Executive Summary

We present an approach to the design of state-of-the-art, magnetic-field sensor systems that can be optimized to detect extremely weak electromagnetic signals over a wide frequency range from ELF through LF (3 Hz – 300 KHz). Our design approach provides a balance between performance and fieldability and offers several ways to trade off design features to achieve optimal solutions for different applications. Features of our approach include an SNR-optimized antenna and front-end amplifier to provide femto-Tesla (fT) sensitivity; a flat, wide-bandwidth frequency response; and high dynamic range. This minimizes requirements for high back-end DSP processing gain (i.e., long integration times).

As an example of the achievable performance, one point design tailored for ultra-sensitive, wide-bandwidth characterization of either natural or man-made signals in the ULF – LF bands provides the following capabilities:

• Flat, Wide-Bandwidth Frequency Response

  • A noise-optimized antenna driving a state-of-the-art transimpedance amplifier provides a transducer frequency response that is flat from <1 KHz to >100 KHz.

• Very High Analog Sensitivity / Very Low Minimum Detectable Signal (MDS)

  • An antenna B-field sensitivity (0 dB SNR) of 1 at 1 KHz and a total system B-field sensitivity of 2 at 1 KHz. The system becomes more sensitive (the spectral density decreases) linearly with increasing frequency. The sensitivity provided is below the natural noise floor of ~5 over the entire frequency range.

• Very High Dynamic Range

  • Precision amplifier provides high linearity with a dynamic range of more than 95 dB to accommodate high-levels of manmade interference and natural impulsive noise (spherics).

• Easily Fieldable Antenna and Electronics Package

  • The antenna for this example is a relatively lightweight, planar loop with an area of only 1 . It requires no high-permeability materials and can easily be constructed to meet specific deployment requirements.

Introduction

Radiometric and polarimetric measurements in the electromagnetic spectrum from a few Hz to a few hundred KHz can yield significant insights into ionospheric and magnetospheric dynamics. This realm of radio science exhibits a rich range of natural phenomena, such as Schumann resonances; whistlers and other “spherics” resulting from lightning discharges [1]; polar chorus and auroral hiss; and propagation enhancement due to sudden ionospheric disturbances (SIDs). Man-made signals in this portion of the electromagnetic spectrum include navigation signals such as Omega, LORAN and nondirectional beacons (NDBs); communication signals intended for reception by submarines; and standard time and frequency signals.

Providing high-sensitivity receivers for signals in the ELF, SLF, ULF, VLF and LF frequency bands (3 Hz to 300 KHz) presents significant challenges. Some approaches are based on electrically small E-field or B-field antennas, often resonated to the frequency of interest, and typically employ high-impedance amplifiers to minimize voltage-signal loading. Performance tradeoffs are usually not well understood and total system noise performance is almost never optimized for the specific signal(s) of interest. Surprisingly, no published technical paper has been found that provides a sensitivity-based analysis and design of electrically small antennas for weak-signal applications. The goal of this paper is to provide an approach for the design of magnetic-field receiver systems for which high sensitivity, wide bandwidth, and high dynamic range are essential.

The natural noise floor in the ELF through LF range is reasonably well characterized [2]. The noise measurements indicate an average spectral density of ~1 at 1 Hz. The noise density decreases at roughly 10 dB/decade to ~1 at 1 KHz. Between 1 and 10 KHz the noise dips to ~0.1 and then rises sharply to ~1-5 at 10 KHz. Above 10 KHz, the noise drops at roughly 20 dB/decade out to 100 KHz, which is the upper frequency limit of the data. Within the frequency range of 1 KHz to 10 KHz, seasonal and location variations in field magnitude may be on the order of 20 dB.

