# Lumped circuit analysis dealing with electromagnetic propagation in silicon

• Engineering
• Kevin2341
In summary: 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?
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?

Kevin2341 said:

## 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?

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

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.)

Kevin2341 said:
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?

## 1. What is lumped circuit analysis?

Lumped circuit analysis is a technique used in electrical engineering to analyze the behavior of electronic circuits by considering the circuit as a collection of discrete components, such as resistors, capacitors, and inductors. This approach simplifies the analysis of complex circuits and is based on the assumption that the physical size of the circuit components is small compared to the wavelength of the signals being studied.

## 2. How does electromagnetic propagation in silicon affect lumped circuit analysis?

Electromagnetic propagation in silicon refers to the way that electromagnetic waves travel through silicon, which is a common material used in electronic circuits. This can affect lumped circuit analysis because silicon has unique electrical properties that can cause changes in the behavior of the circuit components and the overall circuit performance.

## 3. What are some applications of lumped circuit analysis dealing with electromagnetic propagation in silicon?

Lumped circuit analysis is commonly used in the design and analysis of integrated circuits, microwave circuits, and high-speed digital circuits. It is also used in the development of electronic devices, such as smartphones, computers, and other consumer electronics.

## 4. What are the limitations of lumped circuit analysis when dealing with electromagnetic propagation in silicon?

One limitation of lumped circuit analysis is that it does not take into account the effects of electromagnetic coupling between different components in the circuit. This can be significant in circuits with high frequencies or complex geometries. Additionally, lumped circuit analysis is only applicable for circuits with relatively small dimensions compared to the wavelength of the signals being studied.

## 5. How can I improve the accuracy of lumped circuit analysis in dealing with electromagnetic propagation in silicon?

To improve the accuracy of lumped circuit analysis when dealing with electromagnetic propagation in silicon, more sophisticated modeling techniques can be used. These may include incorporating more realistic models of the circuit components, considering the effects of electromagnetic coupling, and using numerical simulation tools to account for complex geometries. Additionally, experimental validation of the analysis results can help to verify the accuracy of the analysis.