A little more on missing degrees
 

I havn't much idea on what the present argument is all about. And I
have no wish to take sides.

But -

If Line-1 has impedance Zo1 and is a fractional wavelength L1 long,

and Line-2 has impedance Zo2 and is a fractional wavelength L2 long,

then when both lines are connected together and are brought into
so-called 1/4-wave resonance by pruning the length of one of the
lines, it is IMPOSSIBLE for L1 + L2 to equal 1/4-wavelength or 90
degrees.

There are ALWAYS some degrees "missing" - depending on the ratio
Zo1/Zo2.

Except only when Zo1 = Zo2 will L1 + L2 total 90 degrees.

Can be proved mathematically without invoking standing or reflected
waves. You just have to believe in mathematics.

Line-1, of course, is a loading coil and Line-2 is a whip.

I hope this settles an argument.

For a demonstration download program TWOLINES from website below.
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

A little more on missing degrees
 

Reg Edwards wrote:
I havn't much idea on what the present argument is all about. And I
have no wish to take sides.

But -

If Line-1 has impedance Zo1 and is a fractional wavelength L1 long,

and Line-2 has impedance Zo2 and is a fractional wavelength L2 long,

then when both lines are connected together and are brought into
so-called 1/4-wave resonance by pruning the length of one of the
lines, it is IMPOSSIBLE for L1 + L2 to equal 1/4-wavelength or 90
degrees.

There are ALWAYS some degrees "missing" - depending on the ratio
Zo1/Zo2.

Except only when Zo1 = Zo2 will L1 + L2 total 90 degrees.

Can be proved mathematically without invoking standing or reflected
waves. You just have to believe in mathematics.

Line-1, of course, is a loading coil and Line-2 is a whip.

I hope this settles an argument.

For a demonstration download program TWOLINES from website below.
----
.................................................. .........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. .........



And what is line three and line four?
73,
Tom Donaly, KA6RUH

A little more on missing degrees
 

Reg Edwards wrote:
If Line-1 has impedance Zo1 and is a fractional wavelength L1 long,

and Line-2 has impedance Zo2 and is a fractional wavelength L2 long,

then when both lines are connected together and are brought into
so-called 1/4-wave resonance by pruning the length of one of the
lines, it is IMPOSSIBLE for L1 + L2 to equal 1/4-wavelength or 90
degrees.

If we have three sections and Z02 Z01,

---Z01---+---Z02---+---Z01---

the first impedance discontinuity causes a phase
shift in the *opposite* direction from the second
impedance discontinuity. That's why moving a loading
coil from a base-loaded position to a center-loaded
position requires more degrees of coil.

W8JI has been trying to make a big deal out of that
fact but it is just simple physics.
--
73, Cecil http://www.qsl.net/w5dxp

A little more on missing degrees
 

"Reg Edwards" wrote in message
...
I havn't much idea on what the present argument is all about. And I
have no wish to take sides.

But -

If Line-1 has impedance Zo1 and is a fractional wavelength L1 long,

and Line-2 has impedance Zo2 and is a fractional wavelength L2 long,

then when both lines are connected together and are brought into
so-called 1/4-wave resonance by pruning the length of one of the
lines, it is IMPOSSIBLE for L1 + L2 to equal 1/4-wavelength or 90
degrees.

There are ALWAYS some degrees "missing" - depending on the ratio
Zo1/Zo2.

Except only when Zo1 = Zo2 will L1 + L2 total 90 degrees.

Can be proved mathematically without invoking standing or reflected
waves. You just have to believe in mathematics.

Line-1, of course, is a loading coil and Line-2 is a whip.

I hope this settles an argument.

For a demonstration download program TWOLINES from website below.

I don't understand the argument either. Why would anyone care
how many degrees an antenna has; it radiates all the power
whatever its length.

Frank

A little more on missing degrees
 

Frank's wrote:
I don't understand the argument either. Why would anyone care
how many degrees an antenna has; it radiates all the power
whatever its length.

Some of us care whether that radiation is heat or RF. :-)
--
73, Cecil http://www.qsl.net/w5dxp

A little more on missing degrees
 

"Cecil Moore" wrote in message
. com...
Frank's wrote:
I don't understand the argument either. Why would anyone care
how many degrees an antenna has; it radiates all the power
whatever its length.

Some of us care whether that radiation is heat or RF. :-)
--
73, Cecil http://www.qsl.net/w5dxp

A 15 ft long horizontal dipole, #14 AWG, on 3.8 MHz,
has a radiation efficiency of 90.17%. The loss due to
heat is 0.45 dB.

Designing an efficient matching network may be difficult.
Even with 100 W delivered to the antenna the 52 kV
at the feedpoint may pose a problem.

Frank

A little more on missing degrees
 

Frank's wrote:
"Reg Edwards" wrote in message
...

