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Hall-effect sensor design: What is the best way to suppress switching jitter?

Hall-effect sensor design: What is the best way to suppress switching jitter?

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By eeNews Europe



Hall sensors are increasingly preferred sensing solutions in many applications thanks to their contactless measurement principle and resulting high reliability.
For instance, one trend shows the increasing use of Hall-effect sensors over mechanical switches due to their insensitivity against environmental conditions (e.g. dust, humidity, and vibrations), their constant measurement results under the harshest environmental temperature conditions from -40°C up to 150°C, and their highly repeatable operation without degradation over time. All while maintaining a high level of quality for unlimited use.

In order to fulfil this ever evolving safety and reliability feature, highest accuracy of the switching threshold is the essential parameter in the Hall switch specification.
The actual switching operation, triggered by a magnetic signal crossing the switching threshold, is affected by different effects like switching delay, sampling jitter and threshold noise. All of these are undesirable as an ideal switch should react instantaneously, however they cannot be completely avoided due to the Hall IC’s internal signal processing.

In order to achieve an optimal switching performance, the signal processing inside the latest Hall-effect switch family from Micronas – the HAL 15xy family, was designed to feature the highest suppression of such negative side effects.
This paper provides insight to how the signal path design influences the jitter performance of the output signal and the diverse design approaches taken to solve this problem.

A brief introduction of the signal path and the static switching behavior of a Hall switch are presented in the following section.

Signal path of Hall switches

The simplified signal path of a Hall switch consists of several basic components, as depicted in figure 1:

Figure 1: Simplified Hall switch signal path


The integrated Hall sensor converts magnetic flux density into an electrical signal, the optional low-pass filter limits the signal bandwidth and the sampled or non-sampled comparator decides if the signal is above or below the currently active threshold.

A sampled comparator produces new decisions each time it is triggered by the sampling clock, while a non-sampled comparator operates continuously without trigger.

In case a low-pass filter is present, it suppresses frequency components above the useful signal bandwidth in order to lower noise contribution from these frequency ranges.

Most Hall sensor ICs, including the Micronas Hall switch families, employ the well-known spinning-current technique for superior offset performance. Figure 1 omits any spinning-current related blocks for simplicity.

Static switching behavior with hysteresis

A Hall switch features two different magnetic thresholds, Bon and Boff, forming a hysteresis loop. This behavior is necessary to avoid unwanted toggling or flickering, which would occur without hysteresis. Figure 2 shows a graph of the static output behavior versus the magnetic flux density B, assuming a non-inverted output behavior.

Figure 2: Static hysteresis loop of a Hall Switch

Between Bon and Boff both output states are possible. For B>Bon the OUT state will definitely be 0. The switch remains in this state until B<Boff, toggling the state of OUT to 1.



Threshold noise and minimum reliable hysteresis

Now the question may arise how small this hysteresis loop can be made. To give an answer, the effect of threshold noise has to be considered. Actually, Bon and Boff are not fixed thresholds concentrated at a single value but are blurred by threshold noisecaused by the thermal noise of the Hall sensor itself and of the other circuitry. The noise level can be scaled by design, dependent upon current consumption and filter bandwidth. The noise adds to the assumed otherwise constant threshold values. Figure 3 now shows a probability density function for Bon and Boff (not to scale).

Figure 3: PDF for threshold noise

The height of the probability density is an indicator of how likely it is to find the momentary threshold at the corresponding flux density B. In case of thermal noise the probability is a normal (Gaussian) distribution. The width of the density function is given by the standard deviation σBth, which is identical to the threshold´s RMS noise value Bth,rms.

The tails of the probability densities for Bon and Boff will always leak into each other at the midpoint Bmid of Bon and Boff as the density never reaches 0. This means that for a constant flux density Bmid the Bon threshold can sometimes – at a low likelihood – be found to be below Bmid, turning the switch on. Again, sometimes Boff can be found to be above Bmid, turning the switch off again. So the switch can start toggling even for a constant flux density, which is normally undesired. This phenomenon can never be completely avoided, only the probability of occurrence should be sufficiently reduced. As a rule of thumb, if the distance Bon – Boff equals at least 10…12 σBth,  the occurrence is negligible.



