Noise Coupling

Abstract

Noise coupling is one of the essential and constantly recurring topics in EMC. An EMC design engineer must consider any noise coupling paths constantly during the design and when troubleshooting.

First of all, this chapter discusses coupling paths. Then it is shown which coupling leads typically to differential-mode noise and which coupling does typically lead to common-mode noise.

The only difference between success and failure is the ability to take action.

—Alexander Graham Bell

12.1 Coupling Paths

One of the most important concepts to understand in EMC is the concept of coupling paths . To start off, let’s see what parts are involved when electromagnetic interference (EMI) happens and why focusing on coupling paths is so important:

• 1. Source. In the real world, there are sources of unwanted electric or electromagnetic noise. For EMC immunity tests, the noise sources are well defined with the goal that these sources should be as close as possible to the real world (e.g., ESD generators, burst generators, surge generators, and antennas).

• 2. Coupling path. The noise needs a path from the source to the victim. This path is called the coupling path or coupling channel.

• 3. Victim. The victim is the receiver or receptor of the noise, which could cause interference.

Figure 12.1 shows us that if there are issues with EMI and EMC, one has the following three options to overcome these issues:

• 1. Reduce the noise level of the noise source.

  • Emission testing. When testing for radiated emissions of a product (meaning: the EUT is the source of noise), the noise level can be reduced by adding filters and shields to the EUT, controlling the signal transients (rise-/fall-time), or performing a complete redesign (e.g., change from single-ended to differential signaling).

    Fig. 12.1

    

    Noise coupling

  • Immunity testing. The applicable EMC product standard specifies the noise level of the noise source for EMC immunity tests. Therefore, there is no option to reduce the noise level for EMC immunity tests.

• 2. Make changes to the coupling path. The coupling path is where an EMC engineer usually has to focus on if a product fails an EMC test. With well-considered changes to the coupling path, emissions can be reduced and immunity increased (e.g., improving ground connections, adding filters and shields to cables and PCBs).

• 3. Increase the victim’s immunity level with software or firmware. Possible software features which can increase a product’s EMC immunity are digital filters (e.g., median), spike removers (remove spikes in sensor signals), and sanity checks.

Let us have a closer look. There are different kinds of coupling paths, some of them are conductive (galvanic), and some are nonconductive (radiated). Figure 12.2 shows the four different types of coupling:

• 1. Conductive coupling (common impedance coupling)

  Fig. 12.2

  

  EMI noise coupling paths

• 2. Capacitive coupling (electric field coupling)

• 3. Inductive coupling (magnetic field coupling)

• 4. Radiated coupling (electromagnetic field coupling)

The four coupling types are discussed in Sects. 12.1.1–12.1.4.

12.1.1 Conductive Coupling

Conductive coupling can occur when two or more circuits share a common path or common conductor and, therefore, a common impedance $\underline {Z}_{com}$ [Ω]. This shared path leads typically to ground or another reference plane (see Fig. 12.3a). Why could a common conductor path lead to EMC problems or a failed EMC test case? Here is an example: if one of the two circuits in Fig. 12.3a experiences an ESD, burst, or surge pulse, a high current may flow for a short time through a common conductor segment and introduces a noise voltage to the other circuit, which may lead to a malfunction. This is the reason why it is crucial having low-impedance earth/ground planes. A low-impedance ground plane helps to minimize the conductive coupling. In addition, a common path often leads to bad signal integrity as well.

Fig. 12.3

Conductive coupling examples. (a) Shared path to ground. (b) Shared power supply

Suppose that circuit 1 in Fig. 12.3a drives some power electronics and circuit 2 is a sensitive measurement circuit. The high current of the power electronics (noise current) introduces a noise voltage $\underline {V}_n$ [V] in the said common impedance $\underline {Z}_{com}$ [Ω] and will lead to interference on the measurement circuit 2. Another example is shown in Fig. 12.3b, where two circuits share a power supply. In the case that circuit 2 is switched off and $\underline {I}_2$ [A] suddenly drops to 0 A, voltage $\underline {V}_1$ [V] will increase by $\varDelta \underline {V}_1 = \underline {I}_2\left ( \underline {Z}_{line-supply}+ \underline {Z}_{line-GND}\right )$.

