Longwave (defined here as 500 Hz–500 kHz) radio science drives many scientific and engineering applications, including lightning detection and geolocation, subsea and subsurface sensing and communications, navigation and timing, and ionospheric and magnetospheric remote sensing. The hardware performance (i.e., sensitivity and bandwidth) of the receivers that detect long waves determines the maximum amount of information that can be extracted from the acquired data. In this paper, we present and describe an ultra-sensitive electric field receiver that enables broadband radio reception from near-DC up to 470 kHz, augmenting the legacy of the “Atmospheric Weather Electromagnetic System for Observation Modeling and Education” (AWESOME), a state-of-the-art magnetic field receiver completed previously. The AWESOME electric field receiver uses capacitive coupling with a dipole antenna to detect the electric field components of long waves and attains a sensitivity of 0.677 nV/(mHz). This sensitivity allows the detection of natural radio atmospherics and man-made beacon emissions at a global range. The AWESOME electric field receiver can also be integrated with a magnetic field sensor for simultaneous electric and magnetic field reception. In this paper, we detail the design of the receiver, including the receiver architecture, its working principles, design methodology, and trade-offs. We showcase the receiver performance characterized through both numerical models and empirical measurements. We demonstrate a novel calibration method that is quick and straightforward, suitable for deployments in the field. Finally, we demonstrate some novel applications enabled by this receiver’s excellent sensitivity and simultaneous reception capability of electric and magnetic field components of long waves.

Longwave radio science has been a prominent field of scientific research and engineering development for well over a century. While the longwave spectrum encompasses numerous bands—including ELF (extremely low-frequency; 300 Hz–3 kHz), VLF (very-low-frequency; 3 kHz–30 kHz), LF (low-frequency; 30 kHz–300 kHz), and MF (medium-frequency; 300 kHz–3 MHz)—we define long waves, in this paper, as radio waves of any frequency between 500 Hz and 500 kHz. Long waves, also referred here to as LF waves, are used in various applications due to their relatively long wavelength, long-range propagation, and relatively high penetration into conductive materials.

The first detection of naturally radiated LF waves was serendipitously made in the late 19th century by early telegraph line operators when LF emissions from lightning audibly coupled to long telephone and transmission lines.1,2 They were named clicks, grinders, and sizzles due to the sounds heard by the operators. More deliberate experiments were then conducted to study the nature of these LF waves. The first such attempt was made by Popov in 1895 using a long vertical wire connected to an early radio detector. By observing the LF waves detected by his apparatus, he saw a direct correlation between lightning flashes and LF emissions. Similar experiments were carried out in the following decade that resulted in similar conclusions. By the end of the 19th century, natural LF waves were positively correlated with numerous atmospheric events such as cyclones, polar fronts, and thunderstorms.3 

While these developments were taking place in the reception of LF radio, great strides were also being made on the transmission side. After the conception of the idea to use radio waves to transmit information over long distances, Guglielmo Marconi’s famous spark gap experiments made breakthroughs in the range of wireless radio transmissions. The first breakthrough happened in 1895 when Marconi grounded a spark-gap oscillator and connected it to an elevated wire antenna. With this setup, he was able to break the 0.5-mile range that was theorized to be the upper limit for how far successful radio transmissions could take place. The second breakthrough happened in 1901 when Marconi used his spark-gap transmitter in Cornwall, England, to transmit the letter “s” in Morse code over the Atlantic Ocean and this transmission was received, although disputably, by a 150-m kite-supported antenna in Newfoundland, Canada. While the exact frequency of this transmission was not recorded, it is believed to be around 800 kHz. Marconi assumed that his transmitted radio waves were guided by diffraction from the Earth’s conducting surface, mostly comprised of seawater in this case. In reality, however, the radio waves actually propagated across the Atlantic being guided by the charged particles in the upper atmosphere acting as a reflecting conductor, as well as the Earth that acting as a reflecting ground plane. Marconi had not yet had this knowledge, but these charged particles were found to be a layer of the atmosphere residing between the altitudes of 60 km and 1000 km, later named as the ionosphere. This transatlantic radio transmission marked the beginning of using radio as a form of long-range wireless communications.4,5

Following these breakthroughs, the reception and transmission of LF radio became an active research area that gathered great interest. The radiotelegraphy era saw the modulation of LF radio waves to enable worldwide wireless communications in the early 19th century. This boosted the significance of LF radio as LF radio transmitters and receivers became commonplace throughout World War I and World War II.

Military applications have also taken advantage of LF radio. In addition to LF military communications, LF waves were used for navigation purposes during World War II and thereafter. The Decca Navigation System was invented in the US and implemented by the Royal Navy of the UK to be used by Allied forces during World War II. Utilizing LF transmitters, Decca allowed accurate long-range positioning by comparing phase delays of two single-frequency signals at 70 kHz and 130 kHz. Decca remained in both military and civilian use for the rest of the 20th century.6 A similar system, named “Datatrak,” was used for commercial applications and operated in frequencies between 125 kHz and 150 kHz.7 LORAN-C used another method for navigation using LF transmitters emitting short chirp-frequency pulses around 100 kHz. Comparing the times of the received pulses emitted by different transmitters, a LORAN-C receiver could accurately geolocate the user.8 A breakthrough for global positioning was made by the Omega system established by the US. Omega used a network of VLF transmitters that operated between 10 kHz and 14 kHz to enable accurate geopositioning all around the globe.9 A similar system, named “Alpha,” is currently still in use by Russia. Despite slowly being decommissioned, the Nationwide Differential Global Positioning System (NDGPS) network in the U.S. still uses LF waves between 285 kHz and 325 kHz to broadcast correction messages to compensate for the errors added by ionospheric effects to GPS signals and enhance their accuracy.10 

The LF radio has also been widely used for wireless communications between navy submarines and ground stations since LF waves can penetrate seawater 10s of meters deep due to the skin effect. Numerous LF radio beacons have been built and deployed by multiple countries to establish continuous communication links with submarines globally. These beacons use individual electrically large antennas or arrays of physically large antennas with diameters on the order of kilometers. These transmitting antennas are usually umbrella top-loaded monopoles to increase the radiation resistance as much as possible for the greatest radiation efficiency.11,12 On the receiving side, submarines host physically and electrically small antennas in the form of either loop or dipole antennas. Due to their electrically small size, these antennas cannot transmit power efficiently but can be used to receive the immense amount of power radiated by the beacons.13 Similar to seawater, LF waves can also penetrate rock and soil 10s of meters deep. Hence, the LF radio is also used for subterranean imaging, radiolocation, and through-the-Earth mine communications.

After the first detection of natural LF waves, more discoveries have been made regarding the correlation between lightning and LF radio. When a lightning event occurs, an ionized channel between two charged regions of the atmosphere forms. This ionized channel acts as an electromagnetic source and an antenna kilometers long. During such a discharge event, up to 1 GJ of power is released, mostly as acoustic shock waves or thunder, caused by atmospheric gasses experiencing huge increases in pressure and rapidly expanding outward. However, between 0.01% and 1% of this energy is released electrically, radiating a short burst of broadband electromagnetic waves of great intensity from a few Hz to gamma rays.14 However, the bulk of this electromagnetic energy is radiated in frequencies between 1 kHz and 100 kHz and reflects off the lowest layers of the ionosphere.15 By reflecting off both the ionosphere and ground, these radio atmospherics, colloquially named sferics, propagate globally in this Earth–ionosphere waveguide (EIW) with low attenuation (around 3 dB/1000 km).16 Detecting these sferics with even a sparse network of LF receivers hundreds of kilometers apart enables lightning geolocation at a global scale.17,18 This allows sophisticated LF networks to be put in use for global lightning geolocation.

Sferics propagating in the EIW dominate the global atmospheric noise floor at low frequencies,19 a critical phenomenon to consider in designing systems for the engineering applications outlined above. Since this noise floor is filled with pulses of LF waves emitted by lightning, the atmospheric noise floor has been modeled by some as a Poisson arrival process instead of white Gaussian noise.20 

The aforementioned man-made LF transmitters also pump LF waves into the atmosphere that then propagate globally in the EIW. Therefore, emissions in the LF spectrum can be crudely characterized as short bursts of broadband sporadic spikes—sferics—along with narrowband continuous signals.

As both natural and man-made emissions propagate in the EIW, they are altered by the reflections off the waveguide boundaries. For the ground reflection, some power is dissipated depending on the ground surface conditions. As they reflect off the ionosphere, some mode conversion occurs between TE and TM wave modes due to the anisotropy imposed by the geomagnetic field. Additionally, some power escapes through and roughly follows the magnetic field lines of the Earth.15 These so-called whistlers, named after the sounds they make as they couple to the telephone and telegraph lines, may go back through the ionosphere again on the other end of the magnetic field line and can be detected by a sensitive receiver. The plasma mode of wave propagation is named the whistler mode for this reason, reflecting right-hand circular polarization below the plasma frequency in magnetized plasma. Since these waves propagate through the ionosphere and near-Earth space environment, detecting them is useful for monitoring these environments globally without any need for satellites or sounding rockets.2 

A more useful diagnostic for monitoring the ionosphere and the near-Earth space environment is detecting the power that is trapped in the EIW. As these waves interact with the lowest layers of the ionosphere, their waveforms are altered. However, these alterations are sensitive to the ionospheric conditions, which are affected by various terrestrial and celestial events, including but not limited to solar flares, general solar x-ray activity, solar eclipses, gamma-ray bursts, lunar tides, geomagnetic storms, and lightning-generated electromagnetic pulse (EMP).21 How these events affect the ionosphere can be monitored by detecting LF waves and analyzing their propagation in the EIW. This monitoring is named ionospheric remote sensing, and it is a powerful diagnostic tool in geophysics.

LF receivers are the first step in data acquisition and analysis, and the maximum amount of information that can be extracted from the physical system is set by the hardware performance of these receivers. While the hardware performance has several key characteristics that set the quality of recorded data, the most important parameter is the system sensitivity. The sensitivity of the system characterizes the minimum signal a sensor can detect with a specific signal-to-noise ratio (SNR) per unit bandwidth. Lowering this parameter (or raising the sensitivity) improves the quality of the data recorded by the system, and most LF receiver designs strive to improve this parameter especially in remote sensing applications.

Ultra-sensitive LF receivers have become more sophisticated as new signal processing techniques and data storage technologies allowed ultra-low-noise components and devices readily available for system use. Modern LF receivers can be categorized as magnetic field receivers and electric field receivers based on how they interface with the LF waves propagating in the environment.

