This post will be the first in a series of posts describing the construction of a small transmitting loop antenna. The intended frequency of operation is the 40m amateur band (7 MHz), and the location of the antenna will be on the balcony of a concrete building.
The design parameters
I chose to use 6mm-diameter copper pipe for the loop conductor because it is lightweight and bendable by hand. It should also be fairly easily solderable without requiring a large torch. Though easy to work with, the pipe is solid enough to support itself even when formed into a large loop.
For the tuning capacitor, to be located at the top of the loop, I chose to use a 50 pF butterfly capacitor with welded vanes. The plate spacing is small, but it should be sufficient for my QRP power level of 5 watts.
The 50 pF butterfly capacitor (right) to be used in the small transmitting loop.
A geared motor will be connected directly to the capacitor (with a very short coupler) for remote control, with the motor wires dropping straight down from the motor to the bottom of the loop. 4nec2 simulations showed there should be minimal common-mode current on the motor wires, so I anticipate no choking of the motor wires will be necessary.
The Tamiya geared motor to be connected to the butterfly capacitor.
Loop excitation will be done at the bottom of the loop with a small and galvanically-isolated coupling loop. This should provide excellent suppression of common-mode currents on the feedline, requiring no additional balun.
I chose to make the loop as large as possible to maximise the radiation resistance. I decided the loop should be rectangular, 3 meters wide by 2 meters high, which would barely fit on the balcony where the loop will be mounted.
The challenges
There are two problems with my chosen loop dimensions:
The loop is so large that it cannot fit through the balcony door. It must be constructed from shorter copper pipes, each transported separately to the balcony, with the final soldering of the pipes being done on the balcony.
Once constructed on the balcony, the loop cannot be brought back inside again unless it is dismantled. Some thought needs to be given as to how to disassemble the loop in the event the loop needs to be moved or stored.
Solving the challenges
To allow easy assembly and disassembly of the loop, I considered using mechanical connections, such as hose clamps and bolts, to connect the pipe segments together. However, these would introduce ohmic losses and would require periodic maintenance due to weathering.
Instead, I have decided to use a combination of pipe bending and pipe soldering to construct the loop, as follows:
By hand, bend four copper pipes to 90 degrees, forming four corner elbows.
Transport straight pipes and corner pipes to balcony.
Solder pipes together in the following sequence.
Solder 2 corner pipes and 2 straight pipes together to form the bottom of the loop. After assembly, set this piece aside until the end.
Solder one straight pipe to each side of the butterfly capacitor.
Solder one corner piece to the left pipe.
Solder another corner piece to the right pipe.
Solder a vertical support pipe to the left corner pipe.
Solder a vertical support pipe to the right corner pipe.
Use two wooden poles to support the left and right sides of the loop. Fasten the loop to the support poles by using a hose clamp or similar.
Working alternately on each side of the loop, slowly slide the entire loop assembly upwards vertically along the support poles, to make room for the bottom-most pipes.
Attach and solder the previously-assembled bottom pipe assembly.
Remove the support poles.
Disassembly of the loop must take place in the opposite order as assembly.
Soldering
The loop assembly or disassembly must be done piece-by-piece on the balcony. Due to the small 6mm diameter of the pipes, I do not expect much heat will be needed to solder the pipes together. While it might be possible to use a large 100-watt soldering iron, the iron's electrical cord would make it unwieldy to work with the iron outdoors on the narrow balcony.
A better option would be a torch. Again, since I don't think that a large amount of heat is needed, I plan to use the smallest torch possible: a tiny pocket torch fueled by a cigarette lighter.
This pocket torch should be able to reach a temperature of 1,300 degrees Celsius and can be used continuously in a single burst for up to 60 seconds before it needs to cool down. I believe this should be sufficient for soldering of 6mm copper pipe.
Physically connecting the pipe segments together, prior to soldering, will be done by inserting a short segment of smaller-diameter (5mm) copper pipe to connect two adjoining 6mm pipe segments. The 6mm pipes will be butted together, heated with the torch, then soldered. The solder should flow into the butt joint with the 5mm inner piece providing mechanical stability.
