Another unidirectional small loop: the Coplanar Twin Loop

[qrp-gaijin]

the impedance is around 2 Ohm which means that, to couple the antenna to a receiver we'll need to use a preamp/buffer designed to accept such low impedance and offering an output impedance around 50 (or 75) Ohms,

The CTL article showed a gamma match (tapping at 2 particular locations) on the inner loop to achieve an impedance match to 50-ohm coax. The article also shows how an additional small coupling loop placed inside the inner loop can achieve the impedance transformation to 50 ohms. Both techniques are the same techniques used to match small transmitting loop antennas to 50 ohms.

and this adds another degree on complexity, not that it's bad, but sincerely I prefer simpler stuff in the "SULA" case, the same resistor which gives the cardioid pattern also serves to give a wideband impedance around 450 Ohms, which just using a 9:1 can be easily matched to a coax feeder or to a standard LNA

Yes, the broadband nature of the SULA is interesting. I did a quick run of the 4nec2 model just to make sure it works for me and it did. I wonder how small you can make the SULA and still have acceptable performance. Would 50 cm sides work? 30 cm? The CTL may be have an advantage of smaller size due to the signal boost caused by resonance -- but as you said, the CTL is more complex to build and operate.

One quite interesting thing about the CTL, which is mentioned extensively in the CTL article, is the existence of a magnetic shadow region caused by the outer loop. I had confirmed the existence of the magnetic shadow with some 4nec2 near field simulations several years ago, but I couldn't find my old simulation files and I recreated them just now.

This paragraph is tediously long and can be skipped, but I am writing it just to keep a record of what I did for future reference. Basically I created a test environment with three short vertical dipoles located at x=-100, x=0, and x=100. Then I positioned a 1 meter x 1 meter resonant and resistively-loaded loop at x=0, enclosing the center dipole. The tuning capacitor is located in the vertical center of the positive side (x=0.5m) of the loop, and the null direction of the loop is on the negative side of the loop. Tuning the system requires setting the excitation location to be on the loop and optimizing the capacitance until X=0, then moving the excitation location to the x=0 dipole and optimizing the loading resistance and capacitance for best F/B ratio. Next, two excitation sources are configured: one on the x=0 dipole and one on the x=100 dipole. This produces a very strange pattern due to the dual excitations, but nevertheless in this condition it is possible to again optimize the capacitance and resistance for best F/B ratio. Next, the excitation is removed from the x=0 dipole so that only the excitation on the x=100 dipole remains, which is located on the non-null side of the loop. In this condition, I then plot the magnetic near field data around and inside the loop. Finally, I relocate the excitation to the x=-100 dipole, which is located on the null side of the loop, and again plot the magnetic near field data.

If we compare the magnetic near field data when the loop is excited from the front direction (non-null direction with excitation at x=100) with the magnetic near field data when the loop is excited from the rear direction (null direction with excitation at x=-100), then we see that the front excitation induces a higher magnetic field in the interior of the loop, whereas the rear excitation can only induce a smaller magnetic field in the interior of the loop -- in other words, the magnetic field from the rear of the antenna has been obscured by a magnetic shadow, resulting in less illumination (from the rear direction) in the interior of the loop. The magnetic shadow exists, just as Dr. Villard said -- and I suspect this is exactly the kind of numerical simulation that he ran to confirm the existence of this magnetic shadow.

Below is an image of the magnetic near field data when the loop is excited from the front, non-null direction.

shad1.png (26.88 KiB) Viewed 14235 times

Below is an image of the magnetic near field data when the loop is excited from the rear, null direction. Note that the scale of the image is identical to that of the previous image, so it is valid to compare the colors between the images. Clearly, when excited from the rear, there is less illumination (due to a magnetic shadow) in the interior of the loop.

shad2.png (26.99 KiB) Viewed 14235 times

just as a note, if you want to try a circular loop design, the model below is a vanilla circular loop model

Thanks; that looks useful. The darkness of the above shadow region may be improved with a circular loop instead of a square loop. I'd like to rerun the magnetic shadow simulation with a round loop.

