Coupling Mechanisms

To produce desense, the interfering signal has to reach the receiver. The process by which it does this is called coupling.

9.4.5.1 "Radiated" Coupling

"Radiated" coupling, as generally defined, means any coupling that occurs without a direct connection between threat and victim (e.g., microcontroller and receiver). This does not imply radiation in the strict physical sense; the coupling in nearly all self-desensitization cases occurs within less than one-tenth of a wavelength of the source (threat), and so occurs in the "near field" or induction region, instead of the "far field" or radiation region. Even at 2450 MHz, where a wavelength is 12.25 cm, it is rare to have the coupling distance exceed 2 cm. It becomes even less likely as the maximum dimension of a wireless sensor node approaches this length.

9.4.5.1.1 Inductive Coupling and Current Loops

It was discovered by Faraday in the early 1800s that a changing current in a coil of wire could induce a changing current in a second coil of wire. This phenomenon became known as induction, and is, among other things, the principle of operation of the transformer.

As with most physical phenomena, induction can also occur when it is not desired. This most commonly occurs in small electronic devices when a current loop is created in an integrated circuit V_dd and V_ss supply (such as a microcomputer or DC/DC converter), and couples into the device's loop antenna or, less often, an inductor in a receiver circuit.

9.4.5.1.1.1 Coupling Equation

Suppose one has two conductive loops, of negligible thickness, separated by a distance d. One of the loops, loop 1, is further assumed to carry a current I1. The loops are so close together that all magnetic lines of flux generated by loop 1 are contained in loop 2. Further, it is assumed that d << 1, where 1 is the wavelength of the frequency of interest. See Exhibit 13.

Exhibit 13: Inductive Coupling

It can be shown that a mutual inductance,

exists between the two loops, where:

L_m = mutual inductance, H
μ = permeability of the intervening medium, H/m
A = loop area, m²
d = distance between the loops, m

If loop 2 were opened, a voltage v₂ = L_m (di₁/dt) would exist between the open ends. Stated another way, the mutual inductance produces a current-controlled voltage source at the terminals of loop 2, with a value of v₂ = L_m (di₁/dt). This voltage may interfere with receiver operation.

For example, suppose A = 1 cm², d = 5 mm (a common spacing between receiver and microcomputer circuit boards in miniaturized equipment), and the boards are in air, where μ = 4π × 10⁻⁷ H/m. Then,

This mutual inductance can couple a changing current in loop 1 into loop 2, where it may be expressed as voltage v₂ = L_m (di₁/dt). Suppose that i₁ is a 50 percent duty cycle, 1 mA peak, 1 MHz trapezoidal waveform, with rise and fall times of 10 ns. If one is interested in desensitization at 151 MHz, the 151st Fourier harmonic is examined:

Then,

di_1,151/dt = (c₁₅₁ × 2πf)cos2πft
v₂ = L_m (c₁₅₁ × 2πf)cos2πft = (25 × 10⁻⁹ H) × (888.3 × 10⁻⁹)

× (2π × 151 × 10⁶)cos(2π × 10⁶)t
v₂ = (21 × 10⁻⁶)cos(2π × 151 × 10⁶)t

Loop 2 now has a signal with a peak amplitude of 21 μV riding on it. Ordinarily, this would be of little concern; however, if loop 2 is the antenna, this signal (equivalent to 14.8 μV_rms) is 20 log (14.8/7.07) = 6.4 dB above the receiver's desensitization threshold. Note that this occurred with a loop 1 current of only 1 mA.

This coupling can be reduced in several ways. The area A may be reduced, or the distance d increased; both of these reduce the inductance L_m. The geometry may be changed, so that loop 2 is not parallel to loop 1. Although it will not reduce the coupling, it is clear that reducing the rate of change of i₁, di₁/dt, will directly reduce the voltage v₂ coupled to loop 2. All these methods may be used in product design. It is noteworthy that, with the exception of the last, all alternatives require a change in the physical layout of the components; either a relayout of circuit boards or a change in the physical design of the product (by separating the circuit boards further). This is a common theme in the prevention of EMC problems — it truly is a multidisciplinary task involving mechanical design, electrical engineering, and marketing and product design.

It should also be mentioned that arrangements of the two loops are used to minimize coupling. If two loops of radius R are close together (i.e., d << λ), it can be demonstrated that if they are offset such that their overlap is reduced to an amount D = 0.4783 R, the magnetic coupling is reduced to zero.^[7] This arrangement is illustrated in Exhibit 14.

