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Passive Repeater



 
 
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  #1  
Old February 6th 06, 07:57 PM posted to rec.radio.amateur.antenna
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Default Passive Repeater

Ok, my first test failed so far. Example of what I am doing is here
http://home.triad.rr.com/tempdir/images/layout.jpg. My next thing I am
thinking about trying is to place some kind of somewhat small (no billboard)
passive repeater at the end of the powerline attached to a utility pole
where it meets the field. No power this far out and trenching is not an
option. I can google and find hords of info about people using passive
repeaters to bend the signal but I cannot find an actual passive repeater or
how to build one. Also when dealing with this type of repeater would it
force me to have directional antenna's at both ends where currently I have
only the one directional parabolic grid at the top of the powerline and just
a standard AP inside the building. Anyone think of anything else that may
work. going over the forest is also not an option. I own the land where
the grid antenna is located but I dont own the land where the building is
located as I just have permission to place a AP at that site. I am trying
to make the impact as minimal as possible at that site.

Bryan

--
Poor planning on your part does not constitute an emergency on my part.


  #2  
Old February 6th 06, 09:29 PM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater

Hi again Bryan

A passive repeater is very simple.

You simply take two antennas and join them with feeder, then point one
antenna at one end of the link and the other at the other end of the
link. You may need to separate them some so they dont interfere with
each others capture pattern.

There will be a link budget that defines how much system gain (and thus
antenna gain) you need. You could conceivably get away with using the
standard AP antenna at that one end. As I said previously the software I
use for this is broken and I am not in a position to redo it by hand
just at the moment. There is a simple formula for determining path loss
over a line of sight path. You just do that twice with the received
strength at the repeater being the source power for the next link (minus
about 3dB)

What are the distances from each site to the passive rptr location? If
one does the calclulation then outoput power and receiver sensitivity is
also needed.

Cheers Bob

Bryan Martin wrote:
Ok, my first test failed so far. Example of what I am doing is here
http://home.triad.rr.com/tempdir/images/layout.jpg. My next thing I am
thinking about trying is to place some kind of somewhat small (no billboard)
passive repeater at the end of the powerline attached to a utility pole
where it meets the field. No power this far out and trenching is not an
option. I can google and find hords of info about people using passive
repeaters to bend the signal but I cannot find an actual passive repeater or
how to build one. Also when dealing with this type of repeater would it
force me to have directional antenna's at both ends where currently I have
only the one directional parabolic grid at the top of the powerline and just
a standard AP inside the building. Anyone think of anything else that may
work. going over the forest is also not an option. I own the land where
the grid antenna is located but I dont own the land where the building is
located as I just have permission to place a AP at that site. I am trying
to make the impact as minimal as possible at that site.

Bryan

  #3  
Old February 7th 06, 12:24 AM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater

Bryan Martin wrote:
"I can google and find hordes of info about people using passive
repeaters to bend the signal but I cannot find an actual passive
pepeater or how to build one."

Maybe that is because the billboard reflector is close to 98% efficient,
while back-to-back antennas are only about 30% efficient.

Best regards, Richard Harrison, KB5WZI

  #4  
Old February 7th 06, 01:55 AM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater

The building location is maybe 500 feet away from where the repeater would
be. The parabolic grid is maybe 3000-3500 feet away from the repeater
location.

As for the output we will talk about the grid antenna first. It is
currently at 28mw which is adjustable up to 250mw but I would be way over
the limit with the 24db gain antenna (also the way I understand it which is
a learning in process I should not need to increase the xmit power due to
the focus of the directional type antenna). Plus since this will be out in
the open in a sealed weather proof box I don't want heating problems or bird
nuking etc.... Sadly I am unable to find out what the current MN-700 AP
which is located in the building transmits at or what the gain of the stock
antenna's is. I have purchased another AP similar to the one hooked to the
grid antenna which by default would be transmitting at 28mw with 7db gain
rubber duck antenna.

Passive antenna
"You simply take two antennas and join them with feeder". Help me out a bit
here if possible. So I take two antenna's such as
(http://sharperconcepts.zoovy.com/c=6...ct/YSC-HG2409Y)
and hook the pig tails together? Point one at the grid and one at the
building right? Does the gain really matter? Do they need to both be
directional?

