Pioneers in the fields of electricity and magnetism such as Faraday, Ampere and Maxwell proved both empirically and mathematically that the current running through a conductor can be quantified by measuring the magnetic field it generates.
A magnetic sensor may be used to detect current because the magnitude and direction of the magnetic field are determined by the magnitude and the direction of the current through the conductor, as well as by the distance between the conductor and the magnetic sensor used to measure the field.
Applying Ampere’s Law
Simply stated, Ampere’s Law relates the electric current passing through a conductor to the magnetic field produced around it. If the conductor is circular, then a circular magnetic field of equal magnitude may be found around the conductor. Figure 1 illustrates this concept. Imagine that there is a current, I, flowing through a conductor which is coming out of the page. If we add up the magnetic field along the blue circular path of radius, r, around the conductor, this should equal the field created by the current flowing through the conductor.
Ampere’s Law provides a quick, simple calculation of the magnetic field strength, which is proportional to the current passing through the conductor, and inversely proportional to the distance from the conductor. It is expressed by the following equation:
B = flux of the magnetic field (T),
I = current through the conductor (A),
R = distance from the centre of the conductor to the sensing point (m) and
μ0 = permeability of free space (T*m/A)
Since a magnetic field is a vector quantity, both the magnitude and the direction of the magnetic field must be known in order to fully characterise it. The direction can be calculated mathematically. But the right-hand-rule also works, as shown in Figure 2.
To see how this quantification of field strength can be used to measure current, consider a graphical representation of magnetic field strength as a function of distance (R in Ampere’s Law).
Figure 3 plots the effects of changing the distance from the centre of the conductor on the magnitude of the magnetic field in the air when the conductor is carrying 10A. Notice how the B field value declines quickly as the distance increases.
This same effect can be shown in a practical application example: a four-layer PCB with a board stack-up as shown in Figure 4. The sensor is mounted on the top layer of the PCB and the current-carrying conductor which is generating the magnetic field may be mounted on the bottom layer, or on either of the two inner layers.
Table 1 shows the calculated value of B, the magnetic field magnitude, as seen by the sensor when the current-carrying trace is mounted on each of the three layers.
Table 1: how field strength measured by a magnetic sensor varies with distance from the conductor
All the examples shown here are given for a single fixed current value, 10A. In practice, the current measured by a Crocus magnetic sensor may vary from as little as a few mA up to several hundred Amperes. The impact of changing the value of the current is shown in Figure 5 for currents ranging from -50A to +50A. It is clear that that the higher the current, the greater the distance between the sensor and conductor for the same value of magnetic field strength.
This application note shows the correlation between the current and the magnetic field created by the current. In order to successfully measure different levels of current, the designer must take into account several factors including the physical characteristics of the measurement set-up as well as the dynamic range of the current to be measured.
The concepts and examples in this application note are applicable to all of the following Crocus magnetic sensors: CTSR218C-IQ2, CTSR215C-IQ2, CTSR222C-IQ2, CTSR218C-IS4, CTSR215C-IS4, and CTSR222C-IS4.