Latest update:  13 august 2010: cut copper tubing

Update: 22 July 2010 started collecting ideas and material.

Wanted a small transmitting loop (STL) antenna that covers at least the 80 and 40 meter bands. Why: 1) SNR, directional, hope to pick up less electrical noise generated in our apartment building than with my other antennas (or orient the antenna so as to null it out). 2) Preferably less conspicuous. 3) Don't want to have to mess with radials, 4) can be installed at low height.

A small resonant loop, to be more precise. A loop is generally considered small, if its circumference is less than 1/10 of the operating wavelength. Here < 8 m. Resonant: loop is tuned to resonance on the desired frequency with a variable capacitor across the (opened) loop (self inductance).

schematic diagram of resonant loop, with cap and coupling

Small loop antennas are often referred to as magnetic antennas. This is because they mostly respond to the magnetic component of an electromagnetic wave and transmit a large magnetic component in the extreme near field (<1/10 wavelength distance). In the far field (>1 wavelength distance) the RF from a small loop is the same as that from any other antenna being composed of both electric and magnetic fields.

Purchased a Russian-made capacitor at the 2010 Ham Radio in Friedrichshafen/Germany. It is marked "10 kB 10-500 πФ" in other words: 10 kV,10-500 pF. I measured 15-510 pF with an LCR-meter. Cost me €80 (≈ 100 $US, mid 2010 exchange rate).

Can use an air variable cap "bread slicer" (e.g., tuning cap from an old AM radio)  type split-stator or a butterfly style. With100 W operating power, may get 4-5 kV across the cap, 1mm spacing per kV.

My 10-500 pF 10 kV vacuum variable capacitor

Also did a quick test to verify integrity of the vacuum: put the cap in the refrigerator for about an hour. Should be no formation of condensation on the inside of the glass when in the fridge or after taking it back out (on outside is OK). Size: see scale in the picture above. Weight is a hefty 2140 gr (≈ 4 ¾ lbs). It takes 22 turns to go from minimum to maximum capacitance, or vice versa. I.e., 22 pF per turn. The highest resonance frequency of the loop is determined by the minimum capacitance, and, conversely, the lowest resonance frequency by the maximum capacitance value.

I determined calculator results for the given loop and tubing diameter, at my frequencies of preference: 3580 and 7040 kHz (Hellschreiber and narrow-bandwidth digi-modes, respectively). Theoretical! With my capacitor, it should be useable for 20 mtrs as well ! In this band, ≈14070 and 14230 kHz are my preferred freqs (standard Hellschreiber and SSTV frequency, respectively). Calculator assumptions about installation height, resistance, coupling, etc? So, just used to get an feel:

The tables show that the calculated / predicted efficiency for 80 mtrs is rather low, but my other antennas for 80 mtr are (very) short verticals (see this page). I do not know what their efficiency is, but I am sure that it is very low as well. In the end, what counts is performance at my location, for the available space, for the prevailing conditions (proximity to the building, QRM levels, etc), and with respect to other antennas that I can install there.

Mike Underhill, G3LHZ, has a very interesting view on the efficiency estimates obtained with traditional models. I recommend reading this:

	"Small Loop Antenna Efficiency", May 2006
	"All sorts of small antennas – they are better than you think – heuristics shows why!", February 2008

The above tables are for a circular loop. The values for an octagonal loop are very similar: for the same circumference, an octagon has nearly the same area as a circle. For those who like (or need) formulas, this is shown below.

For a circle with radius R and diameter D:

For an octagon with side L:

After some basic manipulations, we can derive that for equal circumferences:

  q.e.d.

The height of an octagon (i.e., distance between parallel sides, not the largest distance between corners of the octagon):

Note that  if you make an octagon with eight sections of length L, you will require elbow pieces to join these sections. This increases H. In my case by 5 cm (2").

