DDS is no longer alone and works hand in hand with Matlab to create a simulation business

Direct digital frequency synthesis ( DDS) is a new frequency synthesis method that has developed rapidly in recent years. It has the advantages of fast frequency switching speed, easy to improve frequency resolution, and low hardware requirements. Programmable full digitalization facilitates single-chip integration, helps reduce costs, improves reliability, and is easy to produce. DDS technology performs frequency synthesis based on the concept of phase, stores digital sampling waveform tables, and can generate various forms of signals such as point frequency, linear frequency modulation, ASK, FSK, etc. Linear frequency modulation signals can obtain a large compression ratio, have good distance resolution and radial velocity resolution, and as a