[TowerTalk] Answer to Pete's (N4ZR) Question

[Eric Gustafson]

>From: sbest@cushcraft.com
>Date: Tue, 25 Aug 98 13:32:12 
>
>Pete:
>
>Let's start with the simplest case.  The 50 ohm antenna fed with
>50 ohm coax, balun (1:1) and 50 ohm transmitter.  Let's first
>assume that the coax and balun are lossless.  If we deliver 1000
>Watts power into the transmission line, 1000 Watts power will be
>delivered to the antenna for radiation.  Let's now assume that
>the coax is 100 feet long and has 2 dB/100 feet attenuation.
>With 1000 Watts power into the transmission line, 369.04 Watts
>will be lost in the coax and 630.96 Watts will be delivered to
>the antenna for radiation.

OK so far...


>
>Now lets consider the more complex case of the same antenna
>connected to the transmitter with a 600 ohms feeder and a tuner.
>I will assume that the tuner is lossless.  I will also assume
>that the feeder line has no spurious radiation.
>
>I will first assume that the feeder line is 100 feet long and
>lossless.  The steady state input impedance at the input of the
>feeder will be 63.524 - j310.662 ohms. Using a conjugate match
>tuner the following power distribution will occur:
>
>The initial power delivered to the tuner will be 284 Watts.  The
>initial power delivered to the antenna will be 80.67 Watts.  The
>steady state power delivered to the antenna will be 1000 Watts
>(80.67 watts signal, 919.33 watts echo).  A 600 ohm forward
>power meter would read 3521 Watts at the tuner output and a 600
>ohm reverse power meter would read 2521 watts at the tuner
>output.
>
>If the feeder line has 2 dB/100 feet attenuation (no VSWR or
>other effects included so that it is the same level as above
>matched antenna example), the input impedance to the feeder line
>will be 226.373 - j277.493 ohms.  Using a conjugate match tuner
>the following power distribution will occur:  ... SNIP ...

Why are you now introducing a 2 dB/100 ft. loss factor to line
that is at HF essentially lossless?  What is the purpose for
doing this?

It is not necessary to overcomplicate this issue.  It is not
necessary to evaluate brief transient conditions.  It is really
very simple to do this analysis without resorting to voodoo.

What we have here is a source of RF energy connected to a
matching/transmission line/radiating system.  If we feed 1000
watts into this system from the source, 1000 watts will come out
of it.  Some as heat and some as radiation.

The heat is generated in what we routinely refer to as the
losses.  So to find out how much gets radiated all we need to do
is account for the losses.

Radiated energy = Input energy - lost energy

The losses are:

1.  Loss in the Tuner.  Here you allowed us a lossless tuner.
    This is very generous but not entirely accurate.  However,
    the loss is not typically terribly large in a well designed
    and correctly applied tuner.  Normally the tuner losses will
    be 1 dB or less when matching a higher impedance to a 50 ohm
    input port.  So lets use 1 dB for the tuner loss.

2.  Line loss.  Or "matched" line loss.  This is the db/100 feet
    when the line is driving a matched load.  For 600 ohm air
    line at 14 MHz, this is significantly less than 0.1 dB/100 ft
    ('91 Radio Amateur's Handbook, chart on page 16-14).  I think
    that since the 0.1 value happens at 28 MHz, we can safely use
    0.05 dB/100 feet at 14 MHz.

3.  Additional loss in transmission line due to mismatch.  Since
    the line/load mismatch is 600/70 or 8.6:1, the additional
    loss due to mismatch is roughly 0.1 dB (extrapolation from
    left side of figure 24 on page 16-15 '91 Radio Amateur's
    Handbook)

So, the tuner and 100 feet of 600 ohm airline connected to a 70
ohm dipole have a total loss of 1.15 dB at a frequency of 14
MHz.  This will cost us 233 watts of total loss.  767 watts will
radiate. 

Even if we give you a lossless balancing device (you were
generous so we can be), and use your example of RG58 cable and
connectors for 2 dB/100 ft feedline loss, and permit a lossless
transformation of 70 to 50 ohms at the antenna feed point, the
tuner and open line will deliver more radiated energy than the
perfectly matched load and coax.  631 watts radiated for matched
load versus 767 radiated for airline and tuner.  So, a matched
load system will _NOT_ always outperform a mismatched load and
tuner combination.

Of course you can (and should) specify better coax.  If you use
RG213, your losses will be only 0.9 dB approximately.  The
question then becomes "How significant is 0.25 dB in terms of
system performance?".  And, "Can I really get a balancing device
that looses less than 0.25 dB including all the connectors?".

73, Eric  N7CL

--
FAQ on WWW:               http://www.contesting.com/towertalkfaq.html
Submissions:              towertalk@contesting.com
Administrative requests:  towertalk-REQUEST@contesting.com
Problems:                 owner-towertalk@contesting.com
Search:                   http://www.contesting.com/km9p/search.htm