AN296240
MCO-0001106, Rev. 2P0147

APPLICATION INFORMATIONFUNDAMENTAL PROPERTIES OF SPEED SENSORS
By Emil Pavlov, Allegro MicroSystems

INTRODUCTION
The aim of this application note is to provide a solid foundation for understanding and comparing the fundamental
properties of speed sensors that are valid not only for Allegro
products but for speed sensors in general. First, these fundamental properties will be defined, followed by the factorsthat influence these properties and the effect of both on theobservable properties in applications, such as angular position and velocity.

The sensor device outputs pulses at specific angular locations based on the time-varying magnetic input signal, andthe speed can be calculated as the inverse pulse distance.
Figure 1 is an example of such a period measurement. Inaddition, Allegro’s speed sensors have advanced integrated
algorithms that also provide rotation direction robustly evenunder adverse conditions such as temperature and signal
variation, signal drift, various vibration signatures, etc.

Throughout this document, several technical terms are usedthat unfortunately tend to be used interchangeably or withalternative definitions depending on the specific technicalfield or context. Therefore, these terms are formally defined
first in the scope of this document, starting with the most general concepts and continuing to the most fundamental ones.

TERM DEFINITIONS
Figure 1 represents data from a physical measurement,
depicting the observed period of the magnetic input signal
and directly shows how the sensor properties affect themeasurement result.

TargetA target can be a ferrous gear wheel, a ferrous stamped diskor cylinder, or an axially or radially magnetized ring magnet
mounted on a rotation axis, for which angular velocity will bedetermined by the speed sensor. For general recommendationsof target design, refer to the application note Target Designfor Hall Transmission Sensors [1] or Magnetic Encoder Designfor Electrical Motor Driving Using ATS605LSG [2]. As far as
the magnetic properties of the target material are concerned,
Impact of Magnetic Relative Permeability of Ferromagnetic
Target on Back-Biased Sensor Output [3] offers a useful guide.

Figure 1: Histogram of observed period of a rotating magnetic encoder

Accuracy
Accuracy denotes the difference between the true value andaverage of all observations. It is important to differentiate
between absolute and relative accuracy, which, besides being
expressed in different units, also denotes different properties
in the context of speed sensors.

[1] https://allegromicro.com/-/media/files/application-notes/an296178-hall-transmission-sensor-target-design.pdf[2] https://www.allegromicro.com/en/insights-and-innovations/technical-documents/hall-effect-sensor-ic-publications/magnetic-encoder-design-electricalmotor-driving-ats605lsg[3] https://www.allegromicro.com/en/insights-and-innovations/technical-documents/hall-effect-sensor-ic-publications/magnetic-relative-permeabilityferromagnetic-target-back-biased-sensor-output

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Relative Accuracy
Relative accuracy quantifies the difference of the averagemeasured period or speed and actual input frequency. In theexample of Figure 1, there is an input signal with 1 kHz and amean observed period of 1 ms, therefore having no deviation.
It is generally more convenient to express the relative accuracy
in angular degrees normalized by the signal period or simply
in percent of the signal period. First, this makes accuracy arelative measure. Second and more importantly, accuracy
then becomes independent of both the input speed and target period (consequently the number of teeth or pole pairs).

Absolute Accuracy

APPLICATION INFORMATION

of all measurement would fall (either left or right) less than thejitter value away from the average.
Another convention is to report the jitter at either the three orsix sigma level, which is achieved by multiplying the 1-sigma
value by 3 or 6 respectively. The general formula for the proportion of observations laying within the double-sided intervalfrom –n × sigma up to +n × sigma is calculated with the error
function, shown in Equation 2.
Equation 2:

In summary, relative accuracy is for velocity and absoluteaccuracy is for angles. It is important to keep in mind thatboth the relative and absolute accuracy are averaged values
and represent a systematic bias from the correct measure. For
an instantaneous (or random) deviation, jitter must be used.

Jitter is most conveniently expressed in percent of the target
period, as this value is independent of rotational speed andnumber of teeth/pole pairs. It is important to note that thesignal period is not necessarily equal to the target period, assome sensors output multiple pulses per period. Not taking
this into account would lead to substantial overestimation ofjitter (precisely by a factor equal to the number of pulses perperiod). Moreover, some Allegro sensors offer configurable
number of pulses per period, so disregarding the above note
would result in fictitious variation of the jitter value without any
physical foundation for it. More on the topic can be found in
the section about the source of jitter.

Precision

Single- and Double-Edge Jitter

Precision represents the spread of multiple measurements
and quantifies the repeatability of the results. It describes only
the random fluctuations from the true value per definition. In
the context of speed sensors, the temporal fluctuations of theoutput pulses are called jitter.

