In the 19th century, British physicist James Clerk Maxwell established a set of partial differential equations describing the relationship between electric and magnetic fields and charge and current densities. Maxwell believed that a changing magnetic field could induce an electric current in a conductor because it generated vortex electric fields.
The working principle of a zero-flux current sensor is based on magneto-electric conversion, relying on the strong nonlinearity of the magnetic material. According to Maxwell's equations, the static magnetic field generated by a direct current has no measurable electrical effect. In a linear system, there is no relationship between the system's output and input current; that is, a linear system cannot measure direct current through magnetic flux induction. Nonlinear systems, however, can establish a relationship between the input direct current and the output.
Schematic diagram of zero flux current sensor
Since direct current has no measurable electrical effect, to make the system "move," we first need to construct an alternating current Iac superimposed with the DC input current Idc. These two currents act together on the nonlinear magnetic material, i.e., a "magnetic modulation" process. Let the system's response function be f(Idc + Iac), which is a nonlinear equation. For simplicity, we only consider the quadratic term here, ignoring higher orders, i.e., the form is:
Formula (1) is f(x) = ax + bx²
The "modulation" process can be described as follows:
f(Idc+Iac)=a(Idc+Iac)+b(Idc+Iac)2
=(a*Idc+b*Idc2)+(a*Iac+b*Iac2+2b*Idc*Iac) formula (2)
Since direct current has no measurable electrical effect, the first part of formula (2) has no effect, that is, it equals 0, and only the active term is retained:
f(Idc+Iac)=a*Iac+b*Iac2+2b*Idc*Iac formula (3)
Please note the last term 2b*Idc*Iac in formula (3). This term reflects the influence of DC current, that is, through modulation, the nonlinear system can respond to DC current; and the stronger the nonlinearity, that is, the larger the coefficient b, the stronger the DC response. If it is a linear system, the coefficient b=0, and it will not respond to DC current. This is why a nonlinear system must be used. Fortunately, the BH characteristic of magnetic materials is strongly nonlinear.
The output of the aforementioned nonlinear system contains not only useful DC current information but also unwanted "modulated" AC current information. The entire system response is designed to be independent of the "modulated" AC current. Therefore, a "demodulation" process is needed to remove the unwanted "modulated" AC current information, specifically removing the terms a*Iac and b*Iac², and converting Iac in the term 2b*Idc*Iac to a constant. The final form is: f(Idc+Iac)=a*Idc.
The “DCStim&Sense” section in the schematic diagram represents DC current excitation and induction, including the “modulation” process. Two flyback magnetic cores are used to cancel the aIac term in formula (3). The “SignalCondition” section includes a “demodulation” section, which requires a low-pass filter to remove the bIac2 term in formula (3). This results in a low bandwidth for the DC branch signal, which mainly responds to DC and low-frequency AC inputs. To expand the bandwidth, an AC branch is introduced, namely the third magnetic core “ACSense”, which is mainly used for induction of medium and high frequency AC current inputs. The output of the “SignalCondition” section is amplified by the power amplifier (PA) circuit, and the output current Iout cancels the magnetic flux generated by the input current Iin. When balanced, it reaches a zero magnetic flux state, that is, Iin-Iout*NS=0, which is also
Iin:Iout=NS:1 formula (4)
The ratio of input to output current is equal to the coil turns ratio and is independent of other factors such as temperature changes. Formula (4) holds true not only for DC but also for AC current within a certain frequency range, and the response frequency can reach the order of hundreds of kHz to MHz. Therefore, the sensor has wideband operating characteristics, and the operating frequency can range from DC to the order of MHz.
Because the magnetic flux is almost completely enclosed in the toroidal core, the effective permeability is very high and the leakage flux is very low. In addition, the system has a very high open-loop gain, so formula (4) holds true with very high precision, generally on the order of 10⁻⁶. Such high precision brings many benefits. First, the dynamic range of current measurement is very wide, and a single sensor can cover the range from mA to kA. Second, a very large current ratio can be achieved, with Ns values reaching 1000~10000 or higher. On the other hand, the magnetic flux state is very slightly affected by environmental factors such as the relative position of the current bus, temperature, and external electromagnetic interference, generally around the order of 10⁻⁶.
The output current signal Iout can be converted into a voltage V=Iout·RM through a high-precision load resistor RM for measurement.
