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-   -   5/8 wave 2 meter antenna (https://www.radiobanter.com/antenna/66750-5-8-wave-2-meter-antenna.html)

john doe March 14th 05 02:26 PM

5/8 wave 2 meter antenna
 
Can anyone point me to a good site for construction a 5/8 wave 2M antenna???

I tried home-brewing one already with poor results .... a conductor up a
piece of PVC .... same conductor wound into a coil at the bottome
connected in series to the center of the coax. 4 1/4 wave radials
connected to outer conductor.

Thanks,

-- Rob
ka2pbt

Dave Platt March 14th 05 07:09 PM

Can anyone point me to a good site for construction a 5/8 wave 2M antenna???

I tried home-brewing one already with poor results .... a conductor up a
piece of PVC .... same conductor wound into a coil at the bottome
connected in series to the center of the coax. 4 1/4 wave radials
connected to outer conductor.


I believe there's a project in the ARRL Handbook which shows how to
convert a Radio Shack CB whip antenna to a 2-meter 5/8-wave - it has
the details for the matching coil that is required.

http://www.arrl.org/tis/info/pdf/8009022.pdf has another QST article
which shows how to construct one from scratch, using a technique that
doesn't require a matching coil (the matching inductor is made from a
stub).

I haven't tried either of these myself.

With regard to the version you made - did you account for the loading
effect of the PVC when you measured and trimmed the length of your
radiator?

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

[email protected] March 14th 05 10:22 PM




With regard to the version you made - did you account for the loading
effect of the PVC when you measured and trimmed the length of your
radiator?



Hi Dave, I was just about to recommend the QST article, but you beat
me. A few comments on why his antenna did not perform: As you stated,
the PVC will change the input Z of the radiator. Just about anything
that is too close to the radiator will change things.
According to EZNEC, a 5/8 radiator with 1/4 radials 5 WL above ground
is 80-j300. As such, with a single series inductor matching section,
the best 50 ohm match is 1.6:1. This could get worse or better
depending on the antenna's environment. It will also change if you
slope the radials.
There is an article in the ARRL Antenna Compendium #1 pp.101 that
deals with 5/8 antennas. It basically explains why a 5/8, depending on
the application, is NOT the best performing radiator.
Gary N4AST


Dave Platt March 14th 05 11:04 PM

In article .com,
wrote:

Hi Dave, I was just about to recommend the QST article, but you beat
me. A few comments on why his antenna did not perform: As you stated,
the PVC will change the input Z of the radiator. Just about anything
that is too close to the radiator will change things.


On second reading of that QST article, I admit to being a bit curious.
The K4LPQ version (with a shorted inductive stub inside the radiator,
soldered to it) is clear enough. However, the W9WQ version using a
longer, open-circuited inductive stub wire isn't a straightforward
translation of this, because there's no soldered (or other DC)
connection between the radiator and anything else!

I infer that in the W9WQ version, the stub wire is performing two
functions at once - it's adding a series inductance, and it's also
coupling the RF out onto the radiator in a capacitive fashion. This
would imply that the stub needs to provide a bit more inductive
reactance than in the K4LPQ shorted-coax version, with some of this
reactance cancelling out the radiator's -j300 and the rest cancelling
out whatever amount of capacitive reactance exists between the stub
wire and the radiator.

Am I reading this right, or am I missing something?

[Regretfully it seems likely that both W9WQ and K4LPQ are now silent
keys, so I can't ask for advice from the horses' mouths.]

According to EZNEC, a 5/8 radiator with 1/4 radials 5 WL above ground
is 80-j300. As such, with a single series inductor matching section,
the best 50 ohm match is 1.6:1. This could get worse or better
depending on the antenna's environment. It will also change if you
slope the radials.


I've seen a number of 5/8-wave antenna designs which deal with this
issue by using something other than a simple series coil. The
commonest approach seems to be to use a coil which is connected in
shunt between the radiator and the ground plane, with the "hot" side
of the coax being fed to a point tapped partway up on the coil. This
approach transforms the radiator impedance down to the 50 ohms needed
to match the coax, and also provides the series inductance needed to
cancel out the reactance. It also provides DC grounding for the
radiator.

http://www.fluxfm.nl/schema/5-8%20go...20radialen.PDF is one
such design. It requires some amount of tooling (e.g. to lathe down
the plastic parts to the specified configuration) but I suspect that a
version could be homebrewed up using simpler materials and methods.
The photos show the way to build the tapped matching coil assembly,
and could probably be adapted to other coil construction methods. I
believe the ARRL Handbook article which adapts a Radio Shack CB mobile
antenna uses a similar tapped coil.

Another approach might be to change the length of the radiator a bit,
to change the resistive part of the feedpoint impedance from 80 ohms
down closer to 50 ohms, and modify the coil to suit. I haven't run
any simulations to see how much change in the radiator length would be
required, and what this change would do to the antenna's gain pattern.

There is an article in the ARRL Antenna Compendium #1 pp.101 that
deals with 5/8 antennas. It basically explains why a 5/8, depending on
the application, is NOT the best performing radiator.


I'll have to look it up if I can find a copy of that edition to see
what they have to say. I agree, in some cases the horizon-directed
gain of a 5/8 isn't what you want. For in-city and in-the-hills
mobile use, a 1/4-wave might give more reliable performance, precisely
because its RF energy is more broadly directed.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

[email protected] March 14th 05 11:46 PM


Dave Platt wrote:
In article .com,
wrote:

Hi Dave, I was just about to recommend the QST article, but you beat
me. A few comments on why his antenna did not perform: As you

stated,
the PVC will change the input Z of the radiator. Just about

anything
that is too close to the radiator will change things.


On second reading of that QST article, I admit to being a bit

curious.
The K4LPQ version (with a shorted inductive stub inside the radiator,
soldered to it) is clear enough. However, the W9WQ version using a
longer, open-circuited inductive stub wire isn't a straightforward
translation of this, because there's no soldered (or other DC)
connection between the radiator and anything else!

I infer that in the W9WQ version, the stub wire is performing two
functions at once - it's adding a series inductance, and it's also
coupling the RF out onto the radiator in a capacitive fashion. This
would imply that the stub needs to provide a bit more inductive
reactance than in the K4LPQ shorted-coax version, with some of this
reactance cancelling out the radiator's -j300 and the rest cancelling
out whatever amount of capacitive reactance exists between the stub
wire and the radiator.