Magnetic field receivers use magnetic induction to detect the magnetic field components of LF waves. Most notable LF magnetic field receiver designs include the Atmospheric Weather Electromagnetic System for Observation, Modeling, and Education magnetic field receiver, or the AWESOME magnetic field receiver, developed at Stanford University and the Georgia Institute of Technology. Multiple iterations of the AWESOME magnetic field receiver have been developed, but the most recent iteration attains a sensitivity of 0.03 fT/Hz with an operating frequency range between 0.5 kHz and 470 kHz.21 AWESOME magnetic field receivers have been deployed globally over the past two decades for various geophysical experiments and international collaborations22–25 and to form the hardware basis of the global GLD360 lightning detection and geolocation network.17,18,26 Recently, a large repository of data known as the Worldwide Archive of Low-Frequency Data and Observations (WALDO) was set up to also make global AWESOME data collections publicly available.27 Designs of other iterations of the AWESOME magnetic field receiver can be found in Refs. 28–30. Other compact LF magnetic field receiver designs have also been developed to be used in satellites for space research. One of these designs achieved a sensitivity of 4 fT/Hz with the frequency range between 1 Hz and 20 kHz.31 Another notable design is presented in Ref. 32.

Electric field receivers, on the other hand, use capacitive coupling to detect the electric field components of LF waves. There have been fewer published electric field receiver designs due to the challenge of calibration and greater dependence of its noise level on a meticulous front-end circuit design. However, one notable electric field receiver design is described in Ref. 33. An early LF instrument that uses a combination of both electric field and magnetic field sensors is also presented in Ref. 19. Finally, a comprehensive report of LF receiver design methods and trade-offs is presented in Ref. 34. In this paper, we describe a novel end-to-end electric field sensing system, named the AWESOME electric field receiver, that achieves excellent sensitivity with broadband reception capability. While magnetic field receivers are more commonly used for LF radio reception, an electric field receiver, especially when used with a magnetic field sensor, could unearth valuable additional information that could otherwise not be extracted by a magnetic field receiver alone. Therefore, we also demonstrate a few selected novel applications enabled by the AWESOME electric field receiver. Early iterations of this receiver design can also be found in Refs. 35 and 36.

This paper is structured as follows: Sec. II describes the system architecture and components along with their design methodologies and trade-offs. Section III showcases a quick and straightforward calibration method that does not require any specialized equipment. Section IV shows the amplitude response and sensitivity of the receiver characterized empirically. Section V demonstrates several novel applications enabled by this ultra-sensitive receiver. Section VI concludes the paper with a summary of the results and findings.

The electric field receiver is comprised of two main sections, the front end and the back end. The front end contains a dipole antenna and two preamplifiers. The dipole antenna is directly attached to the first preamplifier, named Pre2amp, which includes a custom ultra-low-noise differential amplifier (ULNA) and a driver. Pre2amp is connected to the second preamplifier, named Preamp, via a Cat5e Ethernet cable with three 100-Ω shielded and twisted pairs. The Preamp board or card includes low and high-pass filters, an attenuator, and a driver to drive the signal to the back end. The Preamp card is mounted on a backplane board enclosed by a metal box along with two other cards, allowing the electric field receiver to be used simultaneously with two channels of another receiver—such as two channels of data coming from the two orthogonal loop antennas of a magnetic field receiver.

The back end is identical to the one described by Ref. 21 in detail and contains a line receiver and a data storage unit with a recording software. The line receiver has a GPS synchronization circuitry, anti-aliasing filter, an instrumentation amplifier, and an analog-to-digital converter (ADC). After the incoming data from the front end is processed by the line receiver, the data are sent to a computer, where software saves the data locally or sends them over the internet.

The front end and back end are connected via a specialized audio cable (1217B) made by Belden with four 75-Ω twisted and shielded pairs that drives the signals from the front end to the back end and power from the back end to the front end.

Top panels in Fig. 1 show photographs of the front end, and the bottom panel details the workflow of the receiver in the form of a block diagram. Now, we will go on to explain each system component described in this section in more detail.

FIG. 1.

Photographs and block diagram of the AWESOME electric field receiver. Top left panel: Pre2amp with a connected dipole antenna. Middle left panel: the Preamp card mounted on a backplane with two preamplifier cards of the AWESOME magnetic field receiver, all enclosed in a metal box. Top right panel: front-end waterproof setup showing Pre2amp with a dipole in a polyvinyl chloride (PVC) pipe connected to the Preamp box via a Cat5e Ethernet cable. Bottom panel: block diagram of the receiver showing the system workflow. Switches, S1 and S2, reroute the signal path based on the desired frequency response for data collection.

FIG. 1.

Photographs and block diagram of the AWESOME electric field receiver. Top left panel: Pre2amp with a connected dipole antenna. Middle left panel: the Preamp card mounted on a backplane with two preamplifier cards of the AWESOME magnetic field receiver, all enclosed in a metal box. Top right panel: front-end waterproof setup showing Pre2amp with a dipole in a polyvinyl chloride (PVC) pipe connected to the Preamp box via a Cat5e Ethernet cable. Bottom panel: block diagram of the receiver showing the system workflow. Switches, S1 and S2, reroute the signal path based on the desired frequency response for data collection.

Close modal

Different types of antennas are suited better for the detection of different components of LF waves. Magnetic field receivers usually employ ferrite-core or air-core loop antennas, whereas electric field receivers usually use monopole or dipole whip antennas. A key characteristic in the LF antenna design is antenna sensitivity, which contributes to the system sensitivity described in Sec. I. For both electric and magnetic field antennas, we define antenna sensitivity as the field equivalent of the antenna noise, namely, a normally incident field that would induce the same open circuit voltage as the antenna noise over a 1 Hz bandwidth. Hence, similar to Ref. 34, we broadly define the antenna sensitivity for any antenna as

Sa=VnGa,
(1)

where Vn is the antenna noise spectral density and Ga is the open-circuit voltage gain of an antenna in a system, shown in Fig. 2. This definition describes the lowest field magnitude an antenna can receive before it is dominated by the antenna noise. We will now derive the antenna sensitivity expressions for both electric and magnetic field antennas and compare them. For clarity, in these derivations, we will be using exponents, m and e, on top of variables that correspond to the parameters for magnetic and electric field antennas. Variables without these exponents correspond to both electric and magnetic field antennas.

FIG. 2.

Equivalent circuit model of an arbitrary receiving antenna in a system.

FIG. 2.

Equivalent circuit model of an arbitrary receiving antenna in a system.

Close modal

The coupling of incoming waves to magnetic loop antennas is governed by Faraday’s law of induction. Electromagnetic waves induce a time-varying electric potential across the antenna terminals. At low frequencies, the induced open-circuit voltage can be approximated as Vam=jωNaAaBicos(θ), where Na is the number of turns, Aa is the loop area, Bi is the magnetic flux density, and θ is the angle of incidence of the incoming wave. This approximation is valid due to the electrically small size of a loop antenna. Assuming that the incoming wave satisfies the far-field conditions (i.e., Ei/Bi = c, where c is the speed of light) and is normally incident to the loop, we can derive the open-circuit voltage gain of any loop antenna as Gam=VamEi=2πNaAaλ, where λ is the wavelength and Ei is the electric flux density. To derive the voltage noise spectral density of the loop, we need to define the antenna resistance.

For low-loss conductive antennas in free space, the antenna resistance can be modeled as the radiation and loss resistances in series with each other, Ra = Rr + Rl, where Rr is the radiation resistance and Rl is the loss resistance for both electric and magnetic field antennas. It is worthwhile to investigate the non-linearities of both resistances as they determine the behavior of the antenna sensitivity responses over the LF spectrum.

For electrically small loop antennas, radiation resistance could be approximated as Rrm=8ηπ3(NaAa)23λ4, where η is the intrinsic impedance of the medium (approximated here as the intrinsic impedance of free space, η0 = 120π). For short electric field antennas (monopole or dipole), the radiation resistance is calculated as Rre=20πLaeλ2, where Lae is the total wire length, meaning that the radiation resistance of a monopole is half of that of a dipole in an ideal environment (i.e., monopole with a perfect ground plane in free space and dipole in free space). Loss resistances of both magnetic and electric field antennas can be defined by a piecewise function of two regions to account for the skin effect. The DC region is where the skin depth of the wire is greater than or equal to the wire radius, whereas the AC region is where the skin depth is less than the wire radius. Therefore, the loss resistance is calculated as Rl=4ρLaπd2δ>d2ρLaπδ(dδ)δd2, where d is the wire diameter and δ is the skin depth of the antenna wire defined as δ=ρλπcμ, where ρ is the wire resistivity and μ is the permeability of the wire, approximated here as the permeability of free space. To get rid of the piecewise expression in the derivations, we assume that the loss resistance is comprised of only the DC region expression, but we add a correction function, f(λ), to include the AC resistance. Hence, the loss resistance is approximated as

Rl=4ρLaπd2f(λ)=4ρLaπd2(915.6λ0.5149+0.683),
(2)

where f(λ) is the correction function shown in (A2). This correction function is determined by curve fitting a model power function to a modified version of the loss resistance expression. This regression analysis and its goodness-of-fit parameters are described in the Appendix.

For electrically small loop antennas and electrically short monopole and dipole antennas, the total resistance is dominated by loss resistance at low frequencies. For loop antennas, Johnson–Nyquist or thermal noise of this resistance is Vnm=4kBTRlm, where kB is the Boltzmann constant and T is the temperature in Kelvin. Thus, we can derive the loop antenna sensitivity as

Sam=2λπNaAadkBTρLamπf(λ).
(3)

Equation (3) shows that for differently shaped loop antennas with the same Na, the shape that has the lowest Lam/Aa offers the best sensitivity. This most optimal shape is a circle, so for comparison purposes, we will be using a circular loop antenna, meaning Aa=(Lam)24πNa2. Therefore,

Sam=8NaλLamdkBTρπLamf(λ).
(4)

Another step that will improve this expression is to relate the sensitivity to the two critical characteristics for receiver deployment, antenna weight, and size. The antenna weight can be expressed by the mass of the antenna, calculated as

Ma=14πd2Laσ,
(5)

where σ is the wire mass density. The antenna size can be expressed by the height of the loop antenna, defined as ham=LamπNa. Hence, rewriting (4) as a function of height and mass,

Sam=2dσλMamkBTρNahamf(λ).
(6)

We can apply the same derivation for an electric field antenna, relating its size and weight to its sensitivity. The time-average power of an incident traveling wave is calculated as Pī=Ei22η, where Ei is the incident electric field amplitude, or electric flux density, and η is the intrinsic impedance of the medium (approximated here as the intrinsic impedance of free space, η0 = 120π). Coupling of this power to the antenna is calculated as Pa=PīAem, where Aem is the antenna aperture. For any LF antenna, the antenna aperture is defined as Aem=λ2DRr4πRa, where D is the antenna directivity. Then, in air, the coupled power can be calculated as

Pa=Ei2λ2DRr960π2Ra.
(7)

For a system as shown in Fig. 2, the received power by the load is calculated as PL=12Re{ILVL}=12Va2RL|Za+ZL|2. Hence, for a conjugate matched load, i.e., ZL=Za*,

PL=Va28Ra.
(8)

Using (7) and (8), we can derive the open-circuit voltage gain of any electric field antenna given that Pa = PL for a conjugate matched load,

Gae=λDRre2π30.
(9)

Substituting Rre in (9),

Gae=LaeD6.
(10)

Equation (10) shows that the open circuit voltage gain of a short electric field antenna is entirely dependent on the antenna directivity and length. Therefore, to maximize the signal-to-noise ratio (SNR), a longer antenna is desired.

