## Angle Sensor Units

Measurement performance is quoted in a myriad of different units. Any proper comparison between products should be based on common units.

**Pulses per rev (PPR)**. Pulses per rev is commonly quoted for incremental angle sensors, especially optical devices, and describes the number of pulse that the device outputs per revolution. Importantly, the number of pulses per rev is not necessarily connected to accuracy. A common misconception is that an angle sensor which produces 1000 pulses per rev is accurate to 1/1000th of a rev. Wrong!

**Counts per rev (CPR)**. Many angle sensors output two lots of pulses – usually referred to as A/B pulse streams (in quadrature) so that direction of travel is indicated. Accordingly, for each PPR there are two leading edges and two trailing edges which can then be used to generate CPR. The difference is important – a device with 1024PPR has 4 times the resolution of a device offering 1024CPR.

**Bits**. The number of bits in an angle sensor’s output is an increasingly common term due the increasing use of digital outputs such as RS422, SSI, CAN bus etc. Each additional bit doubles the quoted resolution. Whilst obvious to some it is counter intuitive to many. For example, a 12bit product will output 4,096 steps over a rev whereas a 14bit product (it doesn’t sound that different does it?) will output 16,384 steps. A ‘couple of bits’ makes a huge difference to measurement performance. Note also the difference between x bits of resolution and y bits of accuracy. For example an angle sensor may be specified as 10bits of resolution with 8bits of accuracy – in other words 1024 steps per rev with an accuracy of 1/256 of a rev.

**Radians**. Radians are still widely used by the military, aerospace & scientific sectors – especially in motion control. A radian is the angle subtended by a circle’s arc whose length is numerically equal to the circle’s radius. There are 2P radians per rev. A milliradian (usually ‘millirad’) is 1/1000th of a radian and a micro-radian (usually ‘urad’) is 1/1000th of a milliradian. The ‘mil’ is commonly used by military organizations and provides the handy property of subtension – that 1 mil approximately subtends 1metre at a distance of 1000metres. It’s a useful unit of measure if you’re lobbing shells on to an enemy position.

**Gradians**. The gradian is a unit of angle, equivalent to 1/400 of a revolution. It is also known as a gon, grad, or grade. One grad equals 9/10 of a degree. The unit originated in France as the grade, along with the metric system. Although attempts at a general introduction were made, the unit has only been adopted in some countries and specialised areas, like surveying. Subdivisions of gradian used in surveying are c’s (1c = 0.01grad) and cc’s (1cc = 0.0001grad).

**Degrees, Arc-Minutes & Arc-Seconds**. Wouldn’t life be simpler if everyone used degrees? Well it would but who said life was going to be simple…… especially for a design engineer. So 1revolution = 360degrees (I guess you knew that), but each degree can be divided up in to 60arc-minutes and each arc-minute can be divided up in to 60arc-seconds. Accordingly, 1degree = 3600arc-seconds.

Percentage. Percentage is often used to describe the accuracy or linearity of lower performance angle sensors and should rightly be (but often is not) specified in terms of % of full-scale. Importantly, the full-scale of some angle sensors is not 360degrees but may be 60, 90, 120 or 180degrees. Accordingly, a product with a full-scale of 90degrees and a linearity 0,1% of full-scale is likely to be more accurate than a device with 360degree full-scale and 0,05% linearity over full-scale.

You can use the following look up tables to convert between the most common units:-