INF4420 Data Converters Spring 2012 Jørgen Andreas Michaelsen ([email protected]) Outline Quantization Sampling jitter DFT and windowing Data encoding Introduction Digital signal processor (DSP) Signal processing can be more efficient, robust, and convenient in the digital domain (algorithms in digital circuits and software). Need to convert to and from analog to interface with the world. Introduction Anti-alias filter Reconstruction filter Digital processing Continuous time input and output, but with digital processing. Introduction Data conversion accuracy limits system performance. In-depth understanding of data converter performance is important for the design of mixed-signal systems. How do we quantify data converter performance? Introduction Important to pay attention to mixed signal layout issues. Data converters combine sensitive high accuracy circuits for generating reference levels (bandgaps) with digital switching (current spikes). For high resolution converters, the external environment (e.g. PCB) is very important. Quantization Data converters must represent continuous values in a range using a set of discrete values. A binary code is used to represent the value. Information is Hot or cold lost! Freezing, cold, warm, or hot. -20 °C, -19.5 °C, ..., 20 °C. Open Clipart Library (openclipart.org) Quantization Number of bits, N Quantization The quantization error is restricted to the range -Δ/2 to Δ/2. The quantization process is non-linear! Quantization noise Model the quantization error as noise added to the original signal. Enables linear analysis. Quantization noise Quantization noise assumptions: ● All quantization levels have equal probability ● Large number of quantization levels, M ● Uniform quantization steps, constant Δ ● Quantization error uncorrelated with input Quantization noise is white! Quantization noise Time average power (variance): Quantization noise Assuming sine wave input SNR due to quantization noise Sampling jitter Uncertainty in the timing of the sampling clock due to circuit electrical noise (white noise + 1/f). Reference sampling edge Sampling jitter Sampling clock timing jitter translates to an error in the sampled value. Impacts SNR. Sampling jitter Worst-case full scale sine wave at the Nyquist frequency. Error due to jitter should be less than half the quantization step. Discrete Fourier Transform Many data converter performance metrics are carried out more straightforward in the frequency domain. The Discrete Fourier Transform (DFT) is used to analyze a set of N samples. Assumes the N samples are one period of an infinitely repeating signal. Result is a set of N complex numbers, the frequency domain representation of the signal. Discrete Fourier Transform The DFT can be efficiently computed using the Fast Fourier Transform (FFT). Windowing The DFT assumes periodic input. Window functions are used to introduce artificial periodicity. Time domain Freq. domain Trade-offs ● Amplitude accuracy ● Sidelobes ● Width of signal peak Binary data coding Alternatives for representing the quantized value in binary ● Unipolar ● Bipolar ● Two's complement ● ... Static specifications Static specifications ● Gain ● Offset ● INL ● DNL ● Missing codes (output code which can not be reached by any input value) ● Monotonicity (increasing input value will always produce equal or higher output code) ● ... Dynamic specifications Obtained from the DFT (FFT) ● SNR ● SINAD ● SFDR ● THD ● DR SFDR Spurious free dynamic range. Relative to highest spur (not only harmonics) SNR Signal to noise ratio. Signal power, divided by noise power (exclude harmonics) THD Total harmonic distortion A measure of the distortion excluding noise. SINAD Signal to noise and distortion ratio. Dynamic specifications Other dynamic specifications: ● Intermodulation distortion (IMD) ● Settling time ● Glitching Figure of merit (FoM) Equivalent number of bits: Figure of merit (FoM): Resources Not part of the curriculum Converter Passion (blog covering many aspects of data converters) Kester, The Data Conversion Handbook, Analog Devices, 2004 Heinzel et al., Spectrum and spectral density estimation ..., Max-Planck-Institut für Gravitationsphysik, 2002.