As mentioned earlier, the total electric field antenna resistance is dominated by loss resistance at low frequencies, meaning that the voltage noise of an electric field antenna could be approximated as Vne=4kBTRle. Therefore, using (1), the electric field antenna sensitivity is derived as

Sae=4d6kBTρπDLaef(λ).
(11)

We now include the antenna mass and height in this expression. For mass, expression (5) can be used, and for height, hae=Lae can be used. Therefore,

Sae=dσMae6πkBTρhaeDf(λ).
(12)

Since we now have sensitivity expressions for both electric and magnetic field antennas, we can compare the sensitivities of electric field and magnetic field antennas by dividing (12) by (6). Hence,

SR=SaeSam=12λ6πhaehamDNa.
(13)

Equation (13) gives an expression of the sensitivity ratio of electric field and magnetic field antennas of the same mass. We can set the heights of electric field and magnetic field antennas equal to each other (hae=ham=ha) to obtain an expression that gives the ratio of sensitivities of electric field and magnetic field antennas when they have the same height as well as mass,

SR=ha2λ6πDNa.
(14)

We can further simplify (14) by specifying the electric field antenna directivity. For this, we need to determine whether to use a dipole or a monopole for the electric field antenna. While monopole antennas have double the directivity of dipole antennas, dipole antennas have other advantages over monopole antennas, such as allowing the receiver to have differential architecture, crucial for eliminating the common-mode noise in the system. Therefore, we used a dipole antenna in this design, allowing us to substitute 1.5 for D. Therefore,

SR=haλπNa.
(15)

If this ratio is smaller than 1, the electric field antenna sensitivity is theoretically better than that of a magnetic field antenna and vice versa if it is larger than 1. The worst case scenario for electric field antennas is when Na is 1 turn. Therefore, a frequency sweep of this expression when Na = 1 for various ha is shown in Fig. 3.

FIG. 3.

Sensitivity ratio of electric field and magnetic field antennas of the same mass with varying ha when Na = 1. For Na = 1, SR < 1 when ha < 170 m.

FIG. 3.

Sensitivity ratio of electric field and magnetic field antennas of the same mass with varying ha when Na = 1. For Na = 1, SR < 1 when ha < 170 m.

Close modal

As shown in Fig. 3, electric field antennas theoretically have significantly better sensitivity than magnetic field antennas in the LF spectrum when the antennas are small (ha < 170 m). Furthermore, the sensitivity and gain responses of electric field antennas can be further improved by top-loading the antennas and effectively increasing Lae without changing hae. Due to the excellent sensitivity of electric field antennas, the system sensitivity of electric field receivers is limited by the front-end amplifier noise rather than their antenna thermal noise. This is opposite to the case of magnetic field receivers, whose system sensitivity is limited by their antenna thermal noise.34 This allows the sensitivity of the electric field receiver to be improved by replacing the front-end amplifier, and in most cases only the amplifier’s first stage, with each improved amplifier design.

For the AWESOME electric field receiver, we use a dipole antenna made out of 16 AWG copper wire. The antenna sensitivity of a dipole antenna in the LF spectrum is calculated (using the piecewise loss resistance expression) and shown in Fig. 4.

FIG. 4.

Sensitivity of a dipole antenna of varying antenna lengths.

FIG. 4.

Sensitivity of a dipole antenna of varying antenna lengths.

Close modal

While the dipole antenna’s noise level is quite low, another noise source caused by the antenna parameters affects the receiver system noise. Compared to magnetic loop antennas, electric field antennas have significantly higher capacitive reactance at low frequencies. Highly capacitive reactance of the dipole significantly increases the input impedance, causing any current noise leaking from the amplifier’s first stage to add to the system voltage noise. Therefore, for the amplifier design, finding the dipole input impedance as accurately as possible is crucial.

In order to find the dipole input impedance, we note that all the expressions we have derived so far assumed far-field behavior of LF waves as they interact with the antenna. However, deriving an expression for the input impedance of a dipole requires an exhaustive analysis of the near-field behavior. The induced EMF (IEMF) method is one numerical method used to analyze the near-field behavior and derive a closed-form expression of the dipole input impedance, as shown in Ref. 37. Defining the input impedance as Za = Ra + jXa, we calculate the input resistance and reactance of a dipole antenna,

Ra=Rl+Rr=4ρlπd2+20πlλ2,δ>d2,ρlπδ(dδ)+20πlλ2,δd2,
(16)
Xa=η4πsin2(βl/2)2Si(βl)cos(βl)Si(2βl)2Si(βl)+sin(βl)Ci(2βl)2Ci(βl)+Ci(βd2/2l),
(17)

where η is the intrinsic impedance of free space, E is the Euler constant, β is the phase constant, Si is the sine integral, and Ci is the cosine integral. l is the effective antenna length to account for the gap between the wires of the dipole and is defined as l = L2/(Lx), where x is the gap distance and L is the total wire length of the dipole. For an electrically small dipole, (16) and (17) could be approximated as

Ra=4ρlπd2,δ>d2,ρlπδ(dδ),δd2,
(18)
Xa=120ln(l/d)1tan(βl).
(19)

For different dipole lengths, input resistances and reactances from (16) and (17) using IEMF are calculated over the LF spectrum. Then, each dipole was modeled and simulated with method-of-moments (MoM) analysis and compared with the IEMF results in Fig. 5. As shown in Fig. 5, both models provide fairly consistent results. Furthermore, capacitive input reactance significantly dominates over the input resistance.

FIG. 5.

Modeled input impedances of dipole antennas of different lengths using IEMF and MoM over frequency. (a) Input resistance. (b) Input reactance.

FIG. 5.

Modeled input impedances of dipole antennas of different lengths using IEMF and MoM over frequency. (a) Input resistance. (b) Input reactance.

Close modal

While these models of a dipole in free space provide us with an estimated value of the dipole impedance—accurate enough to serve as a starting point for the Pre2amp design—impedance modeling of a dipole in a real environment requires a more exhaustive analysis. This is caused by the capacitive coupling between the antenna and the surrounding environment, whose effect can be modeled in Fig. 2 as a shunt capacitor with an unknown value. Since this value is unknown and heavily dependent on the environment the antenna is placed in, determining a precise and accurate value for the dipole impedance requires real-time measurements of the dynamic environmental conditions in the near-field region of the antenna.

As shown in Sec. II A, the ULNA in Pre2amp should be designed concurrently with the antenna. Hence, for the amplifier design, we need to use the previously calculated antenna parameters. The circuit design of the ULNA is shown in Fig. 6. The ULNA is made out of two cascaded stages. The first stage serves as both the buffer and the primary amplification stage, and the second stage provides additional variable gain while increasing the common-mode rejection ratio (CMRR) of the ULNA. The amplifier is powered by a differential supply (±10.8 V) driven from the Preamp. A resistor divider with a buffer is used between the rails to create a virtual ground. Instead of driving a ground cable, a virtual ground is used to keep all signals and power differential, minimizing noise and distortion coupled from external sources. This also eliminates the need for a fifth wire to be driven between Pre2amp and Preamp and enables a compact signal and power transmission with two differential wire pairs. A buffer between the resistor divider and Pre2amp circuitry is needed due to possible loading. The buffer is an op-amp in the unity-gain configuration. This op-amp was chosen to be OPA211, a unity-gain stable op-amp with 1.1 nV/Hz RTI (referred-to-input) voltage noise spectral density.38 

FIG. 6.

Differential ultra-low noise amplifier circuit schematic. First stage provides high input impedance and gain. Second stage provides additional variable gain and drives the signal to Preamp.

FIG. 6.

Differential ultra-low noise amplifier circuit schematic. First stage provides high input impedance and gain. Second stage provides additional variable gain and drives the signal to Preamp.

Close modal

Since the dipole antenna serves as the interface between the front-end circuitry and the incoming electromagnetic waves, signals coming from the dipole are highly susceptible to distortion and SNR degradation before they are amplified. Furthermore, having any load such as a long microstrip line or a cable between the antenna and the front-end circuitry could result in loss in signal amplitude due to parasitic capacitances. Therefore, the antenna is directly connected to the inputs of the Pre2amp first stage on the same board with traces as short as possible. For the same reason, the design of the first stage is critical for the successful operation of the receiver.

Since the dipole impedance is the source impedance for the amplifier’s first stage, the first stage needs to be designed according to the source impedance over the LF spectrum. First, as discussed earlier, due to the high source impedance at low frequencies, the voltage noise equivalent of the current noise can be significant if the input current noise of the first stage is not minimized. Second, the input impedance of the first stage and the output impedance of the dipole form a voltage divider. Therefore, the magnitude of the transfer function of this voltage divider can be approximated as

|T(s)|=Rin2+Xin2Rin2+(Xa+Xin)2,
(20)

where Rin is the input resistance of the first stage and Xin is the input reactance of the first stage. For maximum voltage transfer, namely, |T(s)| = 1, the first stage should have a high input resistance and a low input capacitance.

There are various devices that satisfy either or both of these requirements. Due to their low input resistance and high noise, bipolar junction transistors (BJTs) are not suitable for the first stage. Field-effect transistors (FETs), on the other hand, have high input resistance and low noise, making them suitable for this design. Among FETs, junction field-effect transistors (JFETs) have the lowest flicker noise while offering high gain, making them advantageous to be used in the first stage.

There are various off-the-shelf discrete JFETs that offer low RTI voltage and current noise. However, current noise is the most important factor in choosing the right JFET. LSK389A from Linear Systems is a JFET pair that has an RTI voltage noise spectral density of 1.3nV/Hz at 1 kHz, a full conduction transconductance of 20 mS, an input resistance of 1 TΩ, and an input capacitance of 22 pF.39 This JFET pair is used as a common-source amplifier in the first stage. The connection between the first stage and the dipole should also be designed carefully. Since any cable or connector would add significant input capacitance, the dipole is directly soldered onto the pads on Pre2amp, which are connected to first-stage inputs. Traces from these pads to the ULNA are kept as short as possible to minimize parasitic capacitance from the traces [0.05 pF/1 mm for a standard printed circuit board (PCB)]. Shunt resistors at the inputs of the first stage in order to create a return path for the input bias currents are also not necessary due to the extremely small input bias currents of LSK389A. This is beneficial as any resistor at the input would add significant thermal noise to the receiver.

In order to minimize the noise contributions of subsequent stages, the first stage voltage gain is maximized while maintaining linearity. To achieve this, the gain is usually set so that the amplified signal is within the dynamic range of the back-end analog-to-digital converter (ADC). However, in this design, the gain is set so that the input signal is amplified beyond the ADC clipping voltage. Then, the signal is attenuated in Preamp before driving the signal to the ADC to prevent the ADC from being saturated. This is required due to the excellent sensitivity of the receiver as even the smallest noise from subsequent stages will have a substantial effect on the overall sensitivity. Therefore, the first stage gain is maximized at 36 dB so that the amplified signal is at the ceiling of the first stage dynamic range, which is 6.8 V. This puts the maximum input voltage the first stage can amplify at 0.1 V.

