This article focuses on the current probes used in EMC measurements and testing. We begin with the explanation of the Faraday and Lentz’s laws which form the theoretical basis for the current probe measurements. The theory is then followed by a description and explanation of the current probe measurement setup. Finally, the actual measurement results in three different detection modes are shown.

Faraday’s Law

Consider an open surface that has a closed loop contour *c* surrounding it (think of a mouth of a balloon) shown in Figure 1. The “balloon” can be inflated or deflated to create different surfaces but the contour *c* needs to stay unchanged [1], [2].

This contour can be a conducting wire or an imaginary contour of non-conducting material (free space). Magnetic flux passing through the open surface bounded by this contour gives rise to an electric field.

Faraday’s law states that

(1)

The line integral in Eq. (1) is often referred to as an *electromotive force:*

(2)

The surface integral in Eq. (1) is the *magnetic flux* crossing the contour

(3)

Using the notation in Eqs. (2) and (3) the Faraday’s law in Eq. (1) can be alternatively expressed as

(4)

This form clearly shows that the induced voltage is directly proportional to the rate of change of the magnetic flux. If the loop is electrically small, this induced voltage can be inserted anywhere in the loop as shown in Figure 2.

The *magnitude* of this voltage is

(5)

The *polarity* of this voltage is determined from the *Lentz’s law* explained next.

Lenz’s Law

*The original magnetic field **B** gives rise to the induced magnetic field **B*_{ind}. According to Lentz’s law the induced magnetic field *B*_{ind} opposes the change in the original magnetic field *B.*

To facilitate the understating of the Lentz’s law let’s consider several scenarios shown in Figure 3.

As shown in Figure 3, the original magnetic field ** B** can be either pointing up or down and can be either increasing or decreasing. Let’s investigate each case separately and apply the Lentz’s rule to determine the direction of the induced magnetic field.

*Case 1 – The original field **B** is pointing up and increasing* (Figure 4a).

The induced field *B** _{ind}* opposes this change. Thus, the induced field

*B**is pointing down.*

_{ind}*Case 2 – The original field **B** is pointing up and decreasing* (Figure 4b). The induced field *B** _{ind}* opposes this change. Thus, the induced field

*B**is pointing up.*

_{ind}*Case 3 – The original field **B** is pointing down and increasing* (Figure 4c). The induced field *B** _{ind}* opposes this change. Thus, the induced field

*B**is pointing up.*

_{ind}*Case 4 – The original field **B** is pointing up and decreasing* (Figure 4d). The induced field *B** _{ind}* opposes this change. Thus, the induced field

*B**is pointing down.*

_{ind}The knowledge of the direction of the induced field allows us to determine the direction of the induced current (using the right-hand rule). This is shown in Figure 5.

Since the induced current flows out of the positive terminal of the induced voltage, the polarity of the induced voltage is easily determined, as shown in Figure 6.

Current Probe Measurements

Figure 7 shows some typical current probes used in EMC measurements and testing.

The electric current can be measured by connecting the current probe directly to the spectrum analyzer, as shown in Figure 8a, or by using a preamplifier as shown in Figure 8b.

Current probe is essentially a transformer, as shown in Figure 9.

When the probe is clamped around a conductor, the conductor is the primary winding and the probe’s windings are the secondary. The current in the conductor produces a magnetic field that is concentrated in and circulates around the core of the probe. By *Faraday’s law*, this circulating magnetic field induces *V _{ind}* that is measured by a spectrum analyzer.

The probe is calibrated so that the voltage measurement by the probe *V _{ind}* can be translated into the current measurement flowing in the conductor (over the specified frequency range). Typically, the probe’s output voltage is specified with the probe terminated in , as shown in Figure 10.

During the calibration process the current of known magnitude and frequency is passed through the probe and the corresponding induced voltage is measured at that frequency. Then, at each frequency, the ratio of that voltage to current can be calculated

(6)

This quantity is referred to as the *transfer impedance* of the probe. The unknown current measured by the current probe can then calculated from

(7)

The transfer impedance is specified in* dBΩ *instead of the values in *Ωs*

(8)

Therefore,

(9)

This allows a direct determination of the unknown current measured by the current probe by a simple subtraction (instead of division)

(10)

and

(11)

Current probes have an associated calibration chart the one shown in Figure 11.

When performing the current probe measurements the measuring equipment (spectrum analyzer or EMI receiver) needs to be set to the one of three detection modes: peak, average, or quasi-peak. The first two modes are self-explanatory, the quasi-peak mode deserves an explanation.

Quasi-peak detectors weigh signals according to their repetition rate, which is a way of measuring their “annoyance factor”. High amplitude low repetition rate signals could produce the same output as low amplitude high repetition rate signal. As the repetition rate increases, the quasi-peak detector produces a higher voltage output i.e., a response on spectrum analyzer or EMI receiver. Figure 12 shows an EMI receiver and its typical screen output; note the three detection modes displayed.

When properly configured, the quasi-peak detector readings will be less than or equal to the peak detection. Average detector will be less than or equal to the quasi-peak detection. Because quasi-peak readings are much slower, (by 2 or 3 orders of magnitude compared with peak) it is very common to scan initially with the peak detection first, and then if this is marginal or fails, switch and run the quasi- peak measurement against the limits.

This approach is illustrated in Figures 13 – 15 which show the current probe measurements.

Since the peak detector measurement failed, it was followed by the average and the quasi-peak measurements, which passed.

**References**

- Clayton R. Paul,
*Introduction to Electromagnetic Compatibility*, 2^{nd}Ed., Wiley, 2006. - Bogdan Adamczyk,
*Foundations of Electromagnetic Compatibility with Practical Applications*, Wiley, 2017.

**Dr. Bogdan Adamczyk** is a professor and the director of the EMC Center at Grand Valley State University (GVSU) where he performs EMC precompliance testing for industry and develops EMC educational material. He is also the founder and principal educator of EMC Educational Services LLC (www.emcspectrum.com) which specializes in EMC courses for industry. Prof. Adamczyk is the author of the book “Foundations of Electromagnetic Compatibility with Practical Applications” (Wiley, 2017). He can be reached at profbogdan@emcspectrum.com.

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