This article is a desk study of the CirroMazzoni Baby loop.

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.

### Radiation Sphere (for a given antenna)

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.

### Radiation Efficiency

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.

## Loss and Radiation Efficiency

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.

## 7.1MHz

### General analysis

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.

### 2.5m centre height

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.

## 14.2MHz

### General analysis

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.

### 2.5m centre 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.

### Conclusions

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.)

## References / links

- 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.