"K7ITM" wrote in message
...
On Apr 7, 8:36 am, "Antonio Vernucci" wrote:
.................................................. ..................
On the other hand, I'm surprised by the comment from the manufacturer
about difficulties making a 1:1 balun. I have had good luck using
ferrites and/or self-resonant coils of feedline and/or coils of
feedline specifically resonated with additional capacitance. A 4:1
balun from a "hairpin" of 1/2 wave of coax, arranged symmetrically, is
easy enough to make, but I would not rule out using a 1:1, if it has
advantages for you.

Cheers,
Tom
Also, I think the 4:1 , 1/2 wave would be a voltage balun. I am considering
adding a ferrite 1:1 on the feedline side of the the coax balun. There is
some feedline radiation right now.

Tam/WB2TT

On 7 abr, 23:15, "Antonio Vernucci" wrote:
Hello Tom,



First, the matching is being done essentially with an "L" network (or
rather the balanced version of an "L" network), where there is a load
resistance (the resistive part of the feedpoint impedance, which
includes radiation resistance and element loss resistance reflected to
the feedpoint), the series capacitive reactance of the feedpoing
element, and a shunt inductive reactance, provided by the hairpin.
Because shortening the driven element causes a decrease in resistance
and an increase in capacitive reactance, it's possible to find a
length that allows matching to any of a wide range of resistances.
But the higher the resistance to which you match, the shorter you need
to make the element and the lower the feedpoint resistance. The ratio
of feedpoint resistance to matched resistance determines the loaded Q
of the matching network; as you make the matched resistance higher,
the loaded Q goes up rather quickly. If you know the loaded Q and the
unloaded Q of the hairpin, you have a good handle on the amount lost
to heat in the hairpin: if the hairpin Q is two times the loaded Q,
half the power is dissipated in the hairpin, for example.

However, unless you build an antenna with a very low feedpoint
resistance at resonance, there almost certainly won't be an efficiency
problem: the reactance changes quickly enough with changes in driven
element length that the resistance won't drop much by the time you
reach enough reactance to get a match to 200 ohms. It appears that
the loaded Q of the match to 200 ohms for your case will be less than
4. I would think unless you really messed up badly, the hairpin
unloaded Q should be well in excess of 100, and if that's the case,
the power lost in the hairpin would correspond to well under 0.1dB
signal level change.

All OK. I however reckon that, due to the parasitic elements effect, the
radiation resistance of the driven element (before shortening it) would be in
the order of 20 ohm. So, impedance gets brought up by a factor of 10 or so.

On the other hand, I'm surprised by the comment from the manufacturer
about difficulties making a 1:1 balun. I have had good luck using
ferrites and/or self-resonant coils of feedline and/or coils of
feedline specifically resonated with additional capacitance. A 4:1
balun from a "hairpin" of 1/2 wave of coax, arranged symmetrically, is
easy enough to make, but I would not rule out using a 1:1, if it has
advantages for you.

His argument is that, for high-power operation (say 1500W), it is more
convenient for him to provide a quarter-wavelength 4:1 balun made of RG-142
teflon cable than a sealed box with a 1:1 coil on an ironpowder toroidal core. I
mentioned him that, just using some extra length of RG-142 cable, he can easily
build a 1:1 balun, and hence design the antenna matching system for 50 ohm
instead of 200 ohm.

I hope he will listen to me, because that antenna is really narrowband!

73

Tony I0JX

Hello,

Imagine 10 Ohms radiation resistance + capacitive component after
shortening the open dipole radiator. When you convert that to 200 Ohms
via a parallel inductance (hairpin), the Q factor of such a network is
about 4.4. At 50 MHz that will result in a bandwidth (VSWR=2) of 8
MHz.

A 200 Ohms to 50 Ohms coaxial balun will have a lower Q factor. So the
combination of balun and L-network will certainly have a useful
bandwidth 340 kHz.

Maybe the radiation resistance is less (you can derive that from the
hairpin inductance) and/or the antenna is by nature (very) narrow
band.

Best regards,

Wim
PA3DJS
www.tetech.nl
remove abc from the address.

