Duality of Electric and Magnetic Fields
Capacitively Coupled “Displacement” Currents
Monitors, Power Transformers, Mains Power Wiring, Motors, DC-DC Converters
Low/High Source Impedances
Mains Power Noise – 50/60 Hz and Harmonics
Common Mode Rejection Ratio
Electric and Magnetic Field Shielding
Electric and magnetic fields are linked via the phenomena of signal alternation over time. Any time-varying electric field has an associated time-varying magnetic field and vice versa. The relative strengths of the coupled fields changes as a function of the generation and environmental conditions.
Electric or magnetic field coupling efficiency can also be considered by examining the construction of reactive circuit elements, namely the capacitor and inductor. A capacitor is created between any two conductors separated by a dielectric. Capacitor reactance increases in proportion to increases in conductor surface area and also in inverse proportion to the distance between conductors. An inductor is created by any conductor. Inductive reactance increases in proportion to the number of turns a conductor makes in the shape of a spiral.
Antennas couple to time-varying electric and magnetic (electromagnetic) fields. In the simplest form, an antenna is a length of conductive wire. This length of wire can be considered to have both capacitive and inductive aspects. The capacitive aspect is sensitive to electric fields and the inductive aspect is sensitive to magnetic fields.
Interfering noise sources can generate electromagnetic fields. These fields alternate at a variety of rates. A slowly-varying field is one associated with mains power. The field generated by mains power voltage has a very long wavelength because the voltage alternates as such a slow rate (50/60 Hz). An antenna designed to couple to such a field would need to be extremely long. Because the wavelength is so long, in the confines of a typical workspace, the field magnitude difference between any two points in space is very small. Accordingly, this mains-generated electromagnetic field in the workspace manifests signal interference in the form of displacement currents. A displacement current is the current that flows through a capacitor.
In the case of mains power-sourced, low frequency electromagnetic fields transmitted through air, the magnetic field component of the mains power interference is not efficiently transmitted or received. However, mains power interference establishes a varying electric field, in the workspace, this phenomenon results in the movement of displacement currents through the room. These currents result from the capacitances between the various conductors in the room. A subject in the workspace can be considered a volume conductor. This volume conductor is capacitively coupled to the mains power wiring.
The displacement current flowing from mains power wiring, to a subject, results in a voltage manifesting on the subject’s body with respect to mains ground. This voltage can easily be measured using a high impedance oscilloscope probe that is referenced to mains ground. The measured voltage will be typically be 10 volts or less and the waveform observed will be a faithful reproduction of the mains power voltage waveform. Because the subject’s body is conductive, the observed waveform will appear largely identical no matter where the subject is probed. Because this interfering voltage appears everywhere on the subject, this voltage is called a common-mode voltage.
This common mode voltage is very problematic for sensitive laboratory workspace measurements. Special methods are required to measure very small voltages in the presence of much larger common-mode voltages. The primary strategy for performing these types of measurements involves the use of differential amplifiers. A differential amplifier will only amplify the voltage difference between the two amplifier inputs. If an identical voltage signal appears at both inputs, this signal will be largely rejected. The specification which defines this ability is the Common Mode Rejection Ratio (CMRR). If the CMRR is 80dB, then this means that the amplifier will reduce a sensed common mode signal by a factor of 10,000.
In practice, any amplifier’s CMRR specification must be considered in context with the amplifier’s isolation to reference characteristics. If a differential amplifier is powered by a supply whose ground reference is identical to mains ground, then the amplifier will act upon the common mode signal that is referenced to mains ground. Alternatively, if the amplifier is powered by a supply which is referenced to the signal source, then the amplifier acts upon the common mode signal which is referenced to the chosen source location. This location is then referred to as amplifier ground.
The physical phenomena of capacitance is commonly encountered. Capacitance is the ability of an object to store electrical charge. Anything that can be electrically charged will exhibit capacitance. Capacitance is defined as charge divided by voltage. The concept of charge implies polarity. Opposing charges (Q) on conductors, separated by an insulator, and the electric potential (voltage, V) between the conductors, are proportional to each other. This proportionality constant is capacitance.