Disassembly, when eventually needed, will be done by heating the butt joint and pulling it apart.
Issues of weight
Note that there is no center spine in my mechanical design for the loop. Therefore, the pipes themselves must be strong enough to support the weight of the top-mounted capacitor and motor assembly. The butterfly capacitor and motor are both small and lightweight, and in my estimation the 6mm-diameter copper pipes should be able to support their weight.
In my particular loop design, the physical size (and weight) of the butterfly capacitor can be kept small for two reasons. First, the required resonating capacitance is small because of the large loop dimensions and correspondingly large inductance. The small size of the required resonating capacitance allows the physical capacitor dimensions to be small. Second, the loop is designed for QRP use, so the plate spacing can be kept small. This again allows small physical capacitor dimensions.
Physical construction
Construction is in the early stages. Future posts will show the progress of the construction.
The 6mm-diameter pipes used are shown below.
Here are the 90-degree corner pipes, bent by hand.
An idea about the capacitor mounting is shown below.
The following receiver is a remote-controlled regenerative receiver using hybrid Colpitts-Vackar feedback. A detailed write-up of this receiver will be posted in the future. Currently, at certain frequencies in the upper half of its tuning range, the receiver suffers from fringe howl, a crippling phenomenon that manifests itself as a loud audio oscillation just as the set enters RF oscillation. In a regenerative receiver, the point of just entering RF oscillation is where the detector is most sensitive, so fringe howl -- the unwanted AF oscillation at the most sensitive detector setting -- serves to make the detector almost useless, and is a problem that must be addressed.
Schematic diagram of fringe-howling regenerative receiver.
The following video illustrates the fringe howl occurring in the receiver prototype. Although the audio and video quality are low, and the prototype circuit layout is not visually pleasing, I felt it important to create an audio-visual recording of the fringe howl phenomenon, because there is (as far as I know) no existing audio-visual documentation of the phenomenon, only written descriptions.
Before watching the video you may want to review the following labeled screen captures from the video, which explain what you are seeing.
Video from 00:00 to 00:20: close-up of the control board
Video from 00:20 to 00:27: close-up of the control cable connecting the control board
Video from 00:27 to 00:50: close-up of the remotely-located receiver board.
Video from 00:50 to 01:14: smooth operation of regeneration control, with no fringe howl, when the antenna is disconnected. Tuning is set to slightly above the middle of the tuning range (4.5 MHz - 16 MHz).
Video from 01:14 to 01:40: connecting a short antenna to the top of the tank through a 6 pF capacitor.
Video from 01:40 to 01:48: close-up of the short antenna, a ~30cm piece of wire
Video from 01:48 to 02:08: fringe howl occurring right at the RF oscillation threshold. Tuning is same as before. Video from 02:08 to 02:30: fringe howl disappears if regeneration is advanced further.
Video from 02:30 to 02:40: tuning receiver downwards in frequency below the midpoint of the tuning range (4.5 MHz - 16 MHz). Video from 02:40 to 02:57: smooth regeneration control and no fringe howl at lower frequencies.
Video from 02:57 to 03:05: tuning receiver upwards in frequency above the midpoint of the tuning range. Fringe howl re-appears.
Addendum 2014-10-08
Regarding fringe howl: A number of readers have made suggestions as to how to fix the fringe howl, which I am investigating. Again, a full write up of this receiver will follow once the problem has been solved.
Some readers have asked what the V2 component is. For circuit analysis or construction, it can be ignored and considered to be a short circuit. In actuality, it is part of the LTspice circuit simulation that delivers a voltage pulse to the tank inductor as an aid in determining whether the oscillator has enough gain to oscillate with the given circuit parameters (Vcc, emitter resistance, inductor losses, base bias, feedback network). This in turn allows me to optimize the feedback network C1/C2/C5.
