Sensors measure physical quantities that are outputs from electromechanical systems. A sensed signal will go through a few steps before we have access to the data:

  • The physical phenomena, the signal source, will happen
  • The sensor will detect this by some mechanism and output a noisy signal
  • Some signal conditioning/processing will take place to make the signal easier to read
  • Analogue to Digital conversion samples and digitises the data
  • The digitised data is presented to software as binary information

Performance of Sensors

There are a number of metrics used to measure the performance of a sensor, and which metrics are considered will depend upon the use case.

  • Accuracy
    • How close is the output to the true value of the input?
    • A sensor with high accuracy will give readings close to the quantity being sensed
  • Precision
    • How consistent are the readings for the same input?
    • How repeatable are the readings?
    • Precise data is close to each other, but not necessarily to the true value
    • High precision with low accuracy may be acceptable if the systematic inaccuracy can be compensated for
  • Drift
    • Changes in the output of the sensor not related to the input
    • Often related to temperature, as this affects electrical properties
  • Hysteresis
    • The difference between the output when the input is increasing, and the output when the input is decreasing
    • Quantities may be sensed differently depending upon their rate of change
    • Common phenomenon and is often useful in other applications
    • Often provided as an average percentage
  • Linearity
    • How the output changes with input over its operating range
    • Linear behaviour is ideal as it simplifies output processing
    • Many sensors have a linearity error of how much the output deviates from linear behaviour
  • Resolution
    • Changes in measured quantity may be too small to detect
    • Sensor will have a max resolution which is the smallest changes it can sense
    • Resolution also limited by ADC
  • Gain
    • How much the output changes with the input
    • Too high and small changes will give large output swings and low noise tolerance
    • Too low and the system will not respond to small changes
    • Often given as how much voltage changes per measured unit
      • A temperature sensor will have a gain in mV/°C
  • Range
    • The max and min values that can be sensed
    • Can also define a linear range, the range for which the sensor has linear behaviour
    • Can set a fixed operating range, to increase sensitivity or resolution over a smaller range
    • Wider range usually gives lower sensitivity/resolution

Signal Conditioning

Generally sensor output is some voltage, which will be given as input to a microcontroller. Voltage signals can be too large, too small, or too noisy, so some conditioning/processing is required

  • Filtering to remove noise
  • Amplification to increase the range of the signal
  • Attenuation to decrease the range of the signal
    • Too large a voltage may damage the electronics

Op-amp circuits are usually involved in signal conditioning.

    • is the open loop gain
    • Both open loop gain and input resistance are in an ideal op amp
  • No current flows in or out of the inputs
  • The two inputs are always at the same voltage


  • The output is connected to the inverting input
    • Negative feedback
  • Provides decoupling between circuits
  • No current flows into , but will still equal as the two inputs are always at the same voltage
    • Ensures no current flows to provide protection
  • No current is drawn from the supply by the op-amp


  • Amplifies the difference between the two input voltages
  • Output saturates at power rail voltages
  • Useful for indicating when output reaches a threshold

Inverting Op-Amp

  • Inverts and amplifies the input
  • Amplifies small sensor output voltages
  • (see ES191)

Non-Inverting Op-Amp

  • Amplifies and does not invert input


Voltage attenuation can be easily achevied with just a voltage divider

  • has range 0 to 20V
  • , ,
  • has range 0 to 5V

Low Pass Filter

A low pass filter attenuates the high frequency components of a signal:

This is a voltage divider with a capacitor:

  • The impedance of a capacitor is dependant upon frequency:
    • Higher frequency, lower impedance
  • The corner/cutoff frequency is where the output is -3 decibels smaller than the input (about 71%)

Reading Signals and ADC

  • Signals are typically read with microcontrollers
  • Input to microcontrollers has a maximum which if exceeded will damage the part
  • Signals are read and digitised so they can be understood by digital electronics
  • Signal is sampled at discrete time steps, at a sampling frequency
    • Each sample is the value of the signal at time
  • The sample value is held until the next sample, when the sample value is updated
    • This creates a digital signal, an approximation to the input signal
  • Sampling frequency has a large affect on how close the digital signal is to the original
    • To maintain the highest frequency components of the signal
    • is the highest frequency present in the signal, the nyquist frequency
    • In practice, sample rate should be much higher than double
  • Signal sample levels may only take a finite, discrete number of values
    • Quantisation level
    • Samples are rounded to nearest quantum
    • Higher sampling resolution means more accurate digital signal