LSK389A is a tightly matched pair with a differential gate-to-source cut-off voltage, |VGS1 − VGS2|, of 6 mV.39 However, with a gain of 36 dB, this voltage difference adds an offset to the output of around 0.4 V. This offset could be significant especially when the input differential signal is large, since this offset might clip one of the output lines. In order to mitigate this, a variable resistor of 10 Ω, RV, is added at the source of the JFETs. The resistance of RV is tuned until |VGS1 − VGS2| is 0, eliminating any DC offset at the output.

Finally, the bias current for the first stage is supplied by a low-noise BJT pair, SSM2212, which has an RTI voltage noise of 0.85 nV/Hz and a current gain of around 600.40 This current mirror supplies 4 mA current to the first stage.

The second stage is comprised of two instrumentation amplifiers, AD8429, with an RTI voltage noise spectral density of 1 nV/Hz and an RTO (referred-to-output) voltage noise spectral density of 45 nV/Hz. Differential input instrumentation amplifiers are used in order to improve the CMRR of the ULNA and increase the dynamic range by driving two outputs from the first stage into two differential input pairs in the second stage. There is, again, no need for shunt resistors to create a return path for input bias currents as the input bias current (150 nA) for the second stage is within the range of the output current that can be supplied by the first stage.

Furthermore, the second stage provides additional variable gain to the ULNA. The variable gain of the instrumentation amplifiers is between 0 dB and 80 dB, which is set by R6. Overall, with the first stage, the ULNA has four gain configurations: 42 dB, 62 dB, 82 dB, and 102 dB. These gains are set when R5 is open, 667 Ω, 60.6 Ω, and 6 Ω, respectively. The nominal bandwidth of the ULNA is 2.2 MHz (6 Hz–2.2 MHz), enabling broadband radio reception. However, the highest gain setting caps the bandwidth at 150 kHz, and, therefore, should only be used when signal detection at only ELF/VLF is desired. Finally, the maximum differential input signal amplitude that is within the dynamic range of the ULNA is the same as that of its first stage, which is 100 mV.

The second stage also drives the signal through the potentially long cable between Pre2amp and Preamp. This cable is a shielded Cat5e Ethernet cable with 52 pF/m capacitance. With the 10 000 pF capacitive load driving capability, the ULNA can drive any Cat5e Ethernet cable shorter than 192 m, enabling great flexibility in the placement of Pre2amp and dipole antenna.

Selection of the parts is also important in such a low-noise circuit as various types of discrete components add different levels of noise to the system. The components used in Pre2amp and their types are shown in Table I. Resistors have two uncorrelated noise components: thermal noise and excess noise (noise generated in excess of the thermal noise). Thermal noise is independent of the component type and is a characteristic of the resistance value. In order to minimize thermal noise, resistor values ought to be minimized without adding distortion to the system or compromising the system stability. Excess noise usually manifests itself as flicker noise depending on the material the resistor is made out of and the manufacturing process. Out of all resistor types, discrete wire-wound resistors have the lowest excess noise; however, they usually have inductive elements associated with them, allowing external parasitics to couple to the circuit. Integrated thin film resistors have slightly higher excess noise, but they do not have any inductive effects and are more convenient to use due to their small size.41 

TABLE I.

Component list for Pre2amp.

DesignatorComponent typeComponent value
J1, J2 Low-noise JFET pair LSK389A 
Q1, Q2 Low-noise BJT pair SSM2212 
U1, U2 Instrumentation amplifier AD8429 
R1, R2 Thin film resistor, 0.01% 10 kΩ 
R3 Thin film resistor, 0.1% 4.64 kΩ 
R4 Thin film resistor, 0.1% 2.2 kΩ 
R5 Thin film resistor, 0.1% DNL, 667 Ω, 60.6 Ω, 6 Ω 
RV Trimpot, 10%, 12 turns 10 Ω 
C1, C2 Molded tantalum capacitor, 10% 0.1 μ
C3, C4 Molded tantalum capacitor, 10% 10 μ
DesignatorComponent typeComponent value
J1, J2 Low-noise JFET pair LSK389A 
Q1, Q2 Low-noise BJT pair SSM2212 
U1, U2 Instrumentation amplifier AD8429 
R1, R2 Thin film resistor, 0.01% 10 kΩ 
R3 Thin film resistor, 0.1% 4.64 kΩ 
R4 Thin film resistor, 0.1% 2.2 kΩ 
R5 Thin film resistor, 0.1% DNL, 667 Ω, 60.6 Ω, 6 Ω 
RV Trimpot, 10%, 12 turns 10 Ω 
C1, C2 Molded tantalum capacitor, 10% 0.1 μ
C3, C4 Molded tantalum capacitor, 10% 10 μ

Capacitors also have thermal and excess noise. Thermal noise is generated due to the series and leakage resistances the non-ideal capacitors have but is negligible since this resistance is usually on the order of a few Ωs. Excess noise is also usually negligible but can be present in various capacitors in different forms. Class 2 ceramic capacitors (X7R, Z5U, X7S, etc.) have piezoelectric effects, which couple to the circuit as voltage noise.42 Film capacitors can have parasitic inductive effects, as their films are rolled and encapsulated.41 Electrolytic capacitors might generate noise after they are exposed to reverse bias conditions, and aluminum electrolytic capacitors have high series resistance and leakage currents that can degrade the system performance.43 While this information about capacitor noise is good to keep in mind, another critical aspect of choosing capacitors is their frequency of operation. Out of all discrete capacitor types, aluminum and molded tantalum electrolytic capacitors reach the lowest frequencies. Molded tantalum capacitors are the only capacitors whose bandwidth covers almost the entire LF spectrum (∼1 Hz–1 MHz) while having comparable noise performance to other low-noise capacitors, assuming that necessary precautions are taken so that they are never reverse biased.44 

With these considerations, we can create a noise model of the entire system by focusing on the noise contribution of just Pre2amp. The noise model of the system can be reduced to the noise model of the ULNA in Pre2amp since the noise contributions of the subsequent stages after Pre2amp are negligible due to Pre2amp’s high gain. We also neglect any noise contribution from the discrete capacitor and excess noise from the discrete resistor components assuming that the necessary precautions specified above are taken to minimize their parasitic behavior. Therefore, the noise model of Pre2amp is shown in Fig. 7.

FIG. 7.

Circuit model of the ULNA for noise calculations.

FIG. 7.

Circuit model of the ULNA for noise calculations.

Close modal

In this model, a few assumptions are made to simplify the calculations while not degrading its accuracy. Since this system is intended to be used at low frequencies, any reactive components that would be included in a high-frequency model are neglected from this model. Furthermore, due to the high output conductance of BJTs and JFETs used in the Pre2amp, output resistances are also neglected from the model. Calculating the RTI noise spectral density, noise contribution from each uncorrelated noise source can be found at the output of its corresponding stage independently, and the output voltage noise can be divided by the gain of the prior stages to obtain its contribution to the input noise. Correlated noise sources, however, require more exhaustive analysis. Only the correlated noise source in this model comes from the nonlinear aspect of this circuit. Since the noise contribution of the current mirror alters the bias conditions of the JFETs, the current mirror noise multiplies with the differential input signal, ΔVG = VG+VG. ΔVG includes contributions from Vin, iJ, and eJ. However, the differential input signal from the antenna, Vin, dominates over other contributions, so we can approximate ΔVGVin = Vin+Vin. Therefore, this approximation makes the noise contribution of the current mirror uncorrelated as well. Thus, we can use superposition to add all noise contributions and determine the overall RTI noise spectral density.

To begin with, we need to consider the noise contribution of the current mirror. As shown in Fig. 7, the input voltage noise of the BJTs, eQ, and thermal noise of the current-setting resistor, eR3, do not directly contribute to the RTI voltage noise but manifest themselves as current noise in iQ = βib2. Neglecting channel length modulation of the JFETs, this current noise multiplies with the input signal, Vin, at the output of the first stage approximately as45 

ViQout=R4Vin2gmiQ(gmVin)2,|Vin|<iQgm,sign(Vin)R4iQ,otherwise.
(21)

For Vin, we consider the maximum differential input signal the ULNA can have without clipping (Vinmax= 100 mV) to simulate the worst-case scenario. Therefore, the total input voltage noise due to iQ over the bandwidth of the receiver is calculated as

ViQin=ViQout2G1,
(22)

where G1 is the voltage gain of the first stage, which is 36 dB as mentioned earlier. Then, the input voltage noise spectral density due to iQ is

eiQin=e1=ViQinBW,
(23)

where BW is the bandwidth of the receiver with filters turned on (469 kHz). By symmetry, we can see that ib1 is equal to ib2. Therefore, using superposition, we can also derive iQ

iQ=βib2=βR3rπ+R3+1eQrπ+rπ2R3+eR3rπ2rπ(R3+rπrπ)+βib1(R3rπ)rπ+rπR3=β(rπ+2R3)eQrπ2+2rπR3+eR3rπ+2R31βrπR3rπ2+2rπR3,
(24)

where rπ=βVTIC with VT being the thermal voltage (VT = kT/q, where q is the charge of an electron). We now consider the thermal noise of RV, eRV. The input voltage noise due to eRV is calculated as

eRVin=e2=gmeRVR4G1=2gmR4kBTRVG1.
(25)

Then, we consider the thermal noise of R4, eR4. The input voltage noise due to eR4 is calculated as

eR4in=e3=eR4G1=2kBTR4G1.
(26)

The input voltage noise due to the input current noise of the first-stage JFETs depends on the source impedance, which is the impedance of the dipole antenna. Therefore, this noise is highly variable with the frequency, as shown in Sec. II A. The input voltage noise due to iJ is calculated as

eiJin=e4=iJZS2,
(27)

where Zs is the dipole impedance. Since the input voltage noise contribution of the input voltage noise of the JFETs, eJ, is e5 = eJ, we can move on to the second stage. The input voltage noise due to the input voltage noise of the instrumentation amplifiers, eUin, is calculated as

eUinin=e6=eUinG1.
(28)

Calculating the input voltage noise due to the input current noise of the instrumentation amplifiers, iU, we need to add all current noise contributions using superposition. Therefore,

eiUin=e7=1G12iUZout122=iUZout1G12,
(29)

where Zout1 is the output impedance of the first stage, calculated as Zout1=R4gmR4+1. The input voltage noise due to the thermal noise of R5, eR5, is calculated as

eR5in=e8=eR5G1=2kBTR5G1.
(30)

Finally, the input voltage noise due to the output voltage noise of the instrumentation amplifier, eUout, is calculated as

eUoutin=e9=eUoutG1G2,
(31)

where G2 is the voltage gain of the second stage, defined as G2=1+6000R4. Therefore, using superposition, the overall RTI noise spectral density can be calculated as

enin=2i=19ei2.
(32)

All the noise contributions due to thermodynamic effects are additive white Gaussian noise, meaning that their spectral densities are frequency invariant. β and gm are also frequency invariant within the operation conditions of the system. Thus, e2, e3, e6, and e8 can be assumed constant over the frequency spectrum the system is operating in. On the other hand, noise contributions due to the intrinsic noise of the transistors and amplifiers are usually frequency variant. The most significant cause to this frequency variance comes from the flicker noise of these solid-state devices. Therefore, the corner frequencies of their flicker noise are important to specify. The corner frequencies of the voltage flicker noise of SSM2212 and AD8429 are on the order of 1 Hz and 10 Hz, respectively, making e1 and e9 practically frequency invariant. However, the corner frequency of the voltage flicker noise of LSK389A is on the order of 10 kHz, and the corner frequency of the current flicker noise of AD8429 is on the order of 100 Hz.39,40,46 Furthermore, although the current noise of LSK389A might be frequency variant, its voltage noise contribution that heavily depends on the dipole impedance is not. To accurately characterize the noise contributions of the frequency variant contributions—current noise of AD8429 and the voltage and the current noise of LSK389A—we need to plot e4, e5, and e7 with respect to frequency. The overall RTI voltage noise spectral density of the ULNA and the voltage noise contributions of the aforementioned noise sources are shown in Fig. 8.