On Apr 7, 4:02 pm, Wimpie wrote:
On 7 abr, 23:15, "Antonio Vernucci" wrote:



Hello Tom,

First, the matching is being done essentially with an "L" network (or
rather the balanced version of an "L" network), where there is a load
resistance (the resistive part of the feedpoint impedance, which
includes radiation resistance and element loss resistance reflected to
the feedpoint), the series capacitive reactance of the feedpoing
element, and a shunt inductive reactance, provided by the hairpin.
Because shortening the driven element causes a decrease in resistance
and an increase in capacitive reactance, it's possible to find a
length that allows matching to any of a wide range of resistances.
But the higher the resistance to which you match, the shorter you need
to make the element and the lower the feedpoint resistance. The ratio
of feedpoint resistance to matched resistance determines the loaded Q
of the matching network; as you make the matched resistance higher,
the loaded Q goes up rather quickly. If you know the loaded Q and the
unloaded Q of the hairpin, you have a good handle on the amount lost
to heat in the hairpin: if the hairpin Q is two times the loaded Q,
half the power is dissipated in the hairpin, for example.

However, unless you build an antenna with a very low feedpoint
resistance at resonance, there almost certainly won't be an efficiency
problem: the reactance changes quickly enough with changes in driven
element length that the resistance won't drop much by the time you
reach enough reactance to get a match to 200 ohms. It appears that
the loaded Q of the match to 200 ohms for your case will be less than
4. I would think unless you really messed up badly, the hairpin
unloaded Q should be well in excess of 100, and if that's the case,
the power lost in the hairpin would correspond to well under 0.1dB
signal level change.

All OK. I however reckon that, due to the parasitic elements effect, the
radiation resistance of the driven element (before shortening it) would be in
the order of 20 ohm. So, impedance gets brought up by a factor of 10 or so.

On the other hand, I'm surprised by the comment from the manufacturer
about difficulties making a 1:1 balun. I have had good luck using
ferrites and/or self-resonant coils of feedline and/or coils of
feedline specifically resonated with additional capacitance. A 4:1
balun from a "hairpin" of 1/2 wave of coax, arranged symmetrically, is
easy enough to make, but I would not rule out using a 1:1, if it has
advantages for you.

His argument is that, for high-power operation (say 1500W), it is more
convenient for him to provide a quarter-wavelength 4:1 balun made of RG-142
teflon cable than a sealed box with a 1:1 coil on an ironpowder toroidal core. I
mentioned him that, just using some extra length of RG-142 cable, he can easily
build a 1:1 balun, and hence design the antenna matching system for 50 ohm
instead of 200 ohm.

I hope he will listen to me, because that antenna is really narrowband!

73

Tony I0JX

Hello,

Imagine 10 Ohms radiation resistance + capacitive component after
shortening the open dipole radiator. When you convert that to 200 Ohms
via a parallel inductance (hairpin), the Q factor of such a network is
about 4.4. At 50 MHz that will result in a bandwidth (VSWR=2) of 8
MHz.

A 200 Ohms to 50 Ohms coaxial balun will have a lower Q factor. So the
combination of balun and L-network will certainly have a useful
bandwidth 340 kHz.

Maybe the radiation resistance is less (you can derive that from the
hairpin inductance) and/or the antenna is by nature (very) narrow
band.

Best regards,

Wim
PA3DJSwww.tetech.nl
remove abc from the address.

Yes, I had similar thoughts, but a bit different. First, I think it's
safe to say that if, at resonance, the driven element presents about
20 ohms at the feedpoint, shortening the D.E. only a little will give
enough capacitive reactance to allow the hairpin match to 200 ohms.
Even if the D.E. looks like 5 ohms, the "L" network match still gives
a 3dB bandwidth of 8MHz at a 50MHz center, or 3MHz 1.5:1 SWR
bandwidth. I think we need to look somewhere else for the answer to
the narrow bandwidth. My working hypothesis at the moment is that
it's in the antenna, or perhaps rather in the combination of antenna
and matching network. Note that the calc for the L match assumed a
constant capacitance, but the antenna will not, in general, look
anything like a constant C even over a fairly narrow frequency range.
I just ran EZNEC on a frequency-scaled version of the 14MHz 5 element
Yagi included in the sample files, with the D.E. slightly shortened to
allow a decent hairpin match to 200 ohms at the design center
frequency. I did a frequency sweep, 49 to 51 MHz, in 0.25MHz steps.
Over that range, the equivalent series capacitance changes from 59pF
at the low end to 138pF at the high end, and at least by NEC2's
prediction, the impedance changes especially quickly around 51MHz--
both reactive and resistive parts. 50.75MHz: 10.3-j31.76; 51MHz: 3.91-
j22.56, quite a large percentage change in 250kHz. Having the
effective series capacitance change that quickly will cause the
matching network to behave very differently than it would with a
capacitance element that is fixed.

