A digital computer synthesizer (DAC), also known as a direct digital synthesis circuit (DDS), is an electronic device designed to synthesize arbitrary waveforms and frequencies from a single reference frequency supplied by a clock generator . A characteristic feature of the DAC is that the samples of the synthesized signal are calculated digitally, after which they are transmitted to a digital-to-analog converter (DAC), where they are converted to an analog form ( voltage or current ).
This DAC differs from frequency synthesizers based on other principles, for example, PLL .
Content
Principle of Operation
The main functional blocks of the DAC are: phase accumulator, phase-amplitude converter, DAC and low-pass filter . Also, the DAC contains a certain amount of memory , which serves to store the parameters of the synthesized signal, such as frequency , phase , amplitude, shape, etc.
In each clock cycle, the phase accumulator (usually a binary counter) increases its value by the value recorded in the memory cell, the number recorded in which is usually called the phase increment. As a result, the value of the phase accumulator increases in a stepwise-linear fashion with time. Then, the phase value calculated in such a way at each cycle is converted into an amplitude value. In principle, this transformation can be arbitrary and depends on the application. In the case most common in practice, for the synthesis of harmonic oscillations, the sine of the current phase value is calculated. The calculation result is fed to the input of the DAC, the output signal of which is smoothed from the sampling steps by the low-pass filter.
Features
One of the important features of such devices is the high resolution of setting values of reproducible frequencies and their absolute accuracy (believing the master oscillator is ideal). Devices with tuning steps of less than 0.00001 Hz are available, with output frequencies from zero hertz to hundreds of megahertz and a reference frequency of the order of a gigahertz [1] [2] .
The speed (time) of tuning the output frequency from one value to another is very high and stable, and is determined mainly by the duration of the impulse response of the analog recovery filter at the output of the synthesizer; perestroika itself is actually instantaneous. The tuning time is independent of the difference between the start and end frequencies. Some synthesizers of this type include, for example , automatic linear increment or frequency hopping. In this case, the phase increment is not constant, but changes according to a given law.
As a disadvantage, one can note a higher energy consumption compared to PLL solutions due to the large volume of calculations, and a higher level of nonharmonic parasitic components in the spectrum of the synthesized signal.
Practical Implementation
The following C code can serve as a good example of the implementation of the described principle:
#include <math.h>
int next_amp ( int dph )
{
static int phase = 0 ;
int amp ;
phase + = dph ;
amp = 511.5 * sin ( 2 * M_PI * phase / 0x100000000L );
return amp ;
}
Here dph is the phase increment, phase is the current (instantaneous) phase, amp is the current (instantaneous) amplitude of the synthesized harmonic signal. If the next_amp function is called at a clock rate , then its return values will be samples of a sinusoidal signal with a frequency and amplitude 511.5 (despite the fact that the returned values themselves are integer). This amplitude corresponds to the input range of the 10-bit DAC.
Here we also used the periodicity property of the sine function, namely the fact that when the phase accumulator is full , its value changes by 2 32 , and the sine argument - by 2π, which does not affect the result.