I havn't much idea on what the present argument is all about. And I
have no wish to take sides.

But -

If Line-1 has impedance Zo1 and is a fractional wavelength L1 long,

and Line-2 has impedance Zo2 and is a fractional wavelength L2 long,

then when both lines are connected together and are brought into
so-called 1/4-wave resonance by pruning the length of one of the
lines, it is IMPOSSIBLE for L1 + L2 to equal 1/4-wavelength or 90
degrees.

There are ALWAYS some degrees "missing" - depending on the ratio
Zo1/Zo2.

Except only when Zo1 = Zo2 will L1 + L2 total 90 degrees.

Can be proved mathematically without invoking standing or reflected
waves. You just have to believe in mathematics.

Line-1, of course, is a loading coil and Line-2 is a whip.

I hope this settles an argument.

For a demonstration download program TWOLINES from website below.


I don't understand the argument either. Why would anyone care
how many degrees an antenna has; it radiates all the power
whatever its length.

I personally wouldn't use an antenna with any less than a Master's
degree.....

- 73 de Mike KB3EIA -

A little more on missing degrees
 

For those of you who may be unfamiliar with the mathematics of
transmission lines, download program TWOLINES and enter the following
practical values -

Line-1 represents the loading coil.
Line-2 represents the whip to be pruned for 1/4-wave resonance.

Enter Zo1 = 6000 ohms, a practical value.
Enter electrical length L1 = 0.15 wavelengths.
Enter attenuation = 0.1 dB for wire loss in coil.

Enter Zo2 = 400 ohms, a practical value.
Enter electrical length L2 = 0.0077 wavelengths.
Enter attenuation = 0.001 dB

Enter open-circuit load resistance = 100 Megohms and load reactance =
100 Megohms.

To check that the circuit is in 1/4-wave resonance, vary plus or minus
length of Line-2 for zero or minimum input reactance.

The input resistance of the coil or Line-1 is about 16 ohms, a typical
value.

But L1 + L2 = 0.1577 wavelengths = only 57 degrees.

The missing 90 - 57 = 33 degrees are just not needed for resonance.
So why is everybody making such a fuss about it?
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

A little more on missing degrees
 

Reg Edwards wrote:

For those of you who may be unfamiliar with the mathematics of
transmission lines, download program TWOLINES and enter the following
practical values -

Line-1 represents the loading coil.
Line-2 represents the whip to be pruned for 1/4-wave resonance.

Enter Zo1 = 6000 ohms, a practical value.
Enter electrical length L1 = 0.15 wavelengths.
Enter attenuation = 0.1 dB for wire loss in coil.

Ignoring losses and starting at 0-j0, plotting this value
on a Smith Chart normalized to 6000 ohms, the normalized
value is -j1.38

-j1.38 * 6000 = -j8280 ohms

Enter Zo2 = 400 ohms, a practical value.
Enter electrical length L2 = 0.0077 wavelengths.
Enter attenuation = 0.001 dB

Starting at 0-j*infinity and plotting backwards, this value
on a Smith Chart normalized to 400 ohms is -j20.7

-j20.7 * 400 = -j8280 ohms

But L1 + L2 = 0.1577 wavelengths = only 57 degrees.

The abrupt jump from -j1.38 to -j20.7 provides a 66 degree
phase shift in the angle of the reflection coefficient as
read off the Smith Chart.

The missing 90 - 57 = 33 degrees are just not needed for resonance.
So why is everybody making such a fuss about it?

The missing 33 degrees are there, provided by the phase shift
in the reflection coefficient. The angle of the reflection
coefficient in the stinger at the impedance discontinuity is
~6 degrees. The angle of the reflection coefficient in the
coil at the impedance discontinuity is ~72 degrees.

72 - 6 = a 66 degree jump in the angle of the reflection
coefficient.

That equates to the missing 33 degrees of antenna. The wave
that is only 3 degrees back from the tip reflection point
is suddenly only 54 degrees from the current maximum point.

It appears to me that the interference of the forward and
reflected waves at the impedance discontinuity causes an
actual 33 degree phase shift. How to analyze what happens
at such an impedance discontinuity is covered in my energy
analysis article at:

http://www.qsl.net/w5dxp/energy.htm

I will try to do that analysis sometime today.
--
73, Cecil http://www.qsl.net/w5dxp

A little more on missing degrees
 

"Reg Edwards"
The missing 90 - 57 = 33 degrees are just not needed for
resonance. So why is everybody making such a fuss about it?
_____________

An antenna * system * does not need to have X number of degrees to be
resonant. It only needs to have ~zero reactance at its feedpoint -- which,
for electrically short AND long radiators can be achieved by use of a
suitable matching network.

Such networks don't add or subtract electrical degrees, however. They only
reduce/cancel the natural reactance of the physical radiator in use.

RF