For purposes of illustration, consider a situation for which the local natural noise density is ~5 at 10 KHz. Then a weak manmade signal with a 1-Hz bandwidth (e.g., very slow on-off-keyed CW) and a 5-fT amplitude would have an instantaneous SNR of 0 dB at the antenna within a 1-Hz bandwidth. An antenna/amplifier that claims high sensitivity for this signal must maintain this SNR with minimal degradation, which requires antenna + electronic noise at or below the natural noise floor. Alternatively, if the signals of interest are natural in origin, then they are by definition components of the natural noise floor and antenna + electronic noise must again be at or below the natural noise floor to provide high-fidelity reception.

The signal-detection challenge, however, is also affected by man-made interference and natural impulsive noise. This drives the need for high dynamic range in addition to high sensitivity to provide the maximum SNIR possible for the analog signal so the requirements on back-end DSP processing gain are reasonable. Finally, some applications may also require a large relative bandwidth to capture signals with relatively fast risetimes, to enable signal search using DSP techniques, or to support the characterization of phenomena that span a relatively large frequency range. Designing an antenna/receiver system that meets these challenging sensitivity, bandwidth and dynamic-range requirements while keeping the hardware relatively small and easily fieldable is a significant challenge. The technical approach we present below enables these challenges to be address in a rigorous manner.

Antenna Technical Approach

B-field sensing can provide advantages over E-field sensing for high-performance receivers in the ELF-LF range. One advantage is the ability to shield B-field antennas from sources of local E-field noise, such as electrostatic discharges due to wind and rain or switching power supplies. Other advantages may include ease of construction, ease of calibration, and antenna null depth. However, in applications that require operation in noisy industrial environments in which magnetic induction is significant, E-field sensing may have the advantage. This paper does not include an analysis of the B-field vs. E-field performance tradespace because it is highly dependent on the application and receiver environment, but focuses only on the optimal design of B-field antennas and amplifiers.

B-field antennas are conductive loops, and when they are electrically small they provide an electromotive force in response to a time-varying magnetic flux through the surface delineated by the loop according to Faraday’s law of induction. Consider a loop antenna comprised of N identical turns of a thin conductor (wire) in a uniform magnetic field B. The open-circuit, terminal-voltage magnitude V in response to a harmonic B field with frequency f can be shown to be

[1]

where A is the loop area, and is the azimuth angle for a loop with a horizontal axis orientation. Because the voltage response (gain) is proportional to frequency, a receiver that employs a voltage amplifier requires significant compensation if a flat frequency response over a wide relative bandwidth is desired. However, this problem can be resolved by capitalizing on other properties of the conductive loop as follows.

An electrically small loop antenna exhibits both a resistance R and an inductance L that depend primarily on the parameters of the loop. The ohmic resistance, neglecting skin effects and proximity effects, which can be shown to be minimal at our frequencies of interest, is given by

[2]

where is the resistivity of the conductor material (~1.72E-8 for copper), is the length of the conductor, is the cross-sectional area of the conductor, and is the length of the loop perimeter. Radiation resistance can be shown to be very small at our frequencies of interest. (This is the reason why electrically small transmitting loops can have very low efficiency.) The calculation of loop inductance is more involved, and many “handbook” equations are available for different geometries. (Sommerfeld, Grover, Terman and Wheeler are standard references.) The key characteristic of importance for now is that inductance L is proportional to and can be computed with good accuracy for the geometries of interest. Therefore, for a given loop antenna design, the source impedance is well represented by assuming the distributed capacitance is controlled so the self-resonant frequency of the loop is well above the highest frequency of interest. This is usually straightforward to achieve.

Now, consider the magnitude of the short-circuit current for an electrically small loop antenna. With best alignment of the dipole antenna response pattern (), it is given by

. [3]

This is a classic single-pole, high-pass-filter response with a 3-dB corner frequency at . So, if a loop antenna is designed to have a corner frequency less than the lowest frequency of interest, a flat frequency response can be achieved by operating the loop into an amplifier with very low input impedance (resistance), i.e., a transimpedance amplifier (current-to-voltage converter) for which the input is a virtual ground. This yields a front-end receiver gain for frequencies above of

[4]

where is the voltage magnitude at the output of the transimpedance amplifier with a V/I gain of . Furthermore, by managing the value of R, antenna thermal voltage noise can be reduced to any required level.