	Shape: square, octagonal, round: latter has largest possible surface area for the (fixed) circumference.
	Importance of keeping loop loss resistance to an absolute minimum, as the radiation resistance is very low. How achieve this, for the capacitor and the tube ends? Solder / weld / large surface compressed joints,...
	Coupling to feed line. Options, considerations (esp. freq range): coupling loop (1/5 of main loop?), Gamma match, Faraday-loop, ferrite ring transformer (toroid; size such that copper tube & wire turns fit / material / # of turns), ... The gamma match only needs to be tuned ONCE (for 50 ohms) then permanently fixed in place. The vacuum variable capacitor is all that needs to be adjust after that. Gamma Match to coax. Delta Match to ladder line. T-match to ladder line. Ferrite toroid (fixed position) to coax. ... This method resembles the "gamma" style match of Yagi-Uda arrays without the series capacitor.
	Support structure.
	Measurements (SWR etc plots for various couplings, directivity, elevation angle)
	Practical results (noise level, SNR, vs mini vertical, vs Cobra, NL-SDR trace).
	Permanently install TL tube on structure.

First thought I'd use a 5 m roll of soft copper tubing. Yes, this non-annealed (re-cooked) copper is malleable by hand. But it is hard to make a nice round shape by hand, and I do not have access to a professional tube bending machine. So I changed my mind and decided to go for an octagonal loop. Surface area of a circular loop is only about 5% larger than that of an octagon with the same circumference.

CONSTRUCTION

Copper tubing pieces and tube cutting tool

For the loop:

	7 sections of copper tubing, each 62.5 cm (24.6") in length, 16 mm outer diameter (OD).
	2 sections of copper tubing, each 29 cm (11.4") in length, 16 mm outer diameter.
	8 copper elbow pieces, 45º, female-to-female, 16 mm
	2 copper elbow pieces, 90º, female-to-male, 16 mm
	2 copper reduction pieces, 16 mm inner diameter (ID) to 10 mm OD (to connect tube to braid to capacitor)
	1 copper T-piece,2 x 16 mm ID, 1x 10 mm ID, (for Gamma Match coupling)

The required 5 m copper tubing (16 mm OD, ≈ 5/8 inch) cost me €24 (≈ 30 $US, mid 2010 exchange rate). This is readily available from DIY centers). This length will give a loop height of about 1.5 m (≈ 5 ft).

For the PVC structure:

	2 m PVC tubing with 63 mm diameter (≈ 2½")
	1 m PVC tubing with 32 mm diameter (≈ 1¼")

For connecting the capacitor to the loop:

	2 stainless steel hose clamps
	2 x 25 cm (10") thick & wide copper braid, or heavy multi-strand copper wire (e.g., AWG #4)

Terminating of the ends of the loop - connection to the capacitor

("spark" gap between elbow pieces must have at least the same voltage rating as the capacitor: here: 10 kV)

Heavy multi-strand wire and hose clamps for connecting to the capcitor

For mounting the capacitor:

	8 mm thick polyethylene cutting board (from the kitchen). SIZE
	2 xx bolts, M6 x ??
	2 self-locking nuts, M6
	4 large tywraps . Size? Black (better UV)

Parts of the capacitor installation bracket

Tools:

	Blow torch (high temp --> propane, acetylene - preferred); the simple one I used produces 1750 ºC ( 3200 ºF)
	Silver solder (plumbers solder)
	Flux (borax flux powder + water, or non-acid liquid or paste flux)
	Piece of sandpaper or steel wool

Soldering tools: blowtorch, two kinds of silver solder (flux not shown)

This is the most expensive antenna I have ever built!

• photo of assembled copper loop

• photo of parts of PVC structure (tubing, caps, ...)

• photo of assembled structure

• photo of clamps/shells on ends of cap + braid to capped ends of copper tube.