Generally speaking, the noise voltage $\underline {V}_n$ [V] introduced to the victim circuit is proportional to the common impedance $\underline {Z}_{com}$ [Ω]:

$$\displaystyle \begin{aligned} \underline{V}_n = \underline{I}_n \cdot \underline{Z}_{com} {} \end{aligned} $$

(12.1)

where:

• $\underline {I}_n =$ current of the noise source in [A]

• $\underline {Z}_{com} =$ common impedance of noise source and victim in [Ω]

Equation 12.1 states that the noise voltage $\underline {V}_n$ [V] is independent of the frequency f [Hz] of the noise signal. However, it must be mentioned that the common impedance $\underline {Z}_{com}(f)$ [Ω] is a function of frequency, and it is to be expected that $| \underline {Z}_{com}(f)|$ [Ω] will increase with increasing frequency (skin effect, inductance L [H] of $\underline {Z}_{com}$). Note: whether the amplitude of the noise voltage $| \underline {V}_n|$ [V] is acceptable or not must be decided under consideration of the useful signal’s amplitude (signal-to-noise ratio; see Sect. 6.6).

Some possible measures against conductive coupling are given in the list below. However, be aware that not every option is feasible in any case. The best option has to be decided for every case individually, as there is always a trade-off between project timelines, budget, and hardware costs.

• Separate current loop. The best and most effective measure against conductive coupling is separating the noise current loop from the victim’s current loop. In case of a complete separation, $\underline {Z}_{com} = 0$.

• Reduce coupling impedance. Try to make the coupling impedance as low as possible, e.g., by reducing the inductance (using solid copper planes on the PCB) or reducing the resistance (adding additional copper wires for the ground connection).

• Filtering. Adding a filter to the noise source helps prevent undesired noise current, whereas adding a filter to the victim will increase the victim’s immunity to noise signals. These filters are typically low-pass filters with capacitors or ferrites.

12.1.2 Capacitive Coupling

Capacitive coupling can occur if there is a coupling capacitance C [F] between two circuits (see Fig. 12.4). The field of concern for the capacitive coupling is the electric E-field. Thus, capacitive coupling is a near-field coupling (near-field; see Sect. 8.3), which means that the noise source and the victim, which receives the noise, are closely located to each other.

Fig. 12.4

Capacitive coupling between two circuits. (a) Physical representation. (b) Equivalent circuit

It is assumed that the capacitive coupling discussed in this section is a weak coupling. That means that the noise coupling is a one-way effect from the noise source to the victim circuit (negligible back reaction from victim to source).

Why could capacitive coupling lead to problems during EMC testing? For example, several wires are together in the same cable, which means that each wire is capacitively coupled to the other wires inside that cable (the capacitance is the bigger, the longer the cable, and the closer the wires to each other). One of the wires drives the reset signal of a controller system. During EMC testing, an ESD pulse happens to a connector pin that is connected to a wire in that cable. Suppose there are no measures against ESD at the connector pin. In that case, this pulse may discharge through one of the cable’s wires and couple capacitively into the other wires in the same cable and potentially resets the controller (if the controller reset signal is not appropriately filtered).

Capacitive coupling happens due to a noise source v ₁(t) [V] with high dv ₁∕dt [V/s] where a noise current i _n(t) [A] is coupled via a stray capacitance C ₁₂ [F] to the victim. The faster the voltage change dv ₁∕dt [V/s] and the larger the stray capacitance C ₁₂ [F], the higher the noise current i _n(t) [A] through C ₁₂ [F] [6, 7]:

$$\displaystyle \begin{aligned} i_n(t) = C_{12}\frac{dv_1}{dt} {} \end{aligned} $$

(12.2)

The noise voltage $\underline {V}_n$ [V] introduced to the victim circuit of Fig. 12.4 due to a capacitive coupling can be calculated like this [6]:

$$\displaystyle \begin{aligned} \underline{V}_n = \frac{j\omega\left(\frac{C_{12}}{C_{12}+C_{2G}}\right)}{j\omega+\frac{1}{R\left(C_{12}+C_{2G}\right)}}\underline{V}_1 {} \end{aligned} $$

(12.3)

where:

• $\underline {V}_n =$ noise voltage introduced to the victim (circuit 2) in [V]

• $\underline {V}_1 =$ voltage of the noise source (circuit 1) in [V]

• C _1G = total capacitance of the noise source circuit to ground in [F]

• C _2G = total capacitance of the victim circuit to ground in [F]

• C ₁₂ = total couple/stray capacitance between circuit 1 and circuit 2 in [F]

• R = load resistor of the victim circuit in [Ω]

• ω = 2πf = angular frequency of the sinusoidal noise signal in [rad/sec]

In most cases, R [Ω] is of much lower impedance than the parallel impedances of C ₁₂ and C _2G [6]:

$$\displaystyle \begin{aligned} R \ll \frac{1}{\frac{1}{1/\left(j\omega C_{12}\right)}+\frac{1}{1/\left(j\omega C_{2G}\right)}} = \frac{1}{j\omega\left(C_{12}+C_{2G}\right)} {} \end{aligned} $$

(12.4)