Is it possible to lengthen the D.E., causing it to present an
inductive reactance at the feedpoint, and match that (to 200 ohms, or
to 50 ohms) with a shunt capacitance? That may work better, giving a
broader SWR bandwidth. The resistive component should be higher,
further lowering the Q, and I suspect the reactance won't change so
quickly with frequency. I don't have time at the moment to compare
the two, but may this evening. It may also be possible to raise the
resistive part to 50 ohms and match to 50 with a series capacitance.

Cheers,
Tom

K7ITM wrote:

Is it possible to lengthen the D.E., causing it to present an
inductive reactance at the feedpoint, and match that (to 200 ohms, or
to 50 ohms) with a shunt capacitance? That may work better, giving a
broader SWR bandwidth....

Good, constructive suggestion, Tom. Kudos for putting in a bit
of design/analysis effort on this rather than just shooting from
the hip. This is definitely a weird way of driving a yagi. It makes
me yearn for the old TV-antenna schemes that used folded
dipoles for the driven element, suitably split-up between upper
and lower wires so as to give a 300-ohm terminal impedance even
with the resistance-lowering effects of the reflector and directors.

Jim, K7JEB

Over that range, the equivalent series capacitance changes from 59pF
at the low end to 138pF at the high end, and at least by NEC2's
prediction, the impedance changes especially quickly around 51MHz--
both reactive and resistive parts. 50.75MHz: 10.3-j31.76; 51MHz: 3.91-
j22.56, quite a large percentage change in 250kHz. Having the
effective series capacitance change that quickly will cause the
matching network to behave very differently than it would with a
capacitance element that is fixed.

That is exactly the point! It would not be correct to calculate bandwidth on the
basis of the Q factor at resonance and assuming that the capacitive antenna
reactance is equivalent to that of a fixed capacitor.

Today I have discovered another shortcoming of that antenna. After raining cats
and dogs, the antenna resonant frequency gets lowered by about 130 kHz due to
the influence of the wet terrain. That is really a lot if you consider that,
after making very accurate measurements with a Bird wattmeter, the antenna
bandwidth is only 100 kHz at 1.4 SWR!

I am considering to re-build the driven element for 50-ohm match, by using a
longer driven element and a 1:1 balun. However it will not be easy to find the
optimum situation because there are two variables to be adjusted, that is the
driven element length and the hairpin length.

Also, I am not too sure on to which extent using a longer driven element would
influence the antenna radiation pattern.

Any comment?

73

Tony I0JX

Over that range, the equivalent series capacitance changes from 59pF
at the low end to 138pF at the high end, and at least by NEC2's
prediction, the impedance changes especially quickly around 51MHz--
both reactive and resistive parts. 50.75MHz: 10.3-j31.76; 51MHz: 3.91-
j22.56, quite a large percentage change in 250kHz. Having the
effective series capacitance change that quickly will cause the
matching network to behave very differently than it would with a
capacitance element that is fixed.

That is exactly the point! It would not be correct to calculate bandwidth on the
basis of the Q factor at resonance and assuming that the capacitive antenna
reactance is equivalent to that of a fixed capacitor.

Today I have discovered another shortcoming of that antenna. After raining cats
and dogs, the antenna resonant frequency gets lowered by about 130 kHz due to
the influence of the wet terrain. That is really a lot if you consider that,
after making very accurate measurements with a Bird wattmeter, the antenna
bandwidth is only 100 kHz at 1.4 SWR!

I am considering to re-build the driven element for 50-ohm match, by using a
longer driven element and a 1:1 balun. However it will not be easy to find the
optimum situation because there are two variables to be adjusted, that is the
driven element length and the hairpin length.

Also, I am not too sure on to which extent using a longer driven element would
influence the antenna radiation pattern.

Any comment?