Dynamic behavior: Sampling jitter


Filtered sampling Hall switches

The signal processing of the HAL 15xy sensor family is based on a sampled design with low-pass filter. As result, the switch output can toggle only at certain equidistant points in time when a new sample of the filtered input is taken, in the case of the HAL 15xy sensors this occurs every 2 µs. The time point when B crosses the switching threshold is asynchronous to the sampling clock, leading to sampling jitter. Figure 4 shows a timing example for a filtered sampling switch like the HAL 15xy:

Figure 4: Delay in case of a filtered sampling Hall Switch

Here the flux density B(t) is assumed to perform a very fast transition through Bon to keep the effect of threshold noise negligible for now. The Hall signal, proportional to B(t), is then taken through a low-pass filter to eliminate threshold noise at higher bandwidths.

It takes a constant systematic delay Δtsyst until the signal crossing the threshold has travelled through the filter, here for example 15 to 16 µs. Additionally, a random delay phase of a maximum length of 2 µs will appear until the next sampling event happens and the comparator toggles. This random delay is called sampling jitter Δtsampling when the Hall switch toggles repeatedly.

The sampling jitter can be described by a peak-to-peak or root mean square (RMS) value. The HAL 15xy sensors perform a peak-to-peak value of Δtsampling,pp.= ± 1µs – within this 2 µs sampling interval.  All time points are equally likely to be found (probability distribution is shaped like a "box"). The resulting RMS amounts to typically Δtsampling,rms = 0.58 µs and maximum 0.72 µs and shows a better performance compared to competitive ICs.


 
For the HAL 15xy family a sampling comparator operating at 500 kHz sampling rate has been selected to guarantee reliable limits for the sampling jitter of typ. ± 1us. This type of design enables the usage of dynamic offset suppression inside the comparator, increasing the overall precision of the HAL 15xy sensors’ magnetic thresholds.

In addition, the sensors have a unique front-end design which enables a flexible definition of the low-pass filter bandwidth between 3 kHz and 93 kHz through the use of metal mask programming without an increase of the sampling jitter. On one hand, a smaller bandwidth increases the systematic delay of the signal path, but on the other hand lowers the switch´s threshold noise increasing the precision. Higher bandwidth has the opposite effect. Thanks to this feature the HAL 15xy family can be tailored to the customer needs for applications with fast dynamic or static magnetic fields.

Non-filtered sampling Hall Switches

Some Hall switches, like the well-known HAL 5xy family from Micronas, are designed as non-filtered sampling ICs. Depending on customer preference, the absence of filtering is attractive for fast reaction with low delay but comes at the cost of threshold noise increase. For such Hall switches, the sampling jitter remains but the systematic delay vanishes as no filter is active. Figure 5 shows the general dynamic behavior of such a type of switch.

Figure 5: Delay in case of a non-filtered sampling Hall switch

This is why the random delay of a HAL 5xy sensor has a peak-to-peak value of Δtsampling,pp.= ± 8 µs and a RMS value of Δtsampling,rms.= ± 4.6 µs and highlights the improved performance of its successor, the HAL 15xy family of switches from Micronas.


Filtered non-sampling Hall Switches

Some non-sampled Hall switches exhibit a systematic delay caused by filtering and a random delay caused by noise from an internal thermal comparator. Therefore the situation is similar to HAL 15xy, only the probability density of the switching uncertainty is normally distributed, looking like a gauss curve, instead of a “box” shape. Only the total switching jitter is present with no sampling jitter contributing. Figure 6 illustrates this behavior.

Figure 6: Delay in case of a filtered non-sampling Hall Switch

For a normal distribution no peak to peak value can be given (still often ± 3σ are used), only the standard deviation σ is defined, here equal to the switching jitter’s RMS value. Hall ICs based on this design approach show in best case a maximum output RMS jitter of 1 µs and do not provide the same high performance as filtered sampling Hall switches like the ones of the HAL 15xy sensor family.