If the condition of Eq. 12.4 is given, we can simplify the noise voltage $\underline {V}_n$ [V] calculation to [6]:

$$\displaystyle \begin{aligned} \underline{V}_n &= j\omega R C_{12} \underline{V}_1 \text{ , in case of relatively low}\ R {} \end{aligned} $$

(12.5)

$$\displaystyle \begin{aligned} v_n(t) &= i_n(t)\cdot R = C_{12}\frac{dv_1}{dt}\cdot R \text{ , in case of relatively low}\ R \end{aligned} $$

(12.6)

where:

• $\underline {V}_n =$ noise voltage introduced to the victim (circuit 2) in [V]

• v _n(t) = noise voltage introduced to the victim (circuit 2) in [V]

• $\underline {I}_n =$ noise current through coupling capacitance in [A]

• i _n(t) = noise current through coupling capacitance in [A]

• $\underline {V}_1 =$ voltage of the noise source (circuit 1) in [V]

• C ₁₂ = total couple/stray capacitance between circuit 1 and circuit 2 in [F]

• R = load resistor of the victim circuit in [Ω]

• ω = 2πf = angular frequency of the sinusoidal noise signal in [rad/sec]

In case the resistance R [Ω] in circuit 2 to ground is large compared to the parallel impedances of C ₁₂ and C _2G, such that [6]:

$$\displaystyle \begin{aligned} R \gg \frac{1}{\frac{1}{1/\left(j\omega C_{12}\right)}+\frac{1}{1/\left(j\omega C_{2G}\right)}} = \frac{1}{j\omega\left(C_{12}+C_{2G}\right)} {} \end{aligned} $$

(12.7)

then Eq. 12.4 reduces to a capacitive voltage divider [6]:

$$\displaystyle \begin{aligned} \underline{V}_n = \left(\frac{C_{12}}{C_{12}+C_{2G}}\right) \underline{V}_1\text{ , in case of relatively large }R {} \end{aligned} $$

(12.8)

where:

• $\underline {V}_n =$ noise voltage introduced to the victim (circuit 2) in [V]

• $\underline {V}_1 =$ voltage of the noise source (circuit 1) in [V]

• C ₁₂ = total couple/stray capacitance between circuit 1 and circuit 2 in [F]

• C _2G = total capacitance of the victim circuit to ground in [F]

This means for a very large R [Ω], the conductive noise coupling is independent of the frequency ω [rad/sec] and the noise voltage is of larger amplitude than when R [Ω] is small. The frequency response in Fig. 12.5 confirms that.

Fig. 12.5

Frequency response of capacitively coupled noise voltage $| \underline {V}_n|$

Given all this information, we can now define some possible measures against a capacitive coupling (assuming that the voltage level $\underline {V}_1$ [V] of the noise generator and the victim circuit load R [Ω] cannot be changed):

• Reduce transient of noise source. Because the noise current through the stray capacitance i _n(t) = C ₁₂ dv ₁∕dt is directly proportional to the voltage transient dv ₁∕dt [V/s] of the noise source, a reduction of the voltage transient in the noise source helps minimize the capacitive coupling. Note: this measure does not help in the case of very high impedance victim circuits, because in this case, the coupling does not depend on the frequency ω [rad/sec] (see Eq. 12.8).

• Reduce coupling capacitance. No coupling capacitance means no capacitive coupling. In practice, the coupling capacitance cannot be removed completely, but it can be minimized with several measures:

  • Shielding. Adding a shield around the noise source or the victim reduces the coupling capacitance to a minimum (given that the shield does cover the complete noise source and/or victim). Shielding against capacitive coupling is already achieved by connecting only one end of the shield to ground [6].

  • Spatial separation. If possible, the source of noise and the victim circuit could be spatially separated from one another.

  • Change conductor orientation. Let us say the noise source circuit and the victim circuit have conductors parallel to each other. If feasible, a change of the orientation to an angle of 90° between the wires would reduce the coupling capacitance.

• Filtering. With a filter added to the victim circuit, the coupled noise could be reduced. For high impedance victim circuits, adding a filter capacitor parallel to R [Ω] would increase C _2G [F] and therefore help to reduce $| \underline {V}_n|$ [V] (see Eq. 12.8).

12.1.3 Inductive Coupling

Inductive coupling can occur if there is a mutual inductance M [H] between two or more circuits. The field of concern for the inductive coupling is the magnetic H-field. Thus, inductive coupling is a near-field coupling (near-field; see Sect. 8.3), which means that the noise source and the victim, which receives the noise, are closely located to each other.

It is assumed that the inductive coupling discussed in this section is a weak coupling. That means that the noise coupling is a one-way effect from the noise source to the victim circuit (negligible back reaction from victim to source).

How could inductive coupling lead to problems during EMC testing? For example, inductive coupling could lead to issues during EMC testing when high currents flow through cables and PCB traces, e.g., during surge testing where currents up to several [kA] could occur. Large currents often induce voltages in neighboring circuits, which inadvertently disrupts them. These induced voltages are due to inductive coupling.