73

Tony I0JX

Over that range, the equivalent series capacitance changes from 59pF
at the low end to 138pF at the high end, and at least by NEC2's
prediction, the impedance changes especially quickly around 51MHz--
both reactive and resistive parts. 50.75MHz: 10.3-j31.76; 51MHz: 3.91-
j22.56, quite a large percentage change in 250kHz. Having the
effective series capacitance change that quickly will cause the
matching network to behave very differently than it would with a
capacitance element that is fixed.

That is exactly the point! It would not be correct to calculate bandwidth on the
basis of the Q factor at resonance and assuming that the capacitive antenna
reactance is equivalent to that of a fixed capacitor.

Today I have discovered another shortcoming of that antenna. After raining cats
and dogs, the antenna resonant frequency gets lowered by about 130 kHz due to
the influence of the wet terrain. That is really a lot if you consider that,
after making very accurate measurements with a Bird wattmeter, the antenna
bandwidth is only 100 kHz at 1.4 SWR!

I am considering to re-build the driven element for 50-ohm match, by using a
longer driven element and a 1:1 balun. However it will not be easy to find the
optimum situation because there are two variables to be adjusted, that is the
driven element length and the hairpin length.

Also, I am not too sure on to which extent using a longer driven element would
influence the antenna radiation pattern.

Any comment?

73

Tony I0JX

On Apr 8, 12:31 pm, "Antonio Vernucci" wrote:
Over that range, the equivalent series capacitance changes from 59pF
at the low end to 138pF at the high end, and at least by NEC2's
prediction, the impedance changes especially quickly around 51MHz--
both reactive and resistive parts. 50.75MHz: 10.3-j31.76; 51MHz: 3.91-
j22.56, quite a large percentage change in 250kHz. Having the
effective series capacitance change that quickly will cause the
matching network to behave very differently than it would with a
capacitance element that is fixed.

That is exactly the point! It would not be correct to calculate bandwidth on the
basis of the Q factor at resonance and assuming that the capacitive antenna
reactance is equivalent to that of a fixed capacitor.

Today I have discovered another shortcoming of that antenna. After raining cats
and dogs, the antenna resonant frequency gets lowered by about 130 kHz due to
the influence of the wet terrain. That is really a lot if you consider that,
after making very accurate measurements with a Bird wattmeter, the antenna
bandwidth is only 100 kHz at 1.4 SWR!

I am considering to re-build the driven element for 50-ohm match, by using a
longer driven element and a 1:1 balun. However it will not be easy to find the
optimum situation because there are two variables to be adjusted, that is the
driven element length and the hairpin length.

Also, I am not too sure on to which extent using a longer driven element would
influence the antenna radiation pattern.

Any comment?

73

Tony I0JX

Though the Q calculation doesn't give the right SWR bandwidth for the
antenna/matching system, it does tell you that (with such a low loaded
Q), it should not be difficult to make a hairpin or even standard
helical coil inductor that has low enough loss that you can ignore the
effect.

I believe that the physical length of the driven element in a Yagi is
much less important than the tuning and spacing of the parasitic
elements. The question becomes something like this: what is the
relative amplitude and phase of the current in each parasitic element,
for some excitation of the driven element? A Yagi is a system of
coupled resonators, like a system of coupled pendulums. If one of the
pendulums is driven at a particular amplitude and frequency, even if
it's not that pendulum's natural frequency, the rest of the pendulums
will follow along pretty much the same as if the driven pendulum was
tuned to have that natural frequency. In the antenna, the difference
will only be in the coupling from the driven element to the others,
and I believe that changes only slightly as the length of the driven
element changes.

But I may be wrong about that, and await my re-education. ;-) But I
just ran EZNec on the example "NBS" 3-element 50.1MHz Yagi, varying
the nominal 110 inch long D.E. by +/- 10 inches, and saw the expected
fairly large variation in impedance, but only 0.02dB change in gain
over that whole range, with similarly small variation in F/B ratio and
beam width. The longest D.E. I ran was also the highest gain (by that
tiny amount), and provided enough inductive reactance that the
feedpoint could be tuned to resonance and present 200 ohms by shunting
with about 55pF capacitance. Next to try: compare the SWR bandwidths
of the hairpin (inductive) shunt of a shortened D.E. and the
capacitive shunt of a lengthened D.E.. Unless someone offers a better
test case, I'll use the NBS 3 element Yagi...

