Engineering of Distributed Systems

1
Engineering of Distributed Systems

• Lecture 2
• February 7, 2005

2
How are we going to learn about fields the Olin
way?

• How about building a coil gun?
• Available Parts
• 2 Ft. ¼ i.d. plastic pipe
• Length of Wire
• Very Strong (Neodymium Iron Boron) ¼ o.d..
  magnet
• 12 Ampere Power Supply

3
How to we Design it?

• Easy answer
• Use a much current as possible
• Use as many turns of wire as possible
• But
• Every turn of wire adds resistance
• Making the coil longer may not help much
• Harder Answer
• Optimize coil size, shape before building it
• Optimize placement of magnet before firing it
• First step Understand how to quantitatively
  model propulsion force as a function of coil
  current and distance to magnet

4
Last Time

• I V electrical power
• f v mechanical power
• Assume 100 efficient transduction
• I V f v

5
Lab 1

• Drop a magnet through a coil
• Measure velocity v
• Measure voltage V
• I V f v
• f (V / v) I

6
Todays Lecture Lab 2

• Use another approach
• Measure magnetic field generated by coil at
  various distances
• Deduce propulsive forces from fields

7
Why did we measure voltagein lab 1?

• Magnetic field through coil was changing
• Why does this make physical sense?
• Sliding Bar thought experiment

8
Gausss law

• Total field (a.k.a. flux) going through a surface
  surrounding sources of flux is equal to (within a
  constant factor) the flux generated by the
  enclosed flux sources.
• For electric fields

9
Hydraulic Analogy

• Garden Hose Outlet in Bag

10
How fast does the field drop off?

• Coulombs law Says 1/(r2)
• What does Gausss law say this must be true?

11
What if we enclose a volume with no flux sources?

• Divergence Free Field
• What goes in must come out

12
What does this have to do with our coil gun?

• If we know how the magnetic field of the magnet
  decreases with axial distance, then we know how
  much must be going out perpendicular to the axis
• Diagram

13
From radial field strength to force

• F I x B
• Axial force current x radial field
• Problems
• Magnet has non-zero length
• Coil has non-zero length

14
How can we measure how fast magnetic fields drop
off with distance?

• Diagram

15
Lab 2

• Put a 1 MHz sine wave on one transmit coil
• Measure voltage on transmit coil receive coil
  with oscilloscope
• Change Distance between transmit and receive
  coil, repeat measurements
• Do calculations taking into account non-zero
  length of coils

16
Oscilloscope Skills

• Youll be using the RMS and FFT dBV functions
• RMS Root Mean Square
• FFT Fast Fourier Transform
• dBV decibels relative to 1 Volt
• All of these will help us take better
  measurements of somewhat noisy waveforms than
  measuring peaks

17
RMS

• (RMS (x(t)) ) 2 Average power x(t) volts
  would dissipate into a 1 ohm resistor

18
Fourier Transform

• Tells us how much Energy x(t) has an frequency w

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Voltage Decibels (dBV)

• So if x(t) is 1 V RMS, x(t) is 0dBV
• What if x(t) is 10 V RMS?
• What if x(t) is 0.1 V RMS?
• What if x(t) is 1mV RMS?

20
Relationship of zero-length coils and non-zero
length coils

• Voltage on non-zero length coils is the sum of
  voltages on zero-length loops.
• Note that each loop is at a different distance
  from other coil