Above, the Baby loop is a small transmitting loop with a novel remotely controlled loop tuning capacitor and tuning mechanism, and gamma match.

This article will consider NEC-5 models of a similar antenna at 2.5m centre height above ‘average ground’. Key assumptions are

- mean diameter: 1m;
- conductor: 50mm diameter aluminium;
- Tuning capacitor Q: 2000;
- Ground: σ=0.005, εr=13.

Models were run at 7.1 and 14.2MHz at heights from 0.6-10m, detailed analysis was done at 2.5m centre height.

IEEE standard dictionary of electrical and electronic terms (IEEE 1988) defines Radiation Sphere:

A large sphere whose centre lies within the volume of the antenna and whose surface lies in the far field of the antenna, over which quantities characterising the radiation from the antenna are determined.

The definition of Radiation Sphere is important in that it defines **where** radiation is to be observed, it is to be observed in the far field.

IEEE standard dictionary of electrical and electronic terms (IEEE 1988) defines Radiation Efficiency:

The ratio of the total power radiated by an antenna to the net power accepted by the antenna from the connected transmitter.

Radiation fields decay inversely proportional to distance, other fields immediately around an antenna decay more quickly and are insignificant for the purpose of radio communications at great distances. Hence, Radiation is the usual objective of radio communications antennas.

CirroMazzoni give their explanation of efficiency in one of their manuals:

The term “resistive loss” might include loop conductor loss, but it is not clear that it includes loss in the tuning capacitor or loss in the soil under the antenna, and if it did not include those components, it would lead to an overestimate of Radiation Efficiency.

A more complete expression is \(RadiationEfficiency=100\frac{R_{rad}}{R_{rad}+{R_{loss}+}{R_{gnd}}} \%\) where:

- Rrad is the component of feed point impedance due to the total power radiated (ie in the far field);
- Rloss is the component of feed point impedance due to all losses such as conductor loss and dielectric loss in the antenna structure;
- Rgnd is the component of feed point impedance due to loss of energy to the ground.

Failure to properly estimate and include all the loss elements will result in an inflated, even unrealistic, estimate of Radiation Efficiency.

The manufacturer’s brochure claims:

Bandwidth: 4kHz @ 7.0 MHz;

Gain compared to λ/2 dipole: -4dB @ 7.0 MHz,

Converting the stated gain, we have -1.86dBi.

No information is given on the implementation scenario, and it has great bearing on both metrics. One often sees test setups on the kitchen table, in the lounge etc, and I have seen one pic of the “indoor test range at the CirroMazzoni factory” where the antenna was measured in what looked like an ordinary factory space cluttered with conductors and structures.

Like most antennas close to natural ground, this antenna is quite sensitive to height and ground parameters.

Above is a plot of the three components of feed point resistance for the modelled scenario. Note the log resistance scale.

Rrad depends on height, a natural consequence of the effect of the lossy ground reflection.

Rgnd is very sensitive to height close to the ground. If you like, the loop is better at heating dirt when it is closer to it.

Rloss is independent of height, and it dominates the Radiation Efficiency calculation at more than 2m height… so getting this value correct is key to a good estimate of Radiation Efficiency.

Above is a pie chart of the components of feed point resistance at 2.5m centre height. Rrad at 6mΩ is just 7.1% of the total, Radiation Efficiency is 7.1%.

The NEC model also gives us the radiation pattern. The plot above from NEC5GI is the elevation pattern scaled in spherical coordinates as used by NEC.

Maximum gain is -5.66dBi at the zenith and average gain is -11.46dBi, giving Directivity=5.80dB. The model gain is 3.8dBi less than stated in the manufacturer’s manual.

The half power bandwidth calculated from the model is 6.9kHz, Q is 1025.

Calculate small transmitting loop gain from bandwidth measurement is a calculator for a small transmitting loop in free space. With some tweaks, the model can be calibrated to the value of Rrad (Rr), Directivity and Bandwidth calculated from the NEC model.