With a signal from a magnetic encoder with a period of six
degrees (e.g., 60-tooth target with one pulse per period),
then single-edge jitter is the variation of each individual pulse
position around the mean tooth position (0°, 6°, 12°, etc.)
over all revolutions. Double-edge jitter refers to the variationof the periodicity of the signal. It can be calculated either foreach teeth pair individually over all revolutions or as a running
difference of consecutive teeth.

Absolute accuracy is the difference between the angular position of the output pulses and the true mechanical positionof the target. Absolute accuracy is important in applications
where the absolute angular position is required in addition
to angular speed, for example, in absolute encoders or camand crank applications.

Jitter [4]Jitter is the width of the measurement distribution around theaverage. In the case of Figure 1, jitter is around 10 µs. Conventionally, it is reported at one standard deviation level andcan be calculated as shown in Equation 1.

Theoretically, this is shown in Equation 3:
Equation 3:

Equation 1:

where N is the number of measurements, and µ is the averageof all measurement values. It defines that, on average, 68% [5]as it can be derived from the statistical principles; however,in practice, this is rarely the case. The reason is the period-toperiod variation of the input signal, which will be discussed
further in the following sections. Figure 1 shows the doubleedge jitter.

[4] For further information, see application note “Guidelines For Measuring Output Repeatability On Speed Sensors” (available on request; contact Allegro).
[5] Assuming normal distribution, which generally is fulfilled.

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MCO-0001106, Rev. 2P0147

Resolution
Generally, resolution is the minimum possible step/differenceof the output of a measurement device, or how finely the output
is quantized. This term only makes sense for digital devices, as
the resolution for analog devices is zero, i.e., they can output
any arbitrary value. The resolution of the sensor data shownin Figure 1 is the distance between the individual groups,
which in this case is 4 µs. Theoretically, it can be calculated
as the difference between two neighboring clusters, but thisrequires classification of the data. A more practical approachis to take the median of all pairwise distances between consequent measurements. As it can be seen from the histogram,the individual groups do not have discrete values but rather aslight spread, which is caused by jitter of the pulse-capturing
equipment. Using the median instead of the minimum provides
robustness against that. Resolution is typically expressed innanoseconds (ns) or microseconds (µs).

Propagation Delay
Propagation delay is the time it takes from a magnetic edge
until a pulse is output and roughly describes how quickly thesensors react to changes of the input. Due to physical laws,
the magnetic signal does not have any defined edges, but
is rather a smooth (continuously differentiable) curve. Therefore, under a magnetic edge, it is generally meant to be thepoint when the signal crosses an adaptive threshold. The
propagation delay is typically measured in nanoseconds (ns)or microseconds (µs), similar to the resolution.

IMPORTANT INFLUENCING FACTORSThis section details what factors plays an important role fordetermining each of the sensor characteristics previouslydefined. Contrary to the previously given order, this section
is organized from the fundamental properties up, as they
are simpler and often have impact themselves to the more
abstract ones.
Propagation delay is the time necessary for the sensor toprocess the input signal. It is determined by the algorithmic
complexity, IC processing throughput, and fundamentallythe system clock, as each digital operation step takes one
clock cycle. Some applications specifically define a requirement for propagation delay, such the AK protocol for wheelspeed sensors, and it could be an essential part of proper
device functionality.
Sensor resolution depends on the input sampling rate andoutput update rate, and again, ultimately, on the system clock. If
everything else was instantaneous, the propagation delay would
be at minimum zero and at maximum equal to the resolution.