FIG. 8.

Modeled RTI voltage noise spectral density of the ULNA and the voltage noise contributions of all the noise sources.

FIG. 8.

Modeled RTI voltage noise spectral density of the ULNA and the voltage noise contributions of all the noise sources.

Close modal

As shown in Fig. 8, the overall RTI voltage noise is dominated by e4 at high frequencies and by e5 at low frequencies. This cements the argument that the input current noise of the first stage needs to be as small as possible to drive the corner frequency where e4 starts to dominate as low as possible. Furthermore, the input voltage noise of the first stage is critical to make the overall RTI voltage noise as small as possible.

Preamp serves multiple purposes, including signal conditioning and filtering, power regulation, and three-channel data multiplexing for electric and magnetic field receiver integration. Its signal conditioning and filtering circuitry is hosted on a card, named the Preamp card, and is comprised of five cascaded stages, as shown in Fig. 9. The first stage of the Preamp card is a buffer stage to receive the signal driven from Pre2amp. It uses OPA211 in the unity-gain configuration.

FIG. 9.

Preamp circuit schematic when all filters are enabled. First stage is a buffer stage, receiving the incoming signal from Pre2amp. Second and third stages are low and high-pass filters. Fourth stage is a tunable attenuator. Fifth stage is a cable driver, driving the signal to the back end.

FIG. 9.

Preamp circuit schematic when all filters are enabled. First stage is a buffer stage, receiving the incoming signal from Pre2amp. Second and third stages are low and high-pass filters. Fourth stage is a tunable attenuator. Fifth stage is a cable driver, driving the signal to the back end.

Close modal

The second and third stages are passive differential low and high-pass filters with op-amp buffers in between them. The low-pass filter has a cut-off frequency of 500 kHz, and the high-pass filter has a cut-off frequency of 1 kHz. These filters are necessary as there are significant external noise sources whose signals can couple to the receiver as voltage and current noise. At high frequencies, amplitude modulation (AM) radio transmissions (535 kHz–1705 kHz) dominate the external noise environment and are filtered out by the low-pass filter. At low frequencies, 60 Hz emissions and their harmonics from power lines dominate and are filtered out by the high-pass filter. However, there are cases—for instance, when these sources are intended to be observed or at remote locations where noise from power lines and AM transmissions is weak—for which disabling either or both of these filters is beneficial. Therefore, the Preamp card also has jumper connectors, which, if toggled, disable either or both the filters, enabling manual reconfigurability.

Passive filters are used instead of active op-amp filters with reactive feedback due to their lower RTI noise. Modeling the RTI noise of a first-order passive filter and a first-order active filter with the same cut-off frequency (same RC) as shown in Fig. 10, there are two uncorrelated voltage noise sources equal in spectral density, en=4kBTR. Using superposition, we can find the RTO voltage noise spectral densities of both passive and active filters in the passband region. For active filters in Fig. 10 (left), eout=en2RR2+en2=en2. For passive filters in Fig. 10 (right), eout = en. Therefore, active filters have 2 times the RTO noise as passive filters, making the use of passive filters in the Preamp card more beneficial. This passive filter configuration also has the added benefit of having fewer components, reducing the complexity and cost.

FIG. 10.

Noise models of active and passive first-order (a) low-pass filters and (b) high-pass filters.

FIG. 10.

Noise models of active and passive first-order (a) low-pass filters and (b) high-pass filters.

Close modal

The fourth stage is a passive attenuator, tunable via a shunt variable resistor. This attenuation at the end of the front end before driving the signal to the back end is needed to attenuate the high-amplitude signal amplified at the Pre2amp and prevent clipping at the back end. The attenuator is tunable to allow for greater flexibility in the ULNA design process in Pre2amp. However, for this ULNA design, the nominal attenuation is set to be −2.19 dB, bringing down the overall gain of the receiver to 40 dB, 60 dB, 80 dB, or 100 dB. These gains are named low gain, medium gain, high gain, and very high gain, respectively.

The fifth stage is an op-amp driver, which drives the signal from the front end to the back end. LT1206 is a low-noise current feedback amplifier with an RTI voltage noise density of 3.6 nV/Hz at 1 kHz. It is capable of driving loads up to 20 000 pF, allowing the front end to be separated from the back end by the Belden 1217B audio cable as long as 321 m. This separation is crucial since any digital back-end circuitry can couple to the front end as an external noise source.

The Preamp card also hosts a power regulation circuitry in the form of multiple ultra-low-noise linear voltage regulators, taking in unregulated ±15 V and outputting both regulated ±10 V and ±10.8 V that power the entire front end.

After the Preamp card, signals detected by the electric field sensor can be multiplexed with the signals detected by a magnetic field sensor. Two channels are needed to drive the detected signals from the magnetic field sensor’s two orthogonal loop antennas to the back end. A chassis fitted with a backplane board is used to multiplex two channels from a magnetic field sensor with one channel from the AWESOME electric field sensor. The backplane hosts edge connectors to which the Preamp card and magnetic field sensor preamplifier cards can be connected to. The backplane also serves as the interface between the Preamp card and the audio cable the system uses to drive the signals and power between the front end and the back end. Three differential wire pairs of this cable are used to carry the signals from the front end to the back end, and the fourth pair is used to carry power from the back end to the front end. Selection of the parts used in the Preamp follows the same design guidelines outlined in Sec. II B. These components and their types are shown in Table II.

TABLE II.

Component list for Preamp.

DesignatorComponent typeComponent value
U3-8 Low-noise op-amp OPA211 
U9, U10 Low-noise amplifier LT1206 
D1, D2 Semiconductor diode, 100 V 1N914 
R6 Thin film resistor, 0.1% 318 Ω 
R7 Thin film resistor, 0.1% 1.59 kΩ 
R8 Thin film resistor, 0.1% 164 Ω 
R9 Trimpot, 10%, 25 turns 500 Ω 
R10, R11 Thin film resistor, 0.1% 1 kΩ 
C5, C6 Molded tantalum capacitor, 10% 0.1 μ
C7, C8 Molded tantalum capacitor, 10% 10 μ
C9 Molded tantalum capacitor, 10% 500 pF 
C10 Molded tantalum capacitor, 10% 0.1 μ
DesignatorComponent typeComponent value
U3-8 Low-noise op-amp OPA211 
U9, U10 Low-noise amplifier LT1206 
D1, D2 Semiconductor diode, 100 V 1N914 
R6 Thin film resistor, 0.1% 318 Ω 
R7 Thin film resistor, 0.1% 1.59 kΩ 
R8 Thin film resistor, 0.1% 164 Ω 
R9 Trimpot, 10%, 25 turns 500 Ω 
R10, R11 Thin film resistor, 0.1% 1 kΩ 
C5, C6 Molded tantalum capacitor, 10% 0.1 μ
C7, C8 Molded tantalum capacitor, 10% 10 μ
C9 Molded tantalum capacitor, 10% 500 pF 
C10 Molded tantalum capacitor, 10% 0.1 μ

The back end is responsible for providing power to the system, signal processing, and data storage after the signals are driven from the front end to the back end. The back end is comprised of two components: a line receiver and a data storage unit. The architecture and performance of the line receiver are discussed in Ref. 21 and will be briefly reviewed here.

The line receiver rejects common-mode interference coupled into the differential signals driven to the back end, performs anti-aliasing filtering, GPS time-stamping, and synchronization, and digitizes the analog signals with an integrated ADC. The line receiver also provides power to the entire system.

After the differential signals are converted into single-ended signals through the instrumentation amplifier, they are passed onto the anti-aliasing filter. This filter is comprised of three cascaded low-pass filters with a low-pass cut-off at 470 kHz. The anti-aliasing filter can be reconfigured to operate as an 8th order or 12th order elliptical low-pass filter.

The custom ADC, made by National Instruments, provides 16 bit (96 dB) dynamic range at a 1 MHz sampling rate for signal digitization. The 1 MHz sampling clock is generated by using a voltage-controlled oscillator (VCO) synchronized to a GPS receiver. This GPS synchronization circuitry generates a synchronized sampling clock accurate to an rms of 15 ns. This timing accuracy is made possible by an error correction algorithm implemented with a microcontroller, which phase locks the 40 MHz VCO to a 1 pulse-per-second GPS receiver.

After the signals are digitized through the ADC, they are driven and stored in the computer, which also hosts the custom data-acquisition software. This software enables various data recording modes for different applications, as described in Ref. 28. After being stored on the local hard drives or uploaded to the cloud, recorded LF data are consolidated and made publicly available for the entire geoscience and radio science community to use with the establishment of the WALDO database, introduced in Sec. I and discussed in Ref. 27.

The calibration process encompasses characterizing the frequency response of the system and connecting recorded voltages to the driving electric field. For magnetic field receivers,21 this process entails injecting a single-frequency current signal with a known amplitude and phase into the input of the receiver and measuring the amplitude and phase at the receiver output over the entire operating frequency range. For magnetic field receivers with air-core loops, the injected current signal can be analytically matched to its corresponding magnetic flux density due to the electromagnetic model of the loop antenna’s accordance with the Faraday’s law and due to the lack of significant coupling between the loop and the surrounding environment. Because of this predictability of the loop antenna’s electromagnetic behavior, calibration of a magnetic field receiver is rather straightforward.

On the other hand, calibration of an electric field receiver is much more complex due to capacitive coupling of an electric field antenna with the surrounding environment, whose effect on the circuit model is discussed in Sec. II A. Due to this phenomenon, the frequency response of the antenna-amplifier changes based on the environment the receiver is placed in and its dynamic conditions. Consequently, this makes the method of matching the injected signal to its corresponding electric field value imprecise and inaccurate. Since the AWESOME electric field receiver has been and will be deployed in a wide selection of dynamic environments, other calibration methods are needed to precisely and accurately calibrate the system once it is installed.

