A-3-3-2 T8 Noise and Resolution [T-Series Datasheet]

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 24-bit ADC with a ±11 input range can report 16777216 discrete voltages (2²⁴) and has an LSB voltage of 1.311 µV (22 V ÷ 2^24).

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 T8 offers user-selectable effective resolution through the resolution index parameter, which applies to all AIN channels. Increasing the resolution index value will improve the channel resolution, but increasing the resolution often requires the use of slower sampling rates. See section 14.0 AIN for more information on the resolution index parameter and its use.

The default value for RESOLUTION_INDEX is 0, which is an auto setting based upon the configured AIN sampling rate on the T8.

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 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 24-bit aligned values: essentially 24-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:

24-bit Aligned Value = 16777216 * ((Voltage - MinSpanVolts) / (MaxSpanVolts - MinSpanVolts))

RMS Noise = StandardDeviation (24-bit Aligned Values)

Effective Resolution in Bits = 24.0 - log2 (RMS Noise)

See Appendix A-3-3-1 for the supported range settings and corresponding min and max span voltages. For example, with Range = ±11 V, the min is about -11 V and the max is about 11 V.

RMS and Bits Noise Free

In the tables below, the “RMS” columns represent the effective resolution in bits, accounting for RMS noise. The “Bits Noise Free” columns represent the error free code resolution (EFCR).

Range: ±11.0 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	14.8	11.3
1	40.0	14.7	11.3
2	10.0	15.8	12.5
2	40.0	15.6	12.4
3	10.0	16.8	13.5
3	35.5	16.4	13.5
4	10.0	17.3	14.5
4	34.0	16.7	13.9
5	10.0	17.4	14.7
5	32.0	16.7	14.1
6	10.0	17.5	14.7
6	21.3	17.1	14.3
7	10.0	17.5	14.8
7	20.4	17.1	14.4
8	6.0	17.8	15.1
8	16.0	17.3	14.6
9	5.5	18.0	15.3
9	10.6	17.6	14.9
10	5.0	18.0	15.3
10	10.2	17.6	14.9
11	3.5	18.3	15.6
11	8.0	17.8	15.0
12	3.0	18.4	15.7
12	5.3	18.1	15.4
13	2.5	18.5	15.8
13	5.1	18.1	15.4
14	1.5	18.8	16.1
14	4.0	18.3	15.6
15	0.1	19.6	17.0
15	2.0	15.5	10.5
16	0.1	20.3	17.7
16	1.0	19.3	16.5

Range: ±9.6 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.6	12.1
1	40.0	15.6	12.1
2	10.0	16.6	13.3
2	40.0	16.5	13.3
3	10.0	17.6	14.5
3	35.5	17.2	14.2
4	10.0	18.0	15.3
4	34.0	17.4	14.7
5	10.0	18.2	15.5
5	32.0	17.5	14.8
6	10.0	18.3	15.6
6	21.3	17.9	15.2
7	10.0	18.3	15.6
7	20.4	17.9	15.2
8	6.0	18.6	15.9
8	16.0	18.1	15.3
9	5.5	18.8	16.1
9	10.6	18.4	15.7
10	5.0	18.8	16.1
10	10.2	18.4	15.6
11	3.5	19.1	16.4
11	8.0	18.6	15.9
12	3.0	19.2	16.5
12	5.3	18.9	16.1
13	2.5	19.3	16.7
13	5.1	18.9	16.1
14	1.5	19.7	17.0
14	4.0	19.1	16.4
15	0.1	20.4	17.7
15	2.0	19.6	16.8
16	0.1	21.1	18.4
16	1.0	20.1	17.3

Range: ±4.8 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.6	12.1
1	40.0	15.5	12.0
2	10.0	16.6	13.4
2	40.0	16.5	13.4
3	10.0	17.5	14.5
3	35.5	17.2	14.3
4	10.0	18.1	15.3
4	34.0	17.4	14.7
5	10.0	18.2	15.6
5	32.0	17.5	14.8
6	10.0	18.3	15.6
6	21.3	17.9	15.2
7	10.0	18.3	15.6
7	20.4	17.9	15.2
8	6.0	18.6	15.9
8	16.0	18.1	15.4
9	5.5	18.8	16.1
9	10.6	18.4	15.6
10	5.0	18.8	16.2
10	10.2	18.4	15.7
11	3.5	19.1	16.3
11	8.0	18.6	15.8
12	3.0	19.2	16.5
12	5.3	18.9	16.1
13	2.5	19.3	16.6
13	5.1	18.9	16.2
14	1.5	19.6	16.9
14	4.0	19.1	16.3
15	0.1	20.4	17.8
15	2.0	19.6	16.9
16	0.1	21.1	18.5
16	1.0	20.1	17.3

