Appendix B - Noise and Resolution Tables [U6 Datasheet] | LabJack
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Appendix B - Noise and Resolution Tables [U6 Datasheet]

A Note About ADC Noise and Resolution

Analog voltages measured by the U6 are converted to digital representation via the U6's analog to digital converter (ADC).  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 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 (20V ÷ 216).

The stated resolution for an ADC is a best case value, assuming no channel noise.  In reality, every ADC works in conjunction with external circuitry (amplifiers, filters, ect.) which all posses 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 LSB voltage are no longer differentiable from the inherent hardware noise. In addition to defining the smallest measurable analog voltage,  the effective resolution also defines the RMS peak-to-peak noise on a given analog channel.

Closely related to the effective resolution is 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 U6 offers user-selectable resolution through the resolution index parameter on any one AIN channel.  Internally, the ADC hardware uses modified sampling methods to increase measurement resolution beyond the ADC's base resolution.  Valid resolution index values are 0-8 for the U6 and 0-12 for the U6-Pro [2.][3.].  Increasing the resolution index value will improve the channel resolution, but doing so will usually extend channel sampling times.


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 U6 and U6-Pro data are combined and presented together for convenience, where resolution index values 9-12 only apply to the U6-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 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 B-1.  Effective resolution and sampling times for various gains and resolution index settings. Resolution index settings 9-12 apply to the U6-Pro only.

Resolution Effective Effective AIN Sample
Index Resolution Resolution Time
  [bits] [µV] [ms/sample]
Gain/Range: 1/±10V
1 16.0 316 0.05
2 16.5 223 0.06
3 17.0 158 0.08
4 17.5 112 0.12
5 17.9 85 0.20
6 18.3 64 0.36
7 18.8 45 0.69
8 19.1 37 1.33
9 19.6 26 3.58
10 20.5 14 13.5
11 21.3 8.0 66.5
12 21.4 7.5 159
1 15.4 48 0.24
2 16.0 32 0.25
3 16.5 22 0.57
4 16.9 17 0.61
5 17.4 12 1.19
6 17.9 8.5 2.34
7 18.3 6.4 2.67
8 18.7 4.9 3.31
9 19.5 2.8 3.58
10 20.5 1.4 13.5
11 21.4 0.7 66.5
12 21.5 0.7 159
Gain/Range: 100/±0.1V
1 13.3 21 1.04
2 14.2 11 2.04
3 14.7 7.8 5.08
4 15.2 5.5 5.12
5 15.7 3.9 5.20
6 16.3 2.6 10.3
7 16.7 1.9 10.6
8 17.2 1.4 11.3
9 18.3 0.6 3.58
10 19.1 0.4 13.5
11 19.6 0.3 66.5
12 19.7 0.2 159
Gain/Range: 1000/±0.01V
1 10.9 11 5.1
2 12.3 4.1 10.0
3 12.7 3.1 10.0
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 11.3
9 15.4 0.5 3.58
10 16.1 0.3 13.5
11 16.4 0.2 66.5
12 16.4 0.2 159

Figure B-2.  Analog input effective resolution over various gains and resolution index settings.

Figure B-3.  Analog input LSB voltage over various gains and resolution index settings.
Figure B-4.  AIN sample times for analog inputs over various gains resolution index settings.





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.  Resolution index 0 defaults the U6 to resolution index = 8 and the U6-Pro to resolution index = 9 in command response mode.  Stream mode does not support the 24-bit ADC.  Therefore, setting the resolution index to 0 is equivalent to resolution index = 1.

3.  The U6-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 conversion occur on the 24-bit ADC when resolution index values 9-12 are used (command response mode only).

Support - Table Styling Fix


Do you have any noise information for the DACs on the U6?

I put a scope from DAC0 to GND, and the noise I see is the same as if I put the scope from GND to GND.  That just tells us that the noise is less than the scope can detect.