Also note that C1 and C2 are unnecessary. Further simulation has shown that the circuit still oscillates when C1 is removed and when C2 is replaced by a short-circuit. C1 and C2 were intended to provide some small amount of Colpitts-style feedback to boost the Vackar-style feedback formed by D1 and C5, but the Colpitts-style feedback is so small in this case that it is actually not needed, according to the simulation. In hardware, removing C1 and replacing C2 with a short circuit yields identical circuit operation.
Regarding the "Vackar-style" feedback network formed by D1 and C5 (with C1 and C2 removed), please see p. 16 of the following document for the derivation of this feedback network: http://www.kearman.com/vladn/hybrid_feedback.pdf. The following LTspice simulation of a simplified version of my circuit shows the open-loop gain behavior of the D1/C5 Vackar-style feedback network vs. the open-loop gain behavior of the C1/C2 Colpitts-style feedback network. As you can see the Vackar-style feedback has decreasing open-loop gain as the tuning capacitor is tuned higher in frequency, whereas the Colpitts-style feedback has increasing open-loop gain as the tuning capacitance is tuned higher in frequency.
Vackar-style vs. Colpitts-style feedback. Notice the difference in open loop gain as the tuning diode is swept across its capacitance range.
Addendum 2014-10-13: solved fringe howl
The fringe howl has been solved.
Measures tried
Rewire DC control cable to physically move it far away from the hot end of the tank inductor. Result: Fringe howl still occurs.
Remove C6 (RF decoupling for input of AF amp). Result: Fringe howl still occurs.
Increase C20 (Vcc decoupling) to 120uF. Result: Fringe howl still occurs.
Increase R14 (series resistor from emitter to AF amp) from 1k to 10k. Result: Reduced volume. Howling stops, but there is still a seashell sound indicating instability.
Decrease R14 (series resistor from emitter to AF amp) from 10k to 0k. Result: Loud volume, but fringe howl observed at wider range of frequencies.
Add emitter follower stage between detector and AF amp. Remove R14. New emitter follower base connects through 100 nF capacitor to Q1 emitter. Base bias set to Vcc/2 with 20k/20k divider. Emitter resistor set to 1k. Output taken from emitter resistor and fed into C3 (AF amp). Result: Fringe howl still occurs.
Add 10k resistor between Q1 emitter and emitter follower base. Result: Reduced volume. Seashell sound still observed.
Replace emitter follower with DC-coupled common-base buffer. New buffer emitter connects directly to Q1 emitter. Base goes through 100k to collector. Collector goes through 4.7k to decoupled Vcc at R15. AF output taken from collector and fed into AF amp at C3. Result: Fringe howl still occurs.
Change DC-coupled common-base buffer to AC-coupled common-base buffer: Add new 1k emitter resistor to buffer, and connect buffer emitter through 100nF to Q1 detector emitter. Result: Fringe howl still occurs.
Add 10k resistance between common-base buffer and Q1 detector emitter. Result: Fringe howl still occurs.
Remove C7, C8, C9 (RF decoupling for intermediate stages of AF amp). Result: Fringe howl still occurs.
Connect external LM386 amp to output of common-base buffer (at collector 4.7k load resistor). Result: Fringe howl still occurs.
Connect external LM386 amp to Q1 detector emitter directly. Result: AF volume too low to determine whether or not fringe howl occurs.
Remove common-base buffer, reconnect original AF amp (but still with C6, C7, C8, and C9 removed), allow fringe howl to occur, and monitor oscillator signal on nearby receiver. Result: fringe howl heard in radiated signal on monitoring receiver.
Disconnect AF amp when fringe howl is occurring and observe radiated signal on nearby receiver. Result: fringe howl stops in radiated signal on monitoring receiver, indicating it is some interaction between the AF amp and the detector that is causing the howling.
Reconnect AF amp and replace R13 (varactor DC bias at hot end) with 10 mH choke. Result: fringe howl still observed, but the generated AF oscillation has become lower in frequency.
