Cecil, W5DXP wrote:
"---a two foot long section of 50 ohm coax is all the length needed to
force the V/I ratio to be 50 ohms at HF---"

At 3 MHz?

When power is applied to a transmission line, energy from the power
source doesn`t appear everywhere along the line at once. Instead, energy
travels away from the source in the form of an EM wave called the
"incident wave" arriving at various spots along the line in order and at
sequential times.The time it takes to travel through each line segment
depends on the four properties of the line, series resistance (R),
series inductance (L), shunt capacitance (C), and shunt conductance (G).

Source current will start charging the shunt capacitance of the first
line segment. It is delayed by the series inductance and resistance of
the first segment. Resistance does not directly delay current, but
limits current to the capacitace. As the shunt capacitance is charged,
the charging current tapers, but the next line segment starts charging
through its series inductance and resisitance. This energy travel
process continues sequentially throughout the line.

The value of current in an infinite line is the line voltage divided by
the line`s Zo. In a line with reflection, the current in each direction
is the voltage motivating the current in thet direction divided by Zo.

Just how short can a transmission line be and still enforce its Zo? A
1/4-wave matching section inverts impedance between its ends by
enforcing its Zo.

For Zo to equal the square root of L/C, (a resistance), XL must be much
greater than R, and XC must be much greater than G. These restrictions
impose frequency limits on Zo. And, these restrictions may place a low
frequency limit on how short a line can be and still enforce Zo.

Best regards, Richard Harrison, KB5WZI