A signal measured with a 4-bit ADC:

The circuit below shows a 3-bit ADC implemented with a priority encoder and op amps:

Wheatstone Bridge

A wheatsone bridge is a common circuit used to measure an unknown resistance:

  • 4 resistors, one with an unknown value
  • Input is a known voltage
  • Output is the measured difference between and
    • Output of two potential dividers in parallel
  • When , the bridge is balanced

This can be exploited to find the value of an unknown resistance. If , and is unknown and the rest are fixed values:

Can also derive an expression for in terms of the rest of the circuit, if is non-zero:

The unknown resistance may be some sensor which changes its resistance based upon a physical quantity, ie an LDR or strain gauge. The circuit below shows a photoresistor in a wheatstone bridge, with buffered outputs connected to a differential amplifier, which will provide an output voltage:

The gain of the differential amplifier is calculated using the following, where and

Force and Torque Sensors

Strain Gauge

  • A thin strip of semiconductor which is wafer thin and can be stuck onto things
  • The strip deforms as the surface deforms
  • When subject to a strain, its resistance changes
    • is the gauge factor, is the strain
  • Strain is the ratio of change in length to original length, so this will measure how much a material has stretched by
    • The diagram below shows how

Load Cell

A load cell uses strain gauges to measure force:

  • As the force causes the shape to deform, the strain gauges sense this and the applied force can be calculated
  • Important factors to consider are:
    • Maximum force load
    • How the force can be applied to the cell
    • Rated output

Rotary Torque Sensor

Torque sensors work similar to load cells, using strain gauges to detect deformation.

  • The sensor is coupled to a rotating shaft
  • The rotation of the shaft causes small deformations within the torque sensor, which are detected by strain gauges

Position and Speed Sensors

An encoder is a device that gives a digital output dependent upon linear or angular displacement.

  • Incremental encoders detect changes in rotary postition from a starting point
  • Absolute encoders give a rotational position

Incremental Encoder

  • Incremental encodes contain a disc with multiple holes
  • As the disc rotates, the holes will create pulses of light, with each pulse representing a displacement of a certain number of degrees
  • Outer two layers slightly offset so direction of rotation can be determined
  • Innermost hole counts number of revolutions
  • The one shown has 12 holes so a 30° resolution

Absolute Encoder

  • An absolute encoder works on a similar principal to an incremental encoder
  • The output takes the form of binary code whose value is related to the absolute position of the disc
    • Multiple layers used to provide unique encoding for each disc segment
  • Encoders use gray coding so that if any holes are misaligned then error is minimised
  • An 8-bit encoder has 360/256 = 1.4° resolution

Speed sensors

  • Encoders can also be used to measure angular velocity by measuring the time taken between pulses within the encoder
  • Reflective photoelectric sensors work by reflecting light off a disc with reflective and matte colours, and measuring the rate at which the reflected light changes intensity
  • Slotted photoelectric sensors work by detecting if a rotating part is blocking a beam of light or not

Current Sensors

Current Sense Resistors

  • Due to Ohm's law, a current passing through a resistor will cause a voltage drop
  • That voltage can be measured, and the current accross it calculated
  • This will modify the voltage accross the load and cause a power drop
    • A small resistor should be used, typically less than 10 ohms

Hall Effect Sensors

  • Hall effect sensors use the physical phenomena of flowing electrons being deflected in a magnetic field to measure current
  • A magnetic field will cause electrons to be deflected, which will charge either side of a sensor plate depending upon current direction

The potential difference between either side of the plate is given by

  • is hall coefficient
  • is the flux density of the magnetic field
  • is current
  • is plate thickness

Since , , and are constants, the relationship between current and voltage is linear.