Above is the calibrated model, which unsurprisingly reconciles with the NEC model.

The manufacturer’s brochure claims:

Bandwidth: 6kHz @ 14.0 MHz.

Like most antennas close to natural ground, this antenna is quite sensitive to height and ground parameters.

Above is a plot of the three components of feed point resistance for the modelled scenario. Note the log resistance scale.

Rrad depends on height, a natural consequence of the effect of the lossy ground reflection.

Rgnd is very sensitive to height close to the ground. If you like, the loop is better at heating dirt when it is closer to it.

Rloss is independent of height.

Above is a pie chart of the components of feed point resistance at 2.5m centre height. Rrad at 104mΩ is just 28.8% of the total, Radiation Efficiency is 28.8%.

The NEC model also gives us the radiation pattern. The plot above from NEC5GI is the elevation pattern scaled in spherical coordinates as used by NEC.

Maximum gain is -0.10dBi at the zenith and average gain is -5.41dBi, giving Directivity=5.31dB.

The half power bandwidth calculated from the model is 29.8kHz, Q is 476.

Calculate small transmitting loop gain from bandwidth measurement is a calculator for a small transmitting loop in free space. With some tweaks, the model can be calibrated to the value of Rrad (Rr), Directivity and Bandwidth calculated from the NEC model.

Above is the calibrated model, which unsurprisingly reconciles with the NEC model.

The models of a similar antenna structure at 2.5m height over ‘average ground’ suggest that half power bandwidth on 7MHz and 14MHz would be considerably greater than given in the manufacturer’s manual. Along with that, Radiation Efficiency would be low leading to relatively low Gain, lower than stated in the manual in the case of the 7MHz model above.

None of this is to suggest the Baby loop is a bad antenna, the model suggests it will work about as well as a good loop of similar dimensions, no better. Its remote tuning system and tuning capacitor construction may well be a particularly good implementation.

(Revised 23/07/21: Fixed an error in extraction of APG which flowed into some results.)

- CirroMazzoni, 2007. Presentation and instruction manual – loop antenna. Cirro Mazzoni Radiocommunication.
- Duffy, O. 2015. A method for initial ground loss estimates for an STL
- ———. 2015. Accuracy of estimation of radiation resistance of small transmitting loops
- ———. 2015. Small transmitting loop – ground loss relationship to radiation resistance
- ———. 2015. Enhancement of Calculate small transmitting loop gain from bandwidth measurement
- ———. 2015. Antennas and Q
- IEEE. 1988. IEEE standard dictionary of electrical and electronic terms, IEEE Press, 4th Edition, 1988.
- Underhill, M. May 2006. Loop efficiency.
- ———. M. Sep 2013. Impossible Antennas and Impossible Propagation.

The diagram above from the video shows the topology of the series stub match.

Let’s work an example using 50Ω coax where the load is 10-j40Ω at 146MHz.

Above is a naive Simsmith model of the scenario with line lengths adjusted for a ‘perfect’ match. The inset VSWR curve looks great!

Why did I say naive?

Well, when we look at the series stub more completely, along with the differential mode behaviour that is captured in the Simsmith model above, we have the outside surface of the outer conductor of the stub connected to the main line inner conductor on the source side of the stub and it is capable of carrying current.

This stub outer surface current may give rise to radiation and impresses a load impedance across the main line coax in shunt with the perfectly transformed 10-j40Ω load. The value of this unintended impedance depends on the stub physics.

In this case, the stub is just under a quarter of a wavelength, and modelled as a monopole over a ground plane would present a driving impedance of around 15-j80Ω.

Above is the Simsmith model with the addition of the estimated impedance of the stub outer as a radiator in shunt with the main line. The matching result is degraded by the stub exterior’s ‘antenna effect’ and that unintended radiation / pickup may be undesirable.

