# Current-Sensing Topology with Multi Resistors in Parallel and Its Protection Circuit
###### Abstract
Magnitude detection is a necessary part of overcurrent protection circuit design. If peak detection is adopted, the actual protection threshold of waveforms with a low peak factor, such as square and DC wave, is three times the rated effective measurement range. This would damage current sense resistors due to overheating. An RMS-to-DC converter chip can measure the accurate effective value of the input waveform, but its cost is high and the working principle is complex. The dynamic response properties are not easy to be described via mathematical models and it is hard to estimate the response time and the residual ripple of the output waveform [24; 25]. By contrast, the rectified mean circuit could be used to estimate the effective value roughly [24] and the circuit is pretty simple. It is more appropriate for magnitude detection in an overcurrent protection circuit. In order to improve the dynamic range of current measurement, a current-sensing topology with multi resistors in parallel and the design method for its overcurrent protection circuit are proposed. No similar research has been found in the publicly available literature. In order to solve the hiccup issue in protection circuits of parallel sensing topology, a dual threshold-detection circuit is designed. Its working flow and the threshold calculation method are described in detail. For waveforms with various crest factors, the validities of the peak value and rectified mean value detection in the protection circuit are compared. A protection scheme combining these two magnitude-detection methods is proposed. The dynamic characteristics of the rectifier mean-detection circuit are simply determined by the first-order R-C low pass filter. To analyze the dynamic characteristics, Fourier series expressions are given for the absolute value of sinusoidal, triangular and periodic pulse waves. Then Fourier transform and inverse transform are used to obtain the time domain expressions of rectified mean output waveforms. With further transformation and calculation, the estimation formulas for output waveform ripples are obtained. They provide a basis for determining the hysteresis ratio of the comparison circuits. Finally, the advantages of the parallel sensing circuit in improving the dynamic range are verified in the experimental circuit. The conditions for eliminating protection hiccups are given. Notation: \(R_{R}\) denotes the ratio of maximum to minimum current range covered by a single resistor. \(I_{IN}\) means the input current flowing through all sensing paths. \(I_{Rj}\) represents the current sensed by resistor \(R_{j}\) and \(I_{Tj}\) represents the threshold of current sensed by \(R_{j}\) while the involved protection circuit is triggered. \(I_{Tj}\)\({}^{\prime}\) represents the threshold of the input current while the involved protection circuit is triggered. \(C_{F}\) and \(W_{F}\) denote the crest factor and waveform factor of waveforms, respectively. \(P_{F}\) denotes the peak factor of the measurement circuit for a specified range. \(X_{PK}\), \(X_{RMS}\) and \(X_{RM}\) are the peak value, effective value and rectified mean value of waveforms, respectively. \(V_{RA}\) and \(V_{RA}\)\({}^{\prime}\) represent the ripple amplitude evaluated by complete calculation and estimation formulas respectively, for output waveforms of the rectified mean circuit. \(K_{RA}\) denotes the ratio of \(V_{RA}\) to \(V_{RA}\)\({}^{\prime}\). \(\gamma\)denotes the relative error of \(V_{RA}{}^{\prime}\) to \(V_{RA}\). \(R_{RP}\) means the ratio of \(V_{RA}{}^{\prime}\) to \(X_{RM}\). \(\delta_{H}\) means the ratio of half the comparator hysteresis voltage to initial threshold voltage. For all above notations, the subscript \(j\) can be replaced by 1 or 2.