### Construction and Principle of Operation of Closed Loop Hall Effect Current Transducers

While open loop current transducers amplify the Hall generator voltage to provide an output voltage, closed loop transducers use the Hall generator voltage to create a compensation current in a secondary coil to create a total flux, as measured by the Hall generator, equal to zero (see figure above). In other words, the secondary current, I_{S}, creates a flux equal in amplitude, but opposite in direction, to the flux created by the primary current.

Operating the Hall generator in a zero flux condition eliminates the drift of gain with temperature. An additional advantage to this configuration is that the secondary winding will act as a current transformer at higher frequencies, significantly extending the bandwidth and reducing the response time of the transducer.

When the magnetic flux is fully compensated (zero), the magnetic potential (ampere-turns) of the two coils are identical. Hence: \(N_P\cdot I_P=N_S\cdot I_S\), which can also be written as \(I_S=I_P\frac{N_P}{N_S}\).

Consequently, the secondary current, I_{S}, is the exact image of the primary current, I_{P}, being measured. Inserting a "measurement resistor", R_{M}, in series with the secondary coil creates an output voltage that is an exact image of the measured current (see figure above).

To give an order of magnitude, the typical number of secondary turns is N_{S }= 1000…5000 and the secondary current is usually between I_{S }= 25…300 mA, although it could be as high as 2 A. For higher output currents, an output power stage is needed to produce the transducer output current.

At low frequencies, the transducer operates using the Hall generator. At higher frequencies, the secondary coil operates as a current transformer, providing a secondary output current again defined by the turns ratio and converted to a voltage by the measuring resistor. These effects are illustrated in figure 1.

** Figure 1.** *Bandwidth of the "Hall generator" and "current transformer"*

The unique design of closed loop transducers provides an excellent bandwidth, typically from DC to 200 kHz. The challenge is to ensure a flat frequency response across the entire range, especially where the two response curves cross, to provide excellent dynamic response and accuracy for all possible signals.

Finally, while closed loop transducers work theoretically at zero flux, various magnetic imperfections (e.g. leakage flux, non-perfect coupling) imply a residual flux into the core which results in iron losses at high frequencies. Consequently, the heating phenomena described in "Handling Core Losses of Open Loop Transducers" also apply in this case, even if much less significantly.

**For more information, please read:**

Basis for Hall Effect Technologies

Characteristics of Closed Loop Current Transducers

Open Loop Hall Effect Current Transducers

Transducers – Basic Principles of Selection

Handling Core Losses of Open Loop Transducers