The VSWR curve is not so good now when the ‘antenna effect’ of the stub is brought to book. The match could be tweaked some, but it does not remove the radiation / pickup behavior of the stub.

Matchers using series or shunt stub tuners are nearly ideal in waveguide and can be quite good / practical in two wire lines; but while shunt tuners are nearly ideal in coax, series tuners in coax may not be so good and tend to be avoided.

]]>A reader of A common scheme for narrow band match of an end fed high Z antenna commented:

…if the coil is tapped at 1/3, surely then the coil is a 1:3^2 or 1:9 transformer and the capacitor simply ‘tunes out’ the coil reactance, what is the input impedance when it has a 450+j0Ω load?

That is very easy to calculate in the existing Simsmith model.

Above, with load of 450+j0Ω, the input impedance at 50MHz is 8.78+j34.36Ω (VSWR(50)=8.4), nothing like 50+j0Ω.

As for tuning out the reactance…

Somewhat more capacitance does result in a lower VSWR(50), but at 1.6, you could not claim it is matched.

This is not simply a 1:9 transformer by any stretch of the imagination.

As mentioned in the referenced article, solution of these circuits is not intuitive, the amount of flux leakage is critical to behavior, and that depends greatly on the geometry of the coil.

]]>A common variant shows not capacitor… but for most loads, the capacitance is essential to its operation, even if it is incidental to the inductor or as often the case, supplied by the mounting arrangement of a vertical radiator tube to the mast.

A similar arrangement works for vertical radiators around a λ/2, around means from say 3λ/8 to 5λ/8. All of these present an impedance of some fairly high resistance in series with a significant reactance. Because the current at the feed point is relatively low, these are often used as so-called ground independent antennas.

Above is a Simsmith model of such an arrangement. The load L is from an NEC-4.2 model of a 50MHz 5λ/8 vertical over four λ/4 radials in free space.

The tapped coils is a uniform air cored solenoid of radius 10mm, pitch 3mm, 6t tapped at 33% (ie 2t).

C1 represents the equivalent capacitance of self resonance, equivalent mount capacitance, and possibly some additional capacitance.

Though it seems every ham can explain how this circuit works, there is nothing intuitive about the design of the tapped inductor.

The inductor design was assisted by a little python script which found the tap point and c1 for a given inductor, load, etc.

zl: (59.49-175.4j) pitch: 0.00300 m, radius: 0.01000 m, turns: 6.00, length: 0.01800 m, Ql: 300, Qc: 1000 VSWR=1.00009, tap=32.994 (%), c1=4.91618 (pF)

From that starting point, you could play with Simsmith interactively changing the coil parameters and adjusting things for a new match.

#!/usr/bin/env python # coding: utf-8 import math import cmath from scipy.optimize import minimize from scipy import constants f=50e6 zl=59.49-175.4j #network qc=1000 ql=300 #tapped coil p=0.003 r=0.01 n=6 def wcf(n,r,l): return constants.mu_0*n**2*r*(math.log(1+math.pi*r/l)+1/(2.3004+1.622*l/r+0.4409*(l/r)**2)) def vswr(args): tap,c1=args lt=wcf(n,r,l) l1=wcf(n*tap,r,l*tap) l2=wcf(n*(1-tap),r,l*(1-tap)) m=-(lt-l1-l2)/2 rlt=2*math.pi*f*lt/ql y=1/zl y=y+2*math.pi*f*c1*(1/qc+1j) zl2p=rlt*(1-tap)+2*math.pi*f*(l2-m)*1j z=1/y+zl2p y=1/z yl1p=1/(rlt*tap+2*math.pi*f*(l1-m)*1j) y=y+yl1p z=1/y zm=2*math.pi*f*m*1j z=z+zm y=1/z gamma=(z-50)/(z+50) rho=abs(gamma) vswr=(1+rho)/(1-rho) return vswr l=n*p #starting guess tap=0.5 c1=20e-12 x0=[tap,c1] res=minimize(vswr,x0,method='Nelder-Mead') print() print("zl:",zl) print('pitch: {:0.5f} m, radius: {:0.5f} m, turns: {:0.2f}, length: {:0.5f} m, Ql: {:0.0f}, Qc: {:0.0f}'.format(p,r,n,p*n,ql,qc)) print() print('VSWR={:0.5f}, tap={:0.3f} (%), c1={:0.5f} (pF)'.format(res.fun,res.x[0]*100,res.x[1]*1e12))