Add 10k in parallel with R12 (varactor DC bias at cold end) effectively reducing R12 to ~10k. Result: fringe howl still occurs in the same manner as #16.
Change C5 (Vackar feedback capacitor) to 820 pF. Result: fringe howl still occurs in the same manner as #16.
Change oscillator from Vackar-style to Hartley: remove C5, connect varactor anode directly to ground, connect Q1 emitter through 100 nF to tap on L3 (5 turns from cold end). With the Hartley feedback topology, the varactor anode directly grounded, and the varactor cathode biased through a 10 mH choke, most of the original RC networks in the detector itself have now been removed. Result: fringe howl still occurs, though AF frequency has changed. Fringe howl also now occurs with antenna disconnected.
Remove C20 and attempt to take AF output off of collector resistor R15. Result: a constant high-pitched AF oscillation regardless of regeneration setting, indicating AF amp instability.
Connect C3 (AF amp input capacitor) to ground. Result: quiet hissing from AF amp.
Connect C3 (AF amp input capacitor) to decoupled Vcc at R15. Result: a high-pitched AF oscillation indicating insufficient AF amp power supply decoupling.
Add additional 100 ohm resistor and 22uF capacitor (R16 and C23 in new schematic) to decouple Q3 power supply. Reconnect C6, C7, C8, C9. Result: high pitched AF oscillation of #22 stops. However, fringe howl is still observed.
Add additional 100 ohm resistor and 22uF capacitor (R17 and C24 in new schematic) to decouple Q4 power supply. Result: fringe howl is still observed.
Use decoupled AF amp with an older regenerative receiver using a common-collector oscillator, a 176 uH choke as the emitter RF load, and a 100 ohm resistor as the collector AF load. C3 from AF amp is connected to the detector's collector load resistor. Tank inductor is a ferrite rod antenna; no external antenna is connected. Result: no fringe howl observed, but a slight seashell sound is present at some frequencies.
Sleep one night on the problem. In the morning, I think the problem may be the AF amplifier causing the Vcc voltage to vary, and the regeneration control voltage, being taken from the non-decoupled Vcc supply, may be varying in sync with the amplifier-caused Vcc voltage swings, which could cause motorboating: as RF oscillation starts, the detector noise comes up, causing the AF amp to draw more current, causing Vcc to drop, causing the regeneration voltage (taken from the non-decouled Vcc supply) to drop, causing a drop in detector noise, causing a drop in the AF amp current, causing a rise in Vcc, allowing the regeneration voltage to again rise.
Rebuild new regenerative receiver to remove the temporary Hartley feedback of #19 and to again use the original Vackar-style feedback topology. Remove varactor bias choke and again use resistors to supply varactor bias. Reconnect AF amp back to the current regenerative receiver, but supply VR1 voltage (regeneration voltage applied to base) not directly from V4 but instead from the decoupled Vcc supply at R15. Result: fringe howl can no longer be observed in the new receiver when using either a whip antenna or a large antenna connected to C22. However, a slight seashell sound seems to be present around the middle of the tuning range. It is still possible to induce fringe howl by connecting a large antenna (a metal door frame) directly to the top of the tank L3, bypassing the 6 pF antenna coupling capacitor C22.
Rewire older regenerative receiver of #25 to use decoupled Vcc supply for the regeneration control voltage. Result: no fringe howl observed in older receiver, but seashell sound is still present. Connecting whip antenna to the tank inductor (ferrite rod antenna) causes fringe howl at certain frequencies. Even with maximum decoupling the fringe howl could not be completely eliminated from the old circuit, so the decoupling solution -- i.e. decoupling of AF amplifier supply voltage, of detector supply voltage, and of detector regeneration voltage -- is not enough.
Reduce VR1 (regeneration control potentiometer) from 10k potentiometer to 1k potentiometer. Result: some reduction in volume, but no fringe howl observed in any case in either old receiver or new receiver, under all antenna cases (no antenna, short antenna, large antenna, connected directly to tank or through coupling capacitor C22). The reduction in volume was unexpected, but may be due to increased current through the detector transistor's base, leading to decreased AF detection efficiency.