Inductive coupling happens due to a noise current i ₁(t) [A] that changes over time di ₁∕dt [A/s] and induces a noise voltage v _n(t) [V] in a nearby circuit via a mutual inductance M ₁₂ [H]. The faster the current change di ₁∕dt [A/s] and the larger the mutual inductance M ₁₂ [H], the higher the noise voltage v _n(t) [V] induced into the victim circuit [6]:

$$\displaystyle \begin{aligned} v_n(t) = M_{12}\frac{di_1}{dt} {} \end{aligned} $$

(12.9)

The noise voltage $\underline {V}_n$ [V] induced to the victim circuit shown in Fig. 12.6c due to an inductive coupling can be calculated like this [6]:

$$\displaystyle \begin{aligned} \underline{V}_n = j\omega |B| |A| cos\left(\theta\right) = j\omega \varPhi_{12} = j\omega M_{12} |\underline{I}_1| {} \end{aligned} $$

(12.10)

where:

• $\underline {V}_n =$ induced noise voltage to the victim (circuit 2) in [V]

  Fig. 12.6

  

  Inductive coupling between two closely spaced circuits. (a) Physical representation. (b) Equivalent circuit (c) Induced noise depends on the area enclosed by the distributed victim circuit. Magnetic field of magnetic flux density B [T] cuts the area A [m²] at an angle θ [rad]. (d) Frequency response of inductive coupled noise voltage $| \underline {V}_n|$ [V]

• |B| = magnetic flux density caused by the noise source current (circuit 1) in [T]

• |A| = enclosed loop area of the victim circuit (circuit 2) in [m²]

• θ = angle between the magnetic flux vector $\overrightarrow {B}$ and the area vector $\overrightarrow {A}$ in [rad]

• Φ ₁₂ = magnetic flux coupled into the victim circuit area loop (circuit 2) in [Wb]

• $M_{12} = \varPhi _{12}/| \underline {I}_1| =$ mutual inductance between circuit 1 and circuit 2 in [H]

• $\underline {I}_1 =$ noise source current (circuit 1) in [A]

• ω = 2πf = angular frequency of the sinusoidal noise signal in [rad/sec]

Equations 12.9 and 12.10 show the parameters that influence the induced noise voltage $\underline {V}_n$ [V] to the victim. Suppose that the amplitude of the noise current cannot be changed, we still have the following parameters left, which are all directly proportional to the amplitude of the noise voltage: frequency ω [rad/sec], the magnetic flux density B [T], the area A [m²], and the angle θ [rad].

Given all this information, we can now define some possible measures against an inductive coupling (assuming that the amplitude of the noise current $\underline {I}_1$ [A] cannot be changed):

• Reduce current loop area. The most effective and best way to overcome inductive coupling is to reduce the current loop area A [m²] of the victim circuit. Therefore, always take care that the current loop of sensitive circuits is kept as small as possible.

• Spatial separation. The physical separation of the noise source and the victim circuit leads to a reduced magnetic flux density B [T] (when it reaches the victim current loop).

• Shielding. A cable shield for eliminating inductive coupling must be grounded at both ends (a nonmagnetic shield grounded only on one end does not affect a magnetic near-field coupling) [6]. Low-frequency magnetic fields are best shielded with magnetic conductive shielding material ($\mu _r^{\prime }\ll 1$).

• Change circuit orientation. The magnetic flux density is a vector field $\overrightarrow {B}$ [T], which means it has a defined direction. Therefore, a possible option to reduce the noise due to inductive coupling is to change the orientation of the victim current loop area that the term $\cos \left (\theta \right )$ in Eq. 12.10 gets ideally to zero.

12.1.4 Electromagnetic Coupling

Electromagnetic coupling is a far-field coupling (far-field; see Sect. 8.3). This means that the noise source and the victim are located far from each other compared to the wavelength λ [m]. The field of concern for radiated coupling is the electromagnetic field (EM-field; see Sect. 8), where the H-field and the E-field travel perpendicular to each other, and their amplitudes both fall off with the factor 1/d, where d [m] is the distance to the radiating source.

The electromagnetic coupling also plays an important role during EMC tests, e.g., during the radiated immunity test according to IEC 61000-4-3, where the EUT is placed in the far-field of the radiating E-field test antenna (80 MHz to 6 GHz, typically d = 3 m), and, moreover, during radiated emission testing according to CISPR 32, where the EUT is the radiator and the receiving antenna is an E-field antenna placed in the far-field (30 MHz to 6 GHz, typically d = 3 m or d = 10 m).