Above is the code, it elaborates the solution in small steps so that it is easier to understand. The script does not do much error checking, it will produce valid results on sane input.

If you play with the Simsmith model, you may find that there is a solution with c1=0 for some load impedances, but in reality, the incidental capacitances mean that c1 is unlikely to ever be exactly zero.

For the enquiring mind, the relevant files are attached: EFmatch.zip.

]]>Firstly lets set the context, a small loop means less than λ/10 perimeter, and untuned is to mean that the loop is loaded directly, in this case by a receiver which we will assume has an input impedance of 50+j0Ω.

Let’s look at the two cases. The key difference is in the connection at the gap:

- the first has a short circuit coaxial stub of half the perimeter between the inner conductor at the right side of the gap and the outer surface of the outer conductor at the right side of the gap; and
- The second directly connects the inner conductor at the right side of the gap and the outer surface of the outer conductor at the right side of the gap.

Above is a diagram of the loop.

The second case appears in the article Small untuned loop for receiving – it’s not rocket science.

Above is the detail of a simple shielded loop using 50Ω coaxial cable to a 50Ω receiver at the loop terminals.

The additional coaxial stub inserts an impedance is series with the inner conductor at the gap, the impedance is frequency dependent, and its effect in this scenario is mainly in the inductive reactance of the short circuit stub. The influence of that reactance on the recovered power at the load will depend also on the reactance of the loop itself… which is sensitive to the diameter of the conductor.

In other respects, like depth of nulls, symmetry etc, there should be no difference.

Lets compare the two loop connections for two cases, a 1m diameter loop of RG58A/U another of RG213.

Above is a plot of power out for the two scenarios to 10MHz (where perimeter is just over λ/10. The second configuration with the series stub is the lower output.

Above is a plot of power out for the two scenarios to 10MHz (where perimeter is just over λ/10. The second configuration with the series stub is the lower output.

The difference in this case is slightly more than for the previous case as the main loop inductance is lower by virtue of the larger conductor diameter.

]]>Pictured is a dual UnUn. I made this for experimenting. It’s both a 49 and 64 to 1 UnUn.

The 49 to 1 tap uses the SS eye bolt for the feed through electrical connection and the SS machine screw on the top is the 64 to 1 connection. If I want to use the 49 to 1 ratio, there’s a jumper on the eye bolt that connects to the top machine screw where the antenna wire is attached. The jumper shorts out the last two turns of the UnUn. Disconnect the jumper from the top connection and now you have a 64 to 1 ratio.

The advice to short the section of the winding (the white wire in the pic) is really bad advice.

Tapping an air cored solenoid can be effective and with low loss… can be… but not unconditionally. Tapping a ferrite cored inductor almost always has quite high Insertion Loss, it is akin to shorted turns in an iron cored transformer, … so if you try it, measure it to see if the outcome is acceptable.

Keep in mind that flux leakage degrades broadband performance, so conductors wound loosely around the core (as in the pic) and wide spaced single layer windings (as in the core) tend to have higher flux leakage and poorer broadband performance. Measure what you make to verify that it did what you think.

An S parameter file from a two port sweep over HF would be informative.

I offer this analysis without measurement evidence to prove the case, but sometimes an understanding of basic circuit analysis allows one to avoid wasting time on poor designs.