C = Q/V
Capacitance exists between any two electrically conductive surfaces which are separated by an insulator. The capacitance of two electrically conductive parallel identical plates is defined as the permittivity of the insulating material between the plates multiplied by the surface area of one of the plates and divided by the distance between the plates. The permittivity of an insulating material is determined by multiplying the material’s dielectric constant (relative permittivity, Œµr) by the permittivity of free space (Œµo = 8.854√ó10‚àí12 F m‚Äì1)
The concept of displacement current was conceived by James Maxwell in 1861, in his paper “On Physical Lines of Force”. Displacement current is not an electric current of moving electrons, but rather a time-varying electric field that has the units of electric current density and thus has an associated magnetic field. The displacement current can be thought of as the beginning of the flow of current which then precipitates a time-varying electric field. In Maxwell’s 1865 paper, “A Dynamical Theory of the Electromagnetic Field”, Maxwell derived the electromagnetic wave equation. This derivation united electrical, magnetic and optical phenomena into a single theory. The displacement current term, in Maxwell’s electromagnetic wave equation, proved to be a critical element that completed Maxwell’s equations. In particular, the displacement current explains the existence of electromagnetic waves.
In context of physiological measurements, especially those which involve the practical measurement of small biopotentials generated by physiological sources, displacement currents have substantial impacts. In modern laboratory environments, mains power grids are always nearby. High voltage (120/240 VAC) electrical power is well-distributed around such environments. In the case of subjects in a room, displacement currents flow between the high voltage alternating conductors and the subject. The subject can be considered to be a volume conductor that is in the pathway of the displacement current flowing between the high voltage alternating conductors and mains ground. An voltage measurement probe, such as oscilloscope, which is referenced to mains ground, will show a percentage of the alternating mains voltage present on a subject.
External interfering sources can be created by a variety of devices. Common circumstances involve the flow of large currents. Any current flow creates a magnetic field orthogonal to the direction of current flow. Alternating currents result in varying magnetic fields. If a changing magnetic field encounters a conductor perpendicular to the direction of the field, a current will be induced to flow in the conductor.
Nearly all mains connected equipment includes a power transformer, that is described as an AC to AC converter or AC to DC converter. A power transformer converts the typically higher mains voltage of 120 or 240 VAC to lower voltage useful by the equipment (1.8 to 30 VAC or VDC). This conversion process involves two or more coils of wire surrounding a common core that conducts a magnetic field. The magnetic field is induced into the core by the primary coil, the field is established in the core and then the field induces a current in the secondary coil. The ratio of the primary and secondary coil turns is identical to the ratio of the primary to secondary coil voltages and is also identical to the inverse ratio of the primary and secondary coil turns. For example, if a transformer converts from 120 VAC (primary) to 20 VAC (secondary), then the primary coil will have 6 times more turns then the secondary coil. Also, the primary current will be 6 times less than the secondary current.
One interfering aspect of a power transformer is related to the idea of magnetic field leakage. Ideally, the transformer’s magnetic field should be confined to the core. In practice, some magnetic field strays from the core and can induce currents to flow in other conductors which may be nearby the transformer. The basis of transformer action can be observed in very simple geometries. If one conductor carries an electric current, this current will generate a magnetic field. The resulting magnetic field will attempt to induce a current in any nearby conductors. Any current flow in a conductor will generate a related magnetic field. Furthermore, a current is induced in all conductors placed in a changing magnetic field.
An electric motor employs magnetic fields to push on a rotating armature. AC motors use alternating current, usually sourced directly from mains power, to generate alternating magnetic fields to induce armature rotation. DC motors employ direct current, but commute this current into alternating magnetic fields to induce armature rotation. In both types of motors, the generated alternating magnetic fields can stray from the confines of the motor.
DC-DC converters are a special type of transformer which convert a DC voltage of one value to another. These converters operate by creating a primary AC voltage from the primary input DC voltage. This primary AC voltage drives a transformer where the secondary AC voltage is converted back into a secondary DC voltage. Even though the inputs and outputs of a DC-DC converter are DC voltages, the converter still generates stray magnetic fields via the operation of its internal transformer. Generally, magnetic shielding is employed to help reduce stray magnetic field intensity. Furthermore, in order to obtain high power conversion efficiencies, DC-DC converters will employ high speed current switching to minimize power losses in the converter. This high speed current switching results in large common mode noise signals being present on all ports of the converter. Common-mode chokes are typically used to suppress this noise.
Signal source impedances have a great impact on the design methodology of the amplifiers used to record those signals. Generally considered, bipolar junction transistor amplifier inputs are optimal for source impedances less than 1Mohm. For source impedances greater than 1Mohm, JFET transistor input construction is better suited for signal amplification. The determination of optimal amplifier input structure is helped by examining the relationship between the transistor noise voltage (Vn) and the transistor noise current (In). When the source impedance is equal to Vn/In, the amplification performance, in terms of optimal signal to noise ratio, is maximized for that particular amplifier. Ideally, when amplifying a signal, both Vn and In are very low and the ratio (Vn/In) is reasonably close to the signal source impedance.
