Content-Transfer-Encoding: 8bit
Message-ID: <3.0.1.16.20010510132736.2c87c87a@mail.cc.kuleuven.ac.be>
Date: Thu, 10 May 2001 13:27:36
To: rsgb_lf_group@blacksheep.org
From: "Rik Strobbe" <rik.strobbe@fys.kuleuven.ac.be>
Subject: LF: harmonics / LF antenna
In-reply-to: <004401c0d92c$0f19a060$af6e74d5@w8k3f0>
References: <65AECDF1F89AD411900400508BFC869F9C0491@pdw-mail-1.dera.gov.uk> <3AFA2E4C.EBB3C4EF@alg.demon.co.uk>
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii; format=flowed
Precedence: bulk
Reply-To: rsgb_lf_group@blacksheep.org
Sender: <majordom@post.thorcom.com>

Hello group,

few days ago I got a mail from someone new to LF who asked me how efficient
a vertical antenna would surpress the harmonic contests from the TX.
So far I hadn't put much thought on that as my 400W TX has a 3 stage LF
filter, keeping all harmonics at least 50dB down. But calculations seem te
be quite simple, above the resonance frequency the antenna becomes
inductive. The average antenna (few 100pF capacitance) will already at the
second harmonic have an inductive component of several 1000 Ohms, keeping
the (harmonic) current low.
But on the other hand the radiation resistance will increase by the square
of the frequency, making whateven harmonic current that gets through the
coil being radiated more efficient. 
Just out of curiosity I calculated the overall efficiency of a loaded
vertical antenna on the harmonic frequencies and came to the result that
the harmonic supression is rather constant for all harmonics.

Below you find the result for a vertical monopole with a capacitance of
300pF and a loss resistance of 50 Ohm :

FREQUENCY		Impedance	Efficiency (versus fundamental)
fund. (137kHz) 		50 Ohm		0.0dB
2nd harm. (274kHz)	5811 Ohm	-29.3dB
3rd harm. (411kHz)	10330 Ohm	-30.7dB
4rd harm. (548kHz)	14526 Ohm	-31.2dB
6th harm. (822kHz)	22596 Ohm	-31.5dB
8th harm. (1096kHz)	30505 Ohm	-31.6dB
10th harm. (1370kHz)	38349 Ohm	-31.7dB

For the calculations I assumed no stray capacitance in the coil, so in the
'real world' the figures might be a few dB different, probably higher (less
negative).

Further the harmonic surpresssion becomes less is the antenna capacitance
increases (smaller coil needed) and the loss resistance increases.
Eg : for a 'big' antenna with 600pF capacitance and 100 Ohm groundloss the
antenna efficiency on the 2nd harmonic frequency will be only -17.2dB down,
on the 10th harmonic -19.6dB.

So sending a few 100W square wave into a big antenna is not really
recommended.

73, Rik  ON7YD