ECE 353 Introduction to Microprocessor Systems Michael G. Morrow, P.E. Week 14

Topics Digital versus analog Data acquisition systems Quantization and aliasing Analog to Digital Converters (ADCs) Digital to Analog Converters (DACs) Waveform Generation ADuC7026 Analog Peripherals Digital Filtering and Audio Demos

Characteristics of Signals Analog Signals Infinite number of possible signal levels (values) Can change at any instant to any other value  Bandwidth is potentially infinite Analog signals are continuous in both time and value There are no noise margins in analog! Digital Signals Signal level (value) only representable in fixed steps within a finite range Only know the signals value at distinct instants in time  Bandwidth is limited to a finite value Digital signals are discrete in time and value (they are a vector of values) Signal can be exactly identified in the presence of some amount of noise

Why Use Digital Signals? Pros Digital signals can be faithfully stored and copied Allows for numeric processing by digital computers (digital signal processing - DSP) Lossy and lossless data compression possible Can mathematically represent physically unrealizable systems Cons Cannot exactly represent or reconstruct the original analog signal Requires greater bandwidth (uncompressed)

Data Acquisition Systems Block Diagram Isolation/Buffering Amplification Bandwidth-limiting Sample and Hold Analog-to-Digital Converter (ADC) Shannon’s Sampling Theorem F S > 2F MAX Aliasing Must be prevented - it can not be detected in the data Anti-aliasing FiltersFilters

Data Acquisition Systems (cont) Quantization An ADC converts a continuous signal to a discrete digital value at each sample point The ADC uses some scheme to map the analog value to a digital code We will only discuss uniform (linear) quantizationuniform (linear) quantization Quantization Noise There is always uncertainty as to what the actual value of the analog signal value was This is manifested as quantization noise

Types of ADCs Parallel (Flash) Converters Successive Approximation Converters Pipelined Converters Also other types Integrating (Dual-Slope) Converters  Slow, but noise immunity very good, can’t alias Sigma-delta Converters  Commonly used for high resolution (16-24 bits) audio signal conversion at 44.1KHz or higher  Dramatically reduce anti-aliasing filter requirements by oversampling

Digital to Analog Converters (DACs) Device Characteristics Coding scheme Output type and range Resolution Accuracy  Ideal DAC transfer characteristic Ideal DAC transfer characteristic  Errors Offset Gain Nonlinearity Latency and settling time Output glitching

Digital to Analog Converters (DACs) PWM DAC R-2R Ladder DAC Each input bit controls an analog switch Op amp converts current sum to voltage Reconstruction filters What was the value of the signal between the samples?

Waveform Generation DACs allow the generation of analog waveforms under digital control Example – generate sinusoid V OUT = V MAX sin(2πft) Calculate directly as a function of t Calculate as a function of the desired signal phase Use lookup table to obtain sin/cos values, use index as a phase accumulator Use complex vector rotation

ADuC7026 Analog Peripherals 12-channel, 12-bit successive approximation ADC operating at up to 1MS/s Bootloader code uses factory-programmed values to compensate for ADC gain and offset errors Four 12-bit voltage output DACs On-chip precision 2.5V voltage reference External capacitor required On-chip temperature sensor (+/-3°C)

Digital Filters We can implement filters digitally that operate on digital signals Advantages No temperature/aging/drift characteristics Repeatability Can create identical filters Implementation Finite Impulse Response  No feedback  Stability guaranteed Infinite Impulse Response  Uses feedback  Can be unstable

DSP Demos Hardware Quantization Aliasing FIR filter Audio Equalizer Audio Effects Echo Flanger Tremelo Frequency Translation Subharmonic Synthesis Karplus-Strong Guitar Synthesizer Vocoder

Wrapping Up Homework #7 is due on Friday, May 11 th Final Exam is on Wednesday, May 16 th, at 12:25pm, in room 2255EH Coverage is over all course material

Pipelined ADC Conversion is performed in stages by lower resolution (faster!) ADCs.

Parallel (Flash) ADC Simultaneous comparison to all possible quantized values.

Successive Approximation ADC Compares value from DAC with input.

DSP Hardware TMS320C6713 DSP, 225MHz 1350 MFLOPs, 1800 MIPs TLC320AIC23 16-bit stereo CODEC 48KHz sample rate

Aliasing

Anti-aliasing Filters

Anti-aliasing Filters - Ideal

Anti-aliasing Filters - Practical

Uniform Quantization Error function

Ideal DAC Transfer Characteristic

DAC Errors – Offset Error

DAC Errors – Gain Error

DAC Errors – Nonlinearity Errors Differential Non-Linearity (DNL) DNL = actual_step – ideal_step DNL is calculated for each step If DNL<-1, the DAC is not monotonic Integral Non-Linearity (INL) INL is calculated for each output code DNL and INL are normal specified as worst-case values

Digital Filters

Reconstruction Filters Back to our sampled signal – a sinusoid at ¼F S How do we make the DAC output look like the original input signal?

PWM DAC Use PWM digital output driver LPF removes most of AC components

R2R Ladder DAC Resistive current divider network Op amp does current summing

FIR Filter The output y is the sum of the products of the last m samples x and the filter coefficients h.

Audio Equalizer

Audio Effects - Echo

Audio Effects - Flanger The delay B is varied sinusoidally.

Audio Effects - Tremelo Error in diagram – audio signal comes in where the sine generator is shown, modulating sinusoid comes in on upper port.

Audio Effects – Frequency Translation

Audio Effects – Subharmonic Synthesis

Karplus-Strong Queue is filled with noise to start. Output is the sum of the two elements at the head of the queue multiplied by a decay factor. Output is fed back into the queue.

Vocoder Uses the frequency spectrum of one signal to control the frequency response of the other signal. Can also use white noise as the modulated signal.