The Solenoid

Introduction

The solenoid is the component used to convert electric current in to magnetic fields. Since the hall sensor converts magnetic fields in to a voltage potential, the combination of the solenoid and hall sensors implements a current to voltage converter. The first problem to tackle is how to convert current to magnetic fields efficiently. The second problem is how to couple the generated magnetic fields in to the hall sensor with low loss.

Generating Magnetic Field from DC Current

Straight wire

The simplest way to convert current in to magnetic fields is to force the current to travel along a straight conductor. By Maxwell equations, moving electrons will create a magnetic field that are orthogonal to the travel direction. The magnetic fields circle around the moving electron. The more the electrons move (i.e. higher current density), the greater the magnetic field strength generated.

Solenoid

To improve the gain of the straight wire approach, the logical step is to create a coil. A single loop coil will generate 3 times as much gain as a straight wire. To increase the gain even more, mulitple coil loops can be use to increase the gain even further.

Design Considerations

The solenoid looks like a modern on-chip inductor. The main difference is that on-chip inductors strive for high Q and high inductance inductors. Our design strives to reduce series resistance and inductance, but we want high current to magnetic field conversion gain. Inductance is evil in our design because this results in a "non-transparent" measurement of the current. In some cases, adding large series inductance on the DUT's power rails can cause stability issues with the DUT (device under test). Since the solenoid will be connected to the DUT's power rail in series, inductance is highly undesirable. Series resistance in the solenoid causes the solnoid to be non-transparent to the DUT. Series resistance induces a voltage drop across the solenoid. If the voltage drop is too large, the DUT may not function. If the DUT's current consumption changes rapid, the high series resistance will induce noise on the DUT's power rail. Thus, low series resistance and inductance is a must in your solenoid.

Conversion Ratio

From undergraduate eletromagnetic textbooks, the magnetic field generate by a mult-turn solenoid is :

Where :

	B is the magnetic flux density
	u is the magnetic permeability of the medium
	N is the number of turns on solenoid
	I is the current through the solenoid
	L is the length of the solenoid
	R is the radius of the solenoid

This formula calculates the magnetic flux density that is at the end of the solenoid.

Coupling Solenoid to the Hall Sensor with Low Loss

As mentioned above, generating a magnetic field from an electric current is fairly manageable. The only problem with the above techniques is that we want to direct the magnetic field in to the Hall Sensor. The Hall sensor is currently implemented as a N-well tub. Tubs are usually implemented on the silicon wafer substrate. For maximum coupling, the magnetic fields should be perfectly perpendicular to the Tub (i.e. surface of the substrate). The solenoids are usually implemented with metal layers in the CMOS process. As depicted in figure 1, the solenoid's fields are concentrated near the coil. The magnetic field strength decreases with distance to the coil. Hence, the best position for the Hall sensor to be is inside the coil. The magnetic fields are the most uniform and highest field strength inside the coil. Since metal layers are always above the substrate, the metal layers will always be up to a finite distance away from the coil. Thus, there will always be some loss due to the finite distance from the coil.

The solution

To improve the coupling between the solenoid and the Hall sensor, we can move the Hall sensor inside of the solenoid. This may not sound like an easy task since it is physically impossible to move the Hall sensor, which resides on the surface of the substrate, or the Solenoid, which resides in metal layers above the solenoid. The proposed fix is to use N-well as part of the solenoid. But if we backtrack a few paragraphs, low series resistance is one of the primary requirements of the solenoid. N-well is a very resistive material compared to metal layers and it can have a sheet roll resistance as high as 2000 ohms per square. With such a large sheet roll resistance, the low series resistance implementation will not be possible if N-well are part of the solenoid. But without the poly and N-well layers, coupling losses between the Hall sensor and the solenoid will be high.

Suppose the N-well is part of the solenoid but it is not in series with the device. In other words, the solenoid's metal layer closest to the N-well should be shorted together with a N-well ring (see figure 2). The N-well ring should be approximately the same shape as the solenoid's lowest metal layer. This way, Hall sensor will be partially inside of the solenoid (see figure 2). This configuration increases coupling between the Hall sensor and the coil with negelible performance loss (i.e. series coil resistance).

The implementation

As a result, the final implementation of the solenoid is as follows :

	composed of 4 layers of metal with each layer being 1.4 um thick
	composed of N-well with N+ doping (to reduce resistance).
	height of solenoid is 4*1.4um = 5.6um.
	coil looks like a donut with a 5um inner diameter, 25 um outer diameter. R = 7.5um.

With those values, the final gain of the solenoid is 15 mT/A. Do to the location of the hall sensor, not all of the 15mT/A will reach the Hall sensor. We expect a 10% to 20% loss due to non-optimal location of the hall sensor. This is still much better than not using a the N-well with N+ doping and metal layers solenoid.