Appendix B - Resolution Tables

The following tables use typical noise measurements with the LabJack U3 and UE9 to determine the noise-free and effective resolutions that can be expected with the LJTick-InAmp (LJTIA). The LJTIA was connected to an analog input on the LabJack and had IN+ shorted to IN- shorted to GND.

The counts of peak-to-peak noise were determined by collecting 128 points from the analog input and subtracting the minimum binary value from the maximum binary value. For the U3 these are based on 12-bit values, while for the UE9 these are based on 24-bit values.

The noise-free resolution is based on the peak-to-peak noise counts, and corresponds to the resolution where no variation would be seen.

The RMS noise counts is the standard deviation of the 128 collected binary values, and the effective resolution values are based on this RMS value. The effective resolution can be thought of as a specification met by most points, while the noise-free specifications are met by all points.

The “@LJ Inputs” values are in terms of the LabJack U3/UE9 analog input, which is the LJTIA output. Those values are divided by the LJTIA gain to determine the “@LJTIA Inputs” values, which are the resolutions that apply to the signal input to the LJTIA. For instance, a single-ended channel on the LabJack U3 with an LJTIA gain of 201 has a noise-free resolution of about 9 μV and an effective resolution of about 1.8 μV.

LabJack U3

Table B.1. LJTIA Gain = 1-201 with a U3.

LJTIA Gain = 1
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

SE	2	11	0.001191	0.00119141	0.5	13	0.000298	0.00029785
Diff	2	11	0.002383	0.00238281	0.5	13	0.000596	0.0005958
0-3.6	2	11	0.002383	0.00238281	0.5	13	0.000596	0.0005957

LJTIA Gain = 11
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

SE	2	11	0.001191	0.00010831	0.5	13	0.000298	0.00002708
Diff	2	11	0.002383	0.00021662	0.5	13	0.000596	0.00005415
0-3.6	2	11	0.002383	0.00021662	0.5	13	0.000596	0.00005415

LJTIA Gain = 51
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

SE	2	11	0.001191	0.00002336	0.5	13	0.000298	0.00000584
Diff	2	11	0.002383	0.00004672	0.5	13	0.000596	0.00001168
0-3.6	2	11	0.002383	0.00004672	0.5	13	0.000596	0.00001168

LJTIA Gain = 201
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

SE	2	11	0.001806	0.00000898	0.5	12.7	0.000367	0.00000182
Diff	2	11	0.003612	0.00001797	0.5	12.7	0.000733	0.00000365
0-3.6	2	11	0.003612	0.00001797	0.5	12.7	0.000733	0.00000365

LabJack UE9 & UE9-Pro (LJTIA Gain = 1 & 11)

All "counts" data in the following UE9 tables are from 24-bit values. To equate to counts at a particular resolution (Res) use the formula counts/(2^(24-Res)). For instance, with the UE9 set to 12-bit resolution and the 0-5 volt range, there are 8192 counts of noise when looking at 24-bit values. To equate this to 12-bit data, we take 8192/(2^12), which equals 2 counts of noise when looking at 12-bit values.

Table B.2. LJTIA Gain = 1, Resolution 0-18 with a UE9

Resolution=0-12, LJTIA Gain=1
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	12288	10.4	0.0037	0.00370048	2350	12.8	0.000701	0.00070111
0-2.5	20480	9.7	0.003006	0.00300572	4100	12	0.00061	0.00061035

Resolution = 17,LJTIA Gain = 1
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	408	15.3	0.000124	0.00012394	78	17.7	0.000023	0.00002348
0-2.5	620	14.7	0.000094	0.00009393	120	17.1	0.00018	0.0000178

Resolution = 18+ (UE9-PRO, LJTIA Gain = 1)
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	96	17.4	0.000029	0.00002891	20	19.7	0.000006	0.00000587

Table B.3. LJTIA Gain = 11, Resolution 0-18 with a UE9

Resolution = 0-12, LJTIA Gain = 11
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	12288	10.4	0.0037	0.00033641	2350	12.8	0.000701	0.00006374
0-2.5	20480	9.7	0.003006	0.00027325	4100	12	0.00061	0.00005549

Resolution = 17,LJTIA Gain = 11
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	408	15.3	0.000124	0.00001127	78	17.7	0.000023	0.00000213
0-2.5	620	14.7	0.000094	0.00000854	120	17.1	0.00018	0.00000162

Resolution = 18+ (UE9-PRO, LJTIA Gain = 11)
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	110	17.2	0.000033	0.00000302	20	19.7	0.000006	0.00000053

LabJack UE9 & UE9-Pro (LJTIA Gain = 51 & 201):

All "counts" data in the following UE9 tables are from 24-bit values. To equate to counts at a particular resolution (Res) use the formula counts/(2^(24-Res)). For instance, with the UE9 set to 12-bit resolution and the 0-5 volt range, there are 8192 counts of noise when looking at 24-bit values. To equate this to 12-bit data, we take 8192/(2^12), which equals 2 counts of noise when looking at 12-bit values.

Table B.4. LJTIA Gain = 51, Resolution 0-18 with a UE9

Resolution = 0-12, LJTIA Gain = 51
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	12288	10.4	0.0037	0.00007256	2350	12.8	0.000701	0.00001375
0-2.5	20480	9.7	0.003006	0.0005894	4100	12	0.00061	0.00001197

Resolution = 17, LJTIA Gain = 51
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	472	15.1	0.000142	0.00000279	87	17.6	0.000025	0.00000049
0-2.5	776	14.4	0.000116	0.00000227	147	16.8	0.000022	0.00000043

Resolution = 18+ (UE9-PRO), LJTIA Gain = 51
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	172	16.6	0.00005	0.00000099	29	19.2	0.000008	0.00000016

Table B.5. LJTIA Gain = 201, Resolution 0-18 with a UE9

Resolution = 0-12, LJTIA Gain = 201
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	16384	10	0.004883	0.00002429	3500	12.2	0.001063	0.00000529
0-2.5	32768	9	0.004883	0.00002429	6480	11.3	0.00061	0.00000493

Resolution = 17, LJTIA Gain = 201
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	1232	13.7	0.000376	0.00000187	185	16.5	0.000054	0.00000027
0-2.5	2104	13	0.000305	0.00000152	376	15.4	0.000058	0.00000029

Resolution = 18+ (UE9-PRO), LJTIA Gain = 201
Range	Peak-to-peak Noise	Noise-Free Resolution	Noise-Free Res. @LJ Inputs	Noise-Free Res. @LJTIA Inputs	RMS Noise	Effective Resolution	Effective Res. @LJ Inputs	Effective Res. @LJTIA Inputs

volts	counts	bits	volts	volts	counts	bits	volts	volts

0-5	484	15.1	0.000142	0.00000071	106	17.3	0.000031	0.00000015