Analog-to-Digital and Digital-to-Analog Conversion

Analog input cards have only ___________channel(s)

1

In what two ways is the resolution of an ADC or DAD stated?

1. The number of input or output bits the converted uses 2. The voltage size of the LSB, which is one count.

The resolution of the converter is referred to in two ways:

1. The resolution is the number of input or output bits it has 2. Resolution is also the voltage size of the least significant bit (LSB) or one count of the converter's output.

Most Analog output modules have _____channels?

8-16

DAC Rise Time

A DAC's rise time or settling time is the time from a change in the input count until the output signal is generated and remains within specified output tolerance range.

Digital Device

A digital device uses circuitry that represents information as a digital signal, such as two different voltages

Digital Signal

A digital signal represents information as a set of discrete (separate and distinct) numerical values.

Analog Input Card

A distributed control system (DCS) and a programmable logic controller (PLC) have analog input modules that typically use 16-bit ADCs. The programming of an analog input channel for an application requires that the digital output is setup to represent the process variable accurately. This requires determining a digital number that represents the LRV and URV.

ADC Resolution

A four-bit ADC has 16 possible output codes from binary 0000 to binary 1111. An eight-bit ADC has 256 possible output codes from binary 00000000 to binary 11111111. The greater the number of bits is, the greater the binary code range is, and the better the resolution is. The voltage resolution depends on the voltage reference and the number of bits the converter uses

Multiplexer (MUX)

A multiplexer (MUX) is a device that allows selection of one input from many connected channels. The MUX is often an integral part of a data acquisition system. In electronics, a multiplexer (or mux) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line.

Round off

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding. This is a form of quantization error.

Digital Valve Positioners

A valve positioner/controller moves its valve stem to the position specified by the control signal. The control signal to a digital valve positioner can be a digital signal or an analog signal, but it is typically analog, with its faster update speed.

The difference between actual and theoretical analog input voltages required to produce a given output code?

Absolute Accuracy

Nyquist Sampling Theorem

According to the Nyquist sampling theorem, the absolute minimum sample rate necessary to capture an analog waveform is TWICE the waveform's frequency. For an analog input with a frequency of 10 Hz, for example, the ADC sample rate needs to be at least 20 Hz.

Aliasing

Aliasing is a sampling effect that changes the input frequency to another frequency as a result of the conversion process.

Analog Device

An analog device uses circuitry that represents information as an analog signal, such as a electric current.

Analog Signal

An analog signal represents a variable that can be continuously observed and represented.

How does an anti-aliasing filter avoid aliasing effect?

An anti-aliasing filter attenuates the higher frequencies

Anti-aliasing filter

An anti-aliasing filter smooths out the input waveform by preventing any analog signals with frequencies beyond the Nyquist limit to pass through the ADC.

Analog Devices

Analog electronic devices are instantaneous. Any change in the flow rate results in an instantaneous proportional change in Tx output. Similarly, a change in the output of an analog controller is instantaneously received by the current-to-pressure transducer.

The highest frequency that the AI card can read?

Bandwidth

Bandwidth

Bandwidth and roll off frequency indicate the highest frequency that the AI card can read. ADC have filtering circuits to prevent aliasing during sampling.

Resolution

Both DACs and ADCs relate analog voltage signal to binary data. ADC is an electronic device that provides an output that digitally represents the input voltage. DAC is a electronic device that provides an output voltage proportional to its binary data input.

Digital Devices

Computers are found in all levels of instrumentation: - smart tx have a microprocessor controlling their operation - digital valve positioners/controllers have a microprocessor controlling their operation - controllers have evolved to complex control systems that are computers networked together

The time required to do an analog to digital conversion?

Conversion Time

These devices use analog-to-digital or digital-to-analog converters:

Digital transmitter, digital valve positioners, digital controllers, data acquisition cards.

Digital Transmitters

Digital transmitters contain ADCs and a DAC. These transmitter have a sensor that converts the PV to an analog voltage signal. The ADC changes the analog voltage to a digital signal (number).

The Range of analog values

Full-scale range

HART

Highway addressable remote transducer protocol. The HART signal allows for communication of digital data such as process variable, transmitter internal diagnostic information, transmitter internal maintenance information and other measured process data to the control system

ADC Applications

In process control, the resolution of the converter needs to be stated in terms of the process variable. To calculate the resolution in terms of the process variable from the bit resolution, YOU MUST KNOW THE VOLTAGE RANGE OF THE CONVERTER AND HOW THE PROCESS VARIABLE RELATES. THESE ARE APPLICATION DEPENDENT.

the voltage or current range the AI can measure?

Input Range

Linear interpolation

Linear interpolation is used after this to determine the PV value from the ADC output.

Truncated

Not rounded

ADC Quantization Error

Quantization noise is a model of quantization error introduced by quantization in the analog-to-digital conversion (ADC) in telecommunication systems and signal processing. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is non-linear and signal-dependent.

expressed in % , ppm, or factions of 1 LSB, this is the deviation of the analog value at any code from it's theoretical value?

Relative accuracy

# of bits produced. The smallest voltage increment corresponding to a change in LSB

Resolution

The voltage size of the LSB?

Resolution

Resolution Specs

Resolution is based on the module hardware and the selected range.

Scaling

Scaling an analog input channel for a specific PV sets up this relationship.

the amount of time the microprocessor can read and input to each channel?

Scan time

Scan Time

Scan time is the length of time it takes for the module's microprocessor to read and record the input value for each channel. A module scan time of 25 ms indicates that each channel is sampled 40 times every second.

The analog change corresponding to a change in LSB?

Step size

Digital Controllers

The digital circuitry performs the required control function and sends a digital signal to the analog output (AO) block. The AO block converts the digital signal to an analog control signal for transmission to the FCE or passes on the digital control signal to the FCE if the FCE can accept a digital signal.

Flow Rate Characteristics

The flow rate is analog; it can take an infinite number of values and it continuously varies. The output signal of the flow transmitter is a digital signal. For every flow rate, a unique transmitter digital output does not exist.

Data Acquisition Cards (reference voltages)

The input modules are data acquisition cards that gather data from the process variable to pass on to the control system. Output modules take information from the control system and distribute it to multiple FCEs.

Explain why it may not be possible to get an exact output of 4mA from a DAC?

The output steps from one value to another based on its resolution, so it may not be possible to get an exact output value if the value falls between two steps

Analog Variables

The positioning of the stem of a control valve or the speed of a variable speed motor are also analog variables; however, most instruments (tx, controllers and valve positioners) are now digital devices.

Quantization Error

The quantization error of an ADC cannot be calibrated out. This error occurs due to the fact that each binary code represents a range of voltages rather than one precise voltage value. The converter's resolution and whether is truncates or rounds off sets the value of the quantization error.

DAC Resolution

The resolution of a DAC is stated in the same terms as an ADC; as a number of bits or as the size of its voltage output steps.

Anti-aliasing filter

To avoid aliasing, a low-pass filter circuit called an anti-aliasing filter is used before the ADC input. It operates by attenuating the higher frequencies. For example, if the sampling frequency is 10 Hz, the anti-aliasing filter should remove input frequency greater than 5 Hz (half the sampling size).

PLC and DCS systems have a similar modular design?

True

Non-contact stem travel feedback sensor

Valve stem position is typically detected by a non contact stem travel feedback sensor, which produces an analog output signal. This signal is converted to a digital signal by the sensor's ADC.

When calibrating the ADC of an AI card, which two factors are determined?

Zero offset and gain

An analog signal represents a variable that can be _______________ observed and represented?

continuously

A digital signal represents information as a set of __________ ____________ values

discrete numerical