Circuit Corner - Issue 9

In this issue, I will present a simple yet effective way of designing current-sense transformers for any application. Current sense transformers find uses in a wide array of fields, but the design and application of these useful tools is often poorly understood.

Current Sense Transformer Design

The basic design of a current sense transformer. No matter how it is constructed, it will come down to this in the end.

Fundamentally, a current sense transformer is composed of a transformer feeding a resistor. The resistor can be part of the measuring equipment, or it can be next to the transformer, or it can be some combination. When using this design to drive 50ohm coaxial cable, properly terminated, it is more likely that the "resistor" will actually be the 50 ohms resistance looking into the cable, and will not be a discrete component at all. When driving a high impedance input, the resistor is essential.

To design a current sense transformer, you have to decide on a few variables. Specifically, you have to know the characteristic (load) resistance, R_L, the sensitivity resistance R_S, the lowest operating frequency, f, and the expected accuracy A. The sensitivity resistance is expressed in volts per amp, which is just another way of saying ohms. A sensitivity of 10mV/A, for instance, would be 10mOhms.

The accuracy is important because, during operation, the transformer core will begin to magnetize and current will flow in the primary side that is not matched in the secondary side. When the cycle reverses, the current will drain and then build up again in the opposite direction. This effect is caused by the "magnetizing inductance" of the transformer, and is unavoidable. This will cause a slight sag in the output voltage relative to the input current. This sag is predictable and can be reduced to an arbitrarily small amount with careful design, but you must still specify the amount. Specifying too tight an accuracy band will require very large transformers. Accuracy is specified as a number between 0 and 1, that represents the total allowed voltage deviation. It is equivalent to the percent deviation divided by 100.

The minimum operating frequency is required because the transformer will not pass DC. In fact, due to the effects of magnetizing inductance, it will pass lower frequencies considerably more poorly than higher ones.

The first thing to determine when designing such a transformer is the appropriate winding ratio WR, which can be determined as follows:

WR = R_L / R_S

From this equation, we see that, to achieve a buildable current sense transformer, we should try to keep R_L relatively small. While it would seem that R_S should be made large for the same reason, there is a tradeoff in doing so. Specifically, the equivalent resistance to the current sense transformer is determined by:

R_equiv = R_S ² / R_L

This equation suggests that the higher our sensitivity, the more resistance the sense transformer presents to the rest of the circuit. It also points out the downside of lowering R_L too much: the equivalent resistance suffers. This might seem backwards at first, until it is remembered that R_L is reflected through the transformer by the inverse square of the turns ratio.

The final piece of the puzzle is the required primary inductance to achieve the desired transformer:

L_pri = R_S ² / (R_L f A)

This is the inductance required for the primary coil of the transformer, which can be of any construction you prefer. A toroid core is often specified in terms of nH/turn², which allows you to quickly figure out how many primary turns you would need for a given core. Other cores are designed and specified in different ways. Once you know the primary turns count, the secondary simply has that number times the winding ratio of turns.

Any inductance lower than this will cause the output voltage to prematurely drop off. Any inductance higher than this will work better, with better accuracy, but the transformer will be physically larger and/or constructed with more costly materials. As with many things in engineering, this is a case of diminishing returns. Specify the accuracy you actually need in the application you are working with, or you will end up paying for accuracy you have no need of.