Range: ±2.4 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.5	12.1
1	40.0	15.6	12.1
2	10.0	16.6	13.4
2	40.0	16.5	13.3
3	10.0	17.5	14.4
3	35.5	17.2	14.2
4	10.0	18.0	15.3
4	34.0	17.4	14.8
5	10.0	18.2	15.5
5	32.0	17.5	14.9
6	10.0	18.3	15.5
6	21.3	17.8	15.1
7	10.0	18.3	15.5
7	20.4	17.9	15.2
8	6.0	18.6	15.9
8	16.0	18.0	15.4
9	5.5	18.8	16.1
9	10.6	18.4	15.6
10	5.0	18.8	16.2
10	10.2	18.4	15.7
11	3.5	19.1	16.4
11	8.0	18.5	15.8
12	3.0	19.2	16.4
12	5.3	18.9	16.2
13	2.5	19.3	16.6
13	5.1	18.9	16.2
14	1.5	19.6	16.9
14	4.0	19.1	16.3
15	0.1	20.4	17.7
15	2.0	19.6	16.9
16	0.1	21.1	18.4
16	1.0	20.1	17.4

Range: ±1.2 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.5	12.1
1	40.0	15.6	12.2
2	10.0	16.6	13.4
2	40.0	16.5	13.3
3	10.0	17.6	14.4
3	35.5	17.2	14.3
4	10.0	18.0	15.4
4	34.0	17.4	14.8
5	10.0	18.2	15.5
5	32.0	17.5	14.8
6	10.0	18.3	15.6
6	21.3	17.8	15.1
7	10.0	18.3	15.5
7	20.4	17.8	15.2
8	6.0	18.6	16.0
8	16.0	18.0	15.3
9	5.5	18.7	16.1
9	10.6	18.3	15.6
10	5.0	18.8	16.1
10	10.2	18.3	15.6
11	3.5	19.0	16.3
11	8.0	18.5	15.9
12	3.0	19.2	16.5
12	5.3	18.8	16.1
13	2.5	19.3	16.6
13	5.1	18.9	16.2
14	1.5	19.6	16.9
14	4.0	19.0	16.4
15	0.1	20.4	17.8
15	2.0	19.5	16.8
16	0.1	21.0	18.4
16	1.0	20.0	17.3

Range: ±0.6 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.5	12.1
1	40.0	15.5	12.0
2	10.0	16.6	13.3
2	40.0	16.5	13.3
3	10.0	17.5	14.4
3	35.5	17.2	14.2
4	10.0	18.0	15.3
4	34.0	17.3	14.6
5	10.0	18.1	15.5
5	32.0	17.4	14.8
6	10.0	18.2	15.5
6	21.3	17.8	15.1
7	10.0	18.2	15.5
7	20.4	17.8	15.1
8	6.0	18.6	15.8
8	16.0	18.0	15.3
9	5.5	18.7	16.0
9	10.6	18.3	15.5
10	5.0	18.8	16.1
10	10.2	18.3	15.6
11	3.5	19.0	16.3
11	8.0	18.5	15.8
12	3.0	19.1	16.5
12	5.3	18.8	16.1
13	2.5	19.2	16.5
13	5.1	18.8	16.0
14	1.5	19.5	16.9
14	4.0	19.0	16.2
15	0.1	20.3	17.7
15	2.0	19.5	16.8
16	0.1	21.0	18.3
16	1.0	19.9	17.3

Range: ±0.3 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.6	12.1
1	40.0	15.5	12.2
2	10.0	16.6	13.3
2	40.0	16.4	13.2
3	10.0	17.4	14.4
3	35.5	17.0	14.2
4	10.0	17.8	15.0
4	34.0	17.1	14.4
5	10.0	17.9	15.2
5	32.0	17.2	14.5
6	10.0	18.0	15.3
6	21.3	17.5	14.9
7	10.0	18.0	15.4
7	20.4	17.6	14.8
8	6.0	18.4	15.7
8	16.0	17.7	15.1
9	5.5	18.5	15.7
9	10.6	18.0	15.3
10	5.0	18.5	15.9
10	10.2	18.1	15.4
11	3.5	18.8	16.0
11	8.0	18.3	15.5
12	3.0	18.9	16.3
12	5.3	18.5	15.9
13	2.5	19.0	16.3
13	5.1	18.6	15.9
14	1.5	19.3	16.7
14	4.0	18.7	16.1
15	0.1	20.1	17.4
15	2.0	19.2	16.6
16	0.1	20.9	18.3
16	1.0	19.7	17.0