"You may need to separate them some so they dont interfere with each others
capture pattern."
I dont think this would be an issue as one would have to be on 1 side of the
utility pole and one on the other. Do you think this would cause problems?




"Bob Bob" wrote in message
...
Hi again Bryan

A passive repeater is very simple.

You simply take two antennas and join them with feeder, then point one
antenna at one end of the link and the other at the other end of the link.
You may need to separate them some so they dont interfere with each others
capture pattern.

There will be a link budget that defines how much system gain (and thus
antenna gain) you need. You could conceivably get away with using the
standard AP antenna at that one end. As I said previously the software I
use for this is broken and I am not in a position to redo it by hand just
at the moment. There is a simple formula for determining path loss over a
line of sight path. You just do that twice with the received strength at
the repeater being the source power for the next link (minus about 3dB)

What are the distances from each site to the passive rptr location? If one
does the calclulation then outoput power and receiver sensitivity is also
needed.

Cheers Bob

Bryan Martin wrote:
Ok, my first test failed so far. Example of what I am doing is here
http://home.triad.rr.com/tempdir/images/layout.jpg. My next thing I am
thinking about trying is to place some kind of somewhat small (no
billboard) passive repeater at the end of the powerline attached to a
utility pole where it meets the field. No power this far out and
trenching is not an option. I can google and find hords of info about
people using passive repeaters to bend the signal but I cannot find an
actual passive repeater or how to build one. Also when dealing with this
type of repeater would it force me to have directional antenna's at both
ends where currently I have only the one directional parabolic grid at
the top of the powerline and just a standard AP inside the building.
Anyone think of anything else that may work. going over the forest is
also not an option. I own the land where the grid antenna is located but
I dont own the land where the building is located as I just have
permission to place a AP at that site. I am trying to make the impact as
minimal as possible at that site.

Bryan



  #5  
Old February 7th 06, 01:56 AM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater

You lost me somewhere. Was this supposed to help or was it just a slam?


"Richard Harrison" wrote in message
...
Bryan Martin wrote:
"I can google and find hordes of info about people using passive
repeaters to bend the signal but I cannot find an actual passive
pepeater or how to build one."

Maybe that is because the billboard reflector is close to 98% efficient,
while back-to-back antennas are only about 30% efficient.

Best regards, Richard Harrison, KB5WZI



  #6  
Old February 7th 06, 03:34 AM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater

Bryan Martin wrote:
"Was this supposed to help or was it just a slam?"

No, my response was factual, neumeric, and specific. It was not meant as
a slam. Reflectors are less lossy than back-to-back antennas. If you are
using microwaves, the size of the reflector may be practical.

The peflector in the path is most effective when placed near either end
of the path. The reflector can also produce gain over that produced by
the antennas at the path ends. It must be slightly concave to do so.
Commercial reflectors often come equipped with an adjustment to suck in
the center of the reflector for maximum gain once alignment of the
dishes is accomplished. This isn`t speculation. I`ve designed the paths
and performed the adjustments with my own hands.

Best regatds, Richard Harrison, KB5WZI

  #7  
Old February 7th 06, 07:14 AM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater

Example scenario:
There's a mountain between your house and the tv station and you cannot pick
up a tv signal to watch.
SO - you buy 3 high-gain direction tv antennas at radio shack.
You go up to the top of the mountain and set one antenna to point to the tv
station, and one of the other antennas to point toward your house.
The 2 antennas on the mountain feed to each other with 300-ohm ribbon cable-
like the other antenna was the tv set. (one acts like a receiver, and the
other like a transmitter.)
The third high-gain antenna is at your house - pointed to the antenna on top
of the mountain. This antenna feeds to your tv.
So yes - you need directional antennas - three of them.
The antennas need to 'see' each other.
I heard of folks using rhombic antennas on the mtn (uhf and vhf) - good
gain.


"Bryan Martin" wrote in message
...
The building location is maybe 500 feet away from where the repeater would
be. The parabolic grid is maybe 3000-3500 feet away from the repeater
location.

As for the output we will talk about the grid antenna first. It is




  #8  
Old February 7th 06, 11:04 AM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater

I keep hearing about "passive repeaters", but haven't ever seen anything
quantitative about how well they work. I had some measurements done
years ago which showed that a cell phone "passive repeater" in a sedan
doesn't do anything significant, quite obviously because the windows are
such large apertures at that frequency.

