The other flavor is . For example, it is easy to designan op amp circuit to simultaneously handle frequencies between 0.01 Hz and100 kHz (seven decades). When this is tried with a digital system, thecomputer becomes swamped with data. For instance, sampling at 200 kHz, ittakes 20 million points to capture one complete cycle at 0.01 Hz. You may havenoticed that the frequency response of digital filters is almost always plotted ona frequency scale, while analog filters are usually displayed with a frequency. This is because digital filters need
The second inherent advantage of analog over digital is . Thiscomes in two flavors. A is the ratio between thelargest signal that can be passed through a system, and the inherent noise of thesystem. For instance, a 12 bit ADC has a saturation level of 4095, and an rmsquantization noise of 0.29 digital numbers, for a dynamic range of about 14000. In comparison, a standard op amp has a saturation voltage of about 20 volts andan internal noise of about 2 microvolts, for a dynamic range of about . Just as before, a simple op amp devastates the digital system.
In spite of this beating, there are still many applications where analog filtersshould, or must, be used. This is not related to the actual performance of thefilter (i.e., what goes in and what comes out), but to the general advantages thatanalog circuits have over digital techniques. The first advantage is : digitalis slow; analog is fast. For example, a personal computer can only filter data atabout 10,000 samples per second, using FFT convolution. Even simple op ampscan operate at 100 kHz to 1 MHz, 10 to 100 times as fast as the digital system!
Sinceautomated synthesis already exists for digital circuits and is part of the digitalcircuit design flow, this work demonstrates the feasibility of ADC synthesis withlittle or no modification to presently existing software tools.
The step response of the two filters is shown in (e) and (f). The digital filter'sstep response is symmetrical between the lower and upper portions of the step,i.e., it has a linear phase. The analog filter's step response is symmetrical,i.e., it has a nonlinear phase. One more point for the digital filter. Lastly, theanalog filter overshoots about 20% on one side of the step. The digital filterovershoots about 10%, but on both sides of the step. Since both are bad, nopoints are awarded.
Let's compare the two filters blow-by-blow. As shown in (a) and (b), the analogfilter has a 6% ripple in the passband, while the digital filter is perfectly flat(within 0.02%). The analog designer might argue that the ripple can be in the design; however, this misses the point. The flatness achievable withanalog filters is limited by the accuracy of their resistors and capacitors. Evenif a Butterworth response is designed (i.e., 0% ripple), filters of this complexitywill have a residue ripple of, perhaps, 1%. On the other hand, the flatness ofdigital filters is primarily limited by round-off error, making them oftimes flatter than their analog counterparts. Score one point for the digital filter.
The goal will be to provide a low-pass filter at 1 kHz. Fighting for the analogside is a six pole Chebyshev filter with 0.5 dB (6%) ripple. As described inChapter 3, this can be constructed with 3 op amps, 12 resistors, and 6capacitors. In the digital corner, the windowed-sinc is warming up and readyto fight. The analog signal is digitized at a 10 kHz sampling rate, making thecutoff frequency 0.1 on the digital frequency scale. The length of thewindowed-sinc will be chosen to be 129 points, providing the same 90% to 10%roll-off as the analog filter. Fair is fair. Figure 21-1 shows the frequency andstep responses for these two filters.
Next, look at the frequency response on a log scale, as shown in (c) and (d). Again, the digital filter is clearly the victor in both and . Even if the analog performance is improved by adding additionalstages, it still can't compare to the digital filter. For instance, imagine that youneed to improve these two parameters by a factor of 100. This can be done withsimple modifications to the windowed-sinc, but is virtually impossible for theanalog circuit. Score two more for the digital filter.