Range: ±0.15 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.5	12.1
1	40.0	15.4	12.0
2	10.0	16.5	13.3
2	40.0	16.1	13.3
3	10.0	17.2	14.3
3	35.5	16.6	13.8
4	10.0	17.4	14.8
4	34.0	16.6	13.9
5	10.0	17.5	14.8
5	32.0	16.7	14.0
6	10.0	17.6	14.8
6	21.3	17.0	14.4
7	10.0	17.5	14.8
7	20.4	17.0	14.3
8	6.0	17.9	15.2
8	16.0	17.2	14.6
9	5.5	18.0	15.3
9	10.6	17.5	14.8
10	5.0	18.1	15.4
10	10.2	17.5	14.8
11	3.5	18.3	15.6
11	8.0	17.7	15.0
12	3.0	18.4	15.8
12	5.3	18.0	15.3
13	2.5	18.6	15.9
13	5.1	18.1	15.4
14	1.5	18.9	16.2
14	4.0	18.2	15.6
15	0.1	19.6	17.0
15	2.0	18.7	15.9
16	0.1	20.6	17.9
16	1.0	19.2	16.6

Range: ±0.075 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.4	12.0
1	40.0	15.1	11.9
2	10.0	16.2	13.2
2	40.0	15.6	12.8
3	10.0	16.6	13.9
3	35.5	15.8	13.1
4	10.0	16.7	14.0
4	34.0	15.8	13.2
5	10.0	16.7	14.1
5	32.0	15.9	13.2
6	10.0	16.7	14.0
6	21.3	16.2	13.6
7	10.0	16.7	14.0
7	20.4	16.2	13.5
8	6.0	17.1	14.4
8	16.0	16.4	13.7
9	5.5	17.2	14.5
9	10.6	16.7	14.0
10	5.0	17.3	14.5
10	10.2	16.7	14.0
11	3.5	17.5	14.9
11	8.0	16.9	14.2
12	3.0	17.6	14.9
12	5.3	17.2	14.4
13	2.5	17.8	15.1
13	5.1	17.3	14.6
14	1.5	18.1	15.4
14	4.0	17.4	14.7
15	0.1	19.2	16.5
15	2.0	17.9	15.2
16	0.1	19.8	17.1
16	1.0	18.4	15.7

Range: ±0.036 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	15.1	11.8
1	40.0	14.5	11.6
2	10.0	15.5	12.7
2	40.0	14.7	12.0
3	10.0	15.7	13.0
3	35.5	14.9	12.2
4	10.0	15.7	13.0
4	34.0	14.8	12.2
5	10.0	15.8	13.1
5	32.0	14.9	12.2
6	10.0	15.7	13.0
6	21.3	15.2	12.4
7	10.0	15.7	13.0
7	20.4	15.2	12.5
8	6.0	16.1	13.5
8	16.0	15.4	12.7
9	5.5	16.2	13.5
9	10.6	15.7	12.9
10	5.0	16.2	13.6
10	10.2	15.7	13.0
11	3.5	16.5	13.9
11	8.0	15.9	13.3
12	3.0	16.6	14.0
12	5.3	16.2	13.4
13	2.5	16.8	14.0
13	5.1	16.2	13.6
14	1.5	17.1	14.4
14	4.0	16.4	13.6
15	0.1	18.6	15.9
15	2.0	16.9	14.2
16	0.1	18.7	16.2
16	1.0	17.4	14.7

Range: ±0.018 V

Resolution Index	Rate [kHz]	RMS [bits]	Bits Noise Free [bits]
1	10.0	14.6	11.6
1	40.0	13.7	11.1
2	10.0	14.7	12.0
2	40.0	13.7	11.0
3	10.0	14.7	12.1
3	35.5	13.9	11.3
4	10.0	14.8	12.0
4	34.0	13.9	11.2
5	10.0	14.8	12.1
5	32.0	13.9	11.2
6	10.0	14.8	12.1
6	21.3	14.2	11.4
7	10.0	14.8	12.0
7	20.4	14.2	11.6
8	6.0	15.1	12.5
8	16.0	14.4	11.7
9	5.5	15.2	12.6
9	10.6	14.7	12.0
10	5.0	15.3	12.6
10	10.2	14.7	12.0
11	3.5	15.5	12.9
11	8.0	14.9	12.2
12	3.0	15.6	12.9
12	5.3	15.2	12.5
13	2.5	15.8	13.1
13	5.1	15.2	12.5
14	1.5	16.1	13.4
14	4.0	15.4	12.7
15	0.1	17.8	15.2
15	2.0	15.9	13.3
16	0.1	17.9	15.3
16	1.0	16.4	13.7