I'm also curious if the SULA also exhibits a magnetic shadow region in the interior of the loop. I hope to run some simulations soon.

[Andrew (grayhat)]

I'm in a hurry, so I'll keep this short; first, that loop and dipoles setup somewhat recalls at large a yagi (dipoles), did you try changing the size/spacing of the dipoles ? Then, about the CTL, I started wondering if it may be used as a TX antenna, in such a case it would be interesting for lower frequencies, where even a dipole would be huge, just think to the 630m band, a SMALL TX antenna offering an unidirectional lobe would be fantastic and a variation over the "classic" loop !

[Andrew (grayhat)]

forgot, (yes, still ferreting around <sigh>); try the following: load the CTL model, remove the cap/resistor from the outer loop and replace the cap in the inner loop with a resistor (530 Ohms like the SULA will do), now run the NEC model, done so, change the inner loop size and check the result, do the same adding capacitors and/or inductors to the outer loop, also play with the placing of L/C on the outer loop, maybe I'm crazy. but I saw a pattern...

[qrp-gaijin]

I'm in a hurry, so I'll keep this short; first, that loop and dipoles setup somewhat recalls at large a yagi (dipoles), did you try changing the size/spacing of the dipoles ?

Good point. The reason I used 3 fixed dipoles was to have a completely unchanging geometry for the entire test environment, where I only moved the excitation source from one location to another. The goal was to avoid changes in geometry, which might slightly change the tuning of the outer loop, and disturb the null.

But I just now ran another simulation with only (a) one loop (the outer loop of the CTL) which is resistively loaded, high-impedance with additional loading inductance, and capacitively resonated, and (b) one excitation dipole that is moved from x=0 to x=100 to x=-100. The advantage of this scheme is that there is only one excitation dipole (10 cm long) so there are no effects of other distantly-located but inactive dipoles. The disadvantage of this scheme is that the loop's null is optimized when the excitation dipole is located at x=0, inside the loop, but then in the shadow tests (with front illumination and rear illumination), that same dipole is moved from its original x=0 location to the new x=100 or x=-100 location. By removing the dipole from the center of the loop, we may have detuned the loop away from its optimal null condition.

This could all be fixed if we could excite the loop directly when optimizing the F/B ratio. I noticed with interest that the SULA model does this, by placing the excitation source directly opposite of the resistive load. Unfortunately, in the CTL outer loop, that location (directly opposite of the resistive load) is the exact location of the resonating capacitor, and I could never get a proper cardioid pattern with the excitation source located at the capacitor. So I had to use a workaround of using a separate excitation element, which is the small (10 cm long) vertical dipole initially positioned at x=0. The reason I chose a 10 cm-long vertical dipole is that this small geometry should hopefully have little influence on the loop tuning, so that even after it is removed (for the excitation tests at x=100 and x=-100), the loop null should hopefully still be preserved.

Anyway, the result is that even with only one excitation dipole present -- with no additional inactive dipoles present to possibly alter the results -- the magnetic shadow can still be observed.

Below are the results of the front- and rear-illumination tests, with the excitation dipole (10 cm long) positioned at x=100 (front) and x=-100 (rear). No other vertical dipoles are present in the test geometry to eliminate effects of unwanted geometry. The distance between the loop and the excitation source is far enough that the excitation source lies in the far field region of the loop; with the test at 11 MHz, one wavelength is about 27 meters, so the excitation source is several wavelengths away from the loop. The magnetic shadow is still visible, proving that the shadow effect is created solely by the inner loop.

res-far.png (121.96 KiB) Viewed 14199 times

I ran another test with the excitation dipole much closer to the loop, in the near-field zone. The shadow is still visible, but weaker. I suspect this is because the near-field excitation causes unwanted reactive near-field effects like local induction. There may also be some detuning effects.

