Discharge Pulse Characteristics of Charged Transmission Lines
Ivor Catt asked for a small web page linking to my lab notes on charging and discharging characteristics of coax cable.
Transmission Lines, Reflection, and Terminations
Lab Notes on Coax Cable Reflections (html)
Lab Notes on Coax Cable Reflections (pdf)
From his early work in the 1960's, Ivor is keenly aware that at high frequency, not only do capacitors possess inductive characteristics (such as lead inductance), but also possess transmission line characteristics, as well.
These notes are intended to help gain hands-on experience with transmission lines and transmission line effects. These lab notes are easily reproducible at the technical school level. The only requirements are a digital scope, function generator, a standard 500' spool of coax cable, and a handful of terminations and BNC tees.
About myself: I am an instructor of electronics at Austin Community College. I am a MSEE, not a PhD. I teach technicians, not engineers. I prefer experimental results, and use math as a secondary tool for deeper understanding.
Regarding the charging and discharging of open transmission line,
the experimental fact is that the discharge time is twice the
electrical length of the transmission line. My interpretation is that
the charged transmission line has a superposition of left-going and
right-going electromagnetic fields, traversing the line, and
reflecting off the open ends.
In the stationary state, we have a steady voltage between the two
conductors, and no galvanic current flow, yet we have
a dynamical system with electromagnetic fields always in motion at the
local light speed. Because the stationary, charged system has no
gradients in the electric or magnetic field, no dielectric or galvanic
During the pulse charging (or discharging, as these are dual to each
other) I find it convenient to view the field motion as the cause, and
the voltage and current as a response. The leading edge of the
incoming field has a gradient along the direction of motion. This
gradient will cause transient dielectric heating during the initial
traverse. Likewise, there will be a time gradient of the magnetic
field transverse to the direction of motion. This will induce currents
in the outer shield and inner conductor which will cause transient
local heating of the conductors. On each reflection during charging,
these transients diminish in magnitude until steady state (within our
noise basement) is achieved.
Crude estimates of the electric and magnetic fields in the charged coax:
E = V/(r_o - r_i) (better formulas based on ln(r/r_i) exist).
B_+ = +V/(c*(ro - ri)) (From homopolar equation Voltage = B*L*velocity)
B_- = -V/(c*(ro - ri)) reflected wave travelling opposite above.
In steady state, the two magnetic fields null out, leaving the illusion
of no magnetic field.
1) Voltage applied to input of transmission line
2) Electromagnetic Field starts propagating toward far end. Magnetic
field high, proportional to applied voltage.
3) First reflection, reversed propagating field has opposite magnetic
polarity. Superimposed magnetic field has partial cancellation.
Electric field unchanged.
4) Subsequent reflections continue this process until steady state
within noise basement is achieved.
Kurt Nalty. 7 August 2015