• photo of cap installed on vertical part of structure

For connecting the coax feedline

(to base of loop. opposite capacitor):

Option 1: Gamma Match: 1 copper T-piece, 16 ID / 10 OD / 16 OD (to serve as starting point of a Gamma Match) BNC female chassis-mount connector 1 m of thick solid copper wire (e.g., 3 mm)

Option 2: Ferrite toroid transformer coupling; one side of xfrmr winding formed by mag loop, the other by several windings of heavy gauge wire. need broadband coupling; loop this size is least efficient on 80 mtr, so if not broadband coupling, then optimize for 80 mtrs. T140-43 or T240-43; ID of toroid must be large enough to slip it over the copper tube and elbow pieces, and add several turns of thick wire (T140 (1.4" OD, 0.9" ID (≈ 23 mm) is sufficient; T240 has a 2.4" OD and 1.4" (≈ 35 mm) ID). Calculator on this page http://www.smeter.net/antennas/small-transmitting-loop.php suggests 21 turns at 3.5 MHz, 8 at 14.23 MHz. Also see http://www.aa5tb.com/loop.html; http://www.k3jls.net/mlc.html#loop suggests 3 turns. heavy duty installation wire (e.g. AWG 4) dual banana plug to BNC

RF current is not uniform around the loop. It is at maximum directly opposite the tuning component.

When using a coupling loop, it should be fitted eccentric to the main loop such that it is adjacent to the side opposite the tuning component. It can be round or rectangular provided the perimeter length is unchanged.

Delta Match + ladder line: not considered.

Faraday (coupling) Loop, 1/5th size f main loop: clumsy from construction point of view.

Solid wire loop (not cross-wired coax): It's much easier to adjust the coupling between the two loops if one of them is just a self-supporting length of wire no thicker in principle than the diameter of the coaxial inner conductor.

Instead of reducing its diameter it can be rotated a little or bent out of the plane of the main loop to have a similar effect. Or
squashed flatter to reduce the area enclosed.

Add diagrams: eg "several types of coupling.jpg" + source + expand with ferrite over copper, etc.

Decided to insert T-piece, even if not using it for a Gamma Match. This means cannot put a ferrite ring at the center of the bottom of the loop - where the T-piece is located. Decided to put a ferrite ring on both sides of the T-piece, and wind the wire turns through both.

For toroid coupling

For Gamma Match: BNC chassis connector fits perfectly into 10 mm OD end of  a T-piece

INSERT:

• photo of motor drive with reduction gearing (or stepper), coupling, limit switches

• schematic of motor drive + PC I/F

• photo of coupling (ferrite, Gamma match, delta match; ladder line, coax)

• photo of complete antenna, erected in umbrella stand, w/o motor drive

• photo of complete antenna, erected, with motor drive

Connect coax directly to toroid windings,

WARNING: the loop can exhibit several hundred volts when operating at QRP power levels (5-10 W). At higher RF levels, several thousand volts will be present on this antenna. Exercise caution when building and using this antenna. Build this antenna at your own risk.

     

Do not get anywhere near the antenna when transmitting!
Do not let any animals (or people that you care about) get near the antenna when transmitting!

It is very dangerous to touch the loop conductor during transmissions. RF burns do not heal well!
 

TUNING, OPERATION, PERFORMANCE

• miniVNA plots (toroid coupling, Gamma/Delta, at min and max capacitor value, at target frequencies)

• RX noise relative to my other antennas

• signal relative to my other antennas

• RX nulling

• TX to SDR

Text + diagrams about radiation pattern + polarization

theoretical radiation pattern (dependent on circumference as fraction of wavelength ? The doughnut shaped radiation pattern is in the plane of the loop with nulls at right angles to the plane of the loop.)

carrier with XX watt

and add same with photos or video clip

• photo with TL tube (overlay of several pix at various angles)

Below are two short video clips of a demonstration by  Mike Underhill, G3LHZ, of the field around a mag loop antenna. 

	"Field around a loop", HFC2000
	"More field", HFC2000

MOTOR DRIVE FOR THE VARIABLE CAPACITOR

Manually tuning the loop antenna is a real hassle. Run back & forth between the transmitter (or antenna analyzer) and the antenna. Physical presence near the antenna de-tunes it, etc. So: need a motor drive with remote control.