res-near.png (132.67 KiB) Viewed 14198 times

Then, about the CTL, I started wondering if it may be used as a TX antenna

It won't be practical. But it could be an educational exercise to think this through to understand why. For transmission at low HF frequencies, the main loop element would need to be extremely low loss (like 10 cm-diameter copper tubes of 0.2 mm thickness for 7 MHz for barely-acceptable performance). Probably, the shadow-generating outer loop would need also need to be scaled up, which is probably impossible due to the required loading inductances, required because the outer shadow-generating loop needs to be high-impedance. In a receive-oriented CTL, the high impedance is required for the antenna to respond both to the incoming electric field and incoming magnetic field, so that their phase cancellation generates the shadow and the unidirectional effect. For transmission, we could reason that the outer loop would then need to equivalently generate (based on the excitation from the main, inner loop) the proper E-field and H-field in order to cancel out part of the symmetrical pattern generated by the inner loop. So the outer loop would need to be optimized both as an H-field generator (a magnetic loop, with low-loss large-diameter tubing) and simultaneously as an E-field generator, which I guess usually requires things like very low loss loading coils. But the final nail in the coffin is the requirement that the outer loop be resistively loaded in order to generate the unidirectional pattern. Any additional resistive loss is anathema to a small transmitting loop antenna -- milliohms of added resistance are significant, because the radiation resistance is also in the milliohm range. Adding tens or even hundreds of ohms of added resistance -- as done in the CTL and SULA -- will totally ruin the transmitting performance of the loop. Maybe if you had gigawatts of transmitter power -- and a variable capacitor, loading resistor, and loading coils that could handle gigawatts -- then a few milliwatts of radiation might come out of the antenna.

Of course, I could be wrong. My line of thought above assumed that the outer, shadow-generating loop needs to be just as low-loss as a normal small transmitting loop. But maybe that's not true -- maybe its role as a shadow-generator (a generator of mutually-cancelling E- and H-fields) does not require extremely low-loss conductors. Maybe its high value of resistive loading won't negatively affect the performance of the inner small transmitting loop. I have my doubts, but don't let that stop you from experimenting!

[qrp-gaijin]

Did a quick 7 MHz simulation of a CTL over real-ground. Maximum gain is about -22.4 dBi.

7mx.png (65.11 KiB) Viewed 14188 times

The outer loop is loaded with 70 ohms of loss resistance to achieve the unidirectional effect.

The outer loop is also loaded with 20 uH of lumped inductance to achieve the high-impedance necessary for E-field sensitivity.

Assuming a Q of 100 for the 20 uH loading coil, at 7 MHz the coil loss resistance is about 9 ohms.

So in addition to the coil loss resistance of 9 ohms, we need to add about 61 ohms of additional load resistance to the outer loop to achieve the required 70 ohms of loss resistance for the unidirectional effect.

The loss resistance of the outer loop is realistic and feasible to construct in practice, because the loop conductor and the ESR of the capacitor will add some milliohms, but these are small in relation to the total required loss resistance of 70 ohms.

The outer high-impedance loop is resonated at 7 MHz with only 12 pF, so it will be sensitive to the stray capacitance of its surroundings.

The inner loop is resonated with 99 pF and will be less sensitive to stray capacitance.

The above simulation is the best case scenario, assuming that the inner loop is a perfectly lossless conductor and that the inner loop's capacitor is lossless. As a rough guess, I tried adding 1 ohm (1000 milliohms) of added resistance to the inner loop to account for conductor loss and capacitor loss. The effect on the final radiation is very small -- less than 1 dB. The effect of the added 1 ohm resistance is small because larger losses are caused by the large loss resistance of the outer loop being coupled into the inner loop.

In conclusion, a transmitting CTL is not totally out of the question, but it loses efficiency. Here's the same loop simulation, but with the outer loop detuned so that it almost does not affect the inner loop. The radiation increases.

7mnormal.png (58.32 KiB) Viewed 14188 times

As a more realistic simulation of a "normal" small transmitting loop, I deleted the outer loop completely, leaving only the 1m x 1m inner loop. I configured conductor loss to be that of copper conductors with 10 cm diameter, and added 0.5 ohms of additional loss for the capacitor ESR. Here is the result.