]]>A correspondent suggested that with a ferrite core, flux leakage is insignificant. This article calculates the coupled coils scenario.

Above is the ‘schematic’ of the balun. Note the entire path from rig to dipole.

Let’s use the impedance measurement with short circuit termination to find the inductance of the two coupled windings in series opposed.

Above is a plot of the impedance, R+jX. X at 1MHz implies L=8.6µH. Remember that this is the inductance of two series opposed coils, so it includes the effect of mutual inductance.

We can estimate reasonably by calculation that the inductance of one coil L1 @ 1MHz is 114µH.

Measurement of a SC termination gave \(L=(L1-M)+(L2-M)=8.6µH \) and since L1=L2 we can calculate \(M=114e-6-\frac{8.6e-6}{2}=109.7\;µH\) and from that the flux coupling factor \(k=\frac{M}{\sqrt {L1L2}}=\frac{109.7}{114}=0.9623\).

So, k is very high, there is very little flux leakage, but not enough to ignore… it has a huge bearing on the outcome.

]]>Above is the ‘schematic’ of the balun. Note the entire path from rig to dipole.

Above is a plot of VSWR from 1 to 51MHz. It starts off at VSWR=2.8 @ 1MHz, not good, and increases with increasing frequency to VSWR=500 @ 30MHz. (The marker label is misleading, it is a significant software defect, the values are not s11 as stated on the chart but VSWR.)

VSWR @ 10MHz is 96.

You might ask how is this different to the case where the two wires were twisted together and 10 turns wound onto the core. They both seem like coupled inductors… and they are, but there is a significant difference is in the extent of coupling, the extent of flux leakage.

A simple measurement of the input impedance of the balun with a short circuit termination gives us a low frequency inductance of around 8.6µH for 0.6m of two wire transmission line, that is around 14µH/m. That is 25 times the inductance if they were wound as a close spaced pair. The capacitance of the wide space wires is lower than if they were wound as a close spaced pair, so both of these and increases loss drive characteristic impedance Zo up to something of the order of 1400Ω, and velocity factor VF down.

Measurement of the short circuit section shows first resonance (antiresonance actually) at 44MHz which allows calculation of VF as 35%.

The combination of extreme Zo and very low VF causes much greater impedance transformation of a 50Ω load than normally desirable, as can be seen from the VSWR plot above.

Let’s compare that simple model of the balun with a simulation

Above is the measured data presented as a Smith chart. For a low Insertion VSWR balun, we would expect the trace to be entirely very close to the prime centre of the chart. This doesn’t even start off there, and just gets worse with increasing frequency.

Though a very simple model, the series transmission line section of Zo=1400Ω ohms and VF=0.35 captures most of the measured behavior.

A more complete model would indicate higher transmission line loss due to the inclusion of the ferrite based inductance in the transmission line distributed inductance. There is little point in measuring the transmission loss as the balun is impractical due to the extreme Insertion VSWR.

There is a simple explanation for the very poor Insertion VSWR of the N6THN balun, it uses a loaded transmission line section with very high Zo and low VF.

If you want low Insertion VSWR in a Guanella 1:1 balun, ensure that Zo of the transmission line section is close to your load impedance.

]]>In this case, it is described in the referenced video as part of a half wave dipole antenna where you might expect the minimum feed point VSWR to be less than 2.

Apologies for the images, some are taken from the video and they are not good… but bear with me.

Above is the ‘schematic’ of the balun.Note the entire path from rig to dipole.

To the experienced eye, it immediately raises questions.

Above is the implementation.

Cursory analysis suggests this will have very poor Insertion VSWR. When used with a low VSWR(50) load like a half wave dipole, the VSWR looking into the balun will be very poor.

Let’s check it out with the ubiquitous nanoVNA.

Since Insertion VSWR is the initial concern, let’s measure Insertion VSWR from 1 to 51MHz. The original video used a #31 core, I have used a #43 as I have them on hand. Not exactly the same, but the same issue arises either way.