Summary of solution to fringe howl
Ensure AF amp is stable by implementing Vcc decoupling. Test AF amp stability by connecting amp input capacitor to +Vcc rail; if it oscillates, more Vcc decoupling is needed.
Ensure the detector supply voltages, including the voltage used to control regeneration, come from the decoupled Vcc supply to avoid regeneration voltage varying with AF amplifier current draw.
The RC time constant of the regeneration control potentiometer and the bypass capacitors on the potentiometer wiper are important and may be a cause of fringe howl.
The current circuit
Addendum 2015-08-26
The value of R14 (1k) is fairly low, and therefore might cause unwanted interaction between the detector Q1's emitter and C6 (10 nF), the RF bypass capacitor at the input of the AF amp. Because R14 is so low, RF charge buildup on C6 might be able to influence the voltage at the Q1 emitter, which could lead to squegging or fringe howl behavior. Better isolation might be needed between the Q1 emitter and C6. This could be done by increasing R14, but this unfortunately decreases AF output. An alternative isolating approach, with no or negligible signal loss, would be to use an emitter follower stage between Q1 and C6 (e.g. http://qrp-gaijin.blogspot.jp/2015/08/a-12-volt-vackar-style-minimalist.html).
Revision history
2014.10.13: added section on solving fringe howl and new circuit
2014.10.08: added notes on Vackar vs. Colpitts feedback and open loop gain simulations
2014.10.09: added video of fringe howl in operation. Verified in hardware that C1 and C2 are unnecessary.
A regenerative receiver design was published in 2001 by N1BYT called the Wheatstone Bridge Regenerative (WBR) receiver. The design was interesting because it achieves good reverse antenna isolation (little oscillator energy can escape to the antenna) while still allowing antenna energy to enter and be amplified by the regenerative detector. The WBR achieves the reverse antenna isolation passively; no additional isolating amplifier stage is necessary.
I was intrigued by this idea of passive reverse isolation but couldn't completely grasp how the circuit worked. Until now. A 1928 patent clearly describes the WBR operation: https://www.google.com/patents/US1667513. I have seen no references in online discussions to this patent; I found it myself after a lengthy period of investigation, while attempting to understand the operation of and research the background of the WBR receiver.
The key point from the 1928 patent's circuit description is that, unlike a normal regenerative receiver, the antenna signal does not directly excite the oscillator's tank at all! Instead it flows through the inductor's center tap and simultaneously goes through both arms of the bridge, which leaves both ends of the capacitor, and both non-grounded ends of the inductor, at the same voltage -- thus not exciting the tank. By going through the bridge, the signal reaches the input of the amplifying active device. Only after amplification and regenerative feedback does the signal then first appear at the tank.
Another interesting point is that the antenna energy is not filtered by the oscillator tank before it reaches the active device. This means that the antenna signals (in N1BYT's design, where the antenna load Z1 is an untuned inductance) encounter the non-linear active device without the benefit of filtering and thus AM blanketing or IMD are more likely to occur than in a receiver where the antenna signals are first filtered by the oscillator's tank. The 1928 patent uses an additional tuned circuit in place of N1BYT's untuned Z1 for additional input signal filtering.