7m-no2.png (44.07 KiB) Viewed 14188 times

So with a normal 1 m x 1 m loop constructed with best practices, we might get -12 dBi at high angles and -15 dBi at low angles -- even better if we can get the capacitor ESR below 500 milliohms, which is probably possible with a good vacuum-variable capacitor. Compare this with the poor performance of the CTL, where maximum gain is only about -22.4 dBi in the best possible case with lossless conductors.

I would guess it makes more sense to transmit more total energy in all directions, instead of trying to transmit less energy in a more focused and restricted range of directions. So I don't think the CTL concept makes sense for transmitting, unless for some reason you need to reduce your radiation in one particular direction.

[qrp-gaijin]

My previous magnetic shadow simulations were done with one loop only (the outer CTL loop) to show that the outer loop, by itself, can create a magnetic shadow. But the shadow is not so dark in this case.

I found out that when I use the two-loop CTL model (with both the outer high-Z loop and the inner low-Z loop), the generated shadow in the interior of the loop is much darker, indicating a much better rejection of signals from the null direction.

Here is the illumination of the shadow region from the front (x=100). The shadow region is bright, because it is illuminated from the non-null side of the antenna.

ctl-front-ill.png (27.87 KiB) Viewed 14170 times

Here is the illumination of the shadow region from the rear (x=-100). The shadow region is very dark, because the illumination from the null side of the antenna is canceled or "blocked" by the field cancellation of the outer loop, thus creating the dark region, the magnetic shadow.

ctl-rear-ill.png (27.93 KiB) Viewed 14170 times

We need to be careful interpreting these results. The generated shadow from the dual-loops is much darker than the single-loop shadow, but that does not necessarily mean that the single loop cannot generate an equivalently dark shadow. It may be possible that the single loop, if appropriately adjusted, can also generate an equivalently dark shadow. I don't know.

The 4nec2 file used to create the above images is included below. It includes instructions for how to run the simulation to see the shadow region.