The first design parameter is the torque required to overcome the stiction (static friction) and turn the shaft of the variable capacitor. This drives the size of the motor and reduction gear (if required). Variable vacuum capacitors have a torque value that depends on the position of the capacitor (mid-range vs close to the end-stops), and the direction (towards or away from an end-stop). I do not have the data sheet of my Russian capacitor. To get an order-of-magnitude idea, I checked the values for a comparable capacitor (25-500 pF, 10 kV test, 9 inch length) on the Jennings website: 6 inch-pound (in.lb) or 6 x 0.113  ≈ 0.68 Nm = 68 Ncm. I then decided to measure it myself ("trust, but verify!"). This is actually quite easy to do! I clamped a standard 30 cm (1 ft) ruler onto the shaft of the capacitor with a small C-clamp. Pushing slowly down onto a kitchen scale until the shaft barely turns, and read the "weight". Voilà. See photo below. Depending on the turn direction, I measured about 80 and 100 gr. The force was applied to the shaft with half of the ruler, i.e., an arm of 15 cm. So, the applied torque was (0.1 kg x 9.8) x 0.15 m ≈ 0.15 Nm = 15 Ncm. Not a lot, and easily handled by a small motor. I decided to not measure the torque required to go beyond the end-stops of the capacitor, hihi. However, it would be nice if the stalling torque of the motor-drive were less than this unknown value, so I could dispense with end-stops.

Determining the torque value of my capacitor

The second important design parameter is the angular resolution of the motor-drive. The loop antenna has a large Q, or - equivalently - a very narrow bandwidth. The motor-drive must be able to make angular displacements that are small enough, such that the associated capacitance change does not change the resonance frequency more than a fraction of the bandwidth. Otherwise it will be next to impossible to tune the resonance frequency close enough to the desired operating frequency. The calculated bandwidth for my antenna is 3.8 kHz on 3580 kHz, and 61 kHz at the high end of the 20 m band. Assuming that the capacitance changes linearly with rotation of the capacitor's shaft, we get 500 pF / (22 turns x 360 º per turn) ≈ 0.06 pF / degree. I have not (yet) verified the validity of this assumption...

Plugging in various resonance frequency values into  the AA5TB spreadsheet (assuming no additional loss resistance), I obtained the following estimates:

Around maximum capacitance:

	resonance frequency is in middle of the 80 m band.
	bandwidth is about 3.5 kHz
	resonance frequency changes about 4.2 kHz / pF (i.e., 0.24 pF / kHz)

Around minimum capacitance:

	resonance frequency is at the high end of in the 20 m band.
	bandwidth is about 52 kHz
	resonance frequency changes about 275 kHz / pF (i.e., 0.0036 pF / kHz)

Clearly, variation around the minimum capacitance is the critical case!

Let's assume that accurate tuning requires changing the resonance frequency with a resolution that is better than 20% of the bandwidth. The above data implies a required resolution of better than 20% x 52 = 10.4 kHz, i.e., 10.4 / 275 = 0.038 pF !

Based on the 0.06 pF / degree change in capacitance as estimated (assumed) above, I need an angular positioning resolution of better than 0.038 / 0.06 = 0.63 degree.

A secondary design parameter is the drive speed. We don't want to wait an hour for the capacitor position to move from min to max value, and vice versa. My capacitor requires 22 turns for this min-max range, which should cover the 80-20 m bands. If I could live with 1 minute, that would be 22 rpm at the capacitor shaft.

Now we can choose a motor and associated drive electronics.

Basic options: permanent magnet (PM) DC motor and stepper motor

Positioning accuracy and torque requirements are easy to with a stepper-motor: they have a specified torque and step size. Stepper control electronics often have half-stepping capability (though this may be at somewhat reduced torque). Common step sizes are 1.2, 1.8, 3.6, 7.5, and 15 degrees. Smaller step sizes do exist, e.g., 0.36 deg, but at a cost...

