anantham/Linearization of Thermistor

## Linearization of Thermistor

---
title: Industrial Instrumentation Mini Project
layout: Aside
published: true
tags: [Industrial Instrumentation,  Mini Project, thermistor, simulation, Bosson's Law, linearization, time period, temperature ]
category: Industrial Instrumentation
---

##Industrial Instrumentation Mini Project


Both Thermistors and RTD's are basically resistors whose resistance varies with temperature.

Thermistors differ from resistance temperature detectors (RTDs) in that the material used in a thermistor is generally a ceramic or polymer, while RTDs use pure metals. The temperature response is also different; RTDs are useful over larger temperature ranges, while thermistors typically achieve a greater precision within a limited temperature range, typically −90 °C to 130 °C.

### linearization using parallel resistance

![Parallel connection of resistance to thermistor](https://lh3.googleusercontent.com/-drn9kQx1-XE/VjAzFXeUU0I/AAAAAAAAbkM/hsX3siB2AK0/s0/Parallel-Resistor-with-thermistor.png "Parallel-Resistor-with-thermistor.png")

So we have high sensitivity and fast response in favor of thermistor, but the non linear behavior is a drawback that we must try to correct.
In tackling this problem the basic approach can be to connect a parallel resistor to the thermistor.

![Linearization by connecting a resistance in parallel](https://lh3.googleusercontent.com/-il3X2qb8TqM/Vi_P4T1IfSI/AAAAAAAAbjs/NeiAix-tq7Q/s0/parallelLinearization.png "parallelLinearization.png")

But as you can see above even though this improves the resistance - temperature relationship in terms of linearity, the sensitivity of the thermistor is sacrificed.

### Temperature to Period Linearization technique

We will be using a circuit (shown below which functions as a relaxation oscillator) to get a linear relationship between our input variable (Temperature) and output variable (in this circuit it's the time period).
It is important to note the importance of linearization, we have useful tools used in systems analysis which are applicable to linear systems.
So as it's much easier to deal mathematically with linear relationships when compared to non linear systems.

Here the output will be a periodic waveform with a time period $T$, here this output waveforms **time period** is the output variable which is linearised w.r.t. to temperature, unlike the thermistor's resistance which is _non linear_ w.r.t. to temperature.

![Nonlinear behavior of thermistor resistance wrt temprature](https://lh3.googleusercontent.com/-yonYPMEqNg0/Vi_I3hvOEGI/AAAAAAAAbjY/SG5bwODIzEk/s0/thermistorTempratureVSResistance.gif "thermistorTempratureVSResistance.gif")


### Theoretical modeling of T - R characteristics

Now for the modeling of the relationship between the temperature and resistance for the thermistor we can use first order approximation, but this approximation involves assumptions such as carrier mobility's invariance with temperature etc which are not valid across the entire operating range of the temperature.

$\Delta R = k  \Delta \theta$

Note that for a even more accurate description of the thermistor we use third order approximations like the [Steinhart–Hart equation](https://en.wikipedia.org/wiki/Steinhart%E2%80%93Hart_equation) and Becker-Green-Pearson Law which has 3 constants.
Even the original Bosson's law has 3 constants and is written as

$R = A e^{\frac{B}{T_0+\theta}}$

This is approximated to the second order law,

$ R = A B^{-\Theta}$

In the above formula's $A, B, T_0$ are constants and $\theta$ stands for temperature while $R$ stands for thermistor resistance.

The reason why we go for the 2 constant law rather than the 3 constant law even though the third order approximation **fits** better is that comparatively its harder to use _hardware linearization_ techniques.[^Wiley Survey of Instrumentation and Measurement]
Also this relationship closely represents an actual thermistor's behavior over a narrow temperature range.

So if we are going for third order approximations we should use take advantage of the advancements in computing and just obtain a analog voltage proportional to the thermistor resistance, then use ADC to get the digital values which can simply be fed into the 3rd order equation.

###Working of the circuit

![Circuit Diagram for linearization of thermistor output](https://lh3.googleusercontent.com/-MgcJrNyyDHE/Vi--_G6o_vI/AAAAAAAAbjE/eVq3EGviPSQ/s0/linearizationThermistor.png "LinearizationOfThermistor.png")

We should observe the non linearity error is within 0.1K over a range of 30K for this linearization circuit.

Read more from what S.Kaliyugavaradan has [written](http://www.edn.com/design/test-and-measurement/4324221/Temperature-to-period-circuit-provides-linearization-of-thermistor-response).

### References

[^Wiley Survey of Instrumentation and Measurement]: Wiley Survey of Instrumentation and Measurement, by Stephen A. Dyer published by John Wiley & Sons. Page 126
Read [here](https://books.google.co.in/books?id=Wr6l42rEizUC&lpg=PA127&ots=xozwi41sZ_&dq=bossons%20law%20thermistor&pg=PA126#v=onepage&q=bossons%20law%20thermistor&f=false)


> Written with [StackEdit](https://stackedit.io/).