Code: Select all

CM Model of Coplanar Twin Loop antenna at 7 MHz.
CM Created in 4nec2 by qrp-gaijin@yahoo.com (https://qrp-gaijin.blogspot.com).
CM 
CM The model has initially been adjusted for a unidirectional null at 7 MHz over average ground. The null points in the negative X direction.
CM 
CM ---------------------
CM 
CM To view the far-field unidirectional pattern:
CM 
CM 1. Place the current source on the inner loop, opposite of the capacitor C1, by setting excitation_tag=4 and excitation_seg=4.
CM 
CM 2. Run a far-field simulation, and observe that a unidirectional null exists and points in the negative X direction.
CM 
CM ---------------------
CM 
CM To view the near-field magnetic shadow:
CM 
CM 1. Place the current source on the vertical dipole by setting excitation_tag=100 and excitation_seg=1.
CM 
CM 2. Set signal_antenna_x=100, to illuminate the loop antenna from the front side with a signal from a distantly-located vertical dipole.
CM 
CM 3. Run a magnetic near-field simulation over the domain x=[-2,2], y=[0.001,0.001], z=[0.5,2.5], with resolution of 0.01 meters in every dimension. In the results window, click anywhere in the plot to activate it, then from the menu set the maximum scale value on the plot to be 0.020 A/m, and observe that the interior of the loop is brightly illuminated by the signal from the vertical dipole, as shown by a high magnetic near field intensity inside the loop.
CM 
CM 4. Set signal_antenna_x=-100, to illuminate the loop antenna from the rear side (the null direction) with a signal from a distantly-located vertical dipole.
CM 
CM 5. Run a magnetic near-field simulation identical to step 3, and observe that the interior of the loop is almost completly dark, indicating a lack of illumination by the signal from the vertical dipole, as shown by a very low magnetic near field intensity inside the loop. This lack of illumination is the effect caused by the "magnetic shadow" effect of the outer loop.
CM 
CM The magnetic shadow can also be observed even inner loop is omitted, indicating that the magnetic shadow is primarily due to the outer loop. However, the shadow created by the outer loop alone seems to be only partially dark, and the difference between front-illumination and rear-illumination is visible but small. But when both the inner and the outer loops are used in combination (as in this simulation), the shadow effect seems greatly enhanced, as indicated by a stark difference between front-illumination and rear-illumination, with rear-illumination resulting in a very dark shadow in the interior of the loop with almost no resulting magnetic field. It is not known if it is possible to create an equivalently-dark magnetic shadow by using only the outer loop.
CM 
CM ---------------------
CM 
CM For small changes in frequency, adjust the model as follows:
CM 
CM 1. Place the current source on the inner loop, opposite of the capacitor C1, by setting excitation_tag=4 and excitation_seg=4.
CM 
CM 1. Adjust C2 (outer loop capacitance) to be very large (e.g. 1000 pF), so that the outer loop is far away from resonance.
CM 
CM 2. Optimize C1 (inner loop capacitance) to resonate the inner loop such that X=0.
CM 
CM 3. Optimize outer_loop_resistance and C2 for best F/B ratio at Theta=90 degrees, with Phi spanning 0 to 180 degrees. It may be best to optimize each of these variables separately, and to repeat the optimization step several times.
CM 
CM ---------------------
CM 
CM For use at an arbitrary frequency f, adjust the model as follows:
CM 
CM 1. Estimate the loading inductance required to resonate the outer loop at frequency f with C2 at 10 pF. This ensures the outer loop is high-impedance. Add this load to the outer loop, opposite of the capacitor.
CM 
CM 2. Estimate the loading inductance required to resonate the inner loop at frequency f with C1 at 300 pF. This ensures the inner loop is low-impedance. Add this load to the inner loop, opposite of the capacitor. For higher frequencies, above 7 MHz or so, no loading inductance is needed for the inner loop. For lower frequencies, loading inductance will likely be needed for the inner loop.
CM 
CM 3. Detune C1. Place the current source on the outer loop, opposite of C2, by setting excitation_tag=13 and excitation_seg=5. Optimize C2 for resonance such that X=0. C2's final value should be around 10 pF, to ensure that the outer loop is high-impedance. If optimization for X=0 is not possible, then the loading inductance for the outer loop is wrong and needs to be adjusted.
CM 
CM 4. Detune C2 by adding 1000 pF to its value. Place the feedpoint on the inner loop, opposite of C1, by setting excitation_tag=4 and excitation_seg=4. Optimize C1 for resonance such that X=0. C1's final value should be more than about 100 pF, to ensure that the inner loop is low-impedance. If optimization for X=0 is not possible, then the loading inductance for the inner loop is wrong and needs to be adjusted.
CM 
CM 5. Set C2 back to its resonant value. Leave the current source at the same location, on the inner loop.
CM 
CM 6. Again optimize C1 for resonance such that X=0, to account for the possible detuning effects of the resonant outer loop. There should be little, if any, change in the value of C1.
CM 
CM 7. Optimize outer_loop_resistance and C2 for best F/B ratio at Theta=90 degrees, with Phi spanning 0 to 180 degrees. It may be best to optimize each of these variables separately, and to repeat the optimization step several times.
CM 
CM When properly adjusted, the model shows a unidirectional null, both in free space, and above ground.
CM 
CM Note that the outer loop must be high impedance (achieved by a loading inductance), and the inner loop must be low impdeance. The high impedance of the outer loop allows sensitivity to both the E-field and the H-field, and these fields partially cancel in the outer loop to create the magnetic shadow effect and the null region.
CM 
CM 
CE
SY h=1.0	'height of bottom of loop above ground
SY radius=0.0005	'conductor radius
SY c1=92.34222	'resonating capacitance for inner loop in pF (used by optimizer)
SY c1_farad=c1*1e-12	'resonating capacitance for inner loop in F
SY c2=12.02402	'resonating capacitance for outer loop in pF (used by optimizer)
SY c2_farad=c2*1e-12	'resonating capacitance for inner loop in F
SY outer_loop_resistance=67.79112	'load resistance in outer loop to achieve unidirectional effect
SY outer_loop_load_inductance=20e-6	'load inductance in outer loop to achieve high-impedance
SY signal_antenna_x=-100	'x location for vertical diople to generate illumination signal
SY signal_antenna_length=0.1	'length of vertical dipole to generate illumination signal
SY excitation_tag=100	'wire tag where the excitation source should be located
SY excitation_seg=1	'wire segment where the excitation source should be located
GW	1	7	-0.5	0	h	0.5	0	h	radius	'Wire 1, 9 segments, halve wavelength long.
GW	2	7	0.5	0	h	0.5	0	h+1	radius
GW	3	7	0.5	0	h+1	-0.5	0	h+1	radius
GW	4	7	-0.5	0	h+1	-0.5	0	h	radius
GW	10	9	-0.642857	0	h-0.142857	0.642857	0	h-0.142857	radius
GW	11	9	0.642857	0	h-0.142857	0.642857	0	h+1.142857	radius
GW	12	9	0.642857	0	h+1.142857	-0.642857	0	h+1.142857	radius
GW	13	9	-0.642857	0	h+1.142857	-0.642857	0	h-0.142857	radius
GW	100	1	signal_antenna_x	0	h+0.5-0.5*signal_antenna_length	signal_antenna_x	0	h+0.5+0.5*signal_antenna_length	radius
GE	1
LD	0	2	4	4	1	0	c1_farad
LD	0	11	5	5	0	0	c2_farad
LD	0	13	5	5	outer_loop_resistance	outer_loop_load_inductance	0
LD	5	0	0	0	58000000
GN	2	0	0	0	13	0.005
EK
EX	6	excitation_tag	excitation_seg	0	1	0	0
FR	0	0	0	0	7	0
EN

