Lumped circuit analysis dealing with electromagnetic propagation in silicon

[Kevin2341]

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?

 

[berkeman]

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?

In your Relevant Equations section, you really should be including units on all those quantities.

What is the wavelength of a 2GHz waveform in silicon?

How does this compare to the longest path in the IC size that you are given?

Is it an order of magnitude larger?

 

[rude man]

Why did you divide 3e8 m/s by 5 and not by 2?

 

[Kevin2341]

I didn't intend to divide 3e8 m\s by 5, isn't 3e8 divided by 2 = 1.5e8? (300,000,00 \ 2 = 150,000,000)? Never mind.. I see what I did, I wrote " "\5, when I meant 2 .

as for the longest path in the IC size given, I'd think it would be 4inches (1+1+1+1, 1 per side). Convert 4 inches down to cm or whatever size would be appropriate for this application.

As for wavelength in silicon, I found 2ghz is equal to 15cm\2 (because of silicon halves the speed of light). 4 inches = 10.16cm, 15\2 = 7.5, so if I'm doing things correctly here, then the answer should be that there isn't a problem? Or am I missing something? (By the way, I did not expect to see this kind of problem in my circuits class so early.. I'm seriously reconsidering engineering right now because of the vast pool of knowledge I am expected to remember.)

 

[berkeman]

I didn't intend to divide 3e8 m\s by 5, isn't 3e8 divided by 2 = 1.5e8? (300,000,00 \ 2 = 150,000,000)? Never mind.. I see what I did, I wrote " "\5, when I meant 2 .

as for the longest path in the IC size given, I'd think it would be 4inches (1+1+1+1, 1 per side). Convert 4 inches down to cm or whatever size would be appropriate for this application.

As for wavelength in silicon, I found 2ghz is equal to 15cm\2 (because of silicon halves the speed of light). 4 inches = 10.16cm, 15\2 = 7.5, so if I'm doing things correctly here, then the answer should be that there isn't a problem? Or am I missing something? (By the way, I did not expect to see this kind of problem in my circuits class so early.. I'm seriously reconsidering engineering right now because of the vast pool of knowledge I am expected to remember.)

The longest path would just be across the diagonal of the chip, not all around the edges. So what distance is that? What is the wavelength of a 2GHz signal propagating in silicon?