domingo, 14 de febrero de 2010

Amplificadores operacionales como comparador para DAC y ADC, 9na Publicacion (Gerald Soto, EES)

Digital computers and microcomputers are digital information processing systems, but information quite often is in analog form (e.g. speech, music and video signals).

To process this information with digital techniques it must first be converted from its analog to digital form. The device that does this is knows as an analog-to-digital converted (ADC or A/D converter).

In addition, since many types of electronic equipment are inherently analog devices (e.g., stereo amplifiers, radio and television receivers), there are many occasions when it is necessary to transform digital information to analog information. This is accomplished by using a device know as a digital-to-analog converter (DAC or D/A converter).

The Operational Amplifier

The operational amplifier, referred to as the op-amp for short, is a linear amplifier that has two inputs (inverting and noninverting) and one output. The op-amp has a very high voltage gain and a very high input impedance, as well as a very low output impedance. The op-amp symbol is shown in Figure 5-1, note that the noninverting input is indicated by '-' and the inverting input by '+'.
fig5-1.gif (2851 bytes)

Figure 5-1 Operational Amplifier
When used as an inverting amplifier, as indicated in Figure 5-2, the feedback resister and the input resister control the voltage gain as indicated in Equation 5-1.
fig5-2.gif (3650 bytes)
Figure 5-2 Op-amp as an inverting amplifier
Equation 5-1

This is known as the closed-loop voltage gain because it refers to the feedback from output to input provided by RF.
In the inverting amplifier configuration, the inverting input is approximately at ground potential (0 V). This is due to the inherent op-amp properties, the feedback mechanism and the connection of the noninverting input to the ground.
When the op-amp is used as a comparator, as shown in Figure 5-3, two voltages (VIN1 and VIN2) are applied to its inputs. When these voltages differ by a very small amount, the op-amp is driven into one of its saturated states, depending on which input voltage is greater.
fig5-3.gif (2228 bytes)
Figure 5-3 Op-amp as a comparator


Sampling is the technique of controlling the time at which information will be converted. Both digital and analog signals may be sampled. In particular, lets examine the case where analog signals are sampled. Figure 5-4 shows the voltage follower sample-and-hold circuit.
fig5-4.gif (2985 bytes)
Figure 5-4 Sample-and-hold circuit
The input signal charges the capacitor (C) and through the resistor (R) when the switch is in the "sampling" position. At the desired instant, the switch is changed to the "hold" position isolating the input signal and leaving the input potential, at that instant, across the capacitor at the amplifier input. Ideally, this voltage would be maintained (held) indefinitely at the noninverting (+) input and consequently at the output. However, finite currents at the amplifier inputs or through the sampling switch cause the voltage across C to change with time. An ideal sample-and-hold circuit would have infinitesimal sample and hold times.
Digital-to-Analog Converters
A simple 3-bit D/A converter is illustrated in Figure 5-5. The input to the circuit is the 3-bit binary number A2A1A0, where each of the variables takes the value of 0V or 1V and A2 represents the MSB.
fig5-5.gif (4085 bytes)

Figure 5-5 Three-bit DAC circuit
Let us take a look at the operation of this circuit:

Note that V=IR, where V = voltage, I = current and R = resistance.

  1. Summing the currents at the inverting input of the op-amp on the left yields

  1. At the second stage of the op-amp the voltage gain is given by v2/v= -R2/R1 and by the substituting for v1 from above we get:

  1. Lets consider the case where R1=RF and R2=R the
Under the circumstances when A2A1A0=000, v= 0. Similarly when A2A1A0=111, v= 7.

Performance Characteristics for D/A converters

The performance characteristics for D/A converters include resolution, accuracy and linearity just to name a few.

  1. The resolution is the reciprocal of the number of discrete steps in the D/A output.

  2. The accuracy is a comparison of the actual output of a D/A converter with the expected output.
  3. Linearity is a deviation from the ideal straight-line output of a D/A converter

There are a number of approaches that can be taken for the construction of an analog-to-digital converter. One technique incorporates a DAC as shown in Figure 5-6. For this device, an analog input voltage is applied to one if the inputs of a voltage comparator.
fig5-6.gif (5363 bytes)

Figure 5-6 Counting ADC
Circuit Operation

As long as the DAC output is applied to the other input of the comparator, and as long as the DAC output voltage is less than the analog input voltage, the comparator output is HIGH (logical 1) and the clock pulse is applied to the binary counter.
When the count of the binary counter is high enough such that the DAC output value exceeds that of the analog input, the comparator output is LOW (logical 0). Now, additional clock pulses are not applied to the counter and it stops counting.
The output of the counter, , forms the resulting n-bit digital output.

The counter is then reset to zero (provision for this is not shown in the figure).

It is assumed that the analog input remained constant during the interval required for the counter to reach its final state. In practice a sample-and-hold circuit is required to ensure this is indeed the case.

This type of converter is also know as the Stairstep-Ramp A/C converter

Question: What disadvantages are there with the counting ADC?
Note: Binary counter used in the ADC converter is a binary up counter. If this counter is replaced with a binary up/down counter then the converter is referred to as a tracking ADC converter. When a binary '1' is input to the counter it counts up. The reverse occurs when binary '0' is input.
Question: Can you determine the operation of the tracking ADC converter?
Flash converter ADC
The flash (simultaneous) A/D converter uses several voltage comparators that compare reference voltages with the analog input voltage. Figure 5-7 shows a two-bit parallel-comparator ADC converter. Note that no comparator is needed for the all-0s condition. In general a 2n-1comparators are needed for conversion to a n-bit binary code. The advantage of this circuit over the one illustrated in Figure 5-6 is that it provides a faster method of analog-to-digital conversion.
fig5-7.gif (8147 bytes)

Figure 5-7 Flash ADC
Circuit operation
When the analog voltage exceeds the reference voltage for a given comparator, a HIGH is generated. The output of each comparator is connected to the input of the encoder which is sampled by a pulse on the enable input. The output from the encoder is the digital value of the analog input.
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