This article discusses the common-mode and differential-mode radiation from cables and presents the measurement results from the SMPS connecting wires.

**Differential-Mode and Common-Mode Circuit Model**

Consider a typical circuit model shown in Figure 1.

If the fields generated by the forward current cancel the fields of the return currents and no other circuits, or sources, or coupling paths are present, then the forward current equals the return current. In virtually any practical circuit, a different scenario takes place, as shown in Figure 2.

*Î _{D}* is referred to as the

*differential-mode (DM) current*while

*Î*is referred to as the

_{C}*common-mode (CM) current*. The DM currents are usually the functional currents. They are equal in magnitude and of opposite directions. The CM (unwanted) currents are equal in magnitude and of the same direction (See [1] for the discussion of the CM current creation).

In the analysis of the DM and CM currents, we often utilize the *total *currents *Î*_{1} and *Î*_{2}* *flowing in the same direction. The reason for this is that it is easier to apply the classical circuit theory to the total currents than it is to the individual currents. Once the equations are developed for the total currents, we simply substitute the differential or common-mode currents for the total currents in the derived expressions. This approach will be demonstrated in the next section.

The total currents *Î*_{1} and *Î*_{2} flowing are related to the DM and CM currents by

(1a)

(1b)

**Radiation from Differential- and Common-Mode Radiation**

Differential- and common-mode radiation can be modeled as the radiation from two Hertzian dipoles driven by a noise voltage.

Let’s begin with the DM radiation. Consider the scenario shown in Figure 3. where two linear antennas (conductor 1 and conductor 2) placed along the *x-axis*, carry the differential-mode currents along the *z*-direction.

The maximum radiated field is broadside to the antenna (in the *xy*-plane, where θ = 90° and in the *z*-direction, as shown. Note that the radiated fields due to both conductors are of opposite directions, giving a small total radiated field, as shown. This total radiated field at the observation point in the *far* field can be obtained by superimposing the fields due to each antenna.

Treating each antenna as a linear dipole of length *l*, the magnitude of the total field at a distance *d* from the antennas is, [2],

(2)

where *f* is the frequency of the current carried by the antennas.

Now, consider the scenario shown in Figure 4 where two linear antennas carry the common-mode currents.

The radiated fields due to both conductors are of same directions, thus reinforcing each other to give the total radiated field as shown. The magnitude of the total field at a distance *d* from the antennas is

(3)

It should be noted that the CM currents could be several orders of magnitude smaller than the DM currents, yet the radiation from them could exceed the regulatory limits.

For instance, it takes only 8 µA of the CM current to exceed the FCC Class B limit of 100 µV/m at a distance of 3m, as the following calculations show.

From Eq. (2) we can calculate the expression for the CM current in terms of the maximum allowable field strength, [3].

(4)

Letting, *l *= 1m, *d *= 3m, *f* = 30 MHz, *E*_{θ} = 100 µV⁄m, we obtain *I _{C}* = 8 µA.

It is, therefore, no surprise that the CM current is of great interest (or fear) to the EMC engineers. Next, we will discuss the DM and CM current measurements from the cables connecting a SMPS.

**Differential-Mode and Common-Mode Current Measurement**

Figure 5 shows the test setup to measure the differential- and common-mode currents.

The current probe used is shown in Figure 6.

The SMPS used in this experiment is a step-down (buck), 12V to 5V DC, switching at 420 kHz.

The CM currents were measured with the current probe, where both the power and ground wires were placed inside the current probe, as shown in Figure 7.

With both wires inside the probe, the differential current fields (ideally) cancel each other, and the current probe measures only the common-mode currents. To be precise, it (ideally) measures twice the value of the CM current, i.e., 2*I _{C}*. The measurement results are shown in Figure 8 and summarized in Table 1. The measurement values are the relative values in the units of dBµV.

Common-Mode Current | Frequency (MHz) | Magnitude (dBμV) |

CM – A | 1.095 | 12.47 |

CM – B | 1.23 | 9.65 |

CM – C | 1.34 | 13.41 |

CM – D | 1.57 | 11.67 |

##### Table 1: CM-current measurement results

Next, let’s measure the total currents. The total currents were measured with two different setups: current probe over the ground wire and the current probe over the power wire, as shown in Figure 9.

Note that in these setups, we measure the magnitudes of the total currents *Î _{1}* and

*Î*, given by Eqs. (1a) and (1b) and shown in Figure 2. As we shall see, in this experiment, the CM currents exist at the different frequencies than the DM currents, and thus, the total current measurements can be used to extract the DM currents. That’s why we measured the CM currents first.

_{2}The measurement results with the probe over the ground line are shown in Figure 10, while the results for the power line are shown in Figure 11. Both results are summarized in Table 2. The measurement values are the relative values in the units of dBµV.

Differential Mode Current |
Frequency | >Magnitude (dBμV) Ground wire |
Magnitude (dBμV) Power wire |

DM – E | 114.8 kHz | 14.94 | 16.95 |

DM – E | 420.4 kHz | 37.83 | 36.94 |

DM – F | >840.9 kHz | 19.09 | 17.33 |

DM – G | 1.261 MHz | 13.65 | 12.51 |

DM – J | 1.681 MHz | 10.1 | 11.3 |

##### Table 2: DM-current measurement results

**Observations**

Except for the frequency of 114.8 kHz, the DM currents appear at the harmonics of the switching frequency. The ground and the power wire total measurements capture both the DM and the CM currents. The CM currents and are not as predictable as the DM currents. Note that the ground-wire CM-current is present at point A in Figure 10, but it is not present at that frequency on the power wire in Figure 11. Another CM current at a lower frequency, at point K, appears in Figure 11, and it was not present at that frequency in Figure 10.

## Acknowledgment

The author would like to thank Ken Javor for his comments and suggestions included in this revised version.

**References**

- Bogdan Adamczyk,
*Common-Mode Current Creation and Suppression*, In Compliance Magazine, August 2019. - Bogdan Adamczyk,
*Foundations of Electromagnetic Compatibility with Practical Applications*, Wiley, 2017. - Henry W. Ott,
*Electromagnetic Compatibility Engineering*, Wiley, 2009.

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