Cheers,
Tom

I believe that the physical length of the driven element in a Yagi is
much less important than the tuning and spacing of the parasitic
elements. The question becomes something like this: what is the
relative amplitude and phase of the current in each parasitic element,
for some excitation of the driven element? A Yagi is a system of
coupled resonators, like a system of coupled pendulums. If one of the
pendulums is driven at a particular amplitude and frequency, even if
it's not that pendulum's natural frequency, the rest of the pendulums
will follow along pretty much the same as if the driven pendulum was
tuned to have that natural frequency. In the antenna, the difference
will only be in the coupling from the driven element to the others,
and I believe that changes only slightly as the length of the driven
element changes.

But I may be wrong about that, and await my re-education. ;-) But I
just ran EZNec on the example "NBS" 3-element 50.1MHz Yagi, varying
the nominal 110 inch long D.E. by +/- 10 inches, and saw the expected
fairly large variation in impedance, but only 0.02dB change in gain
over that whole range, with similarly small variation in F/B ratio and
beam width. The longest D.E. I ran was also the highest gain (by that
tiny amount), and provided enough inductive reactance that the
feedpoint could be tuned to resonance and present 200 ohms by shunting
with about 55pF capacitance. Next to try: compare the SWR bandwidths
of the hairpin (inductive) shunt of a shortened D.E. and the
capacitive shunt of a lengthened D.E.. Unless someone offers a better
test case, I'll use the NBS 3 element Yagi...

Cheers,
Tom


Hi Tom,

the results you got on EZNEC are encouraging. Nevertheless I would not like to
try using a lengthened element in conjunction with a capacitor, as the
difference between that configuration and the original configuration would be
the maximum (although it would be much easier to adjust a capacitor than the
inductance of an hairpin).

What puzzles me is that the antenna manufacturer reported me having sold several
hundreds of those antennas, and no one has reported him the bandwidth being too
narrow or the exagerated wet terrain influence.

I am not sure on what I am going to do, also because I am not 100% sure on
whether the bandwidth problem is only due to the matching system, or it is also
due to the particular antenna design.

My original intention was to compare this 50-MHz long Yagi antenna (32-foot
boom) against a smaller antenna (11-foot boom) I have on another tower, so as to
determine how much a bigger antenna really helps during multiple-hop sporadic
openings to US and Japan.

Probably for the forecoming sporadic-E season (May-August) I will leave things
as they are, and just try to assess the practical advantages of the bigger
antenna. After that I will see what I shall do.

Thanks very much for the useful discussion.

73

Tony I0JX

On 8 abr, 18:52, K7ITM wrote:
On Apr 7, 4:02 pm, Wimpie wrote:



On 7 abr, 23:15, "Antonio Vernucci" wrote:

Hello Tom,

First, the matching is being done essentially with an "L" network (or
rather the balanced version of an "L" network), where there is a load
resistance (the resistive part of the feedpoint impedance, which
includes radiation resistance and element loss resistance reflected to
the feedpoint), the series capacitive reactance of the feedpoing
element, and a shunt inductive reactance, provided by the hairpin.
Because shortening the driven element causes a decrease in resistance
and an increase in capacitive reactance, it's possible to find a
length that allows matching to any of a wide range of resistances.
But the higher the resistance to which you match, the shorter you need
to make the element and the lower the feedpoint resistance. The ratio
of feedpoint resistance to matched resistance determines the loaded Q
of the matching network; as you make the matched resistance higher,
the loaded Q goes up rather quickly. If you know the loaded Q and the
unloaded Q of the hairpin, you have a good handle on the amount lost
to heat in the hairpin: if the hairpin Q is two times the loaded Q,
half the power is dissipated in the hairpin, for example.

However, unless you build an antenna with a very low feedpoint
resistance at resonance, there almost certainly won't be an efficiency
problem: the reactance changes quickly enough with changes in driven
element length that the resistance won't drop much by the time you
reach enough reactance to get a match to 200 ohms. It appears that
the loaded Q of the match to 200 ohms for your case will be less than
4. I would think unless you really messed up badly, the hairpin
unloaded Q should be well in excess of 100, and if that's the case,
the power lost in the hairpin would correspond to well under 0.1dB
signal level change.

All OK. I however reckon that, due to the parasitic elements effect, the
radiation resistance of the driven element (before shortening it) would be in
the order of 20 ohm. So, impedance gets brought up by a factor of 10 or so.