Am I reading this right, or am I missing something?

[Regretfully it seems likely that both W9WQ and K4LPQ are now silent
keys, so I can't ask for advice from the horses' mouths.]

According to EZNEC, a 5/8 radiator with 1/4 radials 5 WL above

ground
is 80-j300. As such, with a single series inductor matching

section,
the best 50 ohm match is 1.6:1. This could get worse or better
depending on the antenna's environment. It will also change if you
slope the radials.


I've seen a number of 5/8-wave antenna designs which deal with this
issue by using something other than a simple series coil. The
commonest approach seems to be to use a coil which is connected in
shunt between the radiator and the ground plane, with the "hot" side
of the coax being fed to a point tapped partway up on the coil. This
approach transforms the radiator impedance down to the 50 ohms needed
to match the coax, and also provides the series inductance needed to
cancel out the reactance. It also provides DC grounding for the
radiator.

http://www.fluxfm.nl/schema/5-8%20go...20radialen.PDF is one
such design. It requires some amount of tooling (e.g. to lathe down
the plastic parts to the specified configuration) but I suspect that

a
version could be homebrewed up using simpler materials and methods.
The photos show the way to build the tapped matching coil assembly,
and could probably be adapted to other coil construction methods. I
believe the ARRL Handbook article which adapts a Radio Shack CB

mobile
antenna uses a similar tapped coil.

Another approach might be to change the length of the radiator a bit,
to change the resistive part of the feedpoint impedance from 80 ohms
down closer to 50 ohms, and modify the coil to suit. I haven't run
any simulations to see how much change in the radiator length would

be
required, and what this change would do to the antenna's gain

pattern.

There is an article in the ARRL Antenna Compendium #1 pp.101 that
deals with 5/8 antennas. It basically explains why a 5/8, depending

on
the application, is NOT the best performing radiator.


I'll have to look it up if I can find a copy of that edition to see
what they have to say. I agree, in some cases the horizon-directed
gain of a 5/8 isn't what you want. For in-city and in-the-hills
mobile use, a 1/4-wave might give more reliable performance,

precisely
because its RF energy is more broadly directed.

--
Dave Platt

AE6EO
Hosting the Jade Warrior home page:

http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!


Hi Dave, I'm sure you are reading it right, will look and see if I can
add anything later.
Gary N4AST


john doe March 15th 05 02:05 AM

No I didn't account for the PVC ...... but I made it longer than my design
and then trimmed past my design length and it never seemed to make a
difference. Considering my inductor was also formed around the PVC that was
probably way off too.....

I modeled the whole thing with nec first. This is what my input file looked
like:
http://mywebpages.comcast.net/ka2pbt/2M-5-8wave-dat.txt

and this is what my output looked like:
http://mywebpages.comcast.net/ka2pbt/2M-5-8wave-out.txt

Construction was a radiator 58.5 inches long fed along a 1/2" sched-40,
inductor was 19 turns around the same sched-40 2 inches long. The were 4
radials at 90 deg each 19.38"

Any comments welcome ....

Thanks,

-- de ka2pbt

"Dave Platt" wrote in message
...
Can anyone point me to a good site for construction a 5/8 wave 2M
antenna???

I tried home-brewing one already with poor results .... a conductor up a
piece of PVC .... same conductor wound into a coil at the bottome
connected in series to the center of the coax. 4 1/4 wave radials
connected to outer conductor.


I believe there's a project in the ARRL Handbook which shows how to
convert a Radio Shack CB whip antenna to a 2-meter 5/8-wave - it has
the details for the matching coil that is required.

http://www.arrl.org/tis/info/pdf/8009022.pdf has another QST article
which shows how to construct one from scratch, using a technique that
doesn't require a matching coil (the matching inductor is made from a
stub).

I haven't tried either of these myself.

With regard to the version you made - did you account for the loading
effect of the PVC when you measured and trimmed the length of your
radiator?

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!




Dave Platt March 15th 05 02:53 AM

In article ,
john doe wrote:

No I didn't account for the PVC ...... but I made it longer than my design
and then trimmed past my design length and it never seemed to make a
difference. Considering my inductor was also formed around the PVC that was
probably way off too.....

I modeled the whole thing with nec first. This is what my input file looked
like:
http://mywebpages.comcast.net/ka2pbt/2M-5-8wave-dat.txt

and this is what my output looked like:
http://mywebpages.comcast.net/ka2pbt/2M-5-8wave-out.txt

Construction was a radiator 58.5 inches long fed along a 1/2" sched-40,
inductor was 19 turns around the same sched-40 2 inches long. The were 4
radials at 90 deg each 19.38"


Is that 58.5 inch figure a typo? Your NEC model says 51 inches, and
my quickie spreadsheet calculation says 50.9 inches for a 145 MHz
center of band.

I also wonder about the coil - it calculates out to be just over 1
microHenry, or about j910 ohms at 145 MHz. That seems like quite a
bit too much, based on jgboyles's posting earlier today indicating a
feedpoint Z of about 80-j300.

The PDF to which I posted a link earlier today uses a coil of only
10.5 turns, spread out over a distance of about 2.5" on a 3/4" form.
That's about .6 uH or j550 ohms... and it's a shunt-fed design so the
actual series inductance (above the tap point) is even lower.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

Buck March 15th 05 03:54 AM

On Mon, 14 Mar 2005 14:26:57 GMT, "john doe"
wrote:

Can anyone point me to a good site for construction a 5/8 wave 2M antenna???

I tried home-brewing one already with poor results .... a conductor up a
piece of PVC .... same conductor wound into a coil at the bottome
connected in series to the center of the coax. 4 1/4 wave radials
connected to outer conductor.

Thanks,

-- Rob
ka2pbt



Can the 5/8 wave antenna be matched with a tuning stub such as the
J-Pole uses?


--
73 for now
Buck
N4PGW

[email protected] March 15th 05 05:55 AM

Can the 5/8 wave antenna be matched with a tuning stub such as the
J-Pole uses?...