Effective threshold noise and hysteresis narrowing

As described at the beginning, each switch threshold shows abnormal distribution over a certain range, caused by threshold noise. The standard deviation σBth describes the width of the distribution. However, the threshold noise is not directly measureable in the application and cannot be used directly to estimate errors caused by noise as it is distorted by the switches’ hysteresis function.


In an application, only a part of the threshold noise has to be considered depending on the slew rate of the flux density B crossing the noisy threshold region. Fortunately, this observable portion is usually smaller than the true threshold noise and is named in this paper as "effective threshold noise". Furthermore, a “threshold walk” or “hysteresis narrowing” can be observed.  This shifted threshold distribution or effective distribution is observed when measuring the switching characteristics and different from the true threshold distribution. Figure 7 tries to illustrate this effect.

Figure 7: True and effective threshold densities

Here the true distribution of the noisy threshold is shown in the upper graph. Positions marked by "X" indicate the values B(t) relevant for the sampling of the switch at t=T0, T0+T, T0+2T etc. (T: Sampling interval).

At each "X" mark, the Hall switch determines if B(t) is above or below the threshold. At the left tail of the true distribution, the probability to find B(t) above the threshold is still small for each single sample. However, the accumulated switching probability up to the current sample is definitely larger, so the switch will toggle if it performs enough samples with B(t) still in the left tail.


Assuming a slowly travelling B(t), it is unlikely to reach the right half of the true distribution before the switch toggles, jumping to the other threshold. The lower part of Figure 7 now shows the effective distribution of the observable noise effect, which is clearly shifted compared to the true distribution. Of course the mean value is shifted as well, causing a small narrowing of the hysteresis window. The amount of narrowing and width of the effective distribution depend on the slew rate of B(t).

Resulting switching jitter of the HAL 15xy family

Most interesting of all is the resulting switching jitter Δtswitch of a Hall switch. The random distribution of the switching delay – the switching jitter – is considered according to Figure 8.

Figure 8: Switching jitter resulting from threshold noise and sampling jitter

In this case threshold noise and sampling jitter are both present, leading to a combined switching jitter. B(t) slowly crosses the effective threshold, hence threshold noise cannot be ignored any more. A noise band is drawn around the effective threshold. Figure 8 indicates where the momentary threshold may be located. The projection of B(t) in the noise band onto the time axis simply gives the resulting timing jitter from threshold noise Δtthres.noise. This timing jitter appears delayed in the filter output voltage Vfilter. Now, when OUT toggles, the final switching jitter consists of the jitter from threshold noise and additionally the sampling jitter, which is always present.

Note that figure 8 ignores the different probability densities of jitter from threshold noise and sampling jitter, further both were just added to create switching jitter.
For high slew rates (SR), the sampling jitter dominates and can be used to estimate the switching jitter. For low slew rates, the sampling jitter is present as well but here the effective threshold noise is dominating.


The boundary between high and low slew rates can easily be found by setting the sampling jitter Δtsampling,rms equal to the jitter induced by threshold noise Bth,rms:

So for magnetic slew rates well below 124 mT/ms the resulting switching jitter can be estimated to originate from threshold noise alone, while sampling jitter is negligible.

Conclusion
The jitter in Hall switches has two origins. First, the thermal noise of the Hall plates and the signal processing lead to the described threshold noise, second, the sampling causes a system dependent sampling jitter. By the optimal deployment of Micronas proprietary technology, the HAL 15xy sensor family operates with a very high sampling frequency leading to a very small sampling jitter. This new and optimized circuitry was designed to guarantee very low thermal noise while keeping a low current consumption providing best in class noise behavior.  Additionally, the bandwidth of the analog filter can be decreased or increased by a metal option enabling the possibility to minimize noise or delay time.


About the Authors:

David Muthers is analog designer. He holds a Ph.D. in Electrical Engineering from the University of Kaiserslautern. Since 2007 he is working for Micronas, mainly on Hall sensor frontends. His main interest is precise analog signal processing and data converters.

Thomas Kauther, analog designer, earned a Dipl.-Ing. in Solid State Electronics from the University of Darmstadt. He is active for Micronas since 1996 in the areas audio, power management, and Hall sensors.

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