Velocity Factor and resonant frequency
 

Roy, W7EL wrote:
"This means that if we put a current into one end of the inductor, it`ll
take about 40 ns for current to reach the other end, right? So we should
expect a phase delay in current of 180 degrees at 6.15 MHz, from one end
to another?"

Hopper`s rule is one foot traveled per nanosecond. 40 feet of wire takes
40 nanoseconds.

The wavelength of 6.15 MHz is 48,8 or about 160 feet and in that space
the phase rotates 360-degrees. 40 feet is 1/4 of 360-degrees or
90-degrees at 6.15 MHz. At 1 MHz, the wavelength is 300 meters. 12,2
meters of wire is about 15-degrees of delay by my $1-dollar Chinese
calculator.

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

Roy, you are allowing your imagination to stray.

Velocity Factor and resonant frequency
 

Sorry, my mistake. So let me rephrase my question:

This means that if we put a current into one end of the inductor, it'll
take about 40 ns for current to reach the other end, right? So we should
expect a phase delay in the current of 90 degrees at 6.15 MHz, or about
15 degrees at 1 MHz, from one end to the other?

Roy Lewallen, W7EL

Richard Harrison wrote:
Roy, W7EL wrote:
"This means that if we put a current into one end of the inductor, it`ll
take about 40 ns for current to reach the other end, right? So we should
expect a phase delay in current of 180 degrees at 6.15 MHz, from one end
to another?"

Hopper`s rule is one foot traveled per nanosecond. 40 feet of wire takes
40 nanoseconds.

The wavelength of 6.15 MHz is 48,8 or about 160 feet and in that space
the phase rotates 360-degrees. 40 feet is 1/4 of 360-degrees or
90-degrees at 6.15 MHz. At 1 MHz, the wavelength is 300 meters. 12,2
meters of wire is about 15-degrees of delay by my $1-dollar Chinese
calculator.

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

Cecil, W5DXP wrote:
"Dr. Corum`s VF equation predicts a VF of approximately double
Richard`s----."

I wonder why? Dr. Terman wrote that the wave follows the turns in a
coil. My recollection of common solid-dielectric coax VF is about 2/3
that of free-space due to the fense plastic.

Twice the velocity factor in a coil requires a wave traveling faster
than light or taking a short-cut around the turns.

I often learn from my mistakes. Where did I err?

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

"Richard Harrison" wrote:
Twice the velocity factor in a coil requires a wave traveling faster
than light or taking a short-cut around the turns.

I often learn from my mistakes. Where did I err?

The current does take a short-cut due to adjacent coil coupling.
But please note the velocity factor only approximately doubles
from the "round and round the coil" calculation. Even though a
VF of 0.04 is ~double the "round and round the coil" approximation,
it is still 96% away from the VF=1.0 originally asserted by W8JI
which assumes that all the coils couple 100% to all the other coils.
--
73, Cecil, W5DXP

Velocity Factor and resonant frequency
 

Cecil, W5DXP wrote:
"The current does take a short-cut due to adjacent coil coupling."

R.W.P. King wrote on page 81 of Transmission Lines, Antennas, and Wave
Guides:
"The electromagnetic field in the near zone is characterized by an
inverse-square law for amplitude and by quasi-instantaneous action."

I still don`t know what to make of King`s assertion regards
instantaneous action.

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

Richard Harrison wrote:
Cecil, W5DXP wrote:
"The current does take a short-cut due to adjacent coil coupling."

R.W.P. King wrote on page 81 of Transmission Lines, Antennas, and Wave
Guides:
"The electromagnetic field in the near zone is characterized by an
inverse-square law for amplitude and by quasi-instantaneous action."

I still don`t know what to make of King`s assertion regards
instantaneous action.

From the IEEE Dictionary: "instantaneous - A qualifying term
indicating that no delay is purposely introduced in the action
of the device."

