Señales analógicas y digitales. En los procesos existen variables continuas, las cuales pertenecen al espacio de estado de los números reales. Es decir, puede tener infinitos valores en su cambio a través del tiempo. Por otra parte, los sistemas digitales, como por ejemplo controladores funcionan con señales discretas. las señales discretas se expresan en números binarios, o señales digitales.
Por razones de limitación física en la construcción de los dispositivos electrónicos, las señales discretas pertenecen al espacio de estado finito. En otras palabras las variables pueden tener sólo un número finito de valores en el transcurrir del tiempo. Además, se define una variable analógica como aquella que puede tener más de dos valores. En este sentido, las señales continuas son analógicas y las señales discretas de más de un bit también los son.
Variables analógicas
Visto desde el controlador, las variables analógica provienen de los transmisores. El transmisor que convierte una variable física (por ejemplo temperatura, presión, nivel, flujo, etc) a variables eléctricas analógicas estandarizadas (por ejemplo la del rango de 4 a 20 mA). La señales transmitidas deben ser procesadas por los controladores. Para ello son convertidas de analógica a digital usando un convertidor analógico digital (CAD) en el módulo de entrada analógica. Si queremos llevar una señal digital a analógica, es posible usando un convertidor digital analógico (CDA) que se encuentra en el módulo de salida analógico.
Existen varios tipos de convertidores analógico digital. Entre ellos se encuentran, contador, continuo, aproximaciones sucesivas, rampa simple, rampa doble, paralelo y delta-sigma entre otros. Hay dos características de los CAD que resaltan sobre las demás, estas son el número de bits y el tiempo de conversión. Los mejores convertidores tienen un número de bits alto y un tiempo de conversión reducido.
Cuantización
El número de bits da paso a otro concepto llamado cuantización. La cuantización no es más que el proceso de representar una señal continua (analógica) con otra discreta.
Por ejemplo se quiere convertir una señal continua que varía entre 0 y 10 VDC (note que entre 0 y 10 VDC hay infinitos valores) con un convertidor de 8 bits (note que con 8 bits sólo se pueden representar 256 (28) números, el cual es finito). El número binario a la salida del convertidor va desde 0 a 255 (28-1), donde, el valor de 0 en la señal digital corresponde a 0 voltios en la señal continua y el valor de 255 en la señal digital corresponde al valor de 10 en la señal continua. El resto de los valores son repartidos desde cero con un incremento de V/(28-1) = 10/255 = 39,215mV, el cual viene a ser la resolución de la señal digital. Mientras mayor es el número de bit, menor es la resolución.
La siguiente tabla muestra los primeros y los últimos valores digitales con sus correspondientes valores continuos.
0 0
1 0,03921569
2 0,07843137
3 0,11764706
…
253 9,92156863
254 9,96078431
255 10
MUESTREO
El tiempo de conversión está relacionado con el tiempo en que se toma la muestra de la señal analógica. En ocasiones se quiere convertir más de una señal analógica con sólo un convertidor, para ello se usan multiplexores. Los multiplexores comparten el uso del CAD entre las señales a convertir.
Cada vez que se hace una conversión de la señal continua se dice que se toma una muestra. El tiempo entre dos muestra se conoce como periodo de muestreo o tiempo de muestreo. Mientras menor es el tiempo de muestreo, la señal digital se parece más a la señal continua, esto es, el error es menor. En la siguiente figura se puede ver una señal analógica convertida a digital con: (a) 8 bits y 100 muestras en un periodo (b), 8 bits 40 muestras (c), 4 bit 100 muestras, (d) 4 bits y 40 muestras y (e) la señal continua.
8 bit, 100 muestras8 bit, 40 muestras
4 bit, 100 muestras
4 bit, 40 muestras
Señal continua
Comparación entre señales analógicas y digitales
Las tarjetas analógicas que se encuentra en el mercado usan convertidores de 12 bits en adelante. Los tiempos de conversión son del orden de lo mili segundos o menos. La siguiente figura muestra la relación entre los diferentes tipos de señales analógicas y digitales.
Señales analógicas y digitales
Señales
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