desired, e.g., one part is 2^16, the maximum frequency that can be counted is only 10 Hz. However, it should be noted that a 10-bit T(digital-to-analog) is not capable of such a fine resolution. For an error of one part in 1024(delta = 2^6), the error is: 2^6/2^16 = 1/2^10 ~ 10^-3 or 0.1%. This provides for a maximum frequency of ~666 Hz. Increasing the allowable error to one part in 2^7 (~0.8%) yields a frequency limit of ~5 KHz. By increasing the frequency to 10,000 Hz, the error increases to (10^4)*(3/2)/10^6=1.5%. What can be done to further increase performance, considering the values for f and error? As has been indicated previously, the ability to make multiple simultaneous register assignments can significantly improve system performance. In this case, the two transfer operations would be performed as: analog-out <- output <- output + delta. This procedure would halve the processing time and double the frequency.
Another parameter not yet examined is the frequency quantization for a fixed sample time, ts. For a fixed sample time, ts, the frequency formula becomes f = K*delta (where K=1/(2^16*ts)) which shows that the frequency varies linearly with respect to delta. For ts= 1.5 microseconds, the frequency change per unit is: f-change/delta =1/(2^16*1.5*10^-6) 10 Hz. The frequencies possible from this function generator with ts=1.5 microseconds are: 10,20,...,10*delta,...,666KHz (independent of error). Different frequencies may be obtained by varying the sample time, ts.
1. In the above generator the amplitude remains fixed. Suppose the amplitude is to be varied over a range and step size by input parameters. What would the parameters be for such a generator? Design such a generator and analyze its characteristics.
2. In the generator presented above, the error varies with respect to the frequency. Using a programmable clock, design a generator which has a constant maximum error for all frequencies; the maximum error should be set by input parameters. Analyze the characteristics of your design.
3. Figure SG-3 shows the output of a triangle waveform generator. Design a generator with such an output and determine the relationship between delta, Error, f, and f-change/delta. How does the sample time, ts, affect the performance of the generator.
4. Design a waveform generator for the exponential function, et-t. Describe the error as a function of t.
5. Design a waveform generator for sin(t), cos(t) for 0<t<2. Note that sin and cos can be defined in terms of each other by integrating.
EVENTS PER UNIT TIME \EPUT METER
KEYWORDS: Waveform, time base, event, frequency limit
An EPUT meter is about the simplest waveform analyzer that can be constructed. It merely counts pulses (events) within a certain measured time period. A description of the structure of an EPUT meter was given in the introduction of time-based systems. The basis of the time period measurement is a clock which produces pulses at a frequency of 1/ts Hertz as shown in Figure EPUT-la. The clock counts for a variable time to give the basic time unit measurement; that is, it forms the basis for a programmable clock. The time base may be any fraction of a second, but it is usually a multiple or submultiple of ten