Harness Crosstalk Research Based On Multi-Conductor Transmission Line Theory

Worst-case estimates of crosstalk in cable bundles are useful for flagging potential problems, but may flag problems that occur only very rarely, due to the random variation of wire positions and other characteristics of the harness. Prediction of crosstalk that may realistically occur requires statistical methods. Monte-Carlo simulation techniques are often used to account for statistical variation, but are time consuming and do not provide intuition toward the cause of or solution to problems. Here we investigate prediction of the statistically"reasonable worst-case"crosstalk by forming probability distributions using inductance and capacitance parameters from a single harness cross-section and using lumped element approximations for crosstalk that account for strong coupling within the harness when the circuit is electrically small.The proposed method does a good job of estimating the reasonable worst-case crosstalk due to random variation of wire position within cable bundles. The advantage of the technique is not only improved estimation speed, but the potential to improve the understanding of why problems occur and how to fix them, since results are found from relatively simple closed form approximations and L and C matrices. Accurate prediction depends on accurate knowledge of harness parameters, like harness height or the rate that wires change position along the harness length. While random variation in harness height or other parameters were not dealt with here, the technique might also be extended to account for these variations.Statistical variations in crosstalk are typically characterized using Monte Carlo simulation techniques which require significant computational effort due to the many random instantiations of the circuit that must be evaluated to obtain an accurate result. Depending on the circuit, simulations may take days to complete. This paper proposes the use of T-parameter (Transfer parameter) matrices to improve the speed of Monte Carlo simulations of cable harness bundles. The method is fast since only simple matrix calculations are required to determine a result. In this method, a reference S-parameter matrix is estimated for a single harness cross-section. Variation of position along the harness length is modeled by splitting the harness into segments, where wire position changes between segments. An S-parameter matrix is found for each segment by swapping rows and columns of the reference S-parameter matrix. T-parameter matrices are found for each segment from the modified S-parameter matrices. The T-parameter matrix representing the overall harness is then found by multiplying the individual T-parameter matrices together.The T-parameter method introduced in the previous sections can quickly estimate statistical crosstalk parameters in cable-harness bundles without sacrificing accuracy. The cable bundle is approximated as cascaded segments of multi-conductor transmission lines. All impedances and values of crosstalk are found using simple matrix calculations once an S-parameter matrix has been calculated for a reference harness segment. The accuracy of the T-parameter method was verified by comparing it with a conventional SPICE analysis of the entire harness. Both methods gave the same result, but the T-parameter method was approximately 300 times faster than the SPICE analysis. This added speed is useful for estimating the statistical variation of crosstalk where hundreds or even thousands of simulations are required for an accurate result. This speed is particularly advantageous as the number of random parameters grows (for example, when modeling the random variation in harness height as well as wire position), because the number of simulations required for an accurate statistical estimate generally increases exponentially with the number of random parameters.