In the case of an electrical apparatus or installation, any structure may be a good antenna for electromagnetic radiation, e.g., wires, cables, circuit loops or structures on PCBAs, or even larger structures like metal chassis. The best option to develop a robust product against EMI, which produces very low unintended radiation, is always achieved by considering EMC right from the beginning of the project. However, once a product fails EMC testing, there are several possible measures to reduce electromagnetic coupled emissions and increase immunity against electromagnetic fields. Note: because most antennas are reciprocal, a measure against unintended radiation also helps to increase immunity and vice versa.

Here are some typical options on how to reduce unwanted electromagnetic coupling:

• Filtering. Suppose a cable is identified as a transmitter or receiver of electromagnetic radiation. In that case, a clamp ferrite bead may reduce the unintended radiation and/or increase the immunity (the clamp ferrite bead attenuates common-mode currents through the cable). Also, filter elements like capacitors placed on the PCB for every IO-line of a cable can help to filter high-frequency signals in either direction. For differential signal interfaces, common-mode chokes are also a good filter option.

• Shielding. Put a shield around the circuit, cable, or unit that unintentionally radiates or acts as a receiver of electromagnetic radiation.

• Grounding. If a metal chassis or a subsystem within the EUT is the source/sink of the electromagnetic radiation, the ground connection should be checked and improved (low-inductance ground connection). Poor grounding of PCBAs, cable shields, or metal structures often leads to unwanted electromagnetic coupling.

12.2 Differential-Mode vs. Common-Mode

In EMC, a distinction is made between common-mode and differential-mode noise currents. Both noise currents could lead to unintended radiation, as shown in Sect. 9.9. Sections 12.3 and 12.4 show how the coupling paths presented above can cause differential-mode and common-mode noise. In practice, things are more complicated than stated in this section because coupling mechanisms often happen in cascades and interfere with each other. Nonetheless, you get an idea of where to focus when designing an electrical system or electronic circuit.

Before we jump into the topic of common-mode and differential-mode noise, let us define the terms differential-mode and common-mode in Sects. 12.2.1 (voltages) and 12.2.2 (currents).

12.2.1 Differential-Mode vs. Common-Mode Voltage

Let us have a look at Fig. 12.7, and let us define the differential-mode and common-mode voltages:

• Differential-mode voltage. The differential-mode voltage $\underline {V}_{DM}$ [V] is defined as the difference of the voltage potentials to ground of conductor 1 and conductor 2 in Fig. 12.7: $\underline {V}_{DM} = \underline {V}_1- \underline {V}_2$.

  Fig. 12.7

  

  Differential-mode vs. common-mode

• Common-mode voltage. In the case of a balanced transmission line (both conductors have equal impedances to ground), the common-mode voltage $\underline {V}_{CM}$ [V] is 0.5 of the sum of the voltages of conductor 1 and conductor 2 to ground: $\underline {V}_{CM} = ( \underline {V}_1+ \underline {V}_2)/2$. However, in the case of an unbalanced transmission line, things are getting a little more complicated, and therefore, we have to define the imbalance factor $\underline {h}$.

For a transmission line with two conductors—like shown in Fig. 12.7,—the imbalance factor $\underline {h}$ is defined as [4]:

$$\displaystyle \begin{aligned} \underline{h} = \frac{\underline{Z}_1}{\underline{Z}_1+\underline{Z}_2} {} \end{aligned} $$

(12.11)

where:

• $\underline {h} =$ imbalance factor or current divisor factor of a transmission line

• $\underline {Z}_1 =$ characteristic impedance of conductor 1 with respect to ground in [Ω]

• $\underline {Z}_2 =$ characteristic impedance of conductor 2 with respect to ground in [Ω]

The imbalance factor $\underline {h}$ is used for calculating the common-mode voltage $\underline {V}_{CM}$ [V] of any transmission line for a given differential-mode voltage $\underline {V}_{DM}$ [V] [4]:

$$\displaystyle \begin{aligned} \underline{V}_{DM} &= \underline{V}_1 - \underline{V}_2 \end{aligned} $$

(12.12)

$$\displaystyle \begin{aligned} \underline{V}_{CM} &= \underline{h}\cdot\underline{V}_1 + (1-\underline{h})\cdot\underline{V}_2 \end{aligned} $$

(12.13)

where:

• $\underline {V}_{DM} =$ differential-mode voltage between conductor 1 and 2 in [V]

• $\underline {V}_{CM} =$ common-mode voltage to ground in [V]

• $\underline {V}_1 =$ voltage of conductor 1 with respect to ground in [V]

• $\underline {V}_2 =$ voltage of conductor 2 with respect to ground in [V]

• $\underline {h} =$ imbalance factor or current divisor factor of a transmission line

12.2.2 Differential-Mode vs. Common-Mode Current

The difference between differential-mode Differential-Mode Current and common-mode current :

• Differential-mode current. A differential-mode current flows in different directions through a cable (see Fig. 12.8).

