Binary Pulse Research Articles

Probability Distributions for the Phase Jitter in Self-Timed Reconstructive Repeaters for PCM

Probability distributions for the timing jitter in the output of an idealized self-timed repeater for reconstructing a PCM signal are approximated. Primary emphasis is focused on self-timed repeaters employing complete retiming. In this case the probability distribution for the timing jitter reduces to the computation of the phase error in the zero crossings at the output of the tuned circuit excited by a jitter-free binary pulse train. It is assumed that the tuned circuit is mistuned from the pulse repetition frequency, and the individual pulses are either impulses or raised cosine pulses. Both random pulse trains and random plus periodic trains are considered. In general, the probability distributions are skewed in the direction of increasing phase error. The approach to the normal law in the neighborhood of the mean when the circuit Q becomes arbitrarily large is demonstrated. Results obtained from the analytical approach are compared with two computer methods for the case of random impulse excitation of a tuned circuit characterized by a Q of 125 and mistuning of 0.1 per cent. Excellent agreement between the three techniques is displayed. For no mistuning and raised cosine excitation two methods for computing the phase error are given and numerical results obtained from both techniques agree closely. Some attention is given to an idealized version of a reconstructive repeater employing partial retiming and it is shown that the timing performance of such a repeater for random signals is very much inferior to the completely retimed repeater.

Deltamodulation for Cheap and Simple Telemetering

Deltamodulation is a simple binary pulse transmission method that can be readily adapted to transmit dc signal levels. It is particularly useful where only a few channels are to be sent, and where one per cent accuracy suffices. A signal-channel demonstration system has been built and tested. The high-speed limitation of such a system takes the form of a finite rate-of-rise, well suited to most telemetering. If, on the other hand, sudden large signal changes are expected, then the system may be modified accordingly. The modified system has the interesting property of giving accuracy varying exponentially with the pulse rate (as in PCM), but still without the necessity of framing the pulses.

Ideal Binary Pulse Transmission by AM and FM

In binary pulse transmission by carrier amplitude or frequency modulation it is ordinarily desirable, both for efficient bandwidth utilization and for improved performance under adverse noise conditions, to use bandpass channels of the minimum practicable bandwidth, as determined by considerations of intersymbol interference and filter design. It is shown that intersymbol interference can be avoided in binary pulse transmission by FM without the need for a wider channel band than in double-sideband AM, for equal pulse transmission rates. Explicit general expressions are derived for the appropriate shaping of the bandpass channel and for the shapes of received pulses, for cases in which rectangular binary pulses are transmitted by FM, without premodulation or postdetection pulse shaping by low-pass filters. Illustrative comparisons are made of binary pulse transmission by AM and FM for two special cases of general interest in communication theory and pulse-system design. The more general case of partial pulse shaping by premodulation and postdetection low-pass filters is also considered. The performance of FM and AM systems in the presence of noise depends on the division of channel shaping between transmitting and receiving filters. The optimum division with FM and AM is determined for random noise, and comparisons are made of signal-to-noise ratios for optimized FM and AM systems. It is shown that there is a single universal relation between error probability and signal-to-noise ratio, applying to an infinite universe of optimized baseband systems and optimized AM systems with ideal synchronous detection, and that this relation is the same as for baseband transmission over an idealized flat channel of minimum bandwidth. The analysis indicates that, with binary FM and appropriate postdetection low-pass filters, it is possible in principle to realize an improvement in signal-to-noise ratio over bipolar double-sideband AM with synchronous detection (phase reversal), for equal channel bandwidths, average signal power and pulse transmission rates, although this may not be feasible with practicable filters.

Microwave Logic Circuits Using Diodes

It is possible to control the transmission of microwave power in a waveguide via external control of the dc bias on a semiconductor diode mounted across the waveguide in a direction parallel to the E field. The combination of a microwave detector with such a modulator affords a means whereby RF power in one waveguide can be made to control RF power in a second waveguide. In order to test the applicability of this circuit to binary logic functions, a regenerative memory loop has been constructed. Traveling-wave tubes were employed to raise the level of a controlled signal to that required by the detector. Using an X-band carrier, binary pulse stability was observed at pulse repetition rates of 685 mc.

