Mixed-Signal System Design and Modeling ©2001 Eric Swanson Lecture 6 Fall Semester 2002

2 Dynamic Range Before we can process real-world signals in the digital domain, we must quantize them Quantization to N bits takes the infinitely many voltage levels possible in the analog world and “rounds” them to a mere 2 N levels The rounding error inherent in quantizing signals is called “quantization error”

3 Dynamic Range Analog-to-Digital Converters (ADCs) are quantizers that operate at the A/D interface –Suppose the ADC full scale input voltage range is V FS –Then, the analog step size  of an N-bit ADC is given by  =V FS /2 N If ADC analog input levels are large, and the input signal is “unrelated” to ADC sampling –Quantization error is essentially random –Error is uniformly distributed between -  /2 and +  /2

4 Dynamic Range The mean-squared quantization error is: This error is commonly referred to as “quantization noise” e 2 =  -  /2 +  /2 x2x2 dx  =  2 12

5 Dynamic Range The dynamic range of an ADC for sinusoidal inputs is the ratio of the rms value of biggest sinewave we can put into the ADC without overload to the rms value of the quantization noise: DR (dB) = 20 log 10 V FS /2/  2  /  12 = 20 log 10 V FS /2/  2 V FS /2 N /  12

6 Dynamic Range Dynamic range for an ADC with sinusoidal input is often just called its “dynamic range” Finite DR is an inevitable consequence of “rounding” a continuous analog input to one of 2 N discrete values DR (dB) = 20 log 10 V FS /2/  2 V FS /2 N /  12 = 20 log 10 2N2N 3232  = 6.021N

7 Dynamic Range 6.02N+1.76dB is the best case DR for an ideal N-bit ADC (or 2 N -level quantizer) –Real ADCs add other noise sources in addition to their quantization noise –Thermal noise typically dominates quantization noise in commercial ADCs Digital signal processing of real-world signals is impossible without at least one ADC’s quantization noise

8 Dynamic Range Note that rounding a 32-bit accumulator value down to 16-bits for storage in a 16-bit register also adds 16b quantization noise –Best-case 16b dynamic range is 98.1dB –Changes in datapath word widths in digital filters must be carefully evaluated for their dynamic range impact Let’s look briefly at real-world ADCs…

9 ADC Dynamic Range DR’s for the best standalone ADCs in the world in 2000 are plotted in the figure Dynamic range decreases as converter bandwidth increases ADC Sampling Frequency (Hz) Dynamic Range (dB)

10 ADC Dynamic Range From , ADC performance at any sampling frequency improved by 2dB/year Since then, the “performance line” has stayed almost stationary ADC Sampling Frequency (Hz) Dynamic Range (dB)

11 ADC Dynamic Range ADCs embedded in IC “Systems on a Chip” (SoCs) have less DR than the best standalone ADCs The embedded ADC performance level is shown in red ADC Sampling Frequency (Hz) Dynamic Range (dB) embedded ADCs

12 ADC Dynamic Range Analog-digital crosstalk and design risk issues limit embedded ADC DR to about 100dB 1 GHz, 30dB DR levels are much more forgiving and the performance gap narrows ADC Sampling Frequency (Hz) Dynamic Range (dB) embedded ADCs

13 ADC Dynamic Range Minimization of analog signal processing is a key goal of mixed-signal IC microarchitecture However, analog signal processing is almost unavoidable “above the red line” ADC Sampling Frequency (Hz) Dynamic Range (dB)

14 Analog vs. Digital DR It’s much less expensive to add dynamic range to digital circuits than analog circuits To double the dynamic range of a digital datapath, we need to add only a bit to an already-wide datapath: dB DR