R > Re. (4) together with the ohmic losses of the cavity in R,. The 1 + W2&R2C2 noise generated by the three sources of loss listed above a noise of is provided by Johnson generator meani-square The highest frequency at which this canl take place is voltage amplitude, called the cutoff frequency, JC,: V2= 4kTCRCB, N/R/Rc- 1 fco .= R (5) where k is the Boltzmiann constant and Te is the ambi- 2r,RC ent temperature of the cavity. L stands for the total and The shot inductance (parasitic inteintional). noise an-d represenits the highest useful frequetncy for a given genierator diode and circuit. Sinice our main initerest is in ani amplifier operatinig at i2= 2eJoB reson-iance, we evaluate the elemenits of the equivalent was discussed above. The load resistance is RL. circuit of Fig. 4 for the coniditioin co rs The result is For the purpose of analysis, it is more convenient to shown in Fig. 5. The effective niegative resistance is now transform the circuit to one in which all the elements are represenited by the series resistanice either in series or in parallel. The series equivalent cir- -R cuit and the new expressions for the equivalent series R - (6)R circuit elemenets are showni in Fig. 4. W02R2C2 1961 Fariv and Cook: A Noise Investigzation of Tunnel-Diode Microwave Amplifiers 741 The bandwidth Af is the distance, in cps, betweeni the half-power frequenicies. It is derived by replacing R, - R' V22 : 4k TC RC B in (7) by the total series impedanice away fromn resonanice as given by Fig. 4. The result is zR2 2 RL-+RC-R' CO)~ R C Af - 2irL I1 \iL( W02R2C2) RL yielding for the voltage gain-baiidwidth product R- , (VG/Z)res,Af(A/Grs\f->/Gfv'G/;AJ _ RL + RC (8) -. 2ei0BR2 y= (A) 2irL - ) v2 -2 R22RC2 VNi~ \ o2R2C2J Eq. (8) takes a meaninlgful formii upoIn substitution of the high gain condition9 Fig. 5-The series equivalent circuit of the Esaki RI ; RG + RL (9) diode amplilier at resonianice. and the definiition of R' as giveln by (6). The result is while the shot noise is niow provided by a voltage gen- (\GAf)high gain = 1 - (10) erator of meall-squLiare amplitude irRC I- --RC 2eIoBR2 CO'"2RC2/ VN12 = wo2RC2C0RC in which form it is ameniable to experimiien-tal veri- ficationi. The physical importance attached to the elements of To increase the gain-bandwidth product, we have to the equivalent circuit of Fig. 5 is of paramount im- use a diode with a small (RC). This happenis, niot onily portance and contains a number of pitfalls, so that a few through the dependenice of V/GA/ on (RC) as giveni by pertinent remarks are in order. Since the resistanices are (10), but also through a less obvious decrease of R,/1'. all in series, they are proportional to power, with the If we assume that the total iniductanice has been made result that onie may wronigly inifer, for instanice, that as smiiall as possible, operation at one frequenicy meanis the power generated by the diode is proportionial to 1 usinig the same C. If one niow goes to a diode imiaterial and, therefore, that for large gain or large power output, with an initrinsically smaller (RC) product, it becomes diodes with large R are superior. In actuality, the geni- possible to operate at the sanie frequenicy with a diode erated power is proportioiial to /IR, xvhich for a given having a smaller R,10 i.e., a diode generatinig more diode material is proportionial to the junictioIn area. power, which corresponids to a smaller R,CR' ratio. Physical significanice caii only be attached to ratios of aiiy pair of resistaInces in Fig. 5. The quanitity R'/IRL is equal to the ratio of power genierated by the diode to IV. THE NOISE TEMPERATURE OF THE AM.PLIFIER that delivered to the load, wvhile RL/Rc, for inistanice, The nioise temperature Tie of the amplifier," wlhich is gives the ratio of the power consumed by the load to somnetimes called the effective iniput nloise tem11perature, that expenided in the cavity.
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