On Bits and Dynamic Range

by Gerald Youngblood, K5SDR

A number of people have asked how you can get more than 96 dB of instantaneous dynamic range out of a 16-bit A/D converter. You may think that one can only achieve 6 dB per bit, which would be 96 dB. Technically the theoretical maximum limit is 6.02n +1.67 dB (where*n* is the number of bits).[1,2] What many people fail to understand is that dynamic range is a meaningless term without knowing the final detection bandwidth (i.e. 500 Hz CW filter).

Instantaneous dynamic range increases with decreasing bandwidth by a factor of 10*log*(bandwidth change). That means that a 50 Hz filter will provide 10 dB higher dynamic range than a 500 Hz filter. That is why you hear less noise in the smaller filter. The actual receiver noise figure (NF) of the radio has not changed but the detection bandwidth has. Thus the SNR and dynamic range improves accordingly.

The dynamic range of any ADC is normally assumed to be specified over the Nyquist bandwidth, which is equal to 1/2 of the converter’s sampling rate. With the ADC used in the FLEX-6000 series, the Nyquist bandwidth is 122.88 MHz. To calculate instantaneous dynamic range, one needs to know the converter’s specified signal to noise ratio (SNR), maximum peak signal handling capability, sampling rate, and final detection bandwidth. There are many application notes available from Analog Devices, Linear Technology, Texas Instruments, etc. that aid in these calculations. It is beyond the scope of this newsletter to provide the detailed education and analysis.

The bottom line is that the FLEX-6000 ADC running at 245.76 Msps provides a nominal instantaneous dynamic range on the order of 130 dB in a 500 Hz bandwidth or about 140 dB in a 50 Hz bandwidth. How much do you need in practice? Let’s look at that question next.

References:

1. “Quantization Noise: An Expanded Derivation of the Equation, SNR= 6.02 N + 1.76 dB”, Ching Man, Analog Devices,Inc.

http:www.analog.com/static/imported-files/tutorials/MT-229.pdf

2. “15.3.2 Quantization – Digitization in Amplitude; DSP and Software Radio Design”, The 2013 ARRL Handbook, American Radio Relay League.