On the other hand, I'm surprised by the comment from the manufacturer
about difficulties making a 1:1 balun. I have had good luck using
ferrites and/or self-resonant coils of feedline and/or coils of
feedline specifically resonated with additional capacitance. A 4:1
balun from a "hairpin" of 1/2 wave of coax, arranged symmetrically, is
easy enough to make, but I would not rule out using a 1:1, if it has
advantages for you.

His argument is that, for high-power operation (say 1500W), it is more
convenient for him to provide a quarter-wavelength 4:1 balun made of RG-142
teflon cable than a sealed box with a 1:1 coil on an ironpowder toroidal core. I
mentioned him that, just using some extra length of RG-142 cable, he can easily
build a 1:1 balun, and hence design the antenna matching system for 50 ohm
instead of 200 ohm.

I hope he will listen to me, because that antenna is really narrowband!

73

Tony I0JX

Hello,

Imagine 10 Ohms radiation resistance + capacitive component after
shortening the open dipole radiator. When you convert that to 200 Ohms
via a parallel inductance (hairpin), the Q factor of such a network is
about 4.4. At 50 MHz that will result in a bandwidth (VSWR=2) of 8
MHz.

A 200 Ohms to 50 Ohms coaxial balun will have a lower Q factor. So the
combination of balun and L-network will certainly have a useful
bandwidth 340 kHz.

Maybe the radiation resistance is less (you can derive that from the
hairpin inductance) and/or the antenna is by nature (very) narrow
band.

Best regards,

Wim
PA3DJSwww.tetech.nl
remove abc from the address.

Yes, I had similar thoughts, but a bit different. First, I think it's
safe to say that if, at resonance, the driven element presents about
20 ohms at the feedpoint, shortening the D.E. only a little will give
enough capacitive reactance to allow the hairpin match to 200 ohms.
Even if the D.E. looks like 5 ohms, the "L" network match still gives
a 3dB bandwidth of 8MHz at a 50MHz center, or 3MHz 1.5:1 SWR
bandwidth.

Hello Tom,

Fully agree with you. I gave the values for a 20 to 200 Ohms match to
show that the problem is not in the matching, but in the antenna. Even
matching from 20 to 50 Ohms will not give sufficient bandwidth,
because actual BW is far below the BW of the matching network (with 20
Ohms termination).

I think we need to look somewhere else for the answer to
the narrow bandwidth. My working hypothesis at the moment is that
it's in the antenna, or perhaps rather in the combination of antenna
and matching network. Note that the calc for the L match assumed a
constant capacitance, but the antenna will not, in general, look
anything like a constant C even over a fairly narrow frequency range.

That rapid Im(Zant) change is the reason for the narrow BW.

I just ran EZNEC on a frequency-scaled version of the 14MHz 5 element
Yagi included in the sample files, with the D.E. slightly shortened to
allow a decent hairpin match to 200 ohms at the design center
frequency.

Did you also scale the thickness of the elements?

I did a frequency sweep, 49 to 51 MHz, in 0.25MHz steps.
Over that range, the equivalent series capacitance changes from 59pF
at the low end to 138pF at the high end, and at least by NEC2's
prediction, the impedance changes especially quickly around 51MHz--
both reactive and resistive parts. 50.75MHz: 10.3-j31.76; 51MHz: 3.91-
j22.56, quite a large percentage change in 250kHz. Having the
effective series capacitance change that quickly will cause the
matching network to behave very differently than it would with a
capacitance element that is fixed.

Is it possible to lengthen the D.E., causing it to present an
inductive reactance at the feedpoint, and match that (to 200 ohms, or
to 50 ohms) with a shunt capacitance? That may work better, giving a
broader SWR bandwidth. The resistive component should be higher,
further lowering the Q, and I suspect the reactance won't change so
quickly with frequency. I don't have time at the moment to compare
the two, but may this evening. It may also be possible to raise the
resistive part to 50 ohms and match to 50 with a series capacitance.

I did use length extension for very thick mesh dipoles for VHF air
band. Their resonant impedance is less then 50 Ohms (because they
become short). Some additional length gives some inductance to use a
parallel capacitor match and (most important) bandwidth increase.

I don't know whether this will give sufficient BW improvement for the
Yagi as the Q is also determined by the reflector en directors. I am
looking forward to your simulation results.


Cheers,
Tom

Wim
PA3DJS
www.tetech.nl
Please remove abc from the address.