Hello, and welcome to the TI Precision Labs video discussing calibration and compensation using temperature sensors. In this video, we'll discuss the concept of calibrating and compensating a system using temperature sensors. Typically, compensation means to migrate the effect of one or more variable parameters on the behavior of a system.

As an example, let us take a small signal inverting amplifier. The gain of the ideal circuit is given as the feedback resistor divided by the input resistor. However, in actual implementation, this may not be true since the resistors used have a temperature dependency. This is known as the Temperature Coefficient of Resistance, or TCR, and is measured in parts per million per degree Celsius. The manufacturer provides the maximum limit for the TCR in the data sheet for the component with respect to a room temperature of 25 degrees Celsius.

In this example, let us further assume that Rf, the feedback resistor, has a value of 2 kilohms. And Rn, the input resistor, has a value of 1 kilohms. And both resistors have a TCR of plus or minus 100 ppm per degree Celsius, specified at 25 degrees Celsius. This results in an ideal inverting gain of 2.

Solving the TCR equation for 125 degrees Celsius results in the delta change of plus or minus 20 ohms for Rf and delta change of plus or minus 10 ohms for Rn. As computed earlier, the magnitude of the ideal gain for the circuit is 2. Let us assume that the input small signal is a sawtooth wave, which is amplified with a gain of 2. The dashed line for V out shows the maximum output signal level possible.

In this ideal case, the output signal is equal to the maximum output level. Now at 125 degrees Celsius, if both resistors drift the maximum positive or negative TCR, the gain remains unchanged. And so does the output signal.

However, if the drift is not the same, the results are quite different. If Rf has a positive drift and Rn has a negative drift, the gain of the circuit changes from 2 to 2.04. This causes the output signal to cross the maximum signal level, resulting in clipping and introducing harmonic distortion into the output. If Rf has a negative drift and Rn has a positive drift, the gain of the circuit changes from 2 to 1.96. This causes the output signal amplification to reduce with the rise of temperature.

Having seen earlier how temperature affects the behavior of a simple inverting amplifier, it is critical that with changing temperature, some form of migration or compensation is applied. A simple method of compensation is to have a variable resistor in series with the input and feedback resistor.

However, to determine the amount of compensation that needs to be done, it is vital that we know the temperature of the system around the component we plan to compensate. That is where a temperature sensor element is required. Once we can accurately determine the temperature, the correct compensation can be applied to the circuit so as to ensure that the output is amplified with the same gain, irrespective of the changing temperature.

Having seen what is temperature compensation, now we will introduce what is temperature calibration and how it is used to perform compensation for a given circuit. As stated earlier, all components have some degree of temperature error introduced due to ambient temperature changes or due to self-heating effects. For this example, we will again take the inverting amplifier circuit.

The x-axis represents the temperature. The y-axis represents the gain. And the green line represents the ideal gain of 2, which we would like the circuit to have across the operating temperature range.

The red box around the ideal gain represents the gain error due to the change of component values-- in this case, the resistors due to temperature. The intent is to reduce the gain error by means of compensation to an acceptable limit, as shown by the green box. This is achieved by calibration.

There are different types of calibration methods used, based on the type of error that needs to be compensated, which we will introduce next. The most basic method is the single point calibration, which is shown in the graph here. A single point calibration technique is used when the error is constant across the operating temperature range.

The error may be positive if the measured gain is more than the ideal gain, or negative if the measured gain is less than the ideal gain. Such a condition may come if the resistors have a tolerance error and TCR such that both of them scale in a ratio, resulting in the actual gain remaining the same across its operating temperature. In such a case, only one of the resistors has to be adjusted, such that overall gain is as close as possible to the ideal gain.

The green box shows the acceptable limits on the error for the application. To perform the single-point calibration, the gain error is measured at a reference temperature. The amount of compensation required is then computed. The variable resistors are then adjusted to bring the overall gain error into the acceptable limits for the application.

The next method of calibration is a two-point calibration. In practice, having the two resistors scaling in exact ratio may not be the case. This results in a gain slope, which results in gain increasing with temperature or decreasing with temperature. The green box shows the acceptable limits on the error for the application.

To perform a two-point calibration, the system output is measured at the lowest temperature of the operating range. The same process is applied on the highest temperature on the operating range. Once the gain area is determined, one or both of the resistors may be scaled accordingly to bring the gain error within the acceptable operating range.

For systems that have a non-linear response, a multi-point calibration is used. This method is the most complicated, as it requires the system designer to understand the actual measured response and best fit it in an equation that can be linearized. As an example, parasitic lead inductance and trace capacitance can change behavior of the small signal amplifier, with frequency of the input signal and temperature resulting in a nonlinear curve.

A multi-point calibration requires measurement of the transfer function, or gain in this example, at multiple temperatures and points across its input signal frequency. This is followed by linearizing the small signal segments to form a more linear gain curve that can be compensated with temperature by adjusting the variable resistors.

In summary, this video discussed how temperature affects the response of all circuits and why compensation is required. Also we discussed the type of calibration techniques that may be used, based on how the transfer function of a system may respond to changes in temperature. Thank you for your time.