A-3-2-2 T7 Noise and Resolution [T-Series Datasheet] | LabJack

# A-3-2-2 T7 Noise and Resolution [T-Series Datasheet]

## T-series Appendix Analog Input Noise and Resolution (Referencable)

#### ADC Noise and Resolution

T-series devices use an internal analog-to-digital converter (ADC) to convert analog voltage into digital representation.  The ADC reports an analog voltage in terms of ADC counts, where a single ADC count is the smallest change in voltage that will affect the reported ADC value.  A single ADC count is also known as the converter's least significant bit (LSB) voltage.  The ADC's resolution defines the number of discrete voltages represented over a given input range.  For example, a 16-bit ADC with a ±10 input range can report 65536 discrete voltages (216) and has an LSB voltage of 0.305 mV (`20 V ÷ 216`).

The stated resolution for an ADC is a theoretical, best-case value assuming no channel noise.  In reality, every ADC works in conjunction with external circuitry (amplifiers, filters, etc.) which all possess some level of inherent noise.  The noise of supporting hardware, in addition to noise of the ADC itself, all contribute to the channel resolution.  In general, the resolution for an ADC and supporting hardware will be less than what is stated for the ADC.  The combined resolution for an in-system ADC is termed effective resolution (aka ENOB).  Simply put, the effective resolution is the equivalent resolution where analog voltages less than the LSB voltage are no longer differentiable from the inherent hardware noise.

The effective resolution is closely related to the error free code resolution (EFCR) or flicker-free code resolution.  The EFCR represents the resolution on a channel immune to "bounce" or "flicker" from the inherent system noise.  The EFCR is not reported in this appendix. However, it may be closely approximated by the following equation:

`EFCR = effective resolution - 2.7 bits` [1]

The T4 and the T7 offer user-selectable effective resolution through the resolution index parameter on any one AIN channel.  Internally, the ADC hardware uses modified sampling methods to reduce noise.  Valid resolution index values are:

• 0-5 for the T4
• 0-8 for the T7
• 0-12 for the T7-Pro [2][3]

Increasing the resolution index value will improve the channel resolution, but doing so will usually extend channel sampling times.  See section 14.0 AIN for more information on the resolution index parameter and its use.

## T7 Appendix Analog Input Noise and Resolution (Referencable)

### T7

The T7 has a 16-bit ADC.  The T7-Pro has the same 16-bit ADC plus a lower speed 24-bit sigma-delta ADC.

#### Noise and Resolution Data

The data shown below summarizes typical effective resolutions and expected channel sampling times over all resolution index values.  Data for the T7 and T7-Pro data are combined and presented together for convenience, where resolution index values 9-12 only apply to the T7-Pro.

The AIN sampling time is the typical amount of time required for the ADC hardware to make a single analog to digital conversion on any channel and is reported in milliseconds per sample.  The AIN sampling time does not include command/response and overhead time associated with the host computer/application.

#### Noise and Resolution Test procedure

Noise and resolution data was generated by collecting 512 successive voltage readings, using a short jumper between the test channel and ground.  To get the effective resolution in volts, we simply take the standard deviation of this array of voltage readings:

Effective Resolution in Volts = StandardDeviation (Data Array in Volts)

To calculate effective resolution in bits, we first convert the voltage readings to 16-bit aligned values.  Essentially 16-bit binary values but with decimal places.  We then take the standard deviation of those values, and then use the last equation below to calculate effective resolution in bits:

16-bit Aligned Value = 65536.0 * ((Voltage - MinSpanVolts) / (MaxSpanVolts - MinSpanVolts))

RMS Noise = StandardDeviation (16-bit Aligned Values)

Effective Resolution in Bits = 16.0 - log2 (RMS Noise)

See Appendix A-3-2-1 for the min and max span voltages.  For example, with Gain = 1 (Range = 10), the min is about -10.6 volts and the max is about 10.1 volts.