High performance, instrumentation amplifier, integrated circuits are typically used in practical amplifier designs. These chips incorporate very low noise front-end input transistor staging, matched and trimmed resistor networks, high common mode rejection and simple gain setting.
Signals from high source impedance generators present multiple challenges for measurement. In these cases, JFET or MOSFET input signal amplifiers are best used. Because of the high source resistances and amplifier input impedances, the conductors running from signal source to amplifier will likely require shielding to eliminate the influences from stray displacement currents. Even though the effective capacitance, from input conductor to mains power lines, might be well under 1pF, interference is likely without the use of shielding to protect the input conductor from impinging displacement currents.
Example: Consider a source impedance of 1G ohm and amplifier input impedance of 100G ohms, assuming a capacitance of 0.00885 pF (8.85 femto farads), from input conductor to 120V @ 60Hz mains wiring:
If the input conductor is 1 meter long, diameter of 1mm and is 1 meters from mains wiring, the capacitance from mains wiring to input conductor will be on the order of 8.85 femto farads.
Xc = 1/2*Pi*F*C = approximately 300G ohms
The mains voltage impressed on the input conductor will be approximately:
120 VAC * 1G ohm/(1G ohm + j300G ohm)
Vp = Vs (sRC/(1+SRC))
Vp = 120VAC * (1*(1/300))/(1+(1*(1/300)) = 0.40 VAC rms = 1.13 V p-p
Assuming a measurement of typical cellular action potential will be about 110 mV p-p, the above interfering signal will be 1.13/0.11 or about 10 times greater! Accordingly, signal shielding is required to reduce the impacts of impinging displacement currents on the signal input conductor. However, a problematic issue that arises, when using input signal shielding, is associated with maintaining wide measurement bandwidth for high source impedances. As source impedance climbs, and if the input conductors are shielded and grounded, input capacitance acts to limit the high frequency response. The signal path incorporates a high series impedance and a shunt capacitance to ground, thus typically introducing a single-pole RC type lowpass filter. Using the above examples, assuming a shunt capacitance of 8.85 pF (1000x higher than non-shielded case), the frequency response is calculated as:
1/2*Pi*R*C = 17.98 Hz
It’s possible to use shielding methods which can drive the shield to the same potential as the input conductor. If the shield is held to the same voltage as the input conductor it will not be possible for a charge difference to develop between input conductor and shield, effectively removing the band limiting effects associated with the shield capacitance. However, driven shield methods will introduce some noise into the shielding, thus negatively impacting signal to noise ratio. Even so, measurement bandwidth can be greatly extended. Starting with the previous case, if effective shield capacitance can be reduced by a factor of 100 (to 88.5 femto-farads) then bandwidth will be 100x greater:
17.98 Hz * 100 = 1.798 kHz
Generally, for best noise performance and highest bandwidth, shielding should be provided by a faraday cage whose boundary is far from the recording site. In this case, shielded input cables are not required and so input capacitance can be very low.
The mains power present in laboratory workspace environments, depending on country of origin, will be nominally 120/240 VAC at 50/60 Hz. In a typical workspace, there may be many wall-mounted mains power outlets. In addition, many of these outlets will typically be filled with mains power cords for a variety of laboratory equipment. Extension cords and power strips may also be present. In total, the usual laboratory workspace holds many meters of 10-16 gauge copper wiring. The environment will usually be permeated by such wiring. The majority of this wiring will be carrying large currents to power the electrically operated systems in the laboratory, including lighting and air handling systems. Much equipment in the laboratory will likely contain digital electronics and switching power supplies, both of which will induce high frequency transient currents on the surrounding mains wiring. The presence of motors and efficient lighting (fluorescent or LED) will introduce additional noise onto the mains power distribution. Individually, these types of added noises, known as conducted emissions, will usually be less than certain specified amounts as determined by CISPR22 and CISPR11. However, when collectively considered, these noises can be substantial.