Probably, but seems easier to to use a 5 turn coil at
the base...But I agree...A 5/8 GP is not a very good 2m
antenna. Better off building a high quality 1/4 wave GP.
Seriously... By high quality, I mean instead of 3-4 sloped
radials, use 6-8 radials, and even better , use a 2nd set
for decoupling. You can also build "sleeve" versions.
5/8's are ok on HF, where the angles are not critical, and on
10m, will usually be the best choice. But on 2m, they are usually
lame.
But, don't take my word. Build a 5/8 GP, and then build a 1/4
GP, and see which is best. I bet the 1/4 wave wins. For a
5/8 to work well on VHF/UHF, it needs to be a collinear dual
5/8 design, or at the least, use sloped 5/8 or 3/4 wave radials.
5/8's with 1/4 wave radials have pretty lousy patterns for 2m use.
MK


john doe March 15th 05 08:14 PM

On Tue, 15 Mar 2005 02:53:22 +0000, Dave Platt wrote:


Is that 58.5 inch figure a typo? Your NEC model says 51 inches, and
my quickie spreadsheet calculation says 50.9 inches for a 145 MHz
center of band.

Actually, the 51 you're seeing in the NEC model is probably the number of
segments. One end is at 0,0,36 and the other is at 0,0,94.5; so yes it's
really 58.5 inches. I came to this number by playing with the model until
the REAL component of the impedance got as close to 50 as I could get it.

I also wonder about the coil - it calculates out to be just over 1
microHenry, or about j910 ohms at 145 MHz. That seems like quite a
bit too much, based on jgboyles's posting earlier today indicating a
feedpoint Z of about 80-j300.


My model comes up with a feedpoint impedance of 5.4485E+01-j2.8560E+03

So I tried to build a coil with an inductive reactance to cancel that .. I
came up with 3.13 microhenries.

Is my model way off?????

[email protected] March 15th 05 09:09 PM

Hummm...Should be about .336 mh for a grounded coil.
About .182 mh for a insulated coil. In the real
world will usually amount to about 5 turns of coil
average on say a .5 to 1 inch form. Trim coil for
best match. MK


Jim Kelley March 15th 05 09:32 PM



wrote:

Hummm...Should be about .336 mh for a grounded coil.
About .182 mh for a insulated coil. In the real
world will usually amount to about 5 turns of coil
average on say a .5 to 1 inch form. Trim coil for
best match. MK


mH = 10e-3 Henry
uH = 10e-6 Henry

73, ac6xg


Dave Platt March 15th 05 09:43 PM

In article ,
john doe wrote:

Is that 58.5 inch figure a typo? Your NEC model says 51 inches, and
my quickie spreadsheet calculation says 50.9 inches for a 145 MHz
center of band.

Actually, the 51 you're seeing in the NEC model is probably the number of
segments. One end is at 0,0,36 and the other is at 0,0,94.5; so yes it's
really 58.5 inches.


Whups... my bad.

I came to this number by playing with the model until
the REAL component of the impedance got as close to 50 as I could get it.


Hmmm. What did that do to the pattern? You no longer have a 5/8-wave
antenna. Adding about 8 inches has brought it very close to being a
3/4-wave radiator. As such, it's going to have a substantially lower
amount of towards-the-horizon energy in its pattern, and a big lobe
aiming upwards at roughly 45 degrees above the horizon.

This is the classic problem with running a 2-meter J-pole on 440 -
it'll load up and radiate, but a lot of its radiation is aimed at
airplanes rather than repeaters :-(

I also wonder about the coil - it calculates out to be just over 1
microHenry, or about j910 ohms at 145 MHz. That seems like quite a
bit too much, based on jgboyles's posting earlier today indicating a
feedpoint Z of about 80-j300.


My model comes up with a feedpoint impedance of 5.4485E+01-j2.8560E+03

So I tried to build a coil with an inductive reactance to cancel that .. I
came up with 3.13 microhenries.

Is my model way off?????


I think you might want to take two looks at it:

- Check the radiation pattern. By lengthening it to get a 50-ohm
resistive component in the feedpoint, I suspect you've given up
much of the gain benefit of a true 5/8-wave radiator. You may
actually have less towards-the-horizon power and sensitivity than
you'd get with a 1/4-wave groundplane or a 1/2-wave J-pole.

- Check the formula and actual inductance for your coil.

With so much capacitive reactance from the radiator to cancel out with
the coil, I suspect that you may also find that you've calculated out
an antenna which is going to be rather narrow-banded. Even slight
frequency shifts, or errors in the coil winding (a fraction of a turn)
could leave you with a lot of residual reactance and an unacceptable
SWR.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

[email protected] March 15th 05 11:56 PM


Dave Platt wrote:
In article .com,
wrote:



On second reading of that QST article, I admit to being a bit

curious.

I infer that in the W9WQ version, the stub wire is performing two
functions at once - it's adding a series inductance, and it's also
coupling the RF out onto the radiator in a capacitive fashion. This
would imply that the stub needs to provide a bit more inductive
reactance than in the K4LPQ shorted-coax version, with some of this
reactance cancelling out the radiator's -j300 and the rest cancelling
out whatever amount of capacitive reactance exists between the stub
wire and the radiator.

Am I reading this right, or am I missing something?


I took a look at the Smith Chart, and for impedances in this region
of the chart, series L and parallel C is not the way to get a match. In
my version, 80-j300, you need 4.7pf shunt C and .15uH series L. I have
no idea how Fig. 1C in the article managed to get a good match with the
single insulated wire up the middle of the radiator.
I seem to recall a tri-band beam (TA-33 jr.?) that used this type of
matching. Must work, so I guess I am missing something.
Gary N4AST


john doe March 15th 05 11:57 PM

Wow, I didn't even consider the pattern ....

Thanks for all the advice ... I'll have another go at it and let you know
how I make out.

-- ka2pbt

"Dave Platt" wrote in message
...
In article ,
john doe wrote:

Is that 58.5 inch figure a typo? Your NEC model says 51 inches, and
my quickie spreadsheet calculation says 50.9 inches for a 145 MHz
center of band.

Actually, the 51 you're seeing in the NEC model is probably the number of
segments. One end is at 0,0,36 and the other is at 0,0,94.5; so yes it's
really 58.5 inches.


Whups... my bad.

I came to this number by playing with the model until
the REAL component of the impedance got as close to 50 as I could get it.


