| Perhaps the most important consideration of an 
    ADC is its resolution. Resolution is the number of binary bits output 
    by the converter. Because ADC circuits take in an analog signal, which is 
    continuously variable, and resolve it into one of many discrete steps, it is 
    important to know how many of these steps there are in total.
    For example, an ADC with a 10-bit output can represent up to 1024 (210) 
    unique conditions of signal measurement. Over the range of measurement from 
    0% to 100%, there will be exactly 1024 unique binary numbers output by the 
    converter (from 0000000000 to 1111111111, inclusive). An 11-bit ADC will 
    have twice as many states to its output (2048, or 211), 
    representing twice as many unique conditions of signal measurement between 
    0% and 100%.  Resolution is very important in data acquisition systems (circuits 
    designed to interpret and record physical measurements in electronic form). 
    Suppose we were measuring the height of water in a 40-foot tall storage tank 
    using an instrument with a 10-bit ADC. 0 feet of water in the tank 
    corresponds to 0% of measurement, while 40 feet of water in the tank 
    corresponds to 100% of measurement. Because the ADC is fixed at 10 bits of 
    binary data output, it will interpret any given tank level as one out of 
    1024 possible states. To determine how much physical water level will be 
    represented in each step of the ADC, we need to divide the 40 feet of 
    measurement span by the number of steps in the 0-to-1024 range of 
    possibilities, which is 1023 (one less than 1024). Doing this, we obtain a 
    figure of 0.039101 feet per step. This equates to 0.46921 inches per step, a 
    little less than half an inch of water level represented for every binary 
    count of the ADC.  
      This step value of 0.039101 feet (0.46921 inches) represents the smallest 
    amount of tank level change detectable by the instrument. Admittedly, this 
    is a small amount, less than 0.1% of the overall measurement span of 40 
    feet. However, for some applications it may not be fine enough. Suppose we 
    needed this instrument to be able to indicate tank level changes down to 
    one-tenth of an inch. In order to achieve this degree of resolution and 
    still maintain a measurement span of 40 feet, we would need an instrument 
    with more than ten ADC bits.  To determine how many ADC bits are necessary, we need to first determine 
    how many 1/10 inch steps there are in 40 feet. The answer to this is 
    40/(0.1/12), or 4800 1/10 inch steps in 40 feet. Thus, we need enough bits 
    to provide at least 4800 discrete steps in a binary counting sequence. 10 
    bits gave us 1023 steps, and we knew this by calculating 2 to the power of 
    10 (210 = 1024) and then subtracting one. Following the same 
    mathematical procedure, 211-1 = 2047, 212-1 = 4095, 
    and 213-1 = 8191. 12 bits falls shy of the amount needed for 4800 
    steps, while 13 bits is more than enough. Therefore, we need an instrument 
    with at least 13 bits of resolution.  Another important consideration of ADC circuitry is its sample 
    frequency, or conversion rate. This is simply the speed at which 
    the converter outputs a new binary number. Like resolution, this 
    consideration is linked to the specific application of the ADC. If the 
    converter is being used to measure slow-changing signals such as level in a 
    water storage tank, it could probably have a very slow sample frequency and 
    still perform adequately. Conversely, if it is being used to digitize an 
    audio frequency signal cycling at several thousand times per second, the 
    converter needs to be considerably faster.  Consider the following illustration of ADC conversion rate versus signal 
    type, typical of a successive-approximation ADC with regular sample 
    intervals:  
      Here, for this slow-changing signal, the sample rate is more than 
    adequate to capture its general trend. But consider this example with 
    the same sample time:  
      When the sample period is too long (too slow), substantial details of the 
    analog signal will be missed. Notice how, especially in the latter portions 
    of the analog signal, the digital output utterly fails to reproduce the true 
    shape. Even in the first section of the analog waveform, the digital 
    reproduction deviates substantially from the true shape of the wave.  It is imperative that an ADC's sample time is fast enough to capture 
    essential changes in the analog waveform. In data acquisition terminology, 
    the highest-frequency waveform that an ADC can theoretically capture is the 
    so-called Nyquist frequency, equal to one-half of the ADC's sample 
    frequency. Therefore, if an ADC circuit has a sample frequency of 5000 Hz, 
    the highest-frequency waveform it can successfully resolve will be the 
    Nyquist frequency of 2500 Hz.  If an ADC is subjected to an analog input signal whose frequency exceeds 
    the Nyquist frequency for that ADC, the converter will output a digitized 
    signal of falsely low frequency. This phenomenon is known as aliasing. 
    Observe the following illustration to see how aliasing occurs:  
      Note how the period of the output waveform is much longer (slower) than 
    that of the input waveform, and how the two waveform shapes aren't even 
    similar:  
      It should be understood that the Nyquist frequency is an absolute 
    maximum frequency limit for an ADC, and does not represent the highest 
    practical frequency measurable. To be safe, one shouldn't expect an ADC 
    to successfully resolve any frequency greater than one-fifth to one-tenth of 
    its sample frequency.  A practical means of preventing aliasing is to place a low-pass filter 
    before the input of the ADC, to block any signal frequencies greater than 
    the practical limit. This way, the ADC circuitry will be prevented from 
    seeing any excessive frequencies and thus will not try to digitize them. It 
    is generally considered better that such frequencies go unconverted than to 
    have them be "aliased" and appear in the output as false signals.  Yet another measure of ADC performance is something called step 
    recovery. This is a measure of how quickly an ADC changes its output to 
    match a large, sudden change in the analog input. In some converter 
    technologies especially, step recovery is a serious limitation. One example 
    is the tracking converter, which has a typically fast update period but a 
    disproportionately slow step recovery.  An ideal ADC has a great many bits for very fine resolution, samples at 
    lightning-fast speeds, and recovers from steps instantly. It also, 
    unfortunately, doesn't exist in the real world. Of course, any of these 
    traits may be improved through additional circuit complexity, either in 
    terms of increased component count and/or special circuit designs made to 
    run at higher clock speeds. Different ADC technologies, though, have 
    different strengths. Here is a summary of them ranked from best to worst:
     Resolution/complexity ratio:  Single-slope integrating, dual-slope integrating, counter, tracking, 
    successive approximation, flash.  Speed:  Flash, tracking, successive approximation, single-slope integrating & 
    counter, dual-slope integrating.  Step recovery: Flash, successive-approximation, single-slope integrating & counter, 
    dual-slope integrating, tracking.  Please bear in mind that the rankings of these different ADC technologies 
    depend on other factors. For instance, how an ADC rates on step recovery 
    depends on the nature of the step change. A tracking ADC is equally slow to 
    respond to all step changes, whereas a single-slope or counter ADC will 
    register a high-to-low step change quicker than a low-to-high step change. 
    Successive-approximation ADCs are almost equally fast at resolving any 
    analog signal, but a tracking ADC will consistently beat a 
    successive-approximation ADC if the signal is changing slower than one 
    resolution step per clock pulse. I ranked integrating converters as having a 
    greater resolution/complexity ratio than counter converters, but this 
    assumes that precision analog integrator circuits are less complex to design 
    and manufacture than precision DACs required within counter-based 
    converters. Others may not agree with this assumption.  |