The first proof of concept voltage measurement and voltage reference stability after the first week

Last week I was busy with making the first proof of concept and establishing communication between ADC, uController and the host computer. Everything goes smooth and I got first voltage measurements from the ADC. The used parts were:

- USB 5V input voltage

- Low noise LDO TC1108 (3.3V) which is used for supplying the voltage reference  

- Voltage reference LTC6655BHMS8 at 2.5V

- ADC LTC2440

- uController Atmega32U4 connected to the ADC via SPI and to the host computer via USART to USB converter. 

I was able also to check first week voltage stability using the Keithley 2002 multimeter. 

The voltage reference will be switched on 24 hours none stop next 5 weeks (which will be ~1000 hours including the last week) to get more stable results.

Samples from Linear Technology arrived!

I asked for a few samples from Mr. Lessnau who is account manager at Linear Technology.
They just arrived and next days I will be busy with soldering, breadboarding and communication with the ADC.
The parts are:
- Voltage reference LTC6655BHMS8 - 2.5V
- ADC LTC2440
- Quad op amps LTC2052
- Quad matched resistor networks : LT5400

Analog Digital Converter accuracy, resolution and sampling rate

Accuracy related errors

The ADC have the following errors which decrease overall DC measurement accuracy:
gain and offset errors, integral non-linearity (INL), differential non-linearity (DNL) and noise.

The first two can be minimized by the software calibration, but the last three are hardware related and have to be consider when an ADC is selected.

Often in ADC data sheets is given Total Unadjusted Error (TUE) which represent the ADC’s worst error without applying any offset or gain error correction:
              _________________________________
TUE = √OffsetError² + GainError² + DNL² + INL²

The noise level usually is reduced with oversampling, digital filtering or averaging.

ADC resolution

ADC resolution is given by number of bits. The minimum absolute resolution is calculated for each voltage range by the following formula:

Min resolution = Voltage range / 2^Bits

Example:

Min Resolution = 10V / 2²⁴  = 10 / 16777216 = 0.000000596 V ( ~ 0.6 uV )

Sampling rate

ADC needs time to convert the analog value into digital one which is give in the datasheets as sampling rate. It can be fixed or selectable depends on particular ADC implementation.
The value of the sampling rate can be several samples per seconds up to several thousand per seconds. The more is the sampling rate, the ADC resolution is decreasing.

Selection of ADC

For voltage measurements usually are used sigma delta ADC integrated circuits or discrete integrated ADC for high end voltmeter where high linearity is desired.

For the first prototype, I selected LTC2400 ADC which is 24 bits with 7.5 samples per seconds. 2.5 voltage reference will be used. The ADC's parameters are shown in the table below. The high accuracy version will use discrete integrated ADC which should will give better linearity.

Parameter Name	Relative value	Absolute value peak to peak
TUE	5 ppm (typ) from the Vref	12.5 uV
INL for Vref = 2.5V	2 ppm (typ) from the Vref	5 uV
DNL calculated via TUE	2.2 ppm (typ) from the Vref	5.45 uV
Offset error	0.5 ppm (typ) from the Vref	1.25 uV
Offset error drift	0.01 ppm/°C (typ) from the Vref	0.025 uV
Gain error	4 ppm (typ) from the Vref	10 uV
Gain error drift	0.02 ppm/°C (typ) from the Vref	0.05 uV
Noise		4.24 uV
Estimated ADC error budget worst case  after offset and gain calibration : INL+DNL+5°C Offset/Gain Drift+Noise		~15 uV

Base block schematics

Here is the base block schematics:

How to achieve better accuracy?

Everything about accuracy starts with the voltage reference used in the DMM.

The voltage references are used by Analog to Digital Converter (ADC) to compare unknown measured voltage with the known referenced one.

The most important characteristics of voltage reference are:

• Absolute voltage value.
• Long-Term stability measured in uV/√kHour or ppm from Vref/√kHour.
• Noise for frequency from DC to 10Hz/10Khz measured in [ppm] or [peak to peak uV] or [RMS uV]
• Voltage reference drift due temperature changes measured in ppm/uV per °C.
• Hysteresis : voltage reference shift due to temperature cycling.

Optional characteristics can include:

• Voltage reference drift due humidity changes.
• Voltage reference drift due mechanical stress of the PCB

One of the best voltage reference which is used in the high end DMMs is the LTZ1000 from a company called Linear technology. DMMs which are using LTZ1000 are HP/Agilent/Keysight 3458A, Keithley 2002, Fluke 8508A, Datron/Wavetek 1271/1281, Prema 6048, Advantest R6581.

The second most popular voltage reference is the LM399 again from the Linear technology company. Used in Keithley 2000. 2001 and 2110

Below can be found a comparison between these two famous voltage references and they typical characteristics values:

VRef Type	LTZ1000	LM399
Reference voltage (typ)	7.2 V	6.95 V
Long-term stability after 1000 hours typical in ppm  (uV peak to peak)	~0.28 ppm (2 uV)	8 ppm (55.6 uV)
Noise typical value in ppm  (uV peak to peak)	~0.16 ppm (1.2 uV)	~2.85 ppm (19.8 uV)
Temperature drift typical value in ppm / °C for 5°C difference (uV peak to peak) [ppm for 1°C]	0.25 ppm (1.8 uV) [0.05 ppm/°C]	1.5 ppm (10.425 uV) [0.3 ppm/°C]
Total error (typical) in ppm after 1000h and 5°C difference  (uV peak to peak)	~0.69 ppm (~5 uV)	~12.35 ppm (~85 uV)
Price, 1 pcs	Min 45 USD	~10 USD

Note, that overall accuracy of DMM includes also accuracy of the used ADC, operational amplifiers, resistors etc..