Hmmm. What did that do to the pattern? You no longer have a 5/8-wave
antenna. Adding about 8 inches has brought it very close to being a
3/4-wave radiator. As such, it's going to have a substantially lower
amount of towards-the-horizon energy in its pattern, and a big lobe
aiming upwards at roughly 45 degrees above the horizon.

This is the classic problem with running a 2-meter J-pole on 440 -
it'll load up and radiate, but a lot of its radiation is aimed at
airplanes rather than repeaters :-(

I also wonder about the coil - it calculates out to be just over 1
microHenry, or about j910 ohms at 145 MHz. That seems like quite a
bit too much, based on jgboyles's posting earlier today indicating a
feedpoint Z of about 80-j300.


My model comes up with a feedpoint impedance of 5.4485E+01-j2.8560E+03

So I tried to build a coil with an inductive reactance to cancel that .. I
came up with 3.13 microhenries.

Is my model way off?????


I think you might want to take two looks at it:

- Check the radiation pattern. By lengthening it to get a 50-ohm
resistive component in the feedpoint, I suspect you've given up
much of the gain benefit of a true 5/8-wave radiator. You may
actually have less towards-the-horizon power and sensitivity than
you'd get with a 1/4-wave groundplane or a 1/2-wave J-pole.

- Check the formula and actual inductance for your coil.

With so much capacitive reactance from the radiator to cancel out with
the coil, I suspect that you may also find that you've calculated out
an antenna which is going to be rather narrow-banded. Even slight
frequency shifts, or errors in the coil winding (a fraction of a turn)
could leave you with a lot of residual reactance and an unacceptable
SWR.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!




[email protected] March 16th 05 12:31 AM





Can the 5/8 wave antenna be matched with a tuning stub such as the
J-Pole uses?


--
73 for now
Buck
N4PGW


Yes, A 5/8 radiator with an input Z of 80-j300 with series 19cm of 450
ohm line will be about 55-j0 ohms. Of course all of this is highly
dependent on the antenna environment on 2m.
Gary N4AST


Dave Platt March 16th 05 01:09 AM

Am I reading this right, or am I missing something?

I took a look at the Smith Chart, and for impedances in this region
of the chart, series L and parallel C is not the way to get a match. In
my version, 80-j300, you need 4.7pf shunt C and .15uH series L. I have
no idea how Fig. 1C in the article managed to get a good match with the
single insulated wire up the middle of the radiator.


It's possible he isn't creating a full match (with an L network) in
this case. He might just be cancelling out the negative reactance,
using a combination of (series L from the stub, and a bit of series C
from the capacitive coupling between stub-feed and radiator), and not
bothering with a shunt component at all. This would, perhaps, result
in an 80+0j feedpoint impedance and about a 1.6 SWR at the feedpoint,
which would probably end up significantly lower at the other end of
the feedline due to feedline losses.

Or, there might be something stranger going on, with the stub giving a
bit of shunt C to ground (in the PL-259), some parallel L/C inside the
radiator, and six other bits of odd voodoo.

The author says that it ought to be possible to get down to below
1.5:1 on the repeater portion of the band... this suggests that the
design isn't one which "tries" to achieve a true 1:1 match. The WA-2
and similar 5/8-wave antennas using a tapped coil seem to be able to
get down arbitrarily close to 1:1 at their best.

Beats me. Almost makes me want to try building one just to measure it
out and see how well it can work. On the other hand, given the
comments by Cebik and others about the somewhat illusory nature of the
gain advantage of a 5/8-wave, I may just stick with J-poles and
quarterwave ground planes.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

John Doe March 16th 05 05:36 AM

Ok,

I have not followed all of this thread.

One of the pdf's shows a shunt tapped inductor
as the base loading.

This is an auto-transformer match.

The entire inductor is set to cancel the capacitive reactance
of the aerial, then the coax feed is tapped to the 50R point,
The result is 50R J0.


For 5/8 aerials you may want to look at a physical short radiator
with a capacity hat to lower the angle of radiation.



wrote in message
ups.com...




Can the 5/8 wave antenna be matched with a tuning stub such as the
J-Pole uses?


--
73 for now
Buck
N4PGW


Yes, A 5/8 radiator with an input Z of 80-j300 with series 19cm of 450
ohm line will be about 55-j0 ohms. Of course all of this is highly
dependent on the antenna environment on 2m.
Gary N4AST




Richard Fry March 16th 05 02:50 PM

"Dave Platt"
... On the other hand, given the comments by Cebik and others
about the somewhat illusory nature of the gain advantage
of a 5/8-wave, I may just stick with J-poles and quarterwave
ground planes.

_______________

Just to note that for AM broadcast verticals, the FCC requires a certain
antenna "efficiency" for various classes of stations, in terms of the
minimum ground wave field strength produced per kilowatt of input power to
the radiator.

The FCC field strength minimum cannot be met by "Class A" stations
(basically the 50kW-ers) using a 1/4-wave vertical radiator. At least a
1/2-wave radiator is needed in most cases.

The most common radiator height for Class A non-directional AM broadcast
stations operating at 50kW day and night is 195°. A radiator height of 225°
(5/8 wave) maximizes ground wave field strength at a given power, but also
produces a high-angle lobe that can interfere with the ground wave during
night-time operation -- so rarely is used by AM broadcast stations. The
ground wave field strength difference between 195° and 225° radiators is
fairly small.

RF
Former staff engineer, WJR Detroit -- (Class A, 760kHz)


john doe March 16th 05 03:24 PM

Interesting .... I changed my number of segments in NEC from 51 to 501 and I
got an impedance more in line with 80-j300 ..... I'll go re-work my coil
now :)

de ka2pbt


"Dave Platt" wrote in message
...
In article ,
john doe wrote:

Is that 58.5 inch figure a typo? Your NEC model says 51 inches, and
my quickie spreadsheet calculation says 50.9 inches for a 145 MHz
center of band.

Actually, the 51 you're seeing in the NEC model is probably the number of
segments. One end is at 0,0,36 and the other is at 0,0,94.5; so yes it's
really 58.5 inches.


Whups... my bad.

I came to this number by playing with the model until
the REAL component of the impedance got as close to 50 as I could get it.


Hmmm. What did that do to the pattern? You no longer have a 5/8-wave
antenna. Adding about 8 inches has brought it very close to being a
3/4-wave radiator. As such, it's going to have a substantially lower
amount of towards-the-horizon energy in its pattern, and a big lobe
aiming upwards at roughly 45 degrees above the horizon.

