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An analysis is presented for the lntrfztiic time variance originating from thermal noise and finite capacitances in high-speed timing circuits using tunnel diodes. The nonlinear differential equation of the transition is solved numerically for a wide range of circuit parameters,and limitations on the minimum attainable time variance are derived. (Submitted as a letter to the Proceedings of the IEEE) *Work supported by the U. S. Atomic Energy Commission. In many high-speed timing circuits significant time variance is contributed by the triggering jitter of the tunnel-diode discriminator. Even when the input waveform to the circuit is deterministic, there always exists a superimposed thermal noise which results in a finite time variance if the tunnel diode has a finite capacitance. This variance is c(~mputea her’i: for the circuit configuration of Fig. 2a. A representative current vs voltage characteristic of the tunnel diode is shown in Fig. 1. The device is biased initially at v = Vi, Ii = I p- IO and transition to v> Vv will take place if the voltage across the diode is increased above V. The P time variance of this transition will be analyzed cncier the following assumptions: (a) The dc i vs v characteristic of the tunnel diode in the vicinity of the peak cur-rent can be approximated by the quadratic i = I- IO 0 (v- Vi- Vo)2 /Vz, where P V. will be determined later. (b) The tunnel diode is imbedded in the circuit shown in Fig. 2a. (c) The tunnel diode can be represented by its dc i vs v characteristic of (a) parallel with a fixed capacitance C (see Fig. 2b). (d) The drive current is is a ramp function: is = Ii + Vi /R for t < 0 and is = IiiVi/R + kt for t> 0,’ Writing the current sum for node X in Fig. 2b, one obtains the nonlinear differential equation Defining S = 1 + Vo/(2RIo) as a measure of the source impedance, x E IoSt/(CVo) as the normalized time, y = (v- Vi)/(VoS) as the normalized voltage, and A E k C Vo/(IfS3) as the normalized slope of is, Eq. (1) becomes dy/dx- y2 + 2y-Ax=O. (2) This nonlinear differential equation was solved numerically for y and dy/dx wit

Year: 1967

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