APPLICATION INFORMATION

Allegro’s sensors have sub-microsecond propagation delay
and resolution, and these properties are optimized so that
there are no adverse effects on the remaining characteristics.
Jitter is not determined by propagation delay or resolution.
However, it must be pointed out that the resolution must besufficiently small for a given jitter; otherwise, it would become
the system’s limiting factor and increase the jitter. Figure 1 isan example of when this condition is still satisfied despite
the small margin. Conversely, the output of the speed sensor
must be sampled with sufficient resolution as to not adversely
affect jitter. A good rule of thumb is to use the same or better
resolution than the sensor itself.
Fundamentally, jitter is caused by the temporal uncertainty ofwhen exactly the magnetic signal crosses the switching threshold. This in turn depends on the ratio of the signal to noise andthe signal slope at the crossing point. For single-edge jitter,
the noise of the sensor is the major contributor. It is inversely
proportional to the temperature (which is inevitable for all
electronic devices), input bandwidth, IC components, noise
spectrum, and sensitivity of the magnetic sensing technology.
Of course, higher sensitivity gives better signal-to-noise ratio fora given signal strength, which is the case for magnetoresistive
technologies. Signal slope is governed by the amplitude andthe specific signal shape at the switching thresholds. Unlessthere is a flat region, which is commonly the case for targets
with a signature region, the slope is generally rather similar
across different targets. So, signal amplitude has a larger
impact on jitter performance, and in order to improve it, it
is advised to use optimized target design, smaller air gap,
stronger magnets, and lower temperature.
Variation of the input signal periodicity has a negative impact
on double-edge jitter performance because it directly impacts
the relative pulse position even if the sensor had perfect precision. Hence, speed variation, tooth-to-tooth variation, poleto-pole variation, run-out, AG variation, and angular vibration
all cause the signal amplitude to fluctuate and consequently
lead to increased double-edge jitter.
In summary, single-edge jitter provides the sensor’s contribution to system precision, whereas double-edge jitteris a combination of sensor and target variation; therefore,
it is worth distinguishing both in evaluations. Henceforth,single-edge jitter will simply be referred to as jitter, as it ismore representative of sensor performance. As mentioned
before, some sensors output multiple pulses per period, but
fundamentally that changes neither the noise level nor thesignal amplitude, so it does not have any real effect on jitter.
Consequently, it is vital that jitter is always normalized to thetarget angular period and not the pulse period.

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AN296240
MCO-0001106, Rev. 2P0147

Allegro’s portfolio consists of sensors with top competitive
jitter performance. Contact Allegro’s representatives to findthe best solution for your application.
Relative accuracy is solely determined by the ratio of detectededges to the actual number. If a sensor outputs only half ofpulses it should, then this would lead to an observer underestimating the velocity by a factor of two and vice versa. Allegro’ssensors incorporate a guarantee for no missing or extra pulses
as part the ASIL-related hardware safety requirements, and assuch have the maximum possible relative accuracy of 100%.
The absolute accuracy is determined by both the propagation
delay and the update rate because it is defined as the absolute
shift with respect to the true timing.
Finally, the specific signal shape of targets is a decisive factor
because it determines the switching position accuracy.

EFFECTS ON OBSERVABLE QUANTITIESAPPLICATION INFORMATION

directly to the absolute accuracy and jitter of the sensor. The
sensor’s relative accuracy is only defined for speed measurements. The resolution could be improved computationally byintegrating speed over a period, but that must be performed
on a system level.
Velocity is the difference of two pulse positions divided by
the elapsed time.
Equation 4:

with A1,2 the angle, T1,2 the timing, N the number of polepairs/teeth. Since the sensor absolute accuracy is a constanttime offset, by definition, it cancels out in the difference, so
the absolute accuracy of the speed signal is perfect. Only inthe case of braking will there be an error to the true velocity
equal to:The most important aspect for customers is the effect all of
the above sensor characteristics have on observable andapplication-relevant quantities such as angular position andvelocity. Although Allegro’s speed sensors are used to measure
speed, as the name suggests, that is only a derived quantity,
and the actual device output are pulses in the time domain.
Consider how that translates to the properties of the aforementioned quantities. For the following analysis, it is assumed
that no additional processing is performed in the ECU besides
registering the pulse timings and performing simple arithmetic
steps to calculate the angle and speed as described below.
Advanced software processing like filtering, averaging, etc.,
add another layer of complexity and are outside the scopeof this document.

Equation 5:

Position is simply the number of observed pulses times thetarget period. Its resolution is only governed by the numberof periods, pulses per period, and typical values ranging from
2° to 30°. Its absolute accuracy and precision correspondEquation 7:

Take for example propagation delay of 100 µs and acceleration of 10 m/s2: the error is only 0.0036 km/h. The sensor
relative accuracy is 100% (due to no missing or extra pulses),so the velocity relative accuracy is also 100%. The relationshipbetween the velocity precision and sensor jitter is the following:
Equation 6:

The velocity resolution is determined by sensor resolution
through:where the speed is measured in rpm, tres in seconds.

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AN296240
MCO-0001106, Rev. 2P0147

APPLICATION INFORMATION

Revision History
NumberDateDescription

Responsibility–June 11, 2021

Initial release

E. Pavlov

1

June 28, 2021

Updated footnote 4 (page 2), equations 1, 5, and 6 (pages 2 and 4), and Single- andDouble-Edged Jitter section (page 2).

E. Pavlov

2

June 10, 2024

Fixed broken link (page 1)

R. Couture

Copyright 2024, Allegro MicroSystems.

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It is the customer’s responsibility to do sufficient qualification testing of the final product to ensure that it is reliable and meetsall design requirements.
Copies of this document are considered uncontrolled documents.

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