This is the classic problem with running a 2-meter J-pole on 440 -
it'll load up and radiate, but a lot of its radiation is aimed at
airplanes rather than repeaters :-(

I also wonder about the coil - it calculates out to be just over 1
microHenry, or about j910 ohms at 145 MHz. That seems like quite a
bit too much, based on jgboyles's posting earlier today indicating a
feedpoint Z of about 80-j300.


My model comes up with a feedpoint impedance of 5.4485E+01-j2.8560E+03

So I tried to build a coil with an inductive reactance to cancel that .. I
came up with 3.13 microhenries.

Is my model way off?????


I think you might want to take two looks at it:

- Check the radiation pattern. By lengthening it to get a 50-ohm
resistive component in the feedpoint, I suspect you've given up
much of the gain benefit of a true 5/8-wave radiator. You may
actually have less towards-the-horizon power and sensitivity than
you'd get with a 1/4-wave groundplane or a 1/2-wave J-pole.

- Check the formula and actual inductance for your coil.

With so much capacitive reactance from the radiator to cancel out with
the coil, I suspect that you may also find that you've calculated out
an antenna which is going to be rather narrow-banded. Even slight
frequency shifts, or errors in the coil winding (a fraction of a turn)
could leave you with a lot of residual reactance and an unacceptable
SWR.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!




Richard Harrison March 16th 05 09:48 PM

Richard Fry wrote:
"The most common radiator height for Class A non-directional AM
broadcast stations operating at 50kW day and night is 195-degrees."

I won`t challenge that as I have conducted no survey. WJR Detroit is
shown on the broadcast allocations map book as an unlimited (day and
night) 50 kilowatt Class 1 station.

Class 1 stations operate in a clear channel (this does not mean alone on
the channel) with an assigned power between 10kW and 50kW

A Class 2 station operates in a clear channel with an assigned power
between 250W and 50kW. They must operate so as to not cause interference
to the Class 1 stations. There are 29 clear channels which permit class
2 station operation.

Class 3 stations share regional channels and operate with assigned
powers between 500W and 5kW. Thyere are 41 regional channels and more
than 2000 Class 3 stations. These numbers were taken before expansion of
the AM broadcast band which has grown the totals.
Class 4 stations operate in assigned local channels with no more than
1kW day and 250W night assignments. There are 6 local channels with 150
or more Class 4 stations on each channel.

Primary service area is the statiob`s groundwave coverage. Secondary
service is uninterfered skywave coverage. Intermittent service lies
between the primary and secondary service areas.

A clear channel has one or more high-powered stations which serve wide
areas. All primary service areas and a substantial portion of their
secondary service areas are cleared of objectional interference.

A regional channel has stations not exceeding 5kW which have coverage
contours which limit the primary service interference between these
stations.

A local channel has stations not exceeding 1 kW daytime and 250 watts at
night. Primary coverage is limited by interference. Assignments are made
to limit interference.

Radio waves are radiated into a hemisphere as space below the antenna is
hidden by the surface of the earth. This results in a formula for the
field power at one mile from a perfect radiator emitting 1 kilowatt:
P = 1000 / 16266419 = 0.00006 watts/sq mtr
E = sq rt (PR)
and R=377 ohms

Volts/mtr=152 at 1 mile from a perfect infinitely short uniform
hemispherical radiator.

From a 1/4-wave vertical, it`s about 195 millivolts per mtr at 1 mile.

From a 1/2-wave vertical, it`s about 236 millivolts per mtr at 1 mile.

From a 5/8-wave vertical, it`s about 267 millivolts per mtr at 1 mile.

Volts vary as the square root of the power. So, for 50 killowatts,
multiply the 1 kilowatt values by 7.07.

The field strengths are the inverse distance or lossless values. Real
earth has losses.

Best regards, Richard Harrison, KB5WZI



[email protected] March 16th 05 11:19 PM

I found that increasing the number of segments had a significant change
in the input Z. The material I read on 5/8 antennas indicated the real
part of the Z was near 50 ohms. I could not get that result until I
increased the number of segments. Guess it is cause 146 MHZ antennas
are a good bit shorter than 3.5 MHZ antennas, and any small deviation
such as lenght, or # of segments will change the end results.
Gary N4AST


Roy Lewallen March 16th 05 11:53 PM

A source is spread out over an entire segment. So when you change the
number of segments, you change both the length and the effective
position of the source. When the source is at the bottom of a quarter
wavelength radiator, small changes in source position don't make much
difference in the impedance seen by the source. However, when the
antenna approaches a half wavelength, the source impedance changes quite
dramatically with source position. Consequently, you'll see substantial
changes in reported source impedance with segmentation in that case.
This might or might not be the cause of what you're seeing. As an
experiment, you might try moving the source up one segment and see how
big a difference it makes.

Whenever the result is very sensitive to small changes in the model, you
shouldn't expect a real antenna to come out exactly like the model
predicts, since small differences between the model and real antenna
will likewise cause significant differences.

The absolute length doesn't matter -- a 146 MHz antenna will be no more
or less sensitive to the same amount of change (in terms of percentage
of the antenna size or of the wavelength) than a 3.5 MHz antenna if both
are proportioned the same. In fact, 146 MHz antennas are typically
considerably fatter in terms of wavelength than 3.5 MHz antennas, and
this makes them less sensitive to small changes.

Roy Lewallen, W7EL

wrote:
I found that increasing the number of segments had a significant change
in the input Z. The material I read on 5/8 antennas indicated the real
part of the Z was near 50 ohms. I could not get that result until I
increased the number of segments. Guess it is cause 146 MHZ antennas
are a good bit shorter than 3.5 MHZ antennas, and any small deviation
such as lenght, or # of segments will change the end results.
Gary N4AST


Richard Fry March 16th 05 11:57 PM

Richard Fry wrote:
"The most common radiator height for Class A non-directional AM
broadcast stations operating at 50kW day and night is 195-degrees."


"Richard Harrison" responded (in part)
I won`t challenge that as I have conducted no survey. WJR Detroit is
shown on the broadcast allocations map book as an unlimited (day and
night) 50 kilowatt Class 1 station.