The balun was hooked up with an accurate 50Ω load (two tiny 1% 100Ω SM resistors at the left of the balun), and connected to the nanoVNA with a transformer to allow the balun balanced drive. The nanoVNA with the attached transformer is OSL calibrated at the terminal block on the transformer board, so we can measure the DUT with 50Ω termination.

Above is the test configuration.

Above is a plot of VSWR from 1 to 51MHz. It starts off at VSWR=2.8 @ 1MHz, not good, and increases with increasing frequency to VSWR=500 @ 30MHz. (The marker label is misleading, it is a significant software defect, the values are not s11 as stated on the chart but VSWR.)

Above is the same data presented as a Smith chart. For a low Insertion VSWR balun, we would expect the trace to be entirely very close to the prime centre of the chart. This doesn’t even start off there, and just gets worse with increasing frequency.

Above is a plot of the impedance, R+jX. For a low Insertion VSWR balun, we would expect that R would be very close to 50Ω over the whole range, and X would be very close to 0Ω over the whole range. This plot starts off with R=50Ω, X=55Ω @ 1MHz, and R just increases way off scale.

It is hard to find an adjective to describe how bad the Insertion VSWR is, it is clearly a total failure on that count alone.

Read widely, be critical of what you read on social media. In respect of balun designs, look for relevant measurements, think about them, analyse the offering.

]]>Take a look at the antenna with a VNA and sweep with the Phase function.

Let’s do that!

There are lots of competing firmwares for the nanoVNA, and having tried many and found them wanting, I use the latest firmware from ttrftech, the ‘originator’ of the nanoVNA. So, my comments are in the context of that firmware.

Let’s look at display of the magic phase quantity with a very good load on the nanoVNA, you might think of this load as the ultimate goal of an antenna system.

Above is a screenshot of my nanoVNA where I have selected the ONLY display format labelled phase, and it can be seen that the yellow trace appears to be quite random.

Above is a screenshot of nanoVNA Saver which seems the preferred PC client of the masses, again the same good load is attached. The upper left plot is the ONLY phase plot derived from s11, again it is quite random. Also show are plots of impedance (which is very good), VSWR (which is very good), and Return Loss (which is very good). Return Loss might look noisy, and it is, but it is always greater than 65dB… excellent! The only plot that has NO VALUE in this case is the phase plot!

In fact, when the magnitude of s11 becomes very small, the phase of s11 becomes dominated my measurement noise and it worthless. Yes, the closer you approach the Nirvana of VSWR=1 (ReturnLoss very high, |s11| very low), the less value in the phase of s11.

Let’s look at a sweep of a real antenna, a 5/8λ 144MHz vertical on my car, looking into 4m of RG58 feedline.

On this chart, the easiest curve to interpret for most hams is the VSWR curve (magenta). The markers show its minimum (1.09) and the VSWR=1.5 bandwidth (145.05-150.05MHz)… this is a good antenna from that point of view… but it could be improved by lengthening a little to move the frequency for minimum VSWR down to 147MHz (… but there is no adjustment left).

So, look at the Return Loss blue curve. Return Loss is related to VSWR and you could make exactly the same conclusions. We should accept Return Loss > 15dB.

Look at the s11 phase curve in red. It does not cross the zero phase line (the middle of the chart, in this sweep, it is 44° at minimum VSWR even though it is sometimes less at higher VSWR. Can you make any rational conclusion from the phase curve, and does the fact it is not zero condemn the antenna system?

Look at the R and X curves, green and black. Can you draw any conclusions from them directly? Can you see where the phase of R+jX would be zero? Hint: it is where X is zero… but hey, that doesn’t happen with this antenna system.

After all that information overload, the VSWR curve is the key performance indicator, and I could have used an ordinary VSWR meter to come to the same conclusions pretty much.

Yet another example where the focus on s11 phase is so misguided.

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