	---
	title: Industrial Instrumentation Mini Project
	layout: Aside
	published: true
	tags: [Industrial Instrumentation, Mini Project, thermistor, simulation, Bosson's Law, linearization, time period, temperature ]
	category: Industrial Instrumentation
	---

	##Industrial Instrumentation Mini Project


	Both Thermistors and RTD's are basically resistors whose resistance varies with temperature.

	Thermistors differ from resistance temperature detectors (RTDs) in that the material used in a thermistor is generally a ceramic or polymer, while RTDs use pure metals. The temperature response is also different; RTDs are useful over larger temperature ranges, while thermistors typically achieve a greater precision within a limited temperature range, typically −90 °C to 130 °C.

	### linearization using parallel resistance

	![Parallel connection of resistance to thermistor](https://lh3.googleusercontent.com/-drn9kQx1-XE/VjAzFXeUU0I/AAAAAAAAbkM/hsX3siB2AK0/s0/Parallel-Resistor-with-thermistor.png "Parallel-Resistor-with-thermistor.png")

	So we have high sensitivity and fast response in favor of thermistor, but the non linear behavior is a drawback that we must try to correct.
	In tackling this problem the basic approach can be to connect a parallel resistor to the thermistor.

	![Linearization by connecting a resistance in parallel](https://lh3.googleusercontent.com/-il3X2qb8TqM/Vi_P4T1IfSI/AAAAAAAAbjs/NeiAix-tq7Q/s0/parallelLinearization.png "parallelLinearization.png")

	But as you can see above even though this improves the resistance - temperature relationship in terms of linearity, the sensitivity of the thermistor is sacrificed.

	### Temperature to Period Linearization technique

	We will be using a circuit (shown below which functions as a relaxation oscillator) to get a linear relationship between our input variable (Temperature) and output variable (in this circuit it's the time period).
	It is important to note the importance of linearization, we have useful tools used in systems analysis which are applicable to linear systems.
	So as it's much easier to deal mathematically with linear relationships when compared to non linear systems.

	Here the output will be a periodic waveform with a time period $T$, here this output waveforms time period is the output variable which is linearised w.r.t. to temperature, unlike the thermistor's resistance which is _non linear_ w.r.t. to temperature.

	![Nonlinear behavior of thermistor resistance wrt temprature](https://lh3.googleusercontent.com/-yonYPMEqNg0/Vi_I3hvOEGI/AAAAAAAAbjY/SG5bwODIzEk/s0/thermistorTempratureVSResistance.gif "thermistorTempratureVSResistance.gif")


	### Theoretical modeling of T - R characteristics

	Now for the modeling of the relationship between the temperature and resistance for the thermistor we can use first order approximation, but this approximation involves assumptions such as carrier mobility's invariance with temperature etc which are not valid across the entire operating range of the temperature.

	$\Delta R = k \Delta \theta$

	Note that for a even more accurate description of the thermistor we use third order approximations like the [Steinhart–Hart equation](https://en.wikipedia.org/wiki/Steinhart%E2%80%93Hart_equation) and Becker-Green-Pearson Law which has 3 constants.
	Even the original Bosson's law has 3 constants and is written as

	$R = A e^{\frac{B}{T_0+\theta}}$

	This is approximated to the second order law,

	$ R = A B^{-\Theta}$

	In the above formula's $A, B, T_0$ are constants and $\theta$ stands for temperature while $R$ stands for thermistor resistance.

	The reason why we go for the 2 constant law rather than the 3 constant law even though the third order approximation fits better is that comparatively its harder to use _hardware linearization_ techniques.[^Wiley Survey of Instrumentation and Measurement]
	Also this relationship closely represents an actual thermistor's behavior over a narrow temperature range.

	So if we are going for third order approximations we should use take advantage of the advancements in computing and just obtain a analog voltage proportional to the thermistor resistance, then use ADC to get the digital values which can simply be fed into the 3rd order equation.

	###Working of the circuit

	![Circuit Diagram for linearization of thermistor output](https://lh3.googleusercontent.com/-MgcJrNyyDHE/Vi--_G6o_vI/AAAAAAAAbjE/eVq3EGviPSQ/s0/linearizationThermistor.png "LinearizationOfThermistor.png")

	We should observe the non linearity error is within 0.1K over a range of 30K for this linearization circuit.

	Read more from what S.Kaliyugavaradan has [written](http://www.edn.com/design/test-and-measurement/4324221/Temperature-to-period-circuit-provides-linearization-of-thermistor-response).

	### References

	[^Wiley Survey of Instrumentation and Measurement]: Wiley Survey of Instrumentation and Measurement, by Stephen A. Dyer published by John Wiley & Sons. Page 126
	Read [here](https://books.google.co.in/books?id=Wr6l42rEizUC&lpg=PA127&ots=xozwi41sZ_&dq=bossons%20law%20thermistor&pg=PA126#v=onepage&q=bossons%20law%20thermistor&f=false)


	> Written with [StackEdit](https://stackedit.io/).