The issue of noise and sensitivity will be covered next, but first an additional important observation is stated. Given a fixed loop shape with area A and a fixed conductor mass , the corner frequency is constant regardless of the number of conductor turns N used to construct the antenna. This observation can be understood by noting that fixing the value of results in the value of R, as expressed by Equation 2, being proportional to since must scale as 1/N to keep the conductor volume , and hence , constant. Therefore, since the value of L is also proportional to , is constant under the conditions of constant loop shape, loop area, and conductor mass.

Receiver sensitivity, which determines the minimum detectable signal (MDS), is limited by antenna thermal noise and amplifier voltage and current noise. The sensitivity of the antenna alone can be defined as the B-field equivalent of the thermal voltage noise density, . Solving Equation 1 for B (with ) and equating V with gives the antenna B-field sensitivity (a spectral density) in units of

. [5]

This indicates the antenna becomes more sensitive ( decreases) with increasing frequency.

Substituting Equation 2 into Equation 5 with the conductor length expressed as , and then incorporating the relationship between conductor mass and conductor volume,, provides two additional expressions for :

. [6]

Here is the geometric shape constant for expressing perimeter length as a function of area (e.g., 4 for a square loop and for a circular loop) and is the conductor density (~8940 for copper).

The additional expressions for in Equation 6 provide further insight into the performance optimization tradespace and are central to the overall receiver design process. In particular, from the second expression in Equation 6 it can be seen that the only (practical) way to improve antenna sensitivity is to increase conductor mass and/or loop area A. To our knowledge (and surprise), this result could not be found in any published treatment of electrically small antennas. Note also that this result does not support the approach taken in many loop-antenna designs, for which increasing the number of turns is incorrectly used as a design strategy to increase antenna sensitivity. More turns of thinner wire might result in an antenna with less sensitivity that fewer turns of heavier wire.

Amplifier Technical Approach

The antenna-sensitivity relationships presented above were derived by considering the B-field equivalent of the thermal noise density. The primary goal, however, is to optimize the overall system noise figure to provide an SNIR that is not limited by the antenna/amplifier combination while providing features such as wide bandwidth, high dynamic range, and fieldability that are important for the application.

As mentioned earlier, the antenna/amplifier design could utilize the unloaded, open-circuit antenna voltage. This requires an amplifier with an input impedance much greater than the antenna source impedance and a 1/f rolloff to achieve a flat system frequency response. Such an amplifier presents challenges with regard to noise and would limit overall system sensitivity. Alternatively, the antenna could be resonated with a tuning capacitor, which provides essentially a high-Q filter for a single frequency of interest. However, that is only appropriate if a narrow-bandwidth signal at single, known frequency is to be received. Finally, an attempt could be made to match the antenna source impedance for maximum power transfer (conjugate match), but this does not provide the flat, wide-bandwidth response that is usually an important design goal.

Returning to the design concept associated with Equation 3, we focus on amplifiers for which the input impedance can be reduced to a very low value. One approach is to use an interstage transformer along with a balanced, common-base amplifier topology for the first stage. That approach, however, adds considerable complexity to the design and introduces additional rollofs and resistance. This increases the corner frequency and generates additional thermal noise over operating the antenna into a virtual ground. Alternatively, a variation on David Norton’s approach for “lossless feedback” (patented with Allen Podell in 1975) could be used in which emitter-base transformer coupling inverts the emitter signal and feeds is back to the base. This reduces emitter input resistance and linearizes the emitter response. However, it again requires a transformer that limits the low-frequency response of the amplifier.