Does anyone have a formula for the coupling factor between
turns in a coil?
--
73, Cecil http://www.qsl.net/w5dxp

Velocity Factor and resonant frequency
 

I'm going with Drs. Corum on this one. Solve equation 28 for tau, get
beta from equation 4. The phase velocity along the axis of the coil is
omega/beta.

The velocity factor in question is that phase velocity over the speed
of light in a vacuum.

The coil modes are surface waves in a weird coordinate system. Note
that the paper is very explicit in saying they're not TEM.

Throw equation 28 into Mathematica or Matlab or something and solve for
tau. The cases given after equation 28 with all the limitations
appear(ed?) to be a point of some contention, but equation 28 seems
*only* to have the limitation of circumferential symmetry of the
surface waves on the coil.


At the junctions between the wire and the coil, there is a transfer of
energy between the surface wave modes on the coil and the usual antenna
mode (I guess it's TEM?)

The coil is like G-line in that it guides surface waves, but the coil
modes are modes specific to the helical geometry; the G-line surface
waves are specific to the straight-wire geometry.

There is a mode on the helix where the waves go round and round the
turns, but the example given is a traveling wave tube for microwave
amplification, and it seems to me that there are a few turns over a few
inches for *microwave* frequencies.

I am not one to argue with a solution to Maxwell's equations.

-Dan

Velocity Factor and resonant frequency
 

I need to proofread more. "At the junctions between the *ANTENNA* wire
and the *LOADING* coil there is a transfer of energy..." would have
been a bit clearer. Also very possibly inaccurate. The energy
transfer may happen somewhere else in space as the fields around the
antenna wire do not have the exponentially decaying radial behavior
that the coil surface wave fields have.

I expect, though, that the current at the antenna wire/coil junction is
what does the exciting of the surface wave modes on the helix.

Also should have said "a few turns over a few inches for a *TWT
OPERATING* at microwave frequencies".

-Dan

Velocity Factor and resonant frequency
 

Dan, N3OX wrote:
"Also should have said "a few turns over a few inches for a "TWT
OPERATING" at microwave frequencies".

That`s interesting. John D. Kraus invented the axial-mode helix antenna
after attending a lecture on traveling wave tubes given by a famous
scientist visiting Ohio tate University. Kraus asked the visitor if he
thought the helix could be used as an antenna. The visitor said no, so
Kraus went home, wound seven turns one wavelength in circumference and
discovered it made a sharp beam off the open end when he used a ground
plane across the driven end. The story appears on page 222 of Hraus` 3rd
edition of "Antennas".

Lenkurt described operation of the traveling wave tube in its August
1965 edition of the "Demodulator". Here is an excerpt:
"The signal to be amplified by the tube is coupled into the gun end of
the helix. This RF signal travels as a surface wave around the turns of
the helix, toward the collector, at about the velocity of light. The
forward or axial velocity of the signal is slower, of course, because of
the pitch and diameter of the helix. This forward movement of the wave
is analogous to the travel of a finely threaded screw where many turns
are required to drive it into position. The signal wave generates an
axial electric field which travels with it along the longitudinal axis
of the helix. This alternating electric field interacts or velocity
modulates the electrons in the beam."

Terman`s description in the 1955 edition of "Electronic and Radio
Engineering" starts on page 678 and is very similar to Lenkurt`s. i`d
bet that it is more than coincidental.

Kraus says of his new helical antenna on page 223 of his 3rd edition of
"Antennas":
"At a low frequency (helix circumference about lambda/2) there was
almost a pure standing wave (VSWR goes to infinity) all along the helix
(outgoing and reflected waves nearly equal) (Fig. 8-3a)--."

Surely an antenna loading coil resembles Kraus` low-frequency helix. It
has an open-circuit whip producing a reflection into one end. The
circumference is well below 1/2-wavelength, giving a current
distribution such as shown in Fig. 8-3a for a frequency below the axial
mode of operation.

Fig. 8-3c shows uniform outgoing and reflected currents over the middle
section of the helix. Kraus` figures were produced from actual
measurements.

Best regards, Richard Harrison, KB5WZI