But here are some numbers to work with. Corrections are welcome.

Assuming perfect efficiency, the maximum effective aperture of an
antenna is Aem = G * lambda^2 / (4 * pi), where

lambda = the wavelength
G = the antenna's numerical power gain in the direction being analyzed

The gain in dBi = 10 * log[base10](G). For convenience, use meters for
length dimensions, so the aperture is in square meters and the
wavelength is in meters.

This means that if we have a field with power density Pdi striking an
antenna with power gain G1 (in the direction the field is coming from),
the antenna can deliver Pdi * Aem watts to a conjugately matched load.

Now let's connect this antenna to a second antenna with numerical power
gain G2, and assume that the two are perfectly matched to each other.
That is, the input impedance of the second antenna is the complex
conjugate of the impedance the first antenna has when driven. Also
assume no loss in the connecting line.

The power delivered to the second antenna is then Pdi * Aem watts.

The second antenna will radiate a field with power density equal to G2
times that of an isotropic antenna supplied with the same power, or

G2 * (Pdi * Aem) / (4 * pi * r^2)

where r is the distance from the antenna in the direction in which the
gain is measured.

Combining these to find the ratio of power density of the field radiated
from the second antenna to the power density of the field striking the
first antenna, we get:

P density ratio = G1 * G2 * (lambda / (4 * pi * r))^2

This is the numerical gain you'll see between the field at the location
of the first passive receiver antenna to the field at a distance r from
the second (radiating) passive receiver antenna. A ratio of less than
one represents attenuation rather than gain. The gain in dB is 10 * the
base 10 logarithm of this ratio, with negative results representing
attenuation. That is,

Overall gain (dB) = 10 * log[base 10](P density ratio)

Now let's look at a couple of examples. For simplicity, assume that none
of the original field arrives at the detector location; that is, there's
a perfect shield or obstruction between the original field and the
detector (technically, the detector's antenna). It doesn't matter what
kind of antenna is physically connected to the detector for this
analysis. In real life, the detector would probably be a receiver, but
I'll call it a detector so hopefully its antenna won't be confused for
either of the two passive receiver's antennas.

Let G1 = G2 = 10 -- both antennas comprising the passive repeater have
10 dBi gain (although don't forget that G1 and G2 are numerical, not dB
gains -- the two numbers just happen to be the same in the case of 10).
Wavelength = 30 meters (10 MHz frequency), and r = 10 meters -- we've
put the detector's antenna 10 meters from the second (radiating) passive
repeater antenna(*).

Working through the numbers, the power density at the detector's antenna
is 5.7 times, or 7.56 dB greater than, the power density striking the
first antenna. So the signal is stronger than it would have been if we'd
put the detector's antenna right where the first passive repeater
antenna is. Don't forget, though, that it took two 10 dBi antennas to
get that 7.56 dB gain.

But now let's look at the same setup but at 150 MHz (2 meter
wavelength). The power density at the detector's antenna in this case is
just 2.5% of (or 15.96 dB less than) the power density of the field
striking the first antenna.

In all cases, if we move the detector's antenna twice as close to the
second (radiating) passive repeater antenna, that is, to 5 meters away,
we'll gain 6 dB; if we double the distance to 20 meters we lose 6 dB.
Before you say, "Aha! let's put the detector antenna 0.000001 meter from
the passive repeater antenna and get incredible gain!" you have to
realize that the antenna gain is achieved only in the far field, so
you've got to keep a good part of a wavelength away for the rules to
hold. Actually, 5 meters is almost certainly too close for the gain to
be valid at 10 MHz. The actual gain at any distance and field strength
for a given input power could easily be determined for a particular
antenna by modeling.

Why does the wavelength make such a big difference? Well, think of the
size of the field each antenna intercepts. Both the 10 MHz and 150 MHz
antennas have the same gain, so the former is dimensionally 15 times
larger than the latter, or 15^2 = 225 times the area. Consquently, the
10 MHz antenna intercepts 225 times the power that the 150 MHz antenna
does(**). 225 is exactly the ratio between the 10 and 150 MHz results of
5.7 and 0.025 (if carried out a few more places).

