Quantization Error Caused by A/D Conversion

Compared to an analog signal, a binary signal which represents only two states contains very little information. If a quantitiy to be represented digitally requires a wider range of values, it must be described by several bits.Analog quantities are processed digitally, when are converted into digital values first. An analog quantity can assume an infinite number of intermediate values while a digital quantity can only assume a limited number of values, therefore when analog signals are converted into discretized digital signals, quantization errors occur. Increasing the number of bits used for digital representation and the sampling rate of the analog signal reduces quantization errors. The complexity of data processing and transmission is increased with an increasing number of bits. The range of values must be adapted to the particular task, while choosing a binary representation that is not too extensive, in order to keep the loss of information during conversion as low as possible.

Quantization error caused by reduced discretization
and sampling rate

Determining the quantization error for displacement measurement:
Analog measuring range --- 0 to 30 cm
Range of values of an 8-bit unit --- 256
Quantization error --- (30/256) cm = 1.2 mm
Range of values of a 12-bit unit --- 4096
Quantization error --- (30/4096) cm = 0.073 mm

Complex Waves

Complex waves include:

• Analog modulated, digitally modulated, pulse-width
• modulated, and quadrature modulated signals
• Digital patterns and formats
• Pseudo-random bit and word streams

Quadrature Modulation

In Signal Modulation waves the amplitude, phase and/or frequency variations embed lower-frequency information into a carrier signal of higher frequency. It gives signals in the form of either speech, data or video. In Analog Modulation the signal varies the carrier’s amplitude and/or frequency. At the receiving end, demodulating circuits interpret the amplitude and/or frequency variations, and extract the content from the carrier. Phase modulation modulates the phase rather than the frequency of the carrier waveform to embed the content. Digital modulation is based on two states which allow the signal to express binary data. In amplitude-shift keying (ASK), the digital modulating signal causes the output frequency to switch between two amplitudes; in frequency-shift keying (FSK), the carrier switches between two frequencies (its center frequency and an offset frequency); and in phase-shift keying (PSK), the carrier switches between two phase settings. In PSK, a “0” is imparted by sending a signal of the same phase as the previous signal, while a “1” bit is represented by sending a signal of the opposite phase. Pulse-width modulation (PWM) is another common digital format; it is often used in digital audio systems. It is applicable to pulse waveforms only. With PWM, the modulating signal causes the active pulse width (duty cycle, explained earlier) of the pulse to vary. Quadrature (IQ) modulation technology is used for building digital wireless communications networks. An in-phase (I) waveform and a quadrature-phase (Q) waveform that is delayed by exactly 90 degrees relative to the “I” waveform are modulated to produce four states of information. An in-phase (I) waveform and a quadrature-phase (Q) waveform are combined and transmitted over one channel, then separated and demodulated at the receiving end. The IQ format delivers far more information than other forms of analog and digital modulation  because it increases the effective bandwidth of the system. A digital pattern consists of multiple synchronized pulse streams. It makes up words of 8, 12, 16, or more bits wide data. The digital pattern generator, specializes in delivering words of data to digital buses and processors via parallel outputs. Digital computers have the inability to produce truly random numbers, therefore Pseudo-random bit streams (PRBS) and pseudo-random word streams (PRWS) are used. Digital video signals can have jagged lines on surfaces that should be smooth. Controlled amount of noise is added to hide these jagged lines from the eye without losing the original information. Serializers or multiplexers are tested using PRWS.

Basic Signal Generator Applications

Signal generators fall into three basic categories: verification, characterization, and stress/margin testing. 

1. Testing Digital Modular Transmitters and Receivers
2. Testing D/A and A/D Converters
3. Stressing Communication Receivers

Wireless equipment designers developing new transmitter and receiver hardware must simulate baseband  I&Q signals to verify conformance with emerging and proprietary wireless standards. Some high-performance arbitrary waveform generators can provide the needed low-distortion, high-resolution signals at rates up to 1 gigabit per second (1 Gbps), with two independent  channels, one for the “I” phase and one for the “Q” phase. Sometimes the actual RF signal is needed to test a receiver. Here, arbitrary waveform generators with sample rates up to 200 S/s can be used to  directly synthesize the RF signal.

Newly-developed digital-to-analog converters (DAC) and analog-to-digital converters (ADC) must be exhaustively tested to determine their limits of linearity, monotonicity, and distortion. A state-of-the-art AWG can generate simultaneous, in-phase analog and digital signals to drive such devices at speeds up to 1 Gbps.

Engineers working with serial data stream architectures (commonly used in digital communications buses and disk drive amplifiers) need to stress their devices with impairments, particularly jitter and timing violations. Advanced signal generators save the engineer untold hours of calculation by providing efficient built-in jitter editing and generation tools. These instruments can shift critical signal edges as little as 200 fs (0.2 ps).