Digital Output Square Root Extraction Formula and Tables

Square root extraction signals are used to simplify closed pipe liquid or gas flow calculations and to improve resolution of the non-linear signal when converted to a flow reading.

The output from a Modbus 12 bit count can be transformed in the following ways:

A linear digital output signal of 0 to 4096 steps can be converted to a non-linear sq rt extraction by applying the following formula or table:

[Output Sq Rt] = Square Root of ([Output Linear] x 4096)

Linear (0 - 4096 steps)	Square Root (0 - 4096 steps)
0	0
256	1024
512	1448
768	1774
1024	2048
1280	2290
1536	2508
1792	2709
2048	2896
2304	3072
2560	3238
2816	3396
3072	3547
3328	3692
3584	3831
3840	3965
4096	4096

A sq rt extraction output of 0 to 4096 steps can be transformed to a linear signal by using the following formula or table:

[Output Linear] = ([Output Sq Rt])^2 / 4096

Square Root (0 - 4096 steps)	Linear (0 - 4096 steps)
0	0
256	16
512	64
768	144
1024	256
1280	400
1536	576
1792	784
2048	1024
2304	1296
2560	1600
2816	1936
3072	2304
3328	2704
3584	3136
3840	3600
4096	4096

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