January 28, 2015

Puzzle: Wire Delay

Technical Tidbit:

You have a long wire of let's say length L. And it has the net delay of 100ps. Now you split the wire into two equal halves of length 0.5L each and insert a buffer at the center of the wire. The delay of buffer is 25ps. What is the total delay of the system: (half wire+ buffer + half wire)?

Option a: 50+25+50= 125ps
Option b: 25+25+25=75ps
Option c: 25+25+50=100ps
Option d: 50+25+25=100ps

Choose the right option, and please give a short explanation.

Thanks!

10 comments:

  1. Option b. Currently studying this so I wish to try it out. I remember wire delay's proportional to the square of the length (0.38RCL^2) so if we split the wire into half the delay goes down from 100ps for L to 25ps for 0.5L. Then the total delay is just the sum of the buffer plus two 0.5L wires.

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
    2. Yes, I do agree with Chirag’s comment

      If R0 is the unit resistance and C0 is the unit capacitance
      Total delay of wire of unit length = R0 L x C0 L
      = R0C0 L^2

      As this buffer dividing the net into equal half’s i.e. L/2

      Now delay offered by wire = R0C0 (L/2)^2 + R0C0 (L/2)^2
      = R0C0 (L^2/4) + R0C0 (L^2/4)
      = 25 + 25

      Total Delay of system = 25 + 25 + 25

      Delete
  2. This comment has been removed by the author.

    ReplyDelete
    Replies
    1. Over all system delay, depends on kind of buffer you add too, in this case a 100ps buffer will increase the overall delay.

      Delete
    2. Also, you cannot divide R and C, its the length that should get divided.

      Delete
  3. Lets take this,
    T=R.C
    R= kL/A
    so T directly proportional to R & R is directly proportional to L
    so T is directly proportional to L
    so 50+25+50=125ps

    Give me explanation if I am wrong..!

    ReplyDelete
    Replies
    1. Your approach is right! But you are missing C component change in your equation. If you consider that too, answer would come out as option b.

      Delete
  4. yes R prop to L..den c prop to L..so T prop to L^2..

    ReplyDelete