GEAR REQUIRED for resolution or torque?

Options: stepper motor (with gearing, if necessary), DC motor with gearing. Piece together controller card, PC interface, ... searched for (relatively) inexpensive off-the-shelf solution.

Decided to go with a Phidgets 1062 controller card. handles up to 4 unipolar stepper motor.  Bought mine at Sawtus Shop (they had the best price I could find at the time (Summer 2010): $66 plus S&H). Phidgets also has a controller card for a single bipolar motor.

This controller card is really tiny: 5 x 6.3 cm (2 x 2½ ")! And: it does not require a heat-sink.

Comes complete with basic software.

Only need to run USB cable (with ferrite ring(s) against RFI) to the antenna + small motor cycle battery to power the motor.

Additional advantage: card can handle up to 4 motors simultaneously: can also build a stepper motor driven light antenna rotor. Supports motor solenoid current of up to 2 A - without a heatsink!

IMPORTANT: Note that this card does not support speeds above 383 half-steps per sec. (about 2 rpm with a 1.8 deg stepper motor (200 full steps/rev) - This is not a problem for my application.

For capacitor, no need to apply holding torque when not moving (unlike other applications); --> no need to keep motor energized.

Half-stepping provides smoother movement than full-stepping (micro-stepping even more).

Options for end protection of cap: calibration / ref. position switch, spindle plus limit switches.

Unipolar vs bipolar: bipolar controller is inherently more complicated (H-bridges); also : http://www.k3jls.net/mlc.html#loop

cog pulley + cog belt. double-flanged timing belt pulley; # grooves ; bore motor + bore cap; pitch; OD; belt width
belt provides isolation between motor and cap; eg fiberlass reinforced neoprene / urethane-polyester, one-sided

www.smallparts.com

One of my colleagues donated a stepper motor (Thank you Helmut!). It is a Slo-Syn SS25-1001, 1.8 deg, 12 V, 440 mA, 20 oz.in (14 N.cm). This is a 5-wire unipolar motor: a common wire (white) and four coil wires (green, green/white, red, red/white, for coil 1-4). It runs great with the Phidgets card. Its shaft has a ¼" diameter. Weighs about 580 gr (≈ 1lb 4 oz),

Half-stepping this motor will give me 0.9 deg positioning increments. So I will need to add gearing with at least a 3:1 ratio (which will increase the torque at the capacitor shaft 3x) to get the desired 0.62 deg when full-stepping, or 1.5:1 when half-stepping. I will try half-stepping at 0.9 deg without gearing first...

Phidgets 1062 USB controller card for up to 4 unipolar stepper motors

The Slo-Syn SS25-1001 motor

• Add: video clip / screen capture of miniVNA plot as cap is driven from goes from min to max

WEATHERIZING

- steel wool + clear coat the copper - not really required for weatherizing, but I like the shiny look.

- capacitor + motor drive: large diam PVC tube, tupperware^® box, ...

- toroid windings to coax: solder + liquid electrical tape

insulate with brush-on Liquid Electrical Tape or DipIt®.

REFERENCES

	"Small, high-efficiency loop antennas", Ted Hart (W5QJR), QST, June 1986, pp. 33-36
	"My Magnetic Loop Antenna", A. Krist (KR1ST), AntennaX, Issue No. 111, July 2006
	"An Overview of the Underestimated Magnetic Loop HF Antenna", by Leigh Turner (VK5KLT)
	"Loop Antennas", Chapter 5 in "ARRL Antenna Handbook, 21st edition
	"Easy Step'n - An Introduction to Stepper Motors for the Experimenter", David Benson, Square 1 Electronics, 200 pp.

LINKS:

	Small Transmitting Loop Antennas - by Steve, AA5TB
	W2BRI's Magnetic Loops (incl. ferrite toroids)
	PA3CNJ Magnetic Loop
	calculators (online, exe)

CALCULATORS:

	AA5TB
	calculators (online, exe)

 


©2010 F. Dörenberg N4SPP

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