__________________

Your text is referenced to out-of-date versions of applicable FCC Rules.
The FCC adopted the metric standard over 15 years ago, and the
classification of AM broadcast stations no longer is defined as Class 1 to 4
but Classes A, B, C & D. The current versions of the applicable Rules are
contained in 47CFR Part 73, and for this topic are dated October 1, 2004.

Minimum radiator heights in meters for Class A, B and C AM broadcast
stations are shown in Figure 7 of 47CFR73.190. Radiator efficiency for
Class A stations (other than in Alaska) must be such as to produce a ground
wave of least 362 mV/m at 1km for 1kW of antenna input power. A 90° omni
radiator cannot do that.

RF


Richard Harrison March 17th 05 01:05 AM

Richard Fry wrote:
"Radiator efficiency for Class A stations (other than in Alaska) must be
such as to produce a groundwave of at least 352 mV/m at 1 km for 1kW of
antenna input power. A 90-degree omni radiator cannot do that."

Most such antennas have long been in place. Surely they are
grandfathered until the station is modified.

Best regards, Richard Harrison, KB5WZI


Richard Fry March 17th 05 11:04 AM

Richard Harrison"
Richard Fry wrote:
"Radiator efficiency for Class A stations (other than in Alaska) must be
such as to produce a groundwave of at least 352 mV/m at 1 km for 1kW of
antenna input power. A 90-degree omni radiator cannot do that."

Most such antennas have long been in place. Surely they are
grandfathered until the station is modified.

________________

The minimum efficiency for Class A is 362mV/m as I posted, not 352mV/m as
you "quoted me" above.

As far as the 50kW / non-D / 24-hr operations are concerned, their
facilities have avoided the use of 90° radiators nearly from their start,
due to the commercial/competitive need to generate a very strong groundwave
while avoiding self interference to that groundwave at night from their own
high-angle radiation. The advantages of using greater fractional wavelength
radiators to accomplish this has long been known and confirmed by field
measurements.

RF


john doe March 17th 05 12:41 PM

I'm trying to understand the shunt tapped inductor as a circuit.

How does it work??? As long as the inductor cancels out the reactance of
the radiator you just need to find the 50 ohm point on the coil ... or for
that matter any feedline impedance???

Pardon my lack of knowledge.

de ka2pbt




Richard Fry March 17th 05 01:52 PM

"Richard Fry" wrote
As far as the 50kW / non-D / 24-hr operations are concerned, their
facilities have avoided the use of 90° radiators...

___________________

The list below illustrates my statement above. This data for most of the
50kW, 24-hr stations with the same radiation pattern day and night was taken
from a secondary source linked to the FCC database, current as of October
2004 (typos, if any, excepted).

The average height of these radiators is 188.8°, not including
WFAN and KDKA.

Data Format =
Freq, Call Letters, Tower Height in Degrees, Notation
640 KFI 175.7
650 WSM 190.3
660 WFAN 155.3 (top loaded)
670 WSCR 181.5
700 WLW 189.3
710 WOR 177
720 WGN 195
750 WSB 179.3
760 WJR 194.7
770 WABC 180.3
780 WBBM 194.1
810 WGY 182.9
820 WBAP 192.1
830 WCCO 194.4
840 WHAS 201.1
850 KOA 207.8
870 WWL 182.1
880 WCBS 207.1
890 WLS 189.3
1020 KDKA 280.28 (sectionalized)
1030 WBZ 188.5
1050 WEPN 186
1060 KYW 180
1070 KNX 193.5
1100 WTAM 185.2
1120 KMOX 192.7
1140 WRVA 185
1160 KSL 193.2
1180 WHAM 177.1
1200 WOAI 193.2
1210 WPHT 186

RF


Richard Harrison March 17th 05 03:44 PM

Richard Fry wrote:
"The list below illustrates my statement above."

Yes, and it proves your point that non-directional 50 KW broadcast
stations in the U.S. use tall towers in terms of wavelength.

The r-f is precious and it makes sense to make the most of it. Thank you
for the list of high-powered stations which can be heard far and wide. I
still regret the end of WLW`s 500 KW days.

Best regards, Richard Harrison, KB5WZI


[email protected] March 17th 05 09:18 PM


john doe wrote:
I'm trying to understand the shunt tapped inductor as a circuit.

How does it work??? As long as the inductor cancels out the reactance

of
the radiator you just need to find the 50 ohm point on the coil ...

or for
that matter any feedline impedance???

Pardon my lack of knowledge.

de ka2pbt


Hi John, Is the shunt tapped inductor you are refering to is a coil
with one end connected to the 5/8 radiator, the other end to the
radials, the coax shield to the radials, and the center conductor
tapped up the coil from the radials? If this is the case, according to
the Smith Chart, you can only get a perfect 50 ohm match if the real
part of the impedance you are trying to match less than 50 ohms. Our
models indicate this is not the case with a 5/8 radiator.
The shunt tapped inductor is actually a 2 element matching system,
with both elements being inductors. As you stated, the inductor in
series with the radiator cancels the reactance, and the tapped shunt
inductor provides a 50+j0 point. Works only if the real part of the
impedance is 50 ohms.
Gary N4AST


Roy Lewallen March 17th 05 10:59 PM

Let's suppose you have a vertical antenna with a base feedpoint
impedance of, say, 75 - j300 ohms (75 ohms resistance in series with 300
ohms of capacitive reactance), typical of a thin 5/8 wave vertical. A
network consisting of 1275 ohms in *parallel* with 319 ohms of
capacitive reactance has the same impedance. (Note how the Xc isn't much
different from the Xc of the series circuit in this case.) If we put an
inductor with 319 ohms of inductive reactance in parallel with the
antenna (that is, from the base feedpoint to ground), the reactance of
the inductor cancels out the capacitive reactance of the antenna, and
we're left with 1275 ohms of pure resistance from the antenna base to
ground (that is, across the inductor).

We can use the inductor as an autotransformer. If we tap up on the
inductor some fraction k of the whole way up, the impedance we'll see at
that tap will be very nearly 1275 * k^2, and it'll be purely resistive
(no reactance) because the impedance across the whole coil is purely
resistive. For example, half way up the coil we'll see 1275 * (.5)^2 =
1275 / 4 = 319 ohms. So to get 50 ohms, we tap up sqrt(50/1275) = 20% of
the way up the coil.