One calibration method that has been used in the literature to precisely and accurately characterize an electric field receiver in a controlled environment is named, in this paper, the direct calibration method. The direct calibration method entails an electric field receiver being placed in a controlled electric field cage in which the receiver is isolated and shielded from the outside environment, as described in Ref. 47. In the cage, the receiver is exposed to a uniform single-frequency electrostatic field with the known amplitude. As the electric field is picked up by the receiver, the amplitude of the receiver output is recorded and compared with the amplitude of the known electric field to obtain the gain of the system at that frequency. This process is then repeated over the entire LF spectrum to obtain the frequency response of the system.48 While this method provides accurate and precise characterization of the receiver, it requires specialized equipment such as a carefully calibrated cage and cannot generally be performed in the field environment where a receiver may be used.

Therefore, we propose and demonstrate a novel calibration method, named, in this paper, the indirect calibration method, through which any electric field receiver could be calibrated in the field. The proposed novel calibration method builds off of the calibrated values of a co-located magnetic field receiver and uses the electromagnetic wave propagation behavior in the far-field region from an LF source. From the magnetic field receiver, a sferic waveform is first identified, which satisfies three conditions:

  1. The source of the sferic is far away enough from the receiver (at least 1000 km) so that the receiver is in the far-field region of the source and that waveguide modes have been established. This is required so that the electric and magnetic fields can be assumed to be in-phase and the electric-to-magnetic field (E-to-B field) amplitude ratio can be approximated as 1/μ, where μ and are the permeability and permittivity of air, respectively.

  2. In the frequency domain, the sferic magnitude is above the noise floor for all the frequencies the receiver is desired to be calibrated for.

  3. The entire great circle path from the lightning stroke to the receiver is either all-daytime or all-nighttime in the lower ionosphere to avoid the complicating propagating effects of the day/night terminator on VLF/LF propagation.

While the first two conditions are more easily understood, the third condition requires more in-depth explanation. Due to greater solar activity during daytime, the ionosphere becomes more heavily ionized, causing the lowest layer of the ionosphere, the D layer, to form at a lower altitude of around 70 km, where LF signals reflect. On the other hand, during nighttime, the reduced solar activity causes the D layer to thin, raising the reflection height to 80 km–90 km. This presents itself as a discontinuity in the ionization altitude at the day/night terminator. This discontinuity scatters LF waves and alters their waveform characteristics, invalidating the assumption of in-phase electric and magnetic fields and E-to-B field amplitude ratio approximation.

After such a sferic magnetic field waveform is identified in the magnetic field data, its corresponding electric field waveform also needs to be identified in the electric field data. Since the magnetic field receiver can be calibrated relatively easily as discussed earlier, the calibrated (absolute) magnetic field phasors of the waveform are calculated in the frequency domain. Assuming that the E-to-B field amplitude ratio is 1/μ and both fields are in-phase, these phasors are multiplied by μ0° to obtain their corresponding absolute electric field phasors. Then, it is assumed that the detected electric field phasors in the frequency domain also correspond to the absolute electric field phasors. Therefore, the ratio of the absolute amplitude to the detected amplitude gives the gain of the electric field receiver at that frequency, and the phase difference between the absolute phase and detected phase gives the phase shift of the receiver at that frequency.

The proposed indirect method could be used with not only broadband sferics but also narrowband signals emitted by LF transmitters to calibrate an electric field receiver for the frequency channel the transmitter operates in. This would not allow for a broadband calibration but could be useful in circumstances where calibrated data are needed only in these frequency channels.

While this method provides a practical and powerful way to calibrate the electric field receiver, it has a couple of shortcomings. The assumption that the identified sferic satisfies the far-field propagation impedance ratio of E-to-B is an important one and is only approximately true. There are situations where this assumption can fall short. However, one way to mitigate this is to repeat the calibration process on sferics from different storms and different times of days and remove outliers or take an average.

Sferics are often above the atmospheric noise floor from near-DC through the LF range (<300 kHz) beyond which the noise from other man-made and natural sources dominate. Therefore, this method allows a system to be calibrated within this frequency range despite the fact that the system’s actual bandwidth might exceed this range. Nonetheless, calibration even only within this range still covers most of the frequency bands of interest in which many man-made transmissions and natural emissions take place.

Thus, the indirect method is useful when a calibration of the receiver is needed without having access to any specialized equipment in the field. The direct method, however, can be more accurate and can enable a more broadband calibration when such necessary equipment is accessible.

We now present the empirical data obtained to characterize the AWESOME electric field receiver and a demonstration of the broadband data acquired by one of the deployed electric field receivers.

The receiver was calibrated and characterized using the indirect calibration process. The AWESOME electric field receiver connected to both 1-m and 2-m dipole antennas was integrated with an AWESOME magnetic field sensor to detect sferics that satisfy the conditions specified in Sec. III. In this case, there were two identified sferics to be used in 1-m and 2-m dipole calibration. The time-domain waveforms and propagation paths of these sferics along with the location of the receiver are shown in Fig. 11.

FIG. 11.

Time-domain waveforms and source locations of the sferics used for indirect calibration along with the location of the calibrated receiver.

FIG. 11.

Time-domain waveforms and source locations of the sferics used for indirect calibration along with the location of the calibrated receiver.

Close modal

The first sferic, used to calibrate the receiver with a 1-m dipole antenna, was radiated by a lightning stroke (stroke A) with a peak current of 144 kA, originating in Cononaco, Ecuador (1°04′31.9″S, 76°16′32.8″W). The second sferic, used to calibrate the receiver with a 2-m dipole antenna was radiated by a lightning stroke (stroke B) with a peak current of 133 kA in Anajás, Brazil (1°00′58.8″S, 49°42′35.7″W). Locations and peak currents of the lightning were obtained from the GLD360 dataset created by Vaisala.26 Since these recordings were taken by the AWESOME receiver in Palmetto, GA (33°34′17.2″N, 84°42′46.1″W), at around 1 PM local time, sferic sources are far away enough (3952 km and 5308 km, respectively) that the receiver is in the far-field region of the sources, satisfying the first condition specified in Sec. III. The sferic magnitude is also above the noise floor for some parts of the LF spectrum, satisfying the second condition. In addition, sferic propagation paths do not cross the day/night terminator, meaning that their paths are entirely in daytime, satisfying the third condition. Since these sferics satisfy all the specified conditions, they were used to calibrate and characterize the electric field receiver. The electric field receiver’s amplitude response obtained via the aforementioned indirect calibration method is shown in Fig. 12.

FIG. 12.

Amplitude response of the receiver at the high gain configuration for 1-m and 2-m dipole antennas obtained via the indirect calibration method.

FIG. 12.

Amplitude response of the receiver at the high gain configuration for 1-m and 2-m dipole antennas obtained via the indirect calibration method.

Close modal

As discussed in Sec. III, the frequency range of the characterized response is limited by the bandwidth of the detected sferics. In this case, the receiver is characterized up to 80 kHz, beyond which the receiver gain obtained via the indirect calibration method is inaccurate due to the weak signal amplitude of the sferic. The amplitude gain is flat from 1 kHz up to 80 kHz hovering around 0.04 VμV/m for 1-m dipole and around 0.08 VμV/m for 2-m dipole. This approximate linear scaling with the dipole length is consistent with the theoretical analysis shown in Sec. II A. There is a significant increase in gain above 80 kHz, which is caused by the amplitude of the detected sferic gradually dropping below the noise floor. The dropoff at 1 kHz can be attributed to the high-pass filter in Preamp. This cutoff can be removed by simply disabling this Preamp filter, enabling a flat amplitude response from near-DC up to 80 kHz.

While frequencies beyond 80 kHz could not be characterized via the indirect calibration process for this particular sferic, the system can still detect and record signals with frequencies between 80 kHz and 470 kHz. Hence, the theoretical bandwidth of the system is from near-DC up to 470 kHz, making this system a broadband receiver capable of detecting signals in the low MF range. The 470 kHz cutoff is set by the anti-aliasing filter in the line receiver and the high-pass filter in Preamp, corresponding with the 1 MHz sampling frequency.

As briefly discussed in Sec. III, the receiver gain also sets the maximum electric field amplitude the receiver can detect before it clips. Higher gain corresponds to the lower clipping threshold and vice versa. Clipping thresholds calculated from the receiver gain data, for this 16-bit ADC, along with the previously detailed information about each configuration are shown in Table III.

TABLE III.

Gain configuration summary.

Configuration nameDipole length (m)Front-end gain (dB)Threshold (mV/m)
Low gain 40 30 
40 15 
Medium gain 60 
60 1.5 
High gain 80 0.3 
80 0.15 
Very high gain 100 0.03 
100 0.015 
Configuration nameDipole length (m)Front-end gain (dB)Threshold (mV/m)
Low gain 40 30 
40 15 
Medium gain 60 
60 1.5 
High gain 80 0.3 
80 0.15 
Very high gain 100 0.03 
100 0.015 

Due to the dependence of the clipping threshold on the receiver gain, the gain configuration should be chosen based on the environment (i.e., intensity of signals of interest) where the receiver is deployed. In our experience, in an urban setting where the signals of interest are sferics and LF man-made transmitters, the medium gain configuration is the most suitable one because of potential clipping due to power line noise. On the other hand, in a rural setting—away from power lines and other man-made noise sources—the high gain configuration is the most suitable one.

Furthermore, if a lower clipping threshold is required for each gain configuration, the tunable attenuator in Preamp can simply be tuned to increase its attenuation—by decreasing R9’s value on the Preamp card—thereby lowering the system gain.

After calibration, the sensitivity of the receiver can be characterized by disconnecting the antenna and measuring the output without any electrically induced voltage at the receiver inputs. The inputs are grounded through a “dummy dipole” to account for the input current noise of Pre2amp. The dummy dipole is a passive network that mimics the impedance of a dipole antenna, as modeled in Sec. II A. Since the dipole impedance is dominated by the capacitive reactance, the dummy dipole is simply a capacitor in series with the Pre2amp inputs. To further minimize the intensity of external signals coupling into the receiver circuitry, the receiver is placed in a metal container for shielding.

After the experimental setup is assembled, the output is measured and divided by the amplitude response obtained from the calibration to obtain the electric field equivalent of the output noise. This signifies the sensitivity of the receiver. Hence, the sensitivity of the receiver at the high gain configuration for both 1-m and 2-m dipole antennas calibrated via indirect calibration is shown in Fig. 13.

FIG. 13.

Sensitivity of the AWESOME electric field receiver at the high-gain configuration for different antenna lengths, also in comparison with the sensitivity of the AWESOME magnetic field receiver used with a right-isosceles loop antenna of 2.6 m in base length and 1.3 m in height with 12 turns.

FIG. 13.

