Analog to digital conversion technique
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This document discusses analog to digital conversion techniques. It explains that analog signals are continuous while digital signals are discrete. It also describes three main techniques in A/D conversion: sampling, quantization, and encoding. Sampling converts a continuous signal to discrete samples. Quantization maps samples to a smaller set of values, introducing quantization error. Encoding converts quantized values into a binary format.
Analog to digital conversion technique
- 2. A signal is the quantity that carry information and varies with time, space, or any independent variable. It can also be define as the function of two or more variable. Analogue signal is continuous in nature, it differ from digital in which a continuous quantity is represented by a discrete function which can take on only one of the finite number of values.
- 3. Man is by nature an analogue, he can interact and understand only an analogue information. However analogue signal is subjected to noise and distortion which progressively degrade the signal-to-noise ratio. This degradation is impossible to recover, since there is no sure way to distinguish the noise from the signal, amplifying the signal to recover attenuated parts of the signal amplifies the noise as well. To avoid or minimise this scenario, and to take advantage of the great capabilities available for digital data storage,
- 4. processing, and computation, requires the conversion of analog to digital. Hence, analog to digital (A/D) conversion techniques have become extremely important. There are three main technique involved in the conversion of analog signals to digital signals, these are:- • Sampling of the continuous signal • Quantization of the sampled signal, and • Encoding. This can be explained below
- 5. sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal). Sampling of the signal can be achieve with sample and hold circuit which can be described below
- 6. The function of the sample and hold circuit is to sample an analog input signal and hold this value over a certain length of time for subsequent processing. Below is the sampled and hold circuit
- 7. The operation of the sample and hold circuit can be explain in the following steps • During sample mode, the SOP behaves just like a regular op-amp, in which the value of the output follows the value of the input. • During hold mode, the MOS transistors at the output node of the SOP are turned off while they are still operating in saturation, thus preventing any channel charge from flowing into the output of the SOP. • In addition, the SOP is shut off and its output is held at high impedance, allowing the charge on Ch to be preserved throughout the hold mode
- 8. On the other hand, the output buffer of this S/H circuit is always operational during sample and hold mode and is always providing the voltage on Ch to the output of the S/H circuit. The frequency at which the continuous signal is sample is explained by the Nyquist and shannon in first half of 20th century.
- 9. Nyquist sampling theory provide the prescription for the minimal sampling frequency required to avoid aliasing during the reconstruction of the signal. It state that:- The sampling frequency should be at least twice the highest frequency contained in the signal, Or in mathematical terms: fs ≥ 2 fc where fs is the sampling frequency (how often samples are taken per unit of time or space), and fc is the highest frequency contained in the signal. Example if the maximum frequency component of a signal to be sample is 2khz, the from nyquist sampling theory
- 10. This signal should be sampled at a frequency which is equal or grater than 4khz. However if this signal is sample at a frequency below this(nyquist rate), then aliasing will occur. Aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled It also refers to the distortion that results when the signal reconstructed from samples is different from the original continuous signal. However this effect of aliasing can be eliminated by using anti-aliasing filter
- 11. Quantization, is the process of mapping a large set of input values to a (countable) smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by quantization is referred to as quantization error. There are two main method of quantization which involved • Truncation and • Rounding
- 12. Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation Rounding is often done to obtain a value that is easier to report and communicate than the original. The following table illustrated sampled values and it equivalent quantized value using rounding technique. s.no Sampled value of the signal. Quantized value 1 0.45 0.5 2 0.44 0.4 3 0.67 0.7 4 0.64 0.6 5 0.55 0.6
- 13. truncation is the term for limiting the number of digits right of the decimal point by discarding the least significant ones. However the error in this processing is twice than the rounding method, below is the table showing the sampled value ofa signal and it equivalent quantized value s.no Sampled value of signal Quantized value using truncation 1 3.3 3 2 4.2 4 3 5.3 5
- 14. The truncation and the rounding technique are important in analog to digital conversion, but they result to quantization error. However the quantization error can be minimise by increasing the resolution of the conversion.
- 15. 1. The quantized signal is then encoded into a sequence of bits(0 and 1), there are different method for which the quantized signal encoded into a bits sequence which can be explained below
- 17. Below is the diagram showing the encoding format of the above