Table A.3.1.1.  T7 resolution data. Effective resolution and sampling times for various gains and resolution index settings. Resolution index settings 9-12 apply to the T7-Pro only.
 Resolution Effective Effective AIN Sample Index Resolution Resolution Time [bits] [µV] [ms/sample] Gain/Range: 1/±10V 1 16.0 316 0.04 2 16.5 223 0.04 3 17.0 158 0.06 4 17.5 112 0.09 5 17.9 85 0.16 6 18.3 64 0.29 7 18.8 45 0.56 8 19.1 37 1.09 9 19.6 26 3.50 10 20.5 14 13.4 11 21.4 7.5 66.2 12 21.8 5.7 159 Gain/Range: 10/±1V 1 15.4 48 0.23 2 16.0 32 0.23 3 16.5 22 0.55 4 16.9 17 0.58 5 17.4 12 1.15 6 17.9 8.5 2.28 7 18.3 6.4 2.55 8 18.7 4.9 3.08 9 19.5 2.8 3.50 10 20.5 1.4 13.4 11 21.4 0.7 66.2 12 21.7 0.6 159 Gain/Range: 100/±0.1V 1 13.3 21 1.03 2 14.2 11 2.03 3 14.7 7.8 5.05 4 15.2 5.5 5.08 5 15.7 3.9 5.15 6 16.3 2.6 10.28 7 16.7 1.9 10.55 8 17.2 1.4 11.08 9 18.3 0.6 3.50 10 19.1 0.4 13.4 11 19.6 0.3 66.2 12 19.7 0.2 159 Gain/Range: 1000/±0.01V 1 10.9 11 5.03 2 12.3 4.1 10.0 3 12.7 3.1 10.1 4 13.3 2.1 10.1 5 13.8 1.5 10.2 6 14.4 1.0 10.3 7 14.7 0.8 10.6 8 15.0 0.6 11.1 9 15.4 0.5 3.50 10 16.1 0.3 13.4 11 16.4 0.2 66.2 12 16.4 0.2 159

Figure A.3.1.2.  T7 analog input effective resolution over various gains and resolution index settings.

Figure A.3.1.3.  T7 analog input LSB voltage over various gains and resolution index settings.

Figure A.3.1.4.  T7 AIN sample times for analog inputs over various gains resolution index settings.

Notes:

[1]  The equation used to approximate the EFCR is determined using +/-3.3 standard deviations from the RMS noise measured on an AIN channel.

[2]  The default value for RESOLUTION_INDEX is 0, which equates to 8 for T7 command-response reads, 9 for T7-Pro command-response reads, and 1 for T7 & T7-Pro stream reads.

[3]  The T7-Pro is equipped with a 24-bit delta-sigma ADC, in addition to the standard 16-bit ADC.  Analog conversions occur on the 16-bit ADC when resolution index values 0-8 are used.  Analog conversions occur on the 24-bit ADC when resolution index values 9-12 are used (command response mode only).

[4]  The hi-resolution 24-bit ADC is not supported in stream mode.

### T7 documentation error

On T7 documentation page:

https://labjack.com/support/datasheets/t-series/appendix-a-3-2-2-t7-nois...

The following text appears:

"
Noise and Resolution Test procedure

Noise and resolution data was generated by collecting 512 successive voltage readings, using a short jumper between the test channel and ground.  The resulting data set represents typical noise measured on any one analog input channel in ADC counts.  The effective resolution is calculated by subtracting the RMS channel noise (represented in bits) from 16-bits.

Effective Resolution = 16 bits - log2 (RMS Noise [in ADC counts])

"

The document goes on to describe effective resolutions of 16 Bits and up.
I think your Effective Resolution = 16 bits - log2 (RMS Noise [in ADC counts]) expression is wrong: It can't calculate the values that are shown.

### That formula matches what I

That formula matches what I see in our source code, and we know that works.

One detail that was not pointed out, is that formula assumes the data has been aligned to 16-bit values.  I added a note #5 about that to the bottom of the page.

We start with an array of voltages.  We then convert them to 16-bit aligned values (kind of like 16-bit binary except with decimal places) using the following:

16-bit aligned Value = 65536 * ( (Value - SpanMin) / (SpanMax - SpanMin) )

We then take the standard deviation of those values.  That is "RMS Noise [in ADC counts]" in the formula in question.

You can try the AIN Noise Test program available on the following page, and the source code is in the LabVIEW_LJM archive.