Exhibit 14: One Method to Reduce Inductive Coupling

Further, if the loops are moved apart, but kept in parallel planes still in the induction region, it can be demonstrated that if the angle between the loop axis and a line drawn between the loop centers is 54.736°, the magnetic coupling is also reduced to zero.^[8] This arrangement is illustrated in Exhibit 15.

Exhibit 15: A Second Method to Reduce Inductive Coupling

Note, however, that although the magnetic coupling may be reduced to zero in these configurations, capacitive (electric) coupling between the two loops may still exist and may, in fact, be the dominant coupling mechanism.

9.4.5.1.1.2 Probably Does Not Involve Inductors

EMC problems involving inductive coupling often do not involve inductors. The main reason is that microcontroller and other digital circuits typically have few inductors; however, the ones they do have (for example, in DC/DC converters) typically carry very large currents with high harmonic content, and are important sources of desensitization energy. The usual inductive coupling problem is caused by current loops on personal computer boards, generally involving microcontroller V_dd and V_ss supplies (about which more will be said later).

9.4.5.1.2 Capacitive Coupling and Voltage Dipoles

Voltage dipoles, in the form of static electricity, have been known since antiquity. It was not until James Clerk Maxwell published his theory of electromagnetism in 1864, however, that it was predicted that a "displacement current" would flow between two conductive objects if the charge on one were allowed to vary. This displacement current is the source of capacitive coupling.

9.4.5.1.2.1 Coupling Equation

Suppose one has two conductive plates, of negligible thickness, separated by a distance d. One of the plates, plate 1, is at potential V₁. The plates are so close together that all electric field lines beginning on plate 1 end on plate 2. Further, it is assumed that d << λ, where λ is the wavelength of the frequency of interest. See Exhibit 16.

Exhibit 16: Capacitive Coupling

It can be shown that a capacitance,

exists between the two plates, where

C_m = capacitance, F
ε = permittivity of the intervening medium, F/m
A = plate area, m²
d = distance between the plates, m

If v₁ were allowed to vary, a displacement current i₂ = C_m (dv₁/dt) would flow between the plates. Stated another way, the mutual capacitance produces a voltage-controlled current source terminating on plate 2, with a value of i₂ = C_m (dv₁/dt). This voltage may interfere with transceiver operation.

For example, suppose A = 1 cm², d = 5 mm, and the boards were in air, where ε ≅ 8.854 × 10⁻¹² F/m. Then

This capacitance can couple a changing voltage on plate 1 into plate 2, via a current i₂ = C_m (dv₁/dt). Suppose that v₁ is a 50 percent duty cycle, 2-V peak, 1-MHz trapezoidal waveform, with a rise time of 10 ns. If one is interested in desensitization at 151 MHz, the 151st Fourier harmonic is examined:

Plate 2 now has a current entering it with a peak amplitude of 298 nA (or 211 nA_rms). Ordinarily, this would be of little concern; however, if plate 2 is an antenna, with an impedance of 50 Ω, the desensitization threshold in terms of current is i_desense = e_desense/R = 7.07 μV_rms/50 Ω = 141 nA. This means the interfering signal is 20 log (211/141) = 3.5 dB above the receiver's desensitization threshold. Note that this occurred with a plate 1 signal voltage of only 2-V peak.

This coupling may be reduced in several ways. The area A may be reduced, or the distance d increased; both of these clearly reduce the capacitance C_m. The geometry may be changed, so that plate 2 is not parallel to plate 1. Importantly, the coupling current is directly proportional to dv₁/dt, so the coupling may be reduced by reducing the rise and fall times of the voltage waveform. The faster the rise time, the greater the coupling; this is a reason why nonsinusoidal (e.g., square) waves typically cause the greatest desense problems.

Further, a "grounded" third plate, called a "Faraday shield," may be placed between plates 1 and 2. The Faraday shield need not be actually grounded, but must be at a constant potential, so that the electric field lines (and so the displacement current) originating on plate 1 terminate on the Faraday shield, instead of on plate 2.

9.4.5.1.2.2 Probably Does Not Involve Capacitors

This coupling mechanism occurs most often due to lack of three-dimensional thinking during the physical design of the product. Commonly, a flex circuit going to a display will pass near the antenna, or the voltage-controlled oscillator on the receiver circuit board will be placed next to a fast-switching circuit on the microcontroller circuit board, when the two boards are mated together. Surprisingly, one of the most common capacitive coupling problems is the capacitive coupling between inductors: inductors tend to be large, and they carry fast-switching voltages.