Sensitivity of the AWESOME electric field receiver at the high-gain configuration for different antenna lengths, also in comparison with the sensitivity of the AWESOME magnetic field receiver used with a right-isosceles loop antenna of 2.6 m in base length and 1.3 m in height with 12 turns.

Close modal

As shown in Fig. 13, the sensitivity of the receiver with a 2-m dipole antenna stays below 45 nV/(mHz), equivalent to 0.15 fT/Hz, and below 80 kHz and reaches as low as 0.677 nV/(mHz), equivalent to 2.26 aT/Hz. Since the amplitude response could only be obtained for frequencies up to 80 kHz for the reasons detailed earlier, the receiver sensitivity could also be characterized for the same frequencies. However, given the assumption that the amplitude response stays flat even above 80 kHz as most of the intrinsic noise is caused by flicker noise, the receiver sensitivity can be expected to stay on the order of 1 nV/(mHz) for the entire LF spectrum.

This result can also be used to compare the AWESOME electric field receiver with another state-of-the-art receiver. The gray curve above the electric field receiver sensitivity is the characterized sensitivity of the AWESOME magnetic field receiver, which is a state-of-the-art LF receiver deployed around the world. For this comparison, AWESOME magnetic field receiver’s noise response was captured via the calibration process described in Ref. 21 while being used with a right-isosceles loop antenna of 2.6 m in base length and 1.3 m in height with 12 turns. The noise level of the magnetic field receiver increases as its antenna becomes smaller, as shown in Refs. 21 and 28. As shown in Fig. 13, the system sensitivity of the electric field receiver is around 20 dB, better than the state-of-the-art, ensuring an improvement in the data quality of any LF receiver network that uses a collection of the AWESOME electric field receivers.

One of the AWESOME electric field receivers integrated with an AWESOME magnetic field sensor was deployed at Briarwood Academy in Briarwood, GA, for real-time 24/7 data collection. One channel of electric field data and two channels of magnetic field data are processed and stored.

Figure 14 displays a sample snippet of the calibrated broadband data acquired by the deployed electric field receiver. The top left panel shows the broadband data in the form of a spectrogram. To display the data in this form, the data are divided into 1 ms segments and a Fourier transform is performed on each segment. Since each time segment is 1-ms long, the frequency resolution is 1 kHz in this instance. Each time segment makes up a column on the spectrogram, and the electric field strength is color-mapped. The data are calibrated at each frequency in every segment using the characterized amplitude response shown in Sec. IV A. While frequencies above 80 kHz could not be characterized at this time, due to the observed flat passband of the system, the amplitude response was assumed to stay flat above 80 kHz for the sake of displaying this sample data. The horizontal axis shows 10 s of data on August 30, 2019 at 22:00:10 UT, with the vertical axis showing the frequency from DC up to 500 kHz.

FIG. 14.

Sample broadband data acquired by the electric field receiver deployed at Briarwood Academy in Briarwood, GA. A detected sferic and signals from man-made transmitters are showcased.

FIG. 14.

Sample broadband data acquired by the electric field receiver deployed at Briarwood Academy in Briarwood, GA. A detected sferic and signals from man-made transmitters are showcased.

Close modal

The spectrogram clearly shows some of the natural and man-made LF waves propagating in the EIW. The vertical lines are the transient but broadband sferics, while the horizontal lines are the continuous but narrowband emissions from man-made LF transmitters. One such sferic and emissions from man-made VLF/LF/MF transmitters are showcased in the bottom left and top right panels. The sferic is showcased on a time-domain plot, whose vertical axis shows the voltage amplitude of the detected sferic. This particular sferic’s brief electric field perturbation lasts over a period of around 1 ms, which is what is normally observed for most sferics. This sferic originated from a thunderstorm in Chihuahua, Mexico, whose location is determined from the GLD360 dataset and is shown on the map in the bottom right panel.

The man-made emissions are showcased and magnified on the spectrogram. Emission on the upper panel is from one of the many LF/MF non-directional beacons (NDBs), which are used for aviation and marine navigation. NDBs send out their call sign periodically in Morse code using on-off keying (OOK), which is then detected by aircrafts and vessels to pinpoint their own location and navigate. This particular NDB is the AA transmitter (341.0 kHz) in Thomson, GA, which is in the vicinity (∼12 km away) of the deployed LF receiver. The spectrogram shows the carrier signal being modulated, reflecting the “dot” portion of the AA (.-.- in Morse code) call sign. Emissions on the lower panel are from navy VLF transmitters used for submarine communications. These particular emissions are radiated by the NAA transmitter (24.0 kHz) in Cutler, ME, NLK transmitter (24.8 kHz) in Seattle, WA, and NML transmitter (25.2 kHz) in LaMoure, ND. The spectrogram shows their minimum-shift keying (MSK modulation patterns, where the center frequencies modulate up and down, reflecting the encoded binary data (1 or 0). Locations of these transmitters along with the location of the Briarwood receiver are shown on the map in the bottom right panel. Thus, the AWESOME electric field receiver can successfully detect both natural and man-made signals throughout the entire LF spectrum as shown.

We now describe a few selected and novel applications enabled by the AWESOME electric field receiver in the field of radio science.

As described in Sec. I, LF radio data can unearth useful information about the state of the ionosphere. One way to extract information from detected LF waves is to detect the signals coming from a reliable LF source. An example of such a reliable source are LF transmitters used by the Navy for global submarine communications. These transmitters transmit information through minimum-shift keying (MSK), which entails shifting the frequency of the signals above or below a certain center frequency to encode 1 or 0 bits while keeping the phase continuous across different frequencies. As these signals propagate in the EIW and reflect off the lower ionospheric layers, the phase and amplitude of the carrier and clocked signals are affected based on the ionospheric conditions. Therefore, information about the ionosphere could be extracted by demodulating the transmitter signal to record the carrier signal amplitude and phase.

The theory of MSK demodulation is well established in the literature and numerous demodulation algorithms have been introduced in the past.49–53 However, demodulating a transmitter signal that propagates in the EIW has its additional challenges.54 Frequency channels of Navy transmitters can be characterized as the summation of the MSK-modulated LF signal, additive Gaussian white noise, and sferic-caused additive impulsive noise. This additional noise makes MSK demodulation of a transmitter signal more difficult. Moreover, as the signal propagates in the EIW, multiple modes appear in order to satisfy the boundary conditions of the waveguide. Well above the cutoff frequency of the EIW (around 1.8 kHz), multi-mode propagation takes place, each with a different amplitude, phase, and group velocity. A novel algorithm that addresses these challenges has already been introduced in Ref. 21. The same algorithm was used to demodulate the signal detected by this system.

Data acquired and stored by all deployed electric field receivers are either broadband data that store all raw data from 0 kHz to 500 kHz or narrowband data that store the raw data within the frequency channels of man-made transmitters and use MSK demodulation to infer and store the carrier amplitude and phase (transmitter parameters).

Figure 15 shows the transmitter parameters of the NAA Navy transmitter in Cutler, ME, recorded in all three channels over a two-day period. These data were acquired by the system deployed at Briarwood Academy described in Sec. IV C.

FIG. 15.

Simultaneous electric and magnetic field recordings of the NAA transmitter parameters in linear form over two days.

FIG. 15.

Simultaneous electric and magnetic field recordings of the NAA transmitter parameters in linear form over two days.

Close modal

The diurnal variations of the ionospheric properties due to solar activity are clearly seen in both phase and amplitude in all three channels. The 12-h time periods (00:00–12:00 UT) when there are erratic fluctuations in amplitude and phase correspond to nighttime and the other 12-h time periods (12:00–00:00 UT) when the amplitude and phase are smooth and consistent correspond to daytime.

The nighttime fluctuations in amplitude sometimes reduces the amplitude of the signal too much for the MSK demodulation algorithm to lose “lock” of the signal’s phase, causing 90° phase aberrations in the phase data. These errors that happen only during nighttime were manually corrected by visually examining the phase plot and changing the phases to be consistent with adjacent data. These errors could also be automatically corrected by an additional error-correcting algorithm that detects 90° phase discontinuities in the data.

In addition to the clear visibility of the diurnal pattern, which is important for ionospheric remote sensing, the amplitude on the electric field channel is very close to the theoretical value of the root sum squared of amplitudes on both magnetic field channels. Hence, the electric field channel adds another set of data points for ionospheric remote sensing through recording of man-made transmitter signals propagating in the EIW.

Finally, while it is expected that phases in all three channels should be the same, the observed variation between channels can be explained by the different propagation paths of the signals in different channels from the source to each antenna.

Cloud to ground (CG) lightning strokes can be characterized as of either positive or negative polarity based on the net charge transferred during the event. Most CG lightning originates in the lower layer of the cloud that is negatively charged. This results in a negative net charge transfer from the cloud to the ground. While being less common, lightning strokes can also form in the upper positively charged region of the cloud, resulting in a net positive charge transfer. Due to the increased distance from the point of origin to the ground, positive lightning strokes are often much more powerful than their negative counterparts.14 

Using only magnetic field sensors in lightning identification and geolocation, there can be an ambiguity in the arrival azimuth of the sferic and polarity of the stroke. For instance, if a positive lightning stroke occurs northeast of the sensor, the magnetic field components will look identical to those of a negative polarity stroke located southwest of the same sensor. For a single magnetic field receiver, this leads to a 180° ambiguity in the arrival azimuth of the sferic, and for networks with only magnetic field receivers, it causes a positive/negative ambiguity in the polarity of the stroke.17 Having additional electric field data recorded by an electric field receiver can solve for this ambiguity and allow lightning detection networks have this critical information at their sensors.55 While such simultaneous magnetic and electric field recordings to resolve these ambiguities have been demonstrated in the past,56 no ultra-sensitive system that records simultaneous magnetic and electric field data has been developed in the recent past to apply this method in a modern system and resolve these ambiguities.

To demonstrate how to resolve such ambiguities, two sferics were identified from the National Lightning Detection Network (NLDN) operated by Vaisala. The two sferics were chosen so that one of them is directly northeast and the other one is directly southwest of the AWESOME electric field receiver deployed at the Briarwood Academy. Figure 16 shows the magnetic and electric field components detected by the receiver. It can be seen from the magnetic field plots of both sferics that the N/S and E/W channels have exactly opposite polarities. With only magnetic field components, it is impossible to resolve the polarity of the stroke. Despite that knowing the arrival azimuth of both sferics allows us to infer whether the polarities of the two sferics are the same or different, it still leaves whether the polarity is positive or negative a mystery. Now adding in the electric field component of the signal, the amplitudes of both strokes at their first peak are observed to be below zero, indicating that that the sources of these sferics are both negative lightning strokes. This resolves the phase ambiguity apparent in lightning detection networks that have only magnetic field receivers.

FIG. 16.

Electric and magnetic field components of the two selected sferics emitted by negative polarity strokes on each channel.

FIG. 16.

Electric and magnetic field components of the two selected sferics emitted by negative polarity strokes on each channel.

