# Characteristics of Sensors

General characteristics of sensors are two, namely

1. Static characteristics
2. Dynamic Characteristics

## Static Characteristics of Sensors

Static characteristics of sensors describe the performance of a transducer with very slow changes in the measurand. Static characteristics include accuracy, linearity, precision, sensitivity…etc

### Error

Accuracy of a sensor is usually specified by error. it tells you how closely the measured value matches the true value.

Error is given by

$$E_a=\frac{X_m – X_t} {X_t} * 100$$

Where t stands for true value, m for measured value and x stands for the measurand.

For multi error systems, the overall error can be assessed either through finding the linear sum of all errors (E1 + E2 +…+En) or through the root mean square approach where total performance error can be assessed as,

$$\sqrt{{E_1}^2+{E_2}^2+…+{E_n}^2}$$

### Precision

Precision describes how close a measured value is to the true value and how far it is reproducible.

Repeatability is the defined as the capability of a sensor to provide the same output repeatedly when used each time to measure the same input.

### Resolution

Resolution is the smallest change in the input that is needed to produce a detectable change in output. For a detectable output Δy, if the minimum change in x is Δxmin, then the maximum resolution is

$$R_{max}=\frac{(\Delta x)_{min}}{MR}*100$$

### Minimum detectable change

It is the minimum signal level that produces a detectable output in the sensor. If the input signal doesn’t contain any noise, the minimum detectable output from the sensor is determined by its noise characteristics. For this, the equivalent noise source is connected to the input of the sensor to produce an output which is the actual output level of the sensor. The RMS equivalent input noise is then taken as the minimum detectable change.

### Threshold

The threshold is the smallest input change that is needed to produce a detectable output at the zero value condition of the measurand.

### Sensitivity

It is the ratio of incremental output to incremental input, that is,

$$S= \frac{\Delta y / \Delta x}{y/x}$$

If the sensitivity of a sensor varies with ambient conditions like time, temperature, humidity..etc without any change in input level, drift is said to occur in the system.

### Selectivity and Specificity

The output of a sensor may change with environmental parameters or other variables. Selectivity is the ability of a sensor to discriminate the response to input changes from other interfering quantities.

### Nonlinearity

Non-linearity is the deviation of a sensor output value (real value) from its ideal output value. The maximum nonlinearity is shown in the figure.

Nonlinearity can be specified either by finding deviation from best fit straight line obtained or by finding the deviation from a straight line joining the endpoints of the scale.

### Hysteresis

Hysteresis is the difference in the output of the sensor for a given input x when x reaches this value in upscale direction and downscale direction.

It is caused by the normal hesitance of a material to come back to its original state after having a physical change. It depends on the hysteresis property of the sensor.

### Output Impedance

Impedance is a measure of the overall opposition of a circuit to the current. The output impedance of a transducer specifies the impedance across its output terminals.

### Isolation and grounding

Isolation eliminates or at least reduces the undesirable coupling in the system. Grounding establishes a common node among different parts of the system with respect to which potential of any point in the system remains constant.

## Dynamic Characteristics of Sensors

Dynamic characteristics of a sensor tell us how fast a transducer responds to the changes in input.

### Transfer function

The transfer function is a measure of the magnitude of the input signal and the magnitude of the output signal.

### Frequency response

It is the relationship between the frequency of the input signal and the magnitude of the output signal.

### Impulse response

The output of a sensor for a brief input signal, called an impulse, is called impulse response.