Revisiting the ELF-LF sensitivity optimization problem with consideration of current technology indicates that the design tradespace can now be extended to include the use of ultralow-noise operational amplifiers in a transimpedance configuration. This has led to the development by the author of an antenna/amplifier performance model for ionospheric and magnetospheric research in the ELF through LF spectrum. When considering device options for an ultralow-noise, transimpedance amplifier, operational amplifiers from Analog Devices, Burr Brown and other companies meet requirements. New device designs are being optimized for operation at low equivalent source impedances. They are anticipated to have an input-referred voltage noise density of ~1 and an input-referred current noise density of ~1-2 at 1 KHz. In addition, these new devices can achieve gain-bandwidth products of >10 MHz, high large-signal bandwidths, and can operate with +/-15-volt rails to provide high dynamic range. The new AD797 from Analog Devices, for example, appears to be an excellent candidate for this application.

Our antenna/amplifier technical approach optimizes the antenna, using the equations presented above, in relationship to the transimpedance amplifier V/I gain and input-referred voltage and current noise densities. This results in sensitivities at the level from <1 KHz to >100 KHz with a <1- antenna area and a copper mass of <5 kg. Our design process can also trade the performance of a ferrite or mu-metal core against an air core. In addition, overall frequency response and bandwidth can be tailored to meet measurement requirements. Analog pulse-blanking techniques are employed after the transimpedance amplifier to suppress spherics (impulse noise and related signals due to lightning) and man-made impulse noise. This provides an optimized analog signal into an analog-to-digital converter. We then employ DSP techniques along with detection vs. false alarm models to provide the necessary back-end processing performance.

Antenna/Amplifier System Design Example

As a design example, we consider performance requirements to provide an ultra-sensitive capability to support broad-bandwidth characterization of ULF/VLF phenomena such as whistlers. The key requirement is a value low enough to ensure the MDS is not limited by the measurement system. Therefore, we specify a of 1 at 1 KHz, which, given that the system becomes more sensitive as f increases, ensures the analog sensitivity is below the natural noise floor. Then, to ensure the measurement system is relatively small and easy to deploy, we specify an antenna area of 1 . Choosing a square loop for ease of construction, Equation 6 gives a very modest required copper mass, , of ~1 kg.

We then balance the antenna noise voltage density against the input-referred voltage and current noise densities for an ultra-low-noise operational amplifier that is optimized for operation at low equivalent source impedances. This involves a number of tradeoffs including transimpedance amplifier V/I gain, system transducer gain, closed-loop bandwidth, and dynamic range. Choosing the number of loop turns used to distribute the required copper mass, , of 1 kg over the loop is a key part of the tradespace analysis. With 100 turns of 0.6-mm diameter wire and a V/I transimpedance gain of 10 , the total combined antenna and amplifier voltage noise spectral density is ~1.2 referred to the amplifier input. This provides an overall system sensitivity of ~2 at 1 KHz, a closed-loop amplifier bandwidth of ~1 MHz, and a dynamic range of ~96 dB. The actual achievable measurement bandwidth is then limited only by the self-resonant frequency of the antenna, which can be maximized by using winding strategies that minimize inter-winding capacitance.

Summary and Conclusions

We presented an approach to the design of state-of-the-art, magnetic-field sensor systems that can be optimized to detect extremely weak electromagnetic signals over a wide frequency range from ELF through LF (3 Hz – 300 KHz). Our design approach provides a balance between performance and fieldability and offers several ways to trade off design features to achieve optimal solutions for different applications. Features of our approach include an SNR-optimized antenna and front-end amplifier to provide femto-Tesla (fT) sensitivity; a flat, wide-bandwidth frequency response; and high dynamic range. This minimizes requirements for high back-end DSP processing gain (i.e., long integration times).

References

[1] Robert. A. Helliwell, Whistlers and Related Phenomena, Stanford University Press, 1965.

[2] E. L. Maxwell and D. L. Stone, “Natural Noise Fields at 1 cps to 100 kc”, IEEE Transactions on Antennas and Propagation, AP-11, No. 3, pp. 339-343, 1963.