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..  

Why accuracy matters?

The accuracy shows what is the real measured value within confidence interval.
Every DMM has accuracy specification from which can be calculated the interval in which the real value of the parameter lies within it.

The accuracy given in the DMM specification is relative, given in last digits, percents (%) or part per millions (ppm) and have to be calculated to absolute value.

The relative accuracy is given for a time period, temperature range and warm-up period. For example :

• 90 days, 1 year, 2 years from the date of the last calibration
• ±5°C difference between the real temperature and the calibrated tempearture
• 2 hours warm-up period

Here an example with 3 real DMM will be given : 

• Low end : Uni-T UT61A which cost ~ 50 USD
• Middle : Keithley 2110 which cost ~ 600 USD
• High end : Keysight 3458A which cost ~ 10000 USD

Lets assume that we measured 5V on the USB power supply with these 3 DMM. 

Tip : how to convert ppm to an absolute value -> ppm/1,000,000 * value

DMM Model	Range	Relative accuracy ±(readings + range)	Absolute accuracy
UT61A	40V	±(0.5% + 1 digit) Resolution for 40V is 0.01V	0.5% * 5V = 0.025V 1 digit * 0.01V = 0.01V Total : ± 0.035V (35mV)
Keithley 2110	10V	±(0.012% + 0.002%) 1 year, 23° ±5°C	0.012%*5V= 0.0006V 0.002%*10V= 0.0002V Total : ± 0.0008V (0.8mV)
Keysight 3458A	10V	±(8 ppm + 0.05 ppm) 1 year, 23° ±5°C	8ppm*5V = 0.00004V 0.05ppm*10V=0.0000005V Total : ± 0.0000405V (0.0405mV)

You can see the difference of absolute accuracy and the price which is paid for.

For ~50 USD, your real measurement value is between 4.965V and 5.035V.

For ~600 USD, your real measurement value is between 4.9992V and 5.0008V.

For ~10000 USD, your real measurement value is between 4.9999595V and 5.0000405V.

Because the voltmeter is used in the current and resistance measurements, the better accuracy in DC Voltage measurement, means also better accuracy of current and resistance measurements.

Preliminary specification for the open DC multimeter

I think to make 2 version of the open DC multi-meter :
- first one (LA stands for low accuracy) with a basic DC accuracy ~ 100 ppm which will be the test bench for the project
- second one (HA stands for high accuracy) with a basic DC accuracy ~ 20 ppm

OSHW DMM Specs

Ranges	Accuracy per year	Resolution	Other characteristics and features
DC Voltage ranges
1V 10V	~ 100 ppm (LA) ~ 20 ppm (HA)	1uV	Input resistance > 1 GOhms Noise floor < 10 uV Auto range
DC Current ranges
5A 1mA	To be estimated later	1mA 1uA	Burden voltage : < 0.02 mV/mA for the 5A range < 0.02 mV/uA for the 1mA range Auto range
Resistance ranges
10KOhms 1MOhms	To be estimated later	0.08 Ohms 8 Ohms	1.25 mA current source 12.5 uA current source 2/4 wire measurement Auto range

Why I started this project

The short answer : because I was not able to find a digital multi-meter (DMM) with accuracy ~ 100 ppm per year for less then 300 USD.

The long answer : I lost somewhere my Kyoritsu DMM 1012 and start looking for a new DMM with a good price for the accuracy. After few days spent on reading datasheets, comparing prices and reading reviews, I was not able to find good enough for the my price limit. So I started to think, why not to make one?

Based on the basic DC accuracy, I found that there are broadly three categories on the market:
- low end, mostly handheld with DC accuracy > 500 ppm.
- middle end, mostly bench top with DC accuracy between 20 ppm and 250 ppm.
- high end, which are used in calibration laboratories with DC accuracy < 10 ppm.

The price starts from few dozens USD and end up with 10000 USD price tag.

The price of several DMM with accuracy ~ 100 ppm was far away from my budget:
Siglent SDM3055 : 150 ppm basic DC accuracy for 449 USD
Rigol DM3058 : 150 ppm basic DC accuracy for 695 USD
Keithley 2110 : 120 ppm basic DC accuracy for  622USD
Keysight U3402A : 120 ppm basic DC accuracy for  759 USD
Keysight 34460A : 75 ppm basic DC accuracy for 945 USD

I made some preliminary calculations which point me that 100 ppm DC only DMM can be made for less than 300 USD. Of course if you have access to calibration grade DMM which in my case was true.

Why open DC Multimeter?
I believe that the openness, transparency and the free, unrestricted access to knowledge and information keeps the technology to move forward.