## ISOLATED CURRENT MEASUREMENT

The simplest method of sensing the current in a electric circuit is by measuring the voltage drop across a known resistance in the current path. This resistor is commonly referred to as a shunt resistor. Although shunt means a parallel resistor, this name is used to refer to the parallel connection with the voltmeter.

The utilization of shunt resistors for current sensing has several drawbacks. Perhaps the most obvious is that the resistor alters the original circuit. The resistor has to withstand the current, and will dissipate some power. A less obvious, but equally important disadvantage is that there is a direct connection between the primary circuit and the sensing circuit. This may be of little concern in electronics, but in power electronics it is a completely different matter. There may be large common mode voltage differentials between various parts of the circuit.

In order to avoid the second problem isolation is required, and as a side benefit most of the isolated sensing technologies has a lower load on the primary circuit when compared to the shunt resistor.

### CURRENT TRANSFORMER

The current transformer is perhaps the most well known isolated current sensing device in the world of power electrics. In reality all transformers are both current, voltage and impedance transformers, the name stems from the application in which the transformer is intended to be used.

A current transformer is typically used with very few(often only one) primary turns, and a large number of secondary turns. Additionally the secondary is designed to be operated in short circuit condition. The transformer is designed such that the current in the secondary circuit in proportional to the primary current. Common standards are secondary currents of either 1 or 5A for nominal primary current.

The reason why this works is that the current in the primary is(nearly) unaffected by the loading on the current transformer, i.e. the primary current is constant. Additionally the high number of turns, and thus high output impedance of the secondary causes the it to act as a current source.

The load on the secondary is usually referred to as the burden. The rated burden is the maximum load i VA, or the highest allowable resistance connected across the secondary terminals. Remember that the current is constant, thus higher resistance implies a higher load.

\[ P = I^2 \cdot R \]

To high burden will cause linearity problems, and a open circuit secondary may(will) even cause destruction of the transformer due to overvoltage.

Current transformers(like all transformers) utilize the effect of magnetic induction, and thus will only work with alternating currents. Another drawback is that the transformer will introduce phase shift between primary and secondary current. At normal power frequencies(50 or 60Hz) this phase shift is usually small however.

### HALL EFFECT TRANSDUCER

The Hall effect is the production of a voltage across a conductor crosswise to an electric current running through the conductor, and perpendicular to a magnetic field in the conductor. The produced voltage depends on the magnitude of both the current and the magnetic field, as well as on the material properties of the conductor.

The Hall voltage is given by:

\[ V_H = \frac{-I B}{n e d} = k \frac{-I B}{d} \]

Where \( I \) is the current through the element, \( B \) is the magnetic flux density, \( n \) is the carrier density, \( d \) is the length of the conductor, and \( e = 1.60217662\cdot10^{-19} \text{Coulomb} \) is the electron charge. \( k \) is a temperature dependent material property, known as the Hall coefficient.

In current sensing applications the wire carrying the primary current is typically run through a core of high permeability material. The magnetic field across the conductor is concentrated and enclosed in the core. A small gap is cut in the core, where the Hall sensing element is placed. A current source is used to maintain a stable current through the Hall element, and the voltage across the element is measured.

In order to improve the performance of the transducer, a system known as closed loop hall sensing is often used. The Hall voltage is amplified and converted to a current running through a second winding on the core. This winding has a large number of turns when compared to the primary winding, and when the polarity is reversed only a small current is required to cancel out the magnetic field produced by the primary winding. The closed loop nature of this system helps to cancel out any nonlinearities in the core, the Hall element and the amplifier.

The current in the secondary is proportional to the primary current related by the turns ratio, and this secondary current is easily measured by a shunt resistor.

The Hall effect is utilized in many applications besides current sensing, but those applications are outside the scope of this article.

### ROGOWSKI-COIL

The Rogowski-coil is a coil of electrically conducting wire wound around a low permeability material(i.e. non-magnetic, or something that does not saturate), and with one end of the coil returning through the center. As both connections are made at one end, this makes it convenient to retrofit around a existing current carrying device.

When subject to a alternating magnetic field, the generated voltage is proportional to the derivative of the field. The voltage is typically integrated, in order to obtain a measure of the field itself.

The voltage is(ideally) given by:

\[ v(t) = \frac{-AN\mu_0}{l} \frac{\mathrm{d}i}{\mathrm{d}t} \]

Where \(A = \pi r^2\) is the area of the small loops, \(N\) is the number of turns, \(\mu_0\) is the permeability of air(vacuum), and \(l = 2\pi R\) is the length of the entire winding.

Due to the high dependence on the physical parameters of the coil, Rogowski-coils are usually sold as a integrated solution with a amplifier calibrated for the specific coil.

Rogowski-coils generally have a high bandwidth when compared to the alternatives. In excess of 1MHz, before the inductance of the coil has a significant negative impact on the performance.

Rogowski-coils only work on alternating currents. While often considered a disadvantage, it may also be regarded as an advantage if the goal is to measure a small AC component in the presence of a large DC current.