Roy Lewallen, W7EL

john doe wrote:
I'm trying to understand the shunt tapped inductor as a circuit.

How does it work??? As long as the inductor cancels out the reactance of
the radiator you just need to find the 50 ohm point on the coil ... or for
that matter any feedline impedance???

Pardon my lack of knowledge.

de ka2pbt




john doe March 18th 05 01:34 AM

Thanks Roy!!!

Is it possible to cancel the capacitive reactance of the antenna by placing
an inductor in series with the radiator??

i.e center of coax connected to one end of a coil with the other end of the
coil connected to the radiator. Coax shield connected to ground plane
radials.

de ka2pbt


"Roy Lewallen" wrote in message
...
Let's suppose you have a vertical antenna with a base feedpoint impedance
of, say, 75 - j300 ohms (75 ohms resistance in series with 300 ohms of
capacitive reactance), typical of a thin 5/8 wave vertical. A network
consisting of 1275 ohms in *parallel* with 319 ohms of capacitive
reactance has the same impedance. (Note how the Xc isn't much different
from the Xc of the series circuit in this case.) If we put an inductor
with 319 ohms of inductive reactance in parallel with the antenna (that
is, from the base feedpoint to ground), the reactance of the inductor
cancels out the capacitive reactance of the antenna, and we're left with
1275 ohms of pure resistance from the antenna base to ground (that is,
across the inductor).

We can use the inductor as an autotransformer. If we tap up on the
inductor some fraction k of the whole way up, the impedance we'll see at
that tap will be very nearly 1275 * k^2, and it'll be purely resistive (no
reactance) because the impedance across the whole coil is purely
resistive. For example, half way up the coil we'll see 1275 * (.5)^2 =
1275 / 4 = 319 ohms. So to get 50 ohms, we tap up sqrt(50/1275) = 20% of
the way up the coil.

Roy Lewallen, W7EL

john doe wrote:
I'm trying to understand the shunt tapped inductor as a circuit.

How does it work??? As long as the inductor cancels out the reactance of
the radiator you just need to find the 50 ohm point on the coil ... or
for
that matter any feedline impedance???

Pardon my lack of knowledge.

de ka2pbt




Jerry Martes March 18th 05 02:02 AM


"john doe" wrote in message
...
Thanks Roy!!!

Is it possible to cancel the capacitive reactance of the antenna by
placing an inductor in series with the radiator??

i.e center of coax connected to one end of a coil with the other end of
the coil connected to the radiator. Coax shield connected to ground plane
radials.

de ka2pbt


John DK2 PBT

I'm no Roy. But, I have thought about Smith Charts alot. I wonder if
you'd consider trying to identify where the antenna's input impedance must
be located so that it might be matched with a series inductor. I'd be way
out of line to assume that you want to look at a Smith Chart for knowledge
about the effectiveness of that series inductance. But, the Smith Chart
can be a real big aid in estimating 'what it takes' to match any antenna's
input impedance.

Jerry




"Roy Lewallen" wrote in message
...
Let's suppose you have a vertical antenna with a base feedpoint impedance
of, say, 75 - j300 ohms (75 ohms resistance in series with 300 ohms of
capacitive reactance), typical of a thin 5/8 wave vertical. A network
consisting of 1275 ohms in *parallel* with 319 ohms of capacitive
reactance has the same impedance. (Note how the Xc isn't much different
from the Xc of the series circuit in this case.) If we put an inductor
with 319 ohms of inductive reactance in parallel with the antenna (that
is, from the base feedpoint to ground), the reactance of the inductor
cancels out the capacitive reactance of the antenna, and we're left with
1275 ohms of pure resistance from the antenna base to ground (that is,
across the inductor).

We can use the inductor as an autotransformer. If we tap up on the
inductor some fraction k of the whole way up, the impedance we'll see at
that tap will be very nearly 1275 * k^2, and it'll be purely resistive
(no reactance) because the impedance across the whole coil is purely
resistive. For example, half way up the coil we'll see 1275 * (.5)^2 =
1275 / 4 = 319 ohms. So to get 50 ohms, we tap up sqrt(50/1275) = 20% of
the way up the coil.

Roy Lewallen, W7EL

john doe wrote:
I'm trying to understand the shunt tapped inductor as a circuit.

How does it work??? As long as the inductor cancels out the reactance of
the radiator you just need to find the 50 ohm point on the coil ... or
for
that matter any feedline impedance???

Pardon my lack of knowledge.

de ka2pbt






Roy Lewallen March 18th 05 05:30 AM

john doe wrote:
Thanks Roy!!!

Is it possible to cancel the capacitive reactance of the antenna by placing
an inductor in series with the radiator??

i.e center of coax connected to one end of a coil with the other end of the
coil connected to the radiator. Coax shield connected to ground plane
radials.

de ka2pbt


Sure. In the example I gave, where the antenna has a 75 - j300 ohm
feedpoint impedance, you'd just need an inductor with 300 ohms of
reactance. Then you'd have a feedpoint impedance of 75 ohms resistive.
Of course, this would be useful in feeding an antenna only if the
resistive part of the feedpoint resistance is close to 50 ohms or some
other value your system can conveniently feed. Unlike the tapped coil
method, it doesn't give you any way of transforming the resistance.

If you need to match any arbitrary impedance, say 250 - j85 or
something, to 50 ohms or some other impedance, you need two things you
can adjust or choose, since you have two things (R and X or magnitude
and phase) which you need to transform. We could get 50 ohms resistive
using the tapped inductor scheme because we could choose the capacitor
and the tap position. Another very common solution is an L network,
which of course has two components. In theory, we can match (or
transform) anything to anything with an L network of some sort. In some
special cases, one of the elements of the L network is zero or infinite,
such as if we're transforming 50 - j200 to 50 + j0, where all we need is
a single inductor. But this isn't generally so.

A 5/8 wave radiator conveniently has a feedpoint resistance in the
neighborhood of 50 ohms, so it can often be matched well enough by
simply adding a series inductor as you suggest.

Roy Lewallen, W7EL

Cecil Moore March 18th 05 03:55 PM

Roy Lewallen wrote:
We can use the inductor as an autotransformer.


