High-speed digital-to-analog conversion by integration of a variable-rate pulse train

The conversion of a binary number into an analog voltage, current, or shaft position is a basic problem which must be solved in a wide variety of digital control systems. Because of this widespread need, many techniques have been devised, each with individual limitations and shortcomings. A conversion of digits-to-shaft position can be made by comparing the digital representation from a code wheel with the binary number to be converted. The shaft attached to the code wheel is made to rotate until the reading obtained from it agrees with the number to be converted. The code wheel reading is subtracted from the number to be converted, and the difference quantity generates an analog error voltage which controls a servo connected to the shaft of the code wheel. A digit-to-voltage or current conversion may be accomplished by the method illustrated in Fig. 1. The principle is that of assigning appropriate analog weights to each binary digit. The individual analog quantities are essentially voltages or currents which are proportional to the significance of the respective digits in the numbering system. The conversion is effected by summing up the analog equivalent for each digit containing a binary one in the number being converted. In Fig. 1, the conversion is to an analog current, I₀, proportional to the binary number, represented by the switch settings. The binary number represented by the switch setting in this figure corresponds to 000101. It will be noted that the current produced is 5/64 E/R. Another system which should be mentioned, because at first glance it appears similar to the one to be described, is the Shannon-Rack converter. In this system, the binary representation of the number to be converted is sampled serially, starting with the lowest-order digit and proceeding to the highest. As the digits are shifted out of the register containing the number, a one digit will cause a pulse to be generated into a shunt RC circuit. The time constant of the RC network is such that in a digit pulse period the charge on the capacitor will decay to one-half of its initial value. Therefore, after n pulse periods, the charge remaining due to a one occurring at the first pulse time is proportional to 1/2^n-1. The exponential decay provides a convenient method of obtaining the appropriate binary weight. The voltage across the capacitor, one pulse period after the most significant digit has been shifted out, will equal a voltage proportional to the digital number which was contained in the register. A simplified circuit of this system is shown in Fig. 2. The circuit consists of a constant current source, a switch, a resistor, and a capacitor. The switch is controlled by the output of the register containing the number being converted. It is closed for a given period of time as each one is shifted from the register.