Calibrating the PSLab’s Analog Features for Maximum Accuracy

The hardware design of the PSLab aims to achieve the maximum possible performance from a very conservative bill of materials. There are several analog components such as Op-amps, voltage dividers, and level-shifters involved in input signal processing that have inherent offsets and slopes that must be corrected in order get the best results. Similarly, some analog output signals from the PSLab are also modified by buffers, amplifiers, and level shifting circuits.

One way to improve the initial accuracy is to choose high performance analog components that are factory calibrated , and do not require any additional correction to achieve error margins that are less than the least count of the PSLab’s measurement capabilities. However, such components such as laser trimmed resistor pairs, and low-offset Op-Amps are quite expensive, and we must instead use software based correction methods to achieve similar performance from affordable parts.

Identifying a suitable calibrator for analog signals

In order to calibrate a device, we must first own a similar device whose measurements we can trust, and which has a finer resolution that the PSLab itself. Calibration is a one-time task that will quantify and store the gain and offset errors, and these errors are not expected to behave very differently unless a significant change in temperature, or mechanical stress is experienced.

Such a device may be as expensive as 24-bit, research-grade multimeters which generally cost upwards of $500 , or can be inexpensive analog to digital convertors that might require some expertise to extract data from them, but can still be used for calibration.

Fortunately, we have been able to identify a cheaply available device that puts the calibration process within the reach and capabilities of the end user. The ADS1115 16-bit ADC is a 4-channel, 0-3.3V ADC that can be interfaced via I2C. Typical initial accuracy of the internal voltage reference 0.01% and data rates higher than 500SPS are possible. It is cost effective, and is available in convenient module formats that can be directly plugged into the PSLab itself. It can be purchased through various vendors ( A , B , C )

Therefore, it appears to be most suited to calibrate individual PSLab devices.

Basic requirements for the calibration process

The process to calibrate the analog inputs and outputs involves looping them externally , and monitoring the actual values via the external calibrator.

We’re killing two birds with one stone by calibrating inputs and outputs in tandem, and it makes for a faster calibration process. The complete calibration process for  Digital to Analog converter outputs has enough complexity to warrant a separate blog post.

Let’s take an example; PV1 ( an analog output that can be set between -5V and +5V) can be connected to CH1 (An analog input which can read voltage values between -16 and +16 Volts) with a small segment of wire, and various voltage values can be set on PV1, and read back by CH1 . At the same time, the external calibration utility will also monitor this voltage, and store the error in PV1 (Set Voltage – Actual Voltage) as well as the error in CH1 ( Read Voltage – Actual Voltage ) .

In a similar manner , PV2 can be connected to CH2, and the second channel of the ADS1115 calibrator can be used to monitor the real value, and so on .

Deviations of various analog input channels and their different voltage ranges from the actual values. As is evident from the graph, errors can be as much as 40mV in a full scale range of +/-16,000mV . But since these errors are quite repeatable, we can apply a calibration polynomial to correct these.

 

Integral Non-linearity of the ADC

In addition to the overall slope and offset, you have probably observed in the previous image, a sawtooth pattern with an amplitude as small as the least count of the analog inputs superimposed on them. This error arises from the integral non-linearity (INL) of the analog to digital convertor of the PIC, and affects all analog inputs uniformly. While in principle we can ignore this for all practical purposes, in order to further improve the analog accuracy, we can also store this INL error of the ADC, and apply this correction to any channel after its slope and offset has been corrected.

The overall slope and offset are caused by the analog references and components, and can be corrected with a simple 3-degree polynomial. However, the sawtooth pattern is characteristics of the INL, and must be stored in a correction array with 4096 elements ( Each element represents the error of the corresponding ADC code of the 12-bit ADC )
The yellow trace represents the error in readings from the ADC after applying polynomial and table based correction. There appears to be a small offset that can be attributed to a change in ambient temperature , but can be neglected as it is in the order of 100uV

 

The following utilities and code are necessary for this process
  • An I2C communication library for ADS1115 must be present in order to acquire data from it via the PSLab
  • The library should be able to handle the following tasks
    • read single ended , and differential voltage values from any of the channels
    • Enable selection of voltage range and voltage reference
  • A graphical interface with the following features and algorithms will be required:
    • Vary the output voltages from PV1,2,3 in small, definite intervals
    • Store the errors in the analog outputs and inputs as a function of the actual voltage
    • Generate Cubic interpolation functions for each input and output channel
    • The Programmable Current Source can be calibrated using a measured Load resistor, and calibrated analog channel. Its interpolation function must also be stored.
    • Write all calibration constants into flash memory after assigning a timestamp
    • Store raw calibration data in a client-side folder
Testing of the analog inputs after applying calibration polynomials. It can be observed that the accuracy has been brought within a +/-5mV range for the wide input channels. For CH3, a +/-1mV accuracy is achieved.
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