Someone should tell that to Kurt N. Sterba. This
month he says: "But for a half-wave or 5/8 wave
vertical you need a parallel tuned circuit at the
base if you want to feed it there with coaxial
cable."

He also says: "A reader is irate because Kurt has
stated that coaxial cable does not radiate. Actually,
Kurt is just quoting from textbooks."

He apparently forgot what he wrote previously: "The
Resonant Feedline Dipole takes advantage of the fact
that coaxial cable acts like a three conductor cable
for RF. There is the inner conductor, the inside of
the shield, and the outside of the shield. RF signals
travel down the inside of the cable with equal currents
on the inner conductor and the shield. The current on
the shield does not penetrate the shield."
--
73, Cecil http://www.qsl.net/w5dxp


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Cecil Moore March 18th 05 04:05 PM

john doe wrote:
Is it possible to cancel the capacitive reactance of the antenna by placing
an inductor in series with the radiator??


That's exactly what happens with the 5/8WL vertical and
base coil.

coil 5/8 WL
GND---/////////--------------------------------------
^
|
50 ohm tap

The coil and 5/8 WL whip form a series-resonant circuit.
--
73, Cecil http://www.qsl.net/w5dxp


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Roy Lewallen March 18th 05 05:31 PM

Cecil Moore wrote:
john doe wrote:

Is it possible to cancel the capacitive reactance of the antenna by
placing an inductor in series with the radiator??



That's exactly what happens with the 5/8WL vertical and
base coil.

coil 5/8 WL
GND---/////////--------------------------------------
^
|
50 ohm tap

The coil and 5/8 WL whip form a series-resonant circuit.
--
73, Cecil http://www.qsl.net/w5dxp


Not quite. If you look at the analysis I posted regarding the tap feed,
you'll see that the inductive reactance required for feeding the antenna
this way isn't equal to the series capacitive reactance of the antenna.
They're often close (as in the example, where the feedpoint series X =
-300 and the required Xl = 319 ohms), but how close they are depends on
the Q (Xs/Rs) of the feedpoint Z. When you feed the antenna this way,
what you have is not a series resonant circuit but a parallel resonant
one, and the required inductance is different for the two. The
requirement for this type of feed is not series resonance, but that the
Z at the top of the coil be completely resistive, which series resonance
doesn't produce. As I pointed out in my most recent posting, you can
make a series resonant circuit consisting of the antenna and an
inductor, and put the source in series with that. But you need a
different size inductor.

Roy Lewallen, W7EL

[email protected] March 18th 05 10:43 PM


Roy Lewallen wrote:

We can use the inductor as an autotransformer. If we tap up on the
inductor some fraction k of the whole way up, the impedance we'll see

at
that tap will be very nearly 1275 * k^2, and it'll be purely

resistive
(no reactance) because the impedance across the whole coil is purely
resistive. For example, half way up the coil we'll see 1275 * (.5)^2

=
1275 / 4 = 319 ohms. So to get 50 ohms, we tap up sqrt(50/1275) = 20%

of
the way up the coil.

Roy Lewallen, W7EL


Hi Roy, I'm OK with 319+j0 half way up the coil, but at 20% of the way
up I keep getting 50+j50. I did it on the Smith Chart, and on a Spice
based circuit analysis program. Too old to do this stuff by hand.
That's not a real good match for 50 ohm coax. The are other taps that
will provide a better match, but no where did I find 50+j0.
In an earlier post I stated that it looked like the real part of the
antenna impedance needed to be less than 50 ohms to get a perfect
match, using this method.
The impedance across the whole coil is not purely resistive, it is at
the 50% point. Apparently I am modeling incorrectly, or missing
something.
Gary N4AST


Rob Roschewsk March 18th 05 11:34 PM

"Roy Lewallen" wrote in message
...
Let's suppose you have a vertical antenna with a base feedpoint impedance
of, say, 75 - j300 ohms (75 ohms resistance in series with 300 ohms of
capacitive reactance), typical of a thin 5/8 wave vertical. A network
consisting of 1275 ohms in *parallel* with 319 ohms of capacitive
reactance has the same impedance.


Roy, how did you come up with "1275 ohms in *parallel* with 319 ohms "
equatating to "75 ohms resistance in series with 300 ohms of capacitive
reactance" ??? Just wondering.

de ka2pbt



Roy Lewallen March 19th 05 01:11 AM

Rob Roschewsk wrote:

Roy, how did you come up with "1275 ohms in *parallel* with 319 ohms "
equatating to "75 ohms resistance in series with 300 ohms of capacitive
reactance" ??? Just wondering.


I got it from a routine I keep on my HP48GX calculator, which comes from
the following series-parallel transformations:

Let:

Rs = resistance of series equivalent circuit
Xs = reactance of series equivalent circuit
Rp = resistance of parallel equivalent circuit
Xp = reactance of parallel equivalent circuit

To convert a series circuit to a parallel circuit which has an identical
impedance:

Rp = (Rs^2 + Xs^2) / Rs
Xp = (Rs^2 + Xs^2) / Xs

To convert a parallel circuit to a series circuit which has an identical
impedance:

Rs = (Rp * Xp^2) / (Rp^2 + Xp^2)
Xs = (Rp^2 * Xp) / (Rp^2 + Xp^2)

These aren't very difficult to derive if you're comfortable with complex
arithmetic. They should be in the toolkit of everyone who works with
electrical circuits.

Important things to keep in mind when using these transformations:

1. Although frequency isn't explicitly involved in the conversions, when
you make an equivalent circuit from a resistor and inductor or
capacitor, Xp and Xs will change with frequency. Therefore a transformed
circuit will have the same impedance as the original only at one
frequency. If the frequency changes, new values of resistance and
capacitance or inductance have to be calculated for the equivalent circuit.

2. Because point 1, one circuit or the other will usually be better for
modeling a real circuit over a range of frequencies, because the
impedance of the real circuit will change with frequency more like one
or the other of the two equivalent circuits.

In the example, where the feedpoint Z = 75 - j300:

Rs = 75
Xs = 300

so

Rp = (75^2 + (-300)^2) / 75 = 1275
Xp = (75^2 + (-300)^2) / (-300) = -318.75

You can check this if you'd like. You'll find that the parallel
combination of 1275 and -j318.75 ohms is 75 - j300.

Roy Lewallen, W7EL


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