## A Brief Overview of A-D Conversion

### by George T. Baker  W5YR

#### (Originally published on the Ten-Tec Contesting reflector, January 3, 2003)

Theoretically, an N-bit A/D converter (ADC) can provide 2n discrete quantization levels or steps or numbers corresponding to some specified analog input signal amplitude range. Since each quantization level represents a change in magnitude of 2, we equate each bit with 6 dB of available dynamic range for the converter.

Example: A 4-bit ADC can output the binary numbers 0000 through 1111, or 0 through 15 decimal. These 16 levels would all be usable except for the effects of indecision in the conversion process which results in the least significant bit (LSB) sometimes being correct and sometimes being incorrect. On average, the correct digital value "falls in the crack between levels" and produces quantization noise in the ADC output. That is, the numbers differ from sample to sample from the "exact values" by being forced to take on only the available values from the converter. This can be thought of as the true sampled signal accompanied by essentially uniformly distributed noise across the spectrum of the "real" signal.

Thus, we regard the LSB as being "lost" to the effects of quantization noise even under the best of conditions. So, our N-bit ADC functions at best as an (N-1)-bit converter, and we have lost 6 dB of its theoretical dynamic range. The working dynamic range thus is reduced from 4 bits at 6 dB per bit or 24 dB to 3 bits or 18 dB. Effectively, we disregard the LSB and use only the remaining higher-order bits.

Realistically, more than just the LSB is lost to quantization noise in the real world of A/D conversion. Common techniques such as sample clock dithering to control the effects of quantization noise can "use up" several low-order bits and therefore further reduce the effective number of quantization levels based on the "6 dB per bit" viewpoint.

Apart from A/D issues, there are a number of other factors at work in a digitally controlled receiver which influence overall dynamic range. Chief among these is the analog response function of the circuitry preceding the A/D converter. Non-linearities in circuit operation can produce aggregate ADC input signal components of larger amplitude than the simple combination of signal amplitudes that would result from purely linear circuit operation ahead of the converter. Thus, more ADC bits are required to represent the input signal than otherwise would be needed with purely linear operation.

Effectively, then, about 100 dB of dynamic range "could" be associated with about 16 or 17 active bits in the A/D conversion process, but this may or may not accurately reflect the actual number of "working" bit levels in the conversion process itself. Realistically, some equivalent "bits" are lost to front-end non-linearities and some to dithering and related ADC operational schemes.

Conclusion: It can be confusing and lead to misunderstanding to think of the dynamic range of a digitally controlled receiver as being determined solely and simplistically by the number of bit levels provided by the ADC. Typically, a 24-bit ADC, theoretically capable of 24*6 = 144 dB overall numerical signal range, may produce a usable dynamic range of only 100 dB as previously reported. The element of design superiority plays into achieving as much of that theoretical 144 dB as possible in a production system; i.e., making the most of the available 24 bits.

Doug Smith KF6DX's very excellent chapter on DSP in the ARRL Handbook is required reading for anyone interested in this subject area. Seldom have so many complex topics been compressed into such small space and explained so clearly. An outstanding contribution . . .

##### References:
1. The ARRL Handbook for Radio Communications (2003) - 80th Edition: Digital Signal Processing, by Doug Smith KF6DX
`Contents copyright © 2002, George T. Baker, W5YR`
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