This article is a natural consequence of that about balanced antenna for VLF, this time no longer investigating the antenna itself, but its "relationship with the surrounding world." We take a moment for the "train of thought", that is, the reasons that led us to develop an active antenna for VLF and ELF of balanced type. The "classics" electric field sensors (like "audio antenna") are typically characterized by: sensitivity proportional to the equivalent heigh receiving only of vertical polarization useful band "limited" at the lower frequencies, also due to the "microphonics effect they suffer". These characteristics “complicate the life” of those who want to go "beyond listening," but do real study of the signals.

The balanced short dipole
The balanced antennas, as we have seen, have built-it the theoretical capacity to overcome these limitations, at least for the most part. It must, however, be installed and connected correctly so as not to frustrate all the advantages.
To get to the general case, we will take a cue from a series of experiments made on the dual polarization antenna, already published on these site.
From the first recordings made on the field, comparing the two polarizations there were no significant differences. Then here came the question: am I really getting into the differential? An important confirmation came from an exchange of views with my friend and expert Renato IK1QFK: he confirmed that the horizontal and vertical fields (electric or magnetic) have to be received very different, such as shown in the following spectrograms .

Who will ever be responsible?
As with all the differential structures, the "culprit" in these cases, is an insufficient CMRR!
Before go further in particular, let see a small explanation.
The common mode rejection ratio CMRR or (acronym from: Common-Mode Rejection Ratio) indicates the tendency of a differential amplifier to reject signals that came to both inputs. An high CMRR is important in applications where the signal of interest is represented by a small voltage fluctuation superimposed to a voltage offset (potentially large), or when the relevant information is contained in the potential difference between two signals.

To calculate the CMRR, you must first define two gains as follows:
Ad differential gain, ie proportionality between the output signal and the difference of the inputs



Acm common mode gain, ie proportionality between the output signal and the common level of the inputs



where Vo  is the output voltage from the amplifier, V+ and V-, the two input voltages Vs and the input voltage applied in equal measure to both inputs.
The CMRR, which is measured in decibels, is now defined by the following equation:

The antenna is considered 4m above the ground, the sensors vertically stacked and  spaced 100mm and the receiver powered by a coaxial cable.
Doing a little of accounts, the relationship between differential field (wanted) and common mode (unwanted) result:



So, with this geometry, if we want the common mode signals do not appear evident in the differential reception, we need 32 "extra dB" of CMRR, to add insulation between modes (at least 30-40dB).
When you try to receive horizontal polarization, we must also keep in mind how the signals are generally lower than the vertical component, and then the "necessity" of CMRR also increases significantly.
From these initial observations, we can say that a CMRR of 80 dB is a reasonable requirement for all situations.
From this point of view, the performance of the component used (INA155) give us assurances. Unfortunately, as we shall see in the following, the values of the datasheet are "best case" and any external component to the amplifier ends to degrade the overall performance.
Continuing the analysis, the first elements to be put "under discussion" in these cases are the power supply line and the direct connection between antenna and receiver. Unfortunately, their liability is limited (but significant!) and also feeding the antenna with a battery on board and installing an electrically isolating transformer along the signal path  do not improve dramatically the situation.

Serching for the guilty..
Said that, it remain the coaxial cable by itself to be investigated. But what role does play the cable? His "sin" is to connect the antenna to the receiver or there is "something else"?
Let slice the problem in smaller pieces and lets try to understand.
First, we redraw the circuit diagram, by inserting the elements sensors with their mutual capacity (C11 and C12), to the ground (C9 and C10) and the parasitic parameters of the structure, in particular the capacity to earth, synthesized in C8.

where: Cp_eq: equivalent capacitance to ground of antenna (and of everything connected to) CAG: capacity of the sensors to ground Zin: input impedance of the amplifier The capacity of the sensors to the ground and the antenna (and connected devices) are in series with the the common mode E-field ! Let try to describe the situation with the help of some equations, emphasizing the circuital parameters. For simplicity of writing, we define the value Cs as the capacity equivalent to the series of Cp_eq and Cag.

Schematization of the receiving system for the purposes of sensitivity to common mode signals

The common mode signal (undesired) at the output of the amplifier will be:



Differential signal (wanted)



The optimal situation occurs looking for the maximum of the following function:


where:

• Zin: input impedance of the differential amplifier
• d: spacing of the sensors
• h: height of the sensors
• CMRRINA155: the CMRR of the instrumental amplifier

Unfortunately, even without developing more complex calculations, it is visible that "the blanket is too short" and any optimization of a variable will be in conflict some other(s).
It 'worth noting the following two ratios:



since the spacing of the sensors is always much smaller that the equivalent height



...decreases with increasing of Cp

which is equivalent to recognize that all the mechanical on constructive components of the antenna, go in the direction of reducing the CMRR of the real system.

If the actions on the geometry of the antenna and its installation can be quite intuitive and limited only by their your imagination and building capacity, it is interesting to see an optimal solution to minimize the ability of the structure to the ground, removing the coaxial cable that carries the signal to the receiver. A big help comes from the world of audio, which now provides a very low cost analog-to-digital converter, with SPDIF optical digital output. An example is shown in the image.

• antenna
• A/D converter with optical output
• signal path into the optical fiber
• sound card with optical input
• Personal Computer

1. vertical polarization antenna, amplifier standard configuration
2. vertical polarization antenna, amplifier with the two inputs connected together at the same sensor
3. horizontal polarization antenna, amplifier standard configuration

Vertical polarization (on left) and horizontal polarization (on right)

• insulated antenna mounting
• self-powered (solar panel & on board battery for example)
• transmission of the digitized signal over an optical fiber