If you know how much signal strength margin you have at the point where
you put the first passive receiver antenna, you can use the equation
above to calculate how much antenna gain you'll need for your passive
repeaters and how close you'll have to put your receiver's antenna to
the second (radiating) passive receiver antenna, or how to trade the
two. Note that I've assumed perfect match and no loss. If, for example,
there's loss in the transmission line between the two passive repeater
antennas, that loss in dB will directly subtract from the overall
passive repeater gain (or add to the overall passive repeater attenuation).

(*) 10 meters is only 1/3 wavelengh so a bit close. The nominal antenna
gain might not actually be realized at that short distance. But I'll
assume it is.

(**) Please don't infer from this that aperture has any obvious
relationship to physical antenna area except in so-called "aperture
antennas" such as horns or parabolic antennas which have large physical
dimensions. The antennas under discussion have apertures proportional to
their physical areas only because they're assumed to be physically
identical except for a scaling factor. In general, antennas with widely
different physical areas can have the same aperture, and antennas with
the same physical area can have widely different apertures.

Roy Lewallen, W7EL
  #9  
Old February 7th 06, 11:32 AM posted to rec.radio.amateur.antenna
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Posts: n/a
Default Passive Repeater


"Roy Lewallen" wrote in message
...
I keep hearing about "passive repeaters", but haven't ever seen anything
quantitative about how well they work. I had some measurements done years
ago which showed that a cell phone "passive repeater" in a sedan doesn't do
anything significant, quite obviously because the windows are such large
apertures at that frequency.

But here are some numbers to work with. Corrections are welcome.

Assuming perfect efficiency, the maximum effective aperture of an antenna
is Aem = G * lambda^2 / (4 * pi), where

lambda = the wavelength
G = the antenna's numerical power gain in the direction being analyzed

The gain in dBi = 10 * log[base10](G). For convenience, use meters for
length dimensions, so the aperture is in square meters and the wavelength
is in meters.

This means that if we have a field with power density Pdi striking an
antenna with power gain G1 (in the direction the field is coming from),
the antenna can deliver Pdi * Aem watts to a conjugately matched load.

Now let's connect this antenna to a second antenna with numerical power
gain G2, and assume that the two are perfectly matched to each other. That
is, the input impedance of the second antenna is the complex conjugate of
the impedance the first antenna has when driven. Also assume no loss in
the connecting line.

The power delivered to the second antenna is then Pdi * Aem watts.

The second antenna will radiate a field with power density equal to G2
times that of an isotropic antenna supplied with the same power, or

G2 * (Pdi * Aem) / (4 * pi * r^2)

where r is the distance from the antenna in the direction in which the
gain is measured.

Combining these to find the ratio of power density of the field radiated
from the second antenna to the power density of the field striking the
first antenna, we get:

P density ratio = G1 * G2 * (lambda / (4 * pi * r))^2

This is the numerical gain you'll see between the field at the location of
the first passive receiver antenna to the field at a distance r from the
second (radiating) passive receiver antenna. A ratio of less than one
represents attenuation rather than gain. The gain in dB is 10 * the base
10 logarithm of this ratio, with negative results representing
attenuation. That is,

Overall gain (dB) = 10 * log[base 10](P density ratio)

Now let's look at a couple of examples. For simplicity, assume that none
of the original field arrives at the detector location; that is, there's a
perfect shield or obstruction between the original field and the detector
(technically, the detector's antenna). It doesn't matter what kind of
antenna is physically connected to the detector for this analysis. In real
life, the detector would probably be a receiver, but I'll call it a
detector so hopefully its antenna won't be confused for either of the two
passive receiver's antennas.

Let G1 = G2 = 10 -- both antennas comprising the passive repeater have 10
dBi gain (although don't forget that G1 and G2 are numerical, not dB
gains -- the two numbers just happen to be the same in the case of 10).
Wavelength = 30 meters (10 MHz frequency), and r = 10 meters -- we've put
the detector's antenna 10 meters from the second (radiating) passive
repeater antenna(*).

Working through the numbers, the power density at the detector's antenna
is 5.7 times, or 7.56 dB greater than, the power density striking the
first antenna. So the signal is stronger than it would have been if we'd
put the detector's antenna right where the first passive repeater antenna
is. Don't forget, though, that it took two 10 dBi antennas to get that
7.56 dB gain.