[qrp-gaijin]

just as a note, if you want to try a circular loop design, the model below is a vanilla circular loop model

[...]

which could be easily modified (e.g. adding a second, smaller size loop inside

Just as a warning, one annoying NEC-2 limitation that we have to be careful about is lining up the segments of closely-spaced parallel wires. As noted at http://on5au.be/content/amod/amod3.html:

NEC-2 documentation specifically recommends that closely space parallel wires be arranged so that the segments are carefully matched, as shown in Figure 2. As noted in the last episode, this practice is a good one to follow with all models.

With a square loop model, this restriction can be implemented (and my CTL model implements it), but with a circular loop model, it will be impossible to implement this restriction.

[Andrew (grayhat)]

first of all, at the moment I'm busy helping some relatives picking olives from trees, so please forgive me if I delay my replies; also, as you can guess. I've no way to run NEC simulations here (note: did you know that ezNEC is now free ? https://www.eznec.com/ ) ... anyhow, your simulations are really interesting, and show that the CTL design has some darn good potential, my only doubt is about how easily it may be realized in practice and about the influence that the feedline may/will have on the antenna behaviour, I'm saying it because I had some issues with that while designing the SULA, and the CTL is even more difficult, due to the outer loop, but ... a step at a time

Ok. getting back to those olive trees... oh and I just had a probably crazy idea, inspired by your loop+dipoles, that is, check if it may be possible to add a passive "reflector" element to the SULA, that is, either a vertical dipole or a V shaped (with the vertex and sides parallel to the SULA back) element... as soon as I'll finish here (that is, most probably next monday) I want to check it on NEC

[Andrew (grayhat)]

forgot (and OT) do you know what happened to Jim's ham forum (the radio board) ? I know you were a member there, and there were a lot of cool folks, but then, it went suddenly "poof" <sigh>

[13dka]

Welcome to the forum, qrp-gaijin! Hope you guys tell me when it's time to charge my little dremel tool.

~20dB more gain / less losses at little more than 1/2 the size of the SULA sounds pretty intriguing, even though the overall coverage seems to be pretty small (7-21Mhz?).

...check if it may be possible to add a passive "reflector" element to the SULA, that is, either a vertical dipole or a V shaped (with the vertex and sides parallel to the SULA back) element... as soon as I'll finish here (that is, most probably next monday) I want to check it on NEC

And if that works, why not adding a director too? (I need a new car then.)