Evaluating the properties of impulse signals transmitted over circuits with distributed and lumped parameters

The dependability of the ABTC-MSh automatic block system entirely depends on the functional safety and operational stability of its component devices, most of which operate in pulse mode. One of the key components of pulse signal converters is various transformers and chokes, whose calculation and development is, in practice, often difficult due to insufficient consideration of stray parameters and operational specificity of such electromagnetic systems when the core is magnetized. The paper estimates the results of coordination of the transformer’s electrical characteristics with the load impedance and that of the pulse signal source suitable for analysing and constructing signal-shaping networks and delay lines based on lumped elements.

Aim. The aim of the work is to substantiate an engineering technique for calculating the duration of the leading edge of a signal in the process of setting its level at the output of the forming circuit of a pulse transformer when matching with loads and estimating the delay time for switching on the actuator at a given response threshold, depending on the parameters of the second-order circuit, which is often used as a feedback element of pulse converters and auto-regulation systems.

Methods. The time characteristics and pulse form are determined for a transformer whose equivalent circuit corresponds to the item’s operation in high frequencies and takes into account the stray parameters normalized to to the primary side. The output signal function is described in accordance with the linear electric circuit theory in operator form and, after a series of Laplace transformations, the generalized expression of the transmission factor is reduced to a standard form for a second-order circuit. The analytical solution was found by determining the values of the zeros and poles of the function on the plane of complex numbers as roots of quadratic equations expressed in terms of the coefficient of circuit damping. Graphs of the field dependences of the processes of establishing the pulse amplitude at the output of the forming circuit and the proportions of the amplitude outlier on the attenuation coefficient are given for various ratios of the coefficients of matching the transformer wave resistance with the load impedances and the pulse signal source. Point estimates of the pulse edge duration are made using the Mathcad programming function and taking into account the dimension of TRUE/FALSE matrices that reflect the transition from zero to one. This allows proposing linear approximations of the duration dependences within the given interval with a single inflection point that corresponds to the condition of complete matching of all resistances. Information is provided on the deviation of the approximation from the calculated data, the delay time of the actuator by the threshold. It is also discussed whether it is admissible to represent distributed parameters in the form of lumped elements while implementing artificial delay lines and higher-order circuits.

Results. Conclusions. The specified problem is resolved by defining a unique calculated dependence that associates the signal edge duration to the transmission coefficient of the examined second-order circuit. The validity of the method for dependence deduction is based on describing the output signal of a pulse transformer in a general form, subsequent analysis of the expression and deduction of an accurate analytical solution, taking into account the primary stray parameters of the transformer and load values.

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