  Fig. 12.8

  

  Differential-mode noise current [8]

• Common-mode current. A common-mode current flows in the same direction—a common direction—through a cable (see Fig. 12.13).

Let us have a look at Fig. 12.7. The imbalance factor $\underline {h}$ defined in Eq. 12.11 can be used for calculating the differential-mode and common-mode current of any transmission line [4]:

$$\displaystyle \begin{aligned} \underline{I}_{DM} &= (1-\underline{h})\cdot\underline{I_1} - \underline{h}\cdot\underline{I}_2 \end{aligned} $$

(12.14)

$$\displaystyle \begin{aligned} \underline{I}_{CM} &= \underline{I}_1 + \underline{I}_2 \end{aligned} $$

(12.15)

where:

• $\underline {I}_{DM} =$ differential-mode current in [A]

• $\underline {I}_{CM} =$ common-mode current through conductor 1 and 2 in [A]

• $\underline {I}_1 =$ current through conductor 1 in [A]

• $\underline {I}_2 =$ current through conductor 2 in [A]

• $\underline {h} =$ imbalance factor or current divisor factor of a transmission line

12.3 Differential-Mode Noise Sources

Differential-mode noise sources cannot be found on any bill of material (BOM) or any schematic. These noise sources are unwanted and unintended. Section 9.9.1 shows how small differential-mode current loops could lead to unwanted radiated emissions.

A not conclusive list of possible differential-mode interference noise sources is given here and then shortly explained in the following sections:

• Conductive coupling to differential-mode noise: Sect. 12.3.1.

• Capacitive coupling to differential-mode noise: Sect. 12.3.2.

• Inductive coupling to differential-mode noise: Sect. 12.3.3.

• Common-to-differential-mode conversion: Sect. 12.3.4.

12.3.1 Conductive Coupling to Differential-Mode Noise

Two or more circuits share a common current path (e.g., a common return current path), and the voltage drop of one of these circuits introduces a differential-mode noise voltage $\underline {V}_{nDM}$ [V] in another circuit(s) and vice versa (see Fig. 12.9). The calculation of the differential-mode noise voltage $\underline {V}_{nDM}$ [V] and more details about conductive coupling—also named common impedance coupling —are given in Sect. 12.1.1.

Fig. 12.9

How conductive coupling causes differential-mode noise (simplified)

Fig. 12.10

How capacitive coupling to a single conductor causes differential-mode noise (simplified)

12.3.2 Capacitive Coupling to Differential-Mode Noise

Assuming a noise current $\underline {I}_{nDM}$ [A] is coupled capacitively to one of the two lines of a differential signal. This noise current causes differential-mode noise voltage $\underline {V}_{nDM}$ [V] and could therefore lead to problematic interference on that circuit or unintended RF emissions (see Fig. 12.10). The calculation of the differential-mode noise current $\underline {I}_{nCM}$ [A] and more details about the capacitive coupling are given in Sect. 12.1.1.

Fig. 12.11

How inductive coupling causes differential-mode noise voltage (simplified)

12.3.3 Inductive Coupling to Differential-Mode Noise

Let’s imagine a magnetic field which induces a noise voltage $\underline {V}_n$ [V] to a differential signal current loop which leads to a differential-mode noise current I _n [A] in that circuit (see Fig. 12.11). This induced noise voltage and the noise current could lead to, e.g., problematic interference on that circuit or unintended RF emissions. The calculation of the induced differential-mode noise voltage $\underline {V}_n$ [V] and more details about inductive coupling are given in Sect. 12.1.3.

Fig. 12.12

How mode conversion (due to unbalanced lines) causes differential-mode noise voltage (simplified)

12.3.4 Common-to-Differential-Mode Conversion

A common-mode noise current $\underline {I}_{nCM}$ [A] can be converted to a differential-mode noise voltage $\underline {V}_{nDM}$ [V] in the case of unbalanced lines. Unbalanced lines mean that the lines are not 100 % balanced;—in other words, the forward and return current lines of a differential signal have [3]:

• 1. Different impedances along their length

• 2. Different impedances to ground.

In both cases, a common-mode current leads to a differential-mode voltage (see Fig. 12.12). This type of conversion is called common-to-differential-mode conversion .

Fig. 12.13

Common-mode noise current [8]

Electronics designers should especially ensure that signal lines at the input of high-gain instrument amplifiers are well balanced. Otherwise, even a tiny common-mode noise current $\underline {I}_{nCM}$ [A] could cause a significant noise voltage $\underline {V}_{nDM}$ [V] at the output of the high-gain amplifier.