9.4.5.1.3 True Radiated Coupling

To get true radiated coupling requires that the source be a relatively efficient radiator that, in turn, implies it must be at least a small fraction of a wavelength in size. This is a rare event in modern electronic equipment, and getting more so with product miniaturization. Problems can arise, however, due to true radiated coupling between separate products. Products incorporating early zero-IF receivers, for example, were often optimized so that their local oscillators (tuned to the frequency of reception) did not interfere with their own reception; however, they could interfere with nearby receivers on the same frequency. This problem, once identified, was easily corrected; however, it was often not detected until late in the product development cycle. One must also consider the possibility of interference with other services; the television receiver interfering with the shortwave radio, described earlier in this chapter, is one example of such an occurrence.

In any event, because radiation occurs when charge is accelerated, for minimum radiation opposing electric charges should be physically as close together as possible. Similarly, opposing magnetic "charges" (i.e., currents flowing in opposite directions) should be placed as close together as possible. Note that if one has minimized both inductive and capacitive coupling in a design, these two criteria are already met.

9.4.5.2 "Conducted" Coupling

"Conducted" coupling, as generally defined, means any coupling that occurs only with a direct connection between threat and victim (e.g., microcontroller and receiver).

9.4.5.2.1 Mutual Impedance Coupling

Suppose one has the circuit illustrated in Exhibit 17. Before the switch is closed, the voltage at point A is V_Aopen = Z₂/(Z₁ + Z₂). After the switch is closed, the voltage is V_Aclosed = (Z₂ || Z₃)/(Z₁ + (Z₂ || Z₃)). The changing current through the Z₃ branch causes a change in the voltage applied to Z₂. If Z₂ were a circuit sensitive to supply voltage variations (e.g., a transceiver, sensor, or other system with significant analog circuitry), and Z₃ a circuit with large changes in supply current over time (e.g., a microcomputer, voltage multiplier coil, or transducer), it is possible to see that Z₂ circuit operation could be impaired with this arrangement.

Exhibit 17: Mutual Impedance Coupling

The culprit, of course, is Z₁, the mutual impedance; if Z₁ = 0 Ω, V_Aopen = V_Aclosed = V at all times. Unfortunately, all practical voltage sources have nonzero internal impedances, so if, as is often the case with wireless sensor network design, a single supply source is mandated, this problem can be minimized but not eliminated.

One is careful to state that Z₁ is an impedance, instead of a resistance. If a series inductor is placed in a line supplying current to more than one circuit and a bypass capacitor is not used, the inductor may also act as a mutual impedance, and lead to mutual impedance coupling.

9.4.5.2.2 The Importance of Current Density

The copper used in most circuit board runners has a nonzero resistivity, so the geometry of a runner has an effect on its resistance. A long, thin runner has more resistance than a short, wide one. To minimize mutual impedance coupling, it is therefore important to place current flow through the widest and shortest possible runners between source and load. Said another way, for minimum mutual impedance coupling one desires to have the current distributed through the most copper cross-sectional area (i.e., the lowest current density), for the shortest distance possible. A numerical example will illustrate the situation.

The resistivity ρ of the electrodeposited copper used in circuit boards is approximately 1.7 × 10⁻⁶ Ωcm = 1.7 × 10⁻⁸ Ωm. The half-ounce copper runners typically used have a thickness T of approximately 18 μm. These runners then have a sheet resistance

If a runner of this material has width W = 5 mil (130 μm) and length L = one inch (2.54 cm), it has a resistance of

If, for example, the 100 mA current of a small motor is sent through this runner, the voltage drop along the runner is E = IR = 10⁻¹ A × 0.188 Ω = 18.8 mV. A receiver supplied from the motor end of this runner would see an 18.8 mV supply variation as the motor cycled on and off. If the runner is replaced with one with W = 100 mils (2.54 mm), R = 940 × 10⁻⁶ Ω (1/0.100) = 0.0094 Ω, resulting in a voltage drop of E = 10⁻¹ A × 0.0094 Ω = 0.94 mV. Although this is a 20-dB improvement, the preferred method to avoid the effects of this voltage drop is to connect the receiver to the voltage source directly, avoiding the voltage drop of the motor circuit board runner entirely.

Sources of mutual impedance coupling include the internal resistance of batteries, capacitors, and voltage multipliers; battery contact resistance; and the resistance of circuit board via holes. High-current runners should have a minimum of circuit board layer changes; however, when layer changes are inevitable, multiple parallel vias should be used to minimize the resistance. Using multiple parallel vias is also good engineering practice for another reason: Vias are the most likely point of failure in a printed circuit board, due to separation between the copper of the trace and the copper in the via. This failure most often occurs due to thermal cycling or mechanical stress, and is often intermittent — the worst type of field failure to have.

Coupling Mechanisms