Closed-form formulas for frequency-dependent resistance and inductance per unit length of microstrip and strip transmission lines

1994 ◽  
Vol 42 (2) ◽  
pp. 241-248 ◽  
Author(s):  
A.R. Djordjevic ◽  
T.K. Sarkar
Keyword(s):  
Closed Form ◽  
Transmission Lines ◽  
Unit Length ◽  
Frequency Dependent

scholarly journals A Method for the Statistical Evaluation of Crosstalk Effect Between Three Parallel Conductors

1999 ◽  
Vol 22 (2) ◽  
pp. 111-119
Author(s):  
P. T. Trakadas ◽  
C. N. Capsalis
Keyword(s):  
Closed Form ◽  
Uniform Distribution ◽  
Transmission Lines ◽  
Statistical Evaluation ◽  
Unit Length ◽  
Surrounding Medium ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Mutual Inductance ◽  
Theoretical Results

There are several cases at which, in order to evaluate the crosstalk effect among transmission lines carrying useful signals, there is a need for probabilistic approach. This paper considers the problem of crosstalk estimation between transmission lines consisting of three conductors in a homogeneous surrounding medium, where the distance between the conductors is a random variable described by uniform distribution. The transmission lines are considered as electrically short. A closed-form equation is developed for the statistical distribution of the per-unit-length mutual inductance(lm)and an analytical one is described for the evaluation of the per-unit-length capacitance(cm). Theoretical results are compared with simulated ones for validation purposes.

scholarly journals TRANSIENT RESPONSE OF A DISTRIBUTED RLC INTERCONNECT BASED ON DIRECT POLE EXTRACTION

2009 ◽  
Vol 18 (07) ◽  
pp. 1263-1285 ◽  
Author(s):  
GUOQING CHEN ◽  
EBY G. FRIEDMAN
Keyword(s):  
Closed Form ◽  
Transient Response ◽  
Transmission Lines ◽  
Average Error ◽  
Proposed Model ◽  
Newton Raphson ◽  
On Chip ◽  
Interconnect Systems ◽  
Interconnect System ◽  
Raphson Method

With higher operating frequencies, transmission lines are required to model global on-chip interconnects. In this paper, an accurate and efficient solution for the transient response at the far end of a transmission line based on a direct pole extraction of the system is proposed. Closed form expressions of the poles are developed for two special interconnect systems: an RC interconnect and an RLC interconnect with zero driver resistance. By performing a system conversion, the poles of an interconnect system with general circuit parameters are solved. The Newton–Raphson method is used to further improve the accuracy of the poles. Based on these poles, closed form expressions for the step and ramp response are determined. Higher accuracy can be obtained with additional pairs of poles. The computational complexity of the model is proportional to the number of pole pairs. With two pairs of poles, the average error of the 50% delay is 1% as compared with Spectre simulations. With ten pairs of poles, the average error of the 10%-to-90% rise time and the overshoots is 2% and 1.9%, respectively. Frequency dependent effects are also successfully included in the proposed method and excellent match is observed between the proposed model and Spectre simulations.

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