But now let's look at the same setup but at 150 MHz (2 meter wavelength).
The power density at the detector's antenna in this case is just 2.5% of
(or 15.96 dB less than) the power density of the field striking the first
antenna.

In all cases, if we move the detector's antenna twice as close to the
second (radiating) passive repeater antenna, that is, to 5 meters away,
we'll gain 6 dB; if we double the distance to 20 meters we lose 6 dB.
Before you say, "Aha! let's put the detector antenna 0.000001 meter from
the passive repeater antenna and get incredible gain!" you have to realize
that the antenna gain is achieved only in the far field, so you've got to
keep a good part of a wavelength away for the rules to hold. Actually, 5
meters is almost certainly too close for the gain to be valid at 10 MHz.
The actual gain at any distance and field strength for a given input power
could easily be determined for a particular antenna by modeling.

Why does the wavelength make such a big difference? Well, think of the
size of the field each antenna intercepts. Both the 10 MHz and 150 MHz
antennas have the same gain, so the former is dimensionally 15 times
larger than the latter, or 15^2 = 225 times the area. Consquently, the 10
MHz antenna intercepts 225 times the power that the 150 MHz antenna
does(**). 225 is exactly the ratio between the 10 and 150 MHz results of
5.7 and 0.025 (if carried out a few more places).

If you know how much signal strength margin you have at the point where
you put the first passive receiver antenna, you can use the equation above
to calculate how much antenna gain you'll need for your passive repeaters
and how close you'll have to put your receiver's antenna to the second
(radiating) passive receiver antenna, or how to trade the two. Note that
I've assumed perfect match and no loss. If, for example, there's loss in
the transmission line between the two passive repeater antennas, that loss
in dB will directly subtract from the overall passive repeater gain (or
add to the overall passive repeater attenuation).

(*) 10 meters is only 1/3 wavelengh so a bit close. The nominal antenna
gain might not actually be realized at that short distance. But I'll
assume it is.

(**) Please don't infer from this that aperture has any obvious
relationship to physical antenna area except in so-called "aperture
antennas" such as horns or parabolic antennas which have large physical
dimensions. The antennas under discussion have apertures proportional to
their physical areas only because they're assumed to be physically
identical except for a scaling factor. In general, antennas with widely
different physical areas can have the same aperture, and antennas with the
same physical area can have widely different apertures.

Roy Lewallen, W7EL

This is way beyond me. Think I'll take up knitting. (if I can get the VSWR
right).

Regards Mike.

  #10  
Old February 7th 06, 05:16 PM posted to rec.radio.amateur.antenna
Guest
 
Posts: n/a
Default Passive Repeater

Thanks for the tutorial. The only time I was (remotely) involved in a
similar set up was in some very early cell phone demos inside buildings
where the cell site was not very close. Two antennas were used, but two
sets of filters and amplifiers were used to get considerable power gain in
both directions. in/out of the demo room.
73, Steve, K9DCI


"Roy Lewallen" wrote in message
...
I keep hearing about "passive repeaters", but haven't ever seen anything
quantitative about how well they work. I had some measurements done
years ago which showed that a cell phone "passive repeater" in a sedan
doesn't do anything significant, quite obviously because the windows are
such large apertures at that frequency.

But here are some numbers to work with. Corrections are welcome.

Assuming perfect efficiency, the maximum effective aperture of an
antenna is Aem = G * lambda^2 / (4 * pi), where

lambda = the wavelength
G = the antenna's numerical power gain in the direction being analyzed

The gain in dBi = 10 * log[base10](G). For convenience, use meters for
length dimensions, so the aperture is in square meters and the
wavelength is in meters.

This means that if we have a field with power density Pdi striking an
antenna with power gain G1 (in the direction the field is coming from),
the antenna can deliver Pdi * Aem watts to a conjugately matched load.

Now let's connect this antenna to a second antenna with numerical power
gain G2, and assume that the two are perfectly matched to each other.
That is, the input impedance of the second antenna is the complex
conjugate of the impedance the first antenna has when driven. Also
assume no loss in the connecting line.

The power delivered to the second antenna is then Pdi * Aem watts.