So to summarise: Forward coupling from the antenna into the detector is high (*NOTE: see addendum below), because the antenna signal flows symmetrically from the tap point through both arms of the bridge (without exciting the tank) whereupon the signal reaches the amplifier input, is amplified, and is regeneratively fed into the tank for the first time. Reverse coupling from the oscillator to the antenna is very low -- almost zero -- because the inductor voltages at opposite sides of the center tap cancel, leaving no oscillator voltage at the center tap to excite the antenna. Addendum, 2014-12 After publishing the above explanation of the WBR circuit, I did some more research, both in the form of circuit simulations and in the form of reading 1920's radio publications. My conclusion from my circuit simulations is that there is a mistake in my previous statement that "forward coupling from the antenna into the detector is high". The forward coupling is not high, because the antenna signal must first go through the amplifier before it reaches the tank. The problem is that this first trip through the amplifier leads to significant loss because the amplifier is configured as a regenerative amplifier, whose output is only a tiny, less-than-unity fraction of its input. That's the essence of a regenerative amplifier: only a tiny fraction of the input appears at the output, but this output is regeneratively fed back to the input, resulting in much larger final regenerative gain after several cycles. With the antenna connected as in the WBR circuit, the signal first gets attenuated by the amplifier stage before the signal is regeneratively amplified, leading to a serious loss of sensitivity. This is especially noticeable with a short whip antenna where signal levels at the antenna are very low to begin with. My conclusion is supported by a 1924 article by Mr. Fitch, who also authored the above-linked 1928 patent on the WBR circuit. The 1924 Fitch article is here: http://www.americanradiohistory.com/Archive-Radio-News/20s/Radio-News-1924-10-R.pdf (see p. 496 of the magazine, i.e. p. 58 of the PDF). The important thing to notice is the difference in tone between the 1928 patent and the 1924 magazine article. The 1928 patent presents the WBR circuit in a positive light and fails to mention its weaknesses, which was probably necessary to convince the patent examiner that the new invention was worthy of a patent. On the other hand, the 1924 magazine article is much more honest about the circuit's shortcomings, and states that the receivers are theoretically interesting but suffer from very poor gain if perfectly balanced. I wrote some more about this on the Yahoo Group "regenrx-simulations" which you can see here: https://groups.yahoo.com/neo/groups/regenrx-simulations/conversations/messages/111.
At the Yahoo Group called regenrx, I got into a good discussion with another user about simulating regenerative receivers, a topic I am particularly interested in. There seems to be a small number of people doing these sorts of simulations and there are various tricks needed to gain insight into the behavior of the almost- or barely-oscillating detector. I've picked up a few tricks here and there, but I felt it would be helpful if all the relevant information could be gathered in one place.
Thus I created a new Yahoo Group called regenrx-simulations. There are already a few working examples posted showing AM detection and CW detection, including regenerative amplification and AF detection. Other examples include frequency determination via FFT and AC sweeps, determining the threshold regeneration level with parameter sweeps, and frequency shift with regeneration adjustment.
No claim of accuracy is made for this calculator. Do not use this calculator for any purpose except entertainment. Refer to the references and perform your own calculations to see if they agree with this calculator's output.
Notes on usage of this calculator
This calculator allows calculation and visualisation of loss components in a small transmitting loop. Unlike other small loop calculators, this loop calculator has a number of unusual features:
Support for multi-turn loops (but see notes below)
Choice of copper, aluminum, or custom conductor material
Support for flat (rectangular cross-section) conductors using W9CF's analytic formulas for RF resistance and self-impedance (see references)
Support for braided conductor loss using a fixed multiplier between 4 and 16 to represent increased losses through wire-to-wire pressure connections in braid
Inclusion of capacitor loss including fixed, dielectric, and metal losses, as per G3RBJ's model (see references); two capacitor models pre-defined, with custom parameters allowed
Inclusion of connecting wire loss (connecting capacitor and loop)
Visualisation of all loss components in both normalised and absolute-value graphs.
Note that for multi-turn loops, the calculator does not include losses due to turn-to-turn proximity effect or turn-to-turn capacitance (circulating currents). The efficiency estimates for multi-turn loops will thus be optimistic.
The validity of W9CF's analytic formulas for rectangular cross-section conductors as used in small transmitting loops, especially multi-turn loops, is not clear.
The following is a multi-turn loop model that achieves 50% efficiency at 7 MHz when simulated in 4nec2. It is a 7-turn square loop, with side length 0.64m, and a total length of 1m. The loop is made of copper conductor 12mm in diameter. A long 20m roll of soft 12mm copper tubing should be rollable by hand into this structure with no joints and minimal loss. Resonating capacitance for 7 MHz is 6 pF.
