## Unit conversion

Code to Voltage Conversion

In general a 14-bit digitizer output samples with codes (raw data value) between -8192 to 8191 (= 2^14 different codes).

The ADQ series of digitizers use the data representation MSB aligned 16 bits words. This means that the 14 bits are mapped onto a 16 bit word using the 14 most significant bits. (16 bits words is the standard format for processing in the PC: signed INT16).

The conversion from 14 bits to 16 bits MSB aligned means that the 14-bit digitizer produce samples with codes between –32768 to 32764 in steps of 4 with 2^14 different unique values. This representation is used in the following calculation.

Different digitizers typically have different voltage input range (maximum amplitude which they can capture). The maximum signal range is found in the datasheet of the respective digitizer.

As an example, on our 14-bit ADQ214 digitizer the input voltage range is 2.2 Volt peak-to-peak (-1.1 to 1.1 Volts).

Therefore the resolution is 2.2 Volts / 2^16 codes = 2.2 Volts / 65536 codes = 0.0336 milliVolts / code.

If you capture a code, let's say 5488 (this is ADC raw 14 bits code 1372 mapped to a 16 bits MSB-aligned word), your corresponding Voltage is 5488 * (2.2 / 2^16) = 5488 *0.0336m = 0.1842... Volts.

As another example, consider capturing the code -32768, then the corresponding Voltage is -32768 *(2.2/2^16) = -1.1 Volts.

And the maximum code, +32764gives 32764*(2.2/2^16) = 1.0998.. Volts.

Voltage to Watt Conversion

Assuming a voltage input range of 2.2 Volt peak-to-peal and 50 Ohm input impedance a full scale single sine wave (0 dBFS) with an amplitude of 1.1 Volt (2.2 Volt peak-to-peak) has a power of (1.1/sqrt(2))^2/50 = 12.1 mW.

Voltage to dBFS Conversion

dBFS means dB with respect to full scale measured with a single sine wave.

For a digitizer with an input voltage range of 2.2 Volt peak-to-peak, 0 dBFS corresponds to a single sine wave with amplitude 1.1 Volt (which is equivalent to 2.2 Volt peak-to-peak).

-6dBFS is a single sine wave with amplitude 0.55 Volt, that is 1.1 Volt peak-to-peak. The value can only be negative for normal operation. A positive value means overflow.

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