The second antenna will radiate a field with power density equal to G2
times that of an isotropic antenna supplied with the same power, or

G2 * (Pdi * Aem) / (4 * pi * r^2)

where r is the distance from the antenna in the direction in which the
gain is measured.

Combining these to find the ratio of power density of the field radiated
from the second antenna to the power density of the field striking the
first antenna, we get:

P density ratio = G1 * G2 * (lambda / (4 * pi * r))^2

This is the numerical gain you'll see between the field at the location
of the first passive receiver antenna to the field at a distance r from
the second (radiating) passive receiver antenna. A ratio of less than
one represents attenuation rather than gain. The gain in dB is 10 * the
base 10 logarithm of this ratio, with negative results representing
attenuation. That is,

Overall gain (dB) = 10 * log[base 10](P density ratio)

Now let's look at a couple of examples. For simplicity, assume that none
of the original field arrives at the detector location; that is, there's
a perfect shield or obstruction between the original field and the
detector (technically, the detector's antenna). It doesn't matter what
kind of antenna is physically connected to the detector for this
analysis. In real life, the detector would probably be a receiver, but
I'll call it a detector so hopefully its antenna won't be confused for
either of the two passive receiver's antennas.

Let G1 = G2 = 10 -- both antennas comprising the passive repeater have
10 dBi gain (although don't forget that G1 and G2 are numerical, not dB
gains -- the two numbers just happen to be the same in the case of 10).
Wavelength = 30 meters (10 MHz frequency), and r = 10 meters -- we've
put the detector's antenna 10 meters from the second (radiating) passive
repeater antenna(*).

Working through the numbers, the power density at the detector's antenna
is 5.7 times, or 7.56 dB greater than, the power density striking the
first antenna. So the signal is stronger than it would have been if we'd
put the detector's antenna right where the first passive repeater
antenna is. Don't forget, though, that it took two 10 dBi antennas to
get that 7.56 dB gain.

But now let's look at the same setup but at 150 MHz (2 meter
wavelength). The power density at the detector's antenna in this case is
just 2.5% of (or 15.96 dB less than) the power density of the field
striking the first antenna.

In all cases, if we move the detector's antenna twice as close to the
second (radiating) passive repeater antenna, that is, to 5 meters away,
we'll gain 6 dB; if we double the distance to 20 meters we lose 6 dB.
Before you say, "Aha! let's put the detector antenna 0.000001 meter from
the passive repeater antenna and get incredible gain!" you have to
realize that the antenna gain is achieved only in the far field, so
you've got to keep a good part of a wavelength away for the rules to
hold. Actually, 5 meters is almost certainly too close for the gain to
be valid at 10 MHz. The actual gain at any distance and field strength
for a given input power could easily be determined for a particular
antenna by modeling.

Why does the wavelength make such a big difference? Well, think of the
size of the field each antenna intercepts. Both the 10 MHz and 150 MHz
antennas have the same gain, so the former is dimensionally 15 times
larger than the latter, or 15^2 = 225 times the area. Consquently, the
10 MHz antenna intercepts 225 times the power that the 150 MHz antenna
does(**). 225 is exactly the ratio between the 10 and 150 MHz results of
5.7 and 0.025 (if carried out a few more places).

If you know how much signal strength margin you have at the point where
you put the first passive receiver antenna, you can use the equation
above to calculate how much antenna gain you'll need for your passive
repeaters and how close you'll have to put your receiver's antenna to
the second (radiating) passive receiver antenna, or how to trade the
two. Note that I've assumed perfect match and no loss. If, for example,
there's loss in the transmission line between the two passive repeater
antennas, that loss in dB will directly subtract from the overall
passive repeater gain (or add to the overall passive repeater

attenuation).

(*) 10 meters is only 1/3 wavelengh so a bit close. The nominal antenna
gain might not actually be realized at that short distance. But I'll
assume it is.

(**) Please don't infer from this that aperture has any obvious
relationship to physical antenna area except in so-called "aperture
antennas" such as horns or parabolic antennas which have large physical
dimensions. The antennas under discussion have apertures proportional to
their physical areas only because they're assumed to be physically
identical except for a scaling factor. In general, antennas with widely
different physical areas can have the same aperture, and antennas with
the same physical area can have widely different apertures.

Roy Lewallen, W7EL



 




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