12.4 Common-Mode Noise Sources

Common-mode noise sources cannot be found on any bill of material (BOM) or any schematic. These noise sources are unwanted and unintended. Common-mode currents are the number 1 source of unintentional radiated emissions (Fig. 12.13). Sections 9.9.2, 9.9.3, and 9.9.4 show how common-mode currents in cables could lead to unintended radiated emissions.

A not conclusive list of possible common-mode interference noise sources is given here and then shortly explained in the following sections:

• Capacitive coupling to common-mode noise: Sect. 12.4.1.

• Electromagnetic coupling to common-mode noise: Sect. 12.1.4.

• Reference point noise to common-mode noise: Sect. 12.4.3

• Differential-to-common-mode conversion: Sect. 12.4.4.

12.4.1 Capacitive Coupling to Common-Mode Noise

Let us imagine that noise currents are coupled capacitively (and equally) onto two differential signal lines, which form a current loop. As a consequence, the coupled common-mode current $\underline {I}_{nCM}$ [A] could lead to radiated or conducted emission issues.

Figure 12.14 shows a simplified setup of how electric near-field coupling could cause common-mode noise. In addition, Sect. 12.1.2 presents the calculation of the coupled noise current and which actions can be taken to reduce it. Finally, how a differential signal leads to common-mode noise with electric field coupling is presented in the following paper [1], where the coupling is called voltage-driven mechanism.

Fig. 12.14

Concurrent capacitive coupling on a pair of wire causes common-mode noise currents, which could lead to high radiated emissions (simplified)

12.4.2 Electromagnetic Coupling to Common-Mode Noise

A cable or a part of an electronic circuit acts as an antenna and receives electromagnetic radiation, e.g., from radio stations or smartphones, etc (Fig. 12.15). The receiving structure is in the far-field of the transmitter. With this coupling, an unintended noise current is brought to an electrical circuit and could lead to interference. Details about the electromagnetic coupling and how to reduce it can be found in Sect. 12.1.4.

Fig. 12.15

Electromagnetic coupling that leads to a common-mode current (simplified)

12.4.3 Reference Point Noise to Common-Mode Noise

A noisy reference point (ground) or a voltage potential difference of spatially divided circuits and systems could cause a common-mode noise current $\underline {I}_{nCM}$ [A] and, therefore, high radiated emissions. Figure 12.16 shows in a simplified form a setup with a noisy reference point. The noise source voltage $\underline {V}_{nCM}$ [V] itself could be caused by a current-driven differential-to-common-mode conversion [1].

Fig. 12.16

Noisy reference point that leads to a common-mode current (simplified)

12.4.4 Differential-to-Common-Mode Conversion

Any change in electrical balance to ground of a transmission line converts some power of the differential-mode signal into a common-mode signal [4]. This differential-to-common-mode conversion happens if—and only if—there is a change in balance of the transmission line [2]. Because this circumstance often causes high radiated emissions and failed EMC tests, the differential-to-common-mode conversion will be analyzed in the following by applying the imbalance difference modeling method (IDM [2, 5]).

Consider a transmission line that experiences a sudden change in the impedance of its lines to ground. This is typically the case when the transmission line leads from a PCB to a cable: in the connector, the individual conductors of the transmission line experience a sudden change in the characteristic impedance to ground (change in balance or imbalance). Let us look at Fig. 12.17, where a differential-mode signal experiences a sudden change in impedance to ground (at the imbalance interface). This sudden change leads to a common-mode voltage $\underline {V}_{AM}$ [V] and common-mode current $\underline {I}_{AM}$ [A], which we call antenna-mode voltage and antenna-mode current because they could lead to unintended radiation. We defined the imbalance factor $\underline {h}$ in Eq. 12.11. On the left side of the imbalance interface, conductors 1 and 2 have an imbalance factor of $\underline {h}_L = \underline {Z}_{1L}/( \underline {Z}_{1L}+ \underline {Z}_{2L})$, and on the right side of the imbalance interface, the conductors have the imbalance factor of $\underline {h}_R = \underline {Z}_{1R}/( \underline {Z}_{1R}+ \underline {Z}_{2R})$. The common-mode voltage $\underline {V}_{AM}$ [V] and current $\underline {I}_{AM}$ [A] that are developed due to the imbalance change are given as [4, 9]:

$$\displaystyle \begin{aligned} \underline{V}_{AM} &= \underline{V}_{DM} \cdot \varDelta \underline{h} \end{aligned} $$

(12.16)

$$\displaystyle \begin{aligned} \underline{I}_{AM} &= \frac{\underline{V}_{AM}}{\underline{Z}_{AM}} \end{aligned} $$

(12.17)

where:

• $\underline {V}_{DM} =$ differential-mode voltage at the imbalance interface in [V]

  Fig. 12.17

  