Statistics of Regenerative Digital Transmission

Statistics of a synchronous binary message pulse train applied to a regenerative repeater are related to those of the original binary message, which is assumed ergodic. It is shown that the ensemble of possible message pulse trains is a nonstationary random process having a periodically varying mean and autocovariance. A spectral density is calculated which shows line-spectral components at harmonics of the pulse rate and a continuous density function, both with intensity proportional to the square of the absolute value of the Fourier transform of the standard pulse at the frequency considered. The continuous component has many properties similar to thermal noise but differs in that, under certain conditions described, it can exhibit regularly spaced axis crossings, can be exactly predicted over finite intervals and is capable of producing discrete components when nonlinear operations are performed on it, even though no line spectral terms are originally present. The analytical results are applied to the problem of deriving a timing wave from the message pulse train by shock-exciting a tuned circuit with impulses occurring at the axis crossings.

A Full Binary Adder Employing Two Negative-Resistance Diodes

Full binary pulse addition may be performed using only two negative-resistance diodes. Amplified Sum and Carry outputs can be provided which are virtually in coincidence with the input signals. A full adder is described, employing Reeves-Cooke positive-gap diodes which operate with pulses of 20-millimicrosecond duration.

Self-Timing Regenerative Repeaters

In self-timing regenerative repeaters, a timing wave for control in pulse regeneration is derived from the binary pulse train at each repeater with the aid of a resonant circuit tuned to the pulse repetition frequency. The timing wave can be made to exercise complete control in retiming of pulses independent of the received pulse train, or it can be combined with the received pulse train to provide partial retiming. The timing principles are discussed here for a particular type of self-timed regenerative repeater invented by Wrathall, in which a timing wave derived from either the received or the regenerated pulse train is combined in a particular way with the received pulse train. The regeneration characteristics of such repeaters as determined by various design parameters are investigated, together with the cumulation of timing deviations in repeater chains and the circuit requirements that must be met to insure satisfactory performance.

Error rates in pulse position coding

An expression for the error rate in a system using a binary pulse position code is derived. In the system considered, the pulses amplitude modulate a carrier and the resultant signal is contaminated by additive Gaussian noise. At the receiver the pulses are recovered by an envelope detector. If synchronization errors and post-detection filtering are neglected, it is shown that the probability of a binary error is approximated well by 1/2 \exp (-a^2/2) , where a^2 is the peak input signal-to-noise power ratio. Finally, the error rate is derived for the case where the signal amplitude is subject to random fading. Some comparisons are made with error rates derived by Montgomery for other systems with and without carrier fading. It is found that when the signal is subject to fading the pulse position system is better than a comparable system using threshold detection.

The Regeneration of Binary Microwave Pulses (Abstract)

The chief advantage of binary pulse systems resides in the possibility of regenerating such pulses at intervals along the transmission route to prevent the accumulation of distortions due to noise, bandwidth limitations, and other disturbing effects. A very important part of any such transmission system is the regenerative repeater employed. This paper reports the results of experiments performed to determine the possibilities of such a repeater operating in the microwave frequency range.

An Electrostatic-Tube Storage System

A storage system which will store binary (on or off) pulses has been constructed, and should prove useful in laboratory studies of certain communication problems. The system comprises two storage channels, each utilizing an MIT electrostatic storage tube and switching circuits which route incoming pulses into one channel while stored pulses are being recovered from the other. Pulses are stored in each tube in a square array of discrete spots of charge; each spot may assume one of two possible potentials, corresponding to the two possible states of a binary pulse. The order of occurrence of incoming pulses is preserved during storage, but the time relationship is not; the time relationship of pulses recovered from storage is determined by an independent pulse source under control of the user. Consequently, the system may be used to compress, expand, or delay a group of pulses. The capacity of each storage channel is, at present, 256 pulses. The system operates reliably at all frequencies up to 33 kc when storing incoming pulses and up to 70 kc when supplying stored pulses.

The Cascaded Binary Counter with Feedback

The count of a cascade of binary pulse counters having any arrangement of feedback connections can be calculated. The calculation is simplified for two special connection patterns. For a particular count, one or the other of these patterns, or a modification of the two, requires a least number of connections.