I decided a good way to measure the noise was to use the U6 itself.  The analog inputs on the U6 will eliminate a lot of noise as the resolution setting is increased, but at a setting of 1 there is no noise reduction and you should see any noise that is there and above the noise of the U6 itself.

So I jumpered AIN0 to GND and jumpered AIN1 to DAC0.  I looked at AIN0 to confirm I was seeing the same noise figures from the table above, then used AIN1 to try and measure the noise on DAC0.

First I used the +/-10V range and looked at voltages across the entire range (>0 and <VS).  I could not see extra noise on AIN1 compared to AIN0, and the noise on both was roughly 1.3mV, so this tells me that the noise of the 12-bit 0-5V DAC is <1 count.

To try and detect the actual noise level I set DAC0 to 0.08V so I could use the +/-100mV AIN range, and was able to see a difference.  The noise on AIN0 was about 100uV, but the noise on AIN1 was about 240uV, so that suggests that the noise on DAC0 is about 240uV.


Does increasing resolution index (from 1-8 for U6) decrease measurement speed?

Can you point me to the link which provides more details on this?

I want to use U6 to measure voltage as min of 80uV in differential mode.

What resolution level should I use so that noise won't affect it and does not compromise on speed.


Usually yes, but there are certain situations where ResIndex=9 is faster than ResIndex=8, as this is the transition from the high-speed ADC to the high-resolution ADC.

See Section 3.1, and use this to decide what Range and ResolutionIndex you will use.

Can you please elaborate the meaning of counts in the above tables. 

Also, is the data for the effective Noise-free resolution bits available for the 16 bit resolution. 

Furthermore, how can we toggle the ADC to capture data in max-resolution mode. 

All "counts" are aligned as 24-bit values.  See the 3rd paragraph above.  If it is still not clear, perhaps give an example of what is not clear and we can help clarify that example.

I am not sure what you are asking in your 2nd sentence.

You control range and resolutionindex to get the desired operation.  Are you using a U6 or U6-Pro, and what software are you using?

tskauli's picture

The tables give the "sample time" for various settings. But when the input signal has noise, what is the equivalent noise bandwidth of the sampling for different resolution settings?

labjack support's picture

The T7 datasheet has more information (applies to the U6 also) in notes 6 & 7 of the Analog Input specs:

For ResolutionIndex 1-8 we don't specify any change in noise bandwidth.  The processor is essentially oversampling & averaging, so you will see noise reduced from higher frequencies, but we have not attempted to quantify a change in the -3dB point.

ElectroLund's picture

The appendix states 10G Ohms for AIN channels.  Yet when we measure across any channel to GND, we see less than 1M!  Is there something I'm missing?

labjack support's picture

Are you saying that you used a DMM to measure resistance from AIN0 to GND?  You could do that on a U12, U3-HV (AIN0-3) or T4 (AIN0-3), and get a pretty meaningful result as they all have front end resistance that dominates the input impedance characteristics.  The device would need to be unpowered with no other connections besides your DMM to AIN0 and GND.

For the U6 & T7, and the low voltage inputs on the U3/T4, we would not expect a DMM measurement of resistance to work whether powered or unpowered.  The input impedance is a characteristic of active circuitry and not the result of resistors.  In the case of the U6/T7 the signal is going through some switches and then to an AD8253 instrumentation amplifier:

The input impedance spec of the AD8253 is stated as 4 Gohms.  So does that mean if you apply 1 volt you will only see 1/4G = 0.3 nA of bias current going into the terminal?  No, from different places in the datasheet you can see that bias current is typically 10s of nA, and in fact might be going in to the terminal or coming out of the the terminal.  The input impedance spec of an instrumentation amp is related to the change of bias current, not the total magnitude.

So why does the T7 Datasheet say 1 Gohm rather than 4 Gohm?  That is because the switches in front of the AD8253 also affect bias current.

All this leads to note #4 where we point out that the key specification for high quality inputs using a high quality instrumentation amp is max source impedance, and we provide a link to our settling time app note for more information.