  Differential-to-common-mode conversion due to imbalance of a transmission line (change of characteristic impedances to ground)

• $\underline {V}_{AM} =$ common-mode voltage developed at the imbalance interface in [V]

• $\varDelta \underline {h} = \underline {h}_L- \underline {h}_R =$ change of imbalance factor $\underline {h}$ at the imbalance interface

• $\underline {I}_{AM} =$ common-mode current through conductor 1 and 2 in [A]

• $\underline {Z}_{AM} =$ input impedance of antenna that is formed by conductors 1 and 2 in [Ω]

Imbalance difference modeling (IDM) is a powerful method for quickly calculating the worst-case common-mode voltage driving a cable (as an antenna). As a worst-case, it can be assumed an imbalance factor change of Δh = 0.5 (perfectly balanced to completely unbalanced and vice versa), which means that the developed common-mode voltage is half the differential-mode amplitude:

$$\displaystyle \begin{aligned} |\underline{V}_{AM}| = |\underline{V}_{DM}| \cdot 0.5 \end{aligned} $$

(12.18)

In EMC, the theoretical maximum field strength E _max [V/m] for a given setup at distance d [m] in the far-field is of primary interest. Therefore, here is a way for a worst-case estimation of the radiated emissions of a digital signal due to transmission line imbalance (e.g., change from an unbalanced microstrip line to a balanced ribbon cable):

• 1. Differential-mode voltage V _DM. Use the Fourier analysis to determine the RMS amplitude V _DM [V] of the sinusoidal harmonics of differential-mode signal. See Sect. M.2 for an estimation of harmonics of an ideal square wave signal.

• 2. Common-mode voltage V _AM. Calculate the assumed worst-case common-mode RMS voltage V _AM [V] developed at the transmission line imbalance change for the harmonics of interest [4]:

  $$\displaystyle \begin{aligned} V_{AM}=0.5\cdot V_{DM}\end{aligned}$$

• 3. Worst-case radiated emissions E _{AM, max}. Use Eq. 9.48 on page 20 to calculate the estimated worst-case radiated emissions E _max [V/m] for the given distance d [m] (far-field) and the antenna-mode voltage V _AM [V] (current, voltage, and field-strength are RMS values):

$$\displaystyle \begin{aligned} E_{AM,max} \approx \begin{cases} \frac{60\cdot I_{AM,max}}{d}\cdot\frac{2}{\sin\left(\sqrt{2}\right)} & \text{when } l_{cable} \leq \frac{\lambda}{2}\\ \frac{60\cdot I_{AM,max}}{d}\cdot\frac{2}{\sin\left(\sqrt{\frac{\lambda}{l_{cable}}}\right)} & \text{when } l_{cable} > \frac{\lambda}{2} \end{cases} \end{aligned} $$

(12.19)

where:

$$\displaystyle \begin{aligned} \underline{I}_{AM,max} = \frac{\underline{V}_{AM}}{\frac{{36.5}\,\Omega}{k_{board}\cdot k_{cable}}} \end{aligned} $$

(12.20)

$$\displaystyle \begin{aligned} k_{board} = \begin{cases} \sin\left(\frac{2\pi \cdot l_{board}}{\lambda}\right) & \text{when } l_{board} \leq \frac{\lambda}{4}\\ 1.0 & \text{otherwise } \end{cases} \end{aligned} $$

(12.21)

$$\displaystyle \begin{aligned} k_{cable} = \begin{cases} \sin\left(\frac{2\pi \cdot l_{cable}}{\lambda}\right) & \text{when } l_{cable} \leq \frac{\lambda}{4}\\ 1.0 & \text{otherwise } \end{cases} \end{aligned} $$

(12.22)

$$\displaystyle \begin{aligned} l_{board} = \frac{1+\frac{2L}{W}}{\frac{2L}{W}}\cdot\sqrt{L^2+W^2} \end{aligned} $$

(12.23)

• V _AM = common-mode RMS voltage driving the monopole antenna (cable) in [V]

• I _AM,max = highest common-mode RMS current that exists on the cable in [A]

• R _min = 36.5 Ω = radiation resistance of a resonant λ∕4-monopole antenna in [Ω]

• l _board = effective board length in [m]

• l _cable = cable length in [m]

• L = length of the PCBA (board) in [m]

• W = width of the PCBA (board) in [m]

• k _board = impact of board size l _board on R _min in case l _board ≤ λ∕4

• k _cable = impact of cable length l _cable on R _min in case l _cable ≤ λ∕4

• d = distance to the radiating structure (PCBA, cable) in [m]

• λ = wavelength of the sinusoidal signal $\underline {V}_{AM}$ in [m]

12.5 Summary

Table 12.1 presents a summary of EMI noise coupling paths.

Table 12.1 EMI noise coupling path summary