To open the model in 4nec2, copy and paste the text between the dashed lines and save it to a file, then open the file in 4nec2.
----------
CM 3D multi-turn loop
CM qrp.gaijin@yahoo.com (2014/04)
CE
SY C=5.85e-12
SY r=6e-3
SY s=5
GW173-2.22e-1613.6-2.22e-1613.75r
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GW20s003.60.450.035714293.15r
GW21s0.450.035714293.155.5511e-170.071428572.7r
GW22s5.5107e-170.071428572.7-0.450.107142863.15r
GW23s-0.450.107142863.15-1.11e-160.142857143.6r
GW24s-1.102e-160.142857143.60.450.178571433.15r
GW25s0.450.178571433.155.5511e-170.214285712.7r
GW26s5.5107e-170.214285712.7-0.450.253.15r
GW27s-0.450.253.15-1.11e-160.285714293.6r
GW28s-1.102e-160.285714293.60.450.321428573.15r
GW29s0.450.321428573.155.5511e-170.357142862.7r
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GW31s-0.450.392857143.15-1.11e-160.428571433.6r
GW32s-1.102e-160.428571433.60.450.464285713.15r
GW33s0.450.464285713.155.5511e-170.52.7r
GW34s5.5107e-170.52.7-0.450.535714293.15r
GW35s-0.450.535714293.15-1.11e-160.571428573.6r
GW36s-1.102e-160.571428573.60.450.607142863.15r
GW37s0.450.607142863.155.5511e-170.642857142.7r
GW38s5.5107e-170.642857142.7-0.450.678571433.15r
GW39s-0.450.678571433.15-1.11e-160.714285713.6r
GW40s-1.102e-160.714285713.60.450.753.15r
GW41s0.450.753.155.5511e-170.785714292.7r
GW42s5.5107e-170.785714292.7-0.450.821428573.15r
GW43s-0.450.821428573.15-1.11e-160.857142863.6r
GW44s-1.102e-160.857142863.60.450.892857143.15r
GW45s0.450.892857143.155.5511e-170.928571432.7r
GW46s5.5107e-170.928571432.7-0.450.964285713.15r
GW47s-0.450.964285713.15-1.11e-1613.6r
GE-1
LD5170058000000
LD5180058000000
LD5190058000000
LD0183300C
LD5200058000000
LD5210058000000
LD5220058000000
LD5230058000000
LD5240058000000
LD5250058000000
LD5260058000000
LD5270058000000
LD5280058000000
LD5290058000000
LD5300058000000
LD5310058000000
LD5320058000000
LD5330058000000
LD5340058000000
LD5350058000000
LD5360058000000
LD5370058000000
LD5380058000000
LD5390058000000
LD5400058000000
LD5410058000000
LD5420058000000
LD5430058000000
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LD5450058000000
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GN200030.0004
EK
EX01830000
FR000070
EN
----------
The simulation results are as shown in the following image.
Addendum 2015-01-03
From the above current diagram (where blue represents lower current flow and red represents higher current flow) it is clear that there is little current flowing in the horizontal section of the antenna connecting the two loop ends. This horizontal section of the antenna contains the loop resonating capacitance of 6 pF. Therefore, there is very little current flowing through the resonating capacitor. This is because the multi-turn loop structure is almost self-resonant by itself with no capacitor.
It follows that by adjusting the turn spacing or diameter, the structure can be made self-resonant with no need for an additional resonating capacitor.
Then, the proper term for this kind of a long, multi-turn, self-resonant radiator is a "normal mode helix". Here is an article describing practical construction and matching of a normal-mode helix for VHF use: w6nbc.com/articles/2011-06QST2mhelices.pdf .
Though I yet haven't built one, I see nothing that would prevent a similar antenna from being built for HF use.
