Sensors

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.

• $V_{\text{out}}=A(V_2-V_1)$
  • $A$ is the open loop gain
  • Both open loop gain and input resistance are $\infty$ in an ideal op amp
• No current flows in or out of the inputs
• The two inputs are always at the same voltage

Buffer

• The output is connected to the inverting input
  • Negative feedback
• Provides decoupling between circuits
• No current flows into $V_2$, but $V_{\text{out}}$ will still equal $V_2$ 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
• $V_{\text{out}}=V_2$

Comparator

• 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

$$\frac{V_{\text{out}}}{V_{\text{in}}}=-\frac{R_2}{R_1}$$

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

Non-Inverting Op-Amp

$$\frac{V_{\text{out}}}{V_{\text{in}}}=1+\frac{R_1}{R_2}$$

• Amplifies and does not invert input

Attenuation

Voltage attenuation can be easily achevied with just a voltage divider

• $V_{\text{in}}$ has range 0 to 20V
• $R_1=30k\Omega$, $R_2=10k\Omega$,
  • $V_{\text{out}}/V_{\text{in}}=0.25$
• $V_{\text{out}}$ 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:

$$V_{\text{out}}=V_{\text{in}}\frac{X_c}{\sqrt{R^2+X_c^2}}$$

• The impedance of a capacitor $X_c$ is dependant upon frequency: $X_c=1/2\pi fC$
  • Higher frequency, lower impedance
• The corner/cutoff frequency $f_c$ is where the output is -3 decibels smaller than the input (about 71%)
  • $f_c=1/2\pi RC$

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 $f_s$
  • Each sample is the value of the signal at time $t$
• 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 $f_s\ge 2f_{max}$
  • $f_{max}$ 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 $V_S$
• Output is the measured difference between $V_C$ and $V_D$
  • Output of two potential dividers in parallel
• When $V_{\text{out}}=0$, the bridge is balanced
  • $R_1/R_2=R_3/R_4$

This can be exploited to find the value of an unknown resistance. If $V_{out}=0$, and $R_1$ is unknown and the rest are fixed values:

$$R_1=R_2\frac{R_3}{R_4}$$

Can also derive an expression for $R_1$ in terms of the rest of the circuit, if $V_{out}$ is non-zero:

$$R_1=R_2\left(\frac{V_S(R_3+R_4)}{V_{out}(R_3+R_4)+V_S{R}_4}-1\right)$$

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 $R_1=R_2$ and $R_3=R_4$

$$V_{out}=\frac{R_3}{R_1}(V_C-V_D)$$

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
  • $\frac{\Delta R}{R}=G\epsilon$
  • $G$ is the gauge factor, $\epsilon$ 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

$$V=K_H\frac{BI}{t}$$

• $K_H$ is hall coefficient
• $B$ is the flux density of the magnetic field
• $I$ is current
• $t$ is plate thickness

Since $K_H$, $B$, and $t$ are constants, the relationship between current and voltage is linear.