Close modal

Therefore, deploying the AWESOME electric field receiver with a magnetic field sensor to form the basis of a lightning detection network would enable global lightning detection and geolocation without these ambiguities in the recorded data.

Propagation of LF waves after they are radiated away from their source makes them exhibit certain characteristics in different regions of the propagation environment around the source. In the near field, the electric and magnetic fields are not orthogonal, and the wave impedance does not follow the intrinsic impedance of the medium. This phenomenon causes electric or magnetic field waves to dominate the near-field environment over one another depending on the source characteristics. Due to the extremely long wavelength of LF waves, this near-field region around an LF source can span an area of tens of kilometers in radius. This makes the reception of the electric field component of LF waves especially useful since remote sensing of LF sources by detecting their electric field or magnetic field emissions in the near field enables various scientific and engineering applications.

One such application is remotely sensing the ratio between the voltage and current amplitudes in an LF radiator. This is enabled by the non-orthogonal nature of electric and magnetic fields in the near field and the fact that electric and magnetic fields are generated by voltage and current radiators, respectively. Therefore, the voltage-to-current ratio in an LF radiator could be derived from measuring the amplitude ratio of the radiated electric fields to magnetic fields in the near field. Such a measurement can be taken by detecting the electric and magnetic fields radiated by the source with the AWESOME electric field receiver integrated with a magnetic field sensor, as shown in Fig. 17.

FIG. 17.

Relative amplitudes of the 60 Hz emissions from the electrical substation in Sligo, NC. Amplitude plots are shifted so that the average amplitude of each channel is the same.

FIG. 17.

Relative amplitudes of the 60 Hz emissions from the electrical substation in Sligo, NC. Amplitude plots are shifted so that the average amplitude of each channel is the same.

Close modal

The AWESOME receiver was deployed near an electrical substation in Sligo, NC, to detect the radiated 60 Hz emissions and their harmonics. In Fig. 17, amplitudes of one channel of electric field data and two channels of magnetic field data from this receiver are shown relative to each other. One second of the data was recorded at the start of every hour and uploaded to a cloud database. Then, a Fourier transform was performed on each second of the data from November 21, 2019 to November 27, 2019. Amplitudes corresponding to the 60 Hz emissions from the substation were extracted and concatenated to be displayed in the figure. Since the important aspect of this time-domain plot visualization is its overall shape, the amplitudes were not calibrated. Instead, the average amplitude of each channel was calculated and the amplitude plots of all three channels were shifted so that their averages are at 0 dB.

While there are numerous periods during which the electric field amplitudes differ from the magnetic field amplitudes, five instances of amplitude perturbations exemplify the significance of recording electric field data. In regions 1, 3, and 6, electric field amplitudes stay on the same level, while magnetic field amplitudes on both channels simultaneously decrease or increase. This could indicate that less current is being drawn from the substation in the cases of region 1 and 6 and more current is being drawn in the case of region 3, possibly caused by a change in the load conditions of the substation. In regions 2 and 5, this contrast in amplitude perturbations is starker as electric field amplitudes spike up, while both magnetic field amplitudes spike down. This engenders the estimation that the voltage-to-current ratio in the substation significantly increases, again possibly due to a change in the substation load conditions.

Region 4 is also notable since both the N/S magnetic field and electric field amplitudes rise, while the E/W magnetic field amplitude falls. This could imply that there was a possible change in the current distribution in the substation (i.e., higher overall current in the E/W direction, while lower overall current in the N/S direction). Higher electric field amplitude, on the other hand, could signal an increase in the overall voltage in the system.

Without correlating the local data from the substation regarding its time-varying conditions to the data recorded by this instrument, it is difficult to confirm the accuracy of these estimations. However, these sample data clearly show the significance of simultaneously recorded electric and magnetic field data in regards to the near-field remote sensing of an LF source, giving rise to many scientific and engineering applications, one concrete and emerging example being better protection of power grids from cyber threats.57 

Another benefit of acquiring electric field data is sensing the effect electromagnetic scattering has on LF signals. Regardless of whether the LF signal is radiated in the far or near field, once it is scattered off of a body, the region around the object becomes near field as the electric and magnetic field components of the LF signal are no longer mutually orthogonal. Therefore, detecting these electric field components become beneficial since electric and magnetic fields are absorbed and re-radiated, namely, scattered, by the scattering object differently. Simultaneous detection of electric and magnetic fields in the near-field region of a scattering object could be used for imaging with LF waves. While near-field LF imaging through magnetic induction has been shown in the literature,58 detection of electric fields would provide additional useful information about the scattering object, enabling more accurate identification and evaluation.

In order to demonstrate how electric field detection provides additional significant data for LF imaging and how electric and magnetic field are scattered off differently from a scattering object, two recordings were taken with an AWESOME receiver with all three channels turned on. Initially, the receiver was run normally in an open area with two square loop antennas of 0.5 × 0.5 m2 in size and a dipole antenna of 1 m in height to detect the LF signals radiated from the NAA transmitter transmitting at 24 kHz. After some time, a square conductive plate, 1.5 × 1.5 m2 in size, made out of stainless steel was placed in front of the antennas in the direction where the NAA transmitter is located for its signals to pass through the plate before reaching the receiver antennas. Amplitude recordings of the signals from the NAA transmitter before and after the plate was placed were then extracted and plotted in Fig. 18.

FIG. 18.

Relative amplitudes of the signals from the NAA transmitter (24 kHz) in Cutler, ME. Amplitude plots are shifted so that the first amplitude data point corresponds to 0 dB. At the 1.0 second mark, a conductive plate was placed in front of the receiver in the direction of the NAA transmitter.

FIG. 18.

Relative amplitudes of the signals from the NAA transmitter (24 kHz) in Cutler, ME. Amplitude plots are shifted so that the first amplitude data point corresponds to 0 dB. At the 1.0 second mark, a conductive plate was placed in front of the receiver in the direction of the NAA transmitter.

Close modal

In Fig. 18, amplitude recordings of all three channels from before and after the conductive plate was placed are shown. At the 1.0 s mark, which corresponds to the exact time when the conductive was placed in front of all three antennas, there is ∼70-dB drop in the electric field amplitude. Contrarily, there is no clear change in the magnetic field amplitudes after the plate’s placement. This significant drop in electric field amplitude with no change in magnetic field amplitude validates the discrepancy in scattering of electric and magnetic fields and confirms how detecting scattered electric fields is useful. Such simultaneous recordings of electric and magnetic fields could pave the way for practical and accurate LF imaging, with various scientific, medical, and security applications. Furthermore, since LF waves penetrate through conductive media with low attenuation, this advancement would enable imaging of objects through conductive media, significantly expanding the application domain of electromagnetic imaging with applications such as non-destructive evaluation of shipments in metal containers at security checkpoints.58 

We have detailed a novel instrument capable of detecting LF electric fields from near-DC up to 470 kHz. This instrument is an end-to-end electric field receiving system with a front end that amplifies and filters the captured waves and a back end that digitizes and stores the data. This instrument is also complementary to the AWESOME magnetic field receiver,21 which can be integrated with this instrument to enable simultaneous electric and magnetic field reception.

We have delineated the instrument’s system architecture and design, including the design methodology and trade-offs. We have described a novel calibration method that uses simultaneously recorded electric and magnetic field data to calibrate the electric field receiver without any need for specialized equipment, useful for receiver deployments in the field. With this calibration method, we have characterized the receiver’s amplitude response as a function of the antenna size and shown that the amplitude response stays flat at around 0.04 VμV/m for a receiver with a 1-m dipole and around 0.08 VμV/m for a receiver with a 2-m dipole between the frequencies of 1 kHz and 80 kHz.

With this empirical data, we have characterized the gain and clipping thresholds of the receiver configured at different gain configurations and with different antenna sizes. We have also characterized the noise level of the system, which stays below 45 nV/(mHz), or 0.15 fT/Hz, and reaches a sensitivity of 0.677 nV/(mHz), or 2.26 aT/Hz, a 20-dB improvement from the AWESOME magnetic field receiver.

Using this ultra-sensitive broadband instrument that enables simultaneous electric and magnetic field reception, we have demonstrated several useful applications within the scope of LF radio science. We have demonstrated the additional scientific information electric field reception provides for ionospheric remote sensing by demodulating signals from LF transmitters at 20 kHz–30 kHz. We have shown how electric field reception resolves the phase ambiguity of sferics detected by magnetic field receivers in lightning detection networks, paving the way for more robust and accurate global lightning detection and geolocation. We have demonstrated the possibility of remote sensing in the near field through simultaneous electric and magnetic field reception either when the LF wave is radiated by a source in the near field of the receiver or when the LF wave is radiated in the far field but is scattered in the near field. We have shown how near-field remote sensing enables remote identification and characterization of LF sources and scattering objects, paving the way for robust cybersecurity protection systems for the power grid: feasible and accurate LF imaging and imaging through conductive media.

This work was supported by the Division of Atmospheric and Geospace Sciences of the National Science Foundation under Grant Nos. AGS 1451142 and 1653114 to the Georgia Institute of Technology. We thank the members of the LF Radio Lab at Georgia Tech for their helpful insight and discussions during the design and development of this instrument. We also thank our friends at Briarwood Academy and the Sligo substation for hosting our receivers.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

In regression analysis, linear regression is used to fit a linear combination of regression parameters (i.e., polynomials) to datasets, whereas non-linear regression is used to fit non-linear combination of regression parameters to datasets. The piecewise loss resistance function was initially modified by dividing it by DC resistance, making the modified expression the prefactor of DC resistance with respect to loss resistance. This prefactor function is defined as

Fl(λ)=1,δ>d2,d24δ(dδ),δd2.
(A1)

Then, the prefactor function was discretized with respect to wavelength, and both linear and non-linear regressions were used to determine the method that minimizes the residual sum of squares (RSS). The RSS is defined as RSS=Σi=1n(yif(xi))2, where yi is the data point and f(xi) is the model function output.

Non-linear regression with a model power function was found to be the most accurate method to approximate the piecewise loss resistance function. With this method, parameters for the model power function were optimized. This correction function used in (2) was found to be

f(λ)=915.6011λ0.5149+0.683.
(A2)

This fitted correction function has an R2 value of 0.9998 with respect to the exact loss resistance function. Hence, a particular dipole antenna’s DC resistance function, piecewise loss resistance function, and loss resistance calculated with the correction function using (2) are shown in Fig. 19.

FIG. 19.

Overall loss resistance and DC resistance of a copper whip antenna of 2 m length and 1.27 cm wire diameter along with the loss resistance calculated with the correction function fitted via non-linear regression.

FIG. 19.

Overall loss resistance and DC resistance of a copper whip antenna of 2 m length and 1.27 cm wire diameter along with the loss resistance calculated with the correction function fitted via non-linear regression.

Close modal

As shown in Fig. 19, the approximated loss resistance closely fits the exact loss resistance, especially compared to DC resistance, showing the necessity of a correction function in the derivations in Sec. II A.

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