The primary mains power frequencies of 50 or 60Hz are not perfectly sinusoidal. Instead, aberrations in the cycle result in the development of harmonics on the mains line. When measuring frequencies of associated displacement currents in the laboratory, it’s not unusually to see large components up to the 5th harmonic. In a 50Hz environment, this means interference may include 50, 100, 150, 200, 250Hz, etc. noise sources. In a 60Hz environment, this means interference may include 60, 120, 180, 240, 300Hz, etc. noise sources.
Computer monitors, due to the large scale multiplexing and display refresh required to drive the screen display, will usually update at rates anywhere from 60Hz to 240Hz. This periodic update results in associated displacement currents in the environment. A monitor behaves similarly to a one large flat conductive plate which is being excited by a rapidly switching alternating current source. This plate creates one-half of a capacitance that is established with the balance of the room’s conductive elements. Because of the high speed switching used in monitor display drives, these update rates will also incorporate harmonics.
CMRR is the ability of an differential amplifier to keep common mode signals from being amplified. Common mode signals are signals that appear identically on both inputs (+/-) of the input differential amplifier.
In the example case of recording biopotentials from a subject, assuming mains power of 60Hz, and sitting within a few feet of a large computer display updating at 72 Hz, it would be likely to measure the following voltage generated, displacement current frequencies present throughout the volume of the subject’s body:
60Hz, 72Hz, 120Hz, 144Hz, 180Hz, 216Hz, 240 Hz, 288Hz, 360Hz, etc.
It’s important to use amplification systems that have high common-mode rejection ratio (CMRR) over the range of biopotential frequencies of interest, primarily in the region of DC-500 Hz, for surface electrode measurements. However, high CMRR is insufficient to remove all environmentally-induced interference. Increasing CMRR past 80dB is ineffective at removing displacement-current-induced voltage signals on the subject, because a myriad of displacement current paths develop through the subject. The body is not a perfect conductor, so small differential voltages will develop on the subject’s body subject to common mode current flow. This is due to the flow of varying displacement currents across and through the subject’s body. Mains power, monitor, motor and lighting system generated displacement currents will turn partly into differential voltages when impressed though a subject’s body. To separate desired biopotential signals from periodic noise, in the amplified signal path, filtering is typically employed. Synchronous removal methods for interference are effective. In some cases, comb bandstop filters are also sufficient. These filters are typically Infinite Impulse Response (IIR) or Finite Impulse Response (FIR) based and can be highly selective.
Both electric and magnetic fields can add interference to a signal. Electric fields and magnetic fields are always coupled. For any alternating electric field (wave) there will be an associated magnetic field, and vice versa. Commonly, the term electromagnetic field is used to identify this wave relationship. Electromagnetic fields are propagated by photons. Electromagnetic energy, depending on the associated frequency of alternation, manifests differently to the human senses. For example, photons with a wavelength of 560nm will appear as green light to the human eye. Photons with a wavelength of 100MHz are not perceived by humans directly. However, photons at this frequency are commonly used as the carrier frequency for frequency modulated (FM) radio. As photon frequency increases, they can manifest as ultraviolet light, X-rays and Gamma rays.
In the frequency range associated with human physiological recording, the electromagnetic wavelength is very long. Most biopotential, surface electrode based, physiological measurements are at a frequency of less than 500 Hz. The most common electromagnetic interference signals are those associated with electrical power distribution. Typically these interfering signals have a fundamental of 50 or 60 Hz, and also include their harmonics. The electromagnetic wavelength at 50 Hz is calculated as:
Wavelength = Speed of Light / Frequency or
300 E 6 (meters/second) / 50 (cycles/second) = 6,000,000 meters
To efficiently couple this electric or magnetic field to an antenna, the antenna would need to be on the order of 1/4 wavelength of 6,000,000 meters or 1,500,000 meters long.
Given that humans are only about 1.5 meters in height, they do not couple efficiently to electromagnetic fields of this frequency. However, because the electric field is alternating in potential, and because a capacitance exists between the subject and the field source, a displacement current may flow from field source to subject. It is this displacement current which typically presents the greatest source of interference for physiological recording.
Because of the very large wavelength of the interfering electromagnetic field, the subject and recording equipment will experience nearly identical field strengths at any point in time. The electromagnetic field becomes common mode for both subject and recording equipment. However, depending upon the location of the dominant capacitive coupling paths, the flow of common mode currents may create differential voltages as the currents move through a variety of pathways.
1. Relativity and its roots
2. Driven shields and input guarding
3. Electric and Magnetic Fields
4. Good electrode/skin interface model and biopotential frequency ranges
5. measure electric field strength
6. field strength meter
7. great paper on electric field sensing