- #1

Kevin2341

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## Homework Statement

One of the conditions that we must obtain for us to use the lumped circuit abstraction is that the timescale of interest in analysis of the circuit must be greater than the speed of electromagnetic propagation. What was discussed in class was how much greater. The answer is very much greater, on the order of a power of 10. Electromagnetic propagation in silicon is about half the speed of light. A priori, is there a problem using the lumped circuit abstraction on a computer chip which is 1 inch square running at 2ghz?

## Homework Equations

...?

3.00x10^8/5=1.5x10^8

2ghz = 2,000,000,000hz or 2.00x10^9

1 sq inch = 6.4516 sq cm

## The Attempt at a Solution

My only thoughts concerning this is that hertz is the unit of frequency (cycles per seconds, correct?). If the speed of light in silicon is 1.5 x 10^8 and it is within a timescale of 2 billion cycles per second, there shouldn't be any issue. I don't know if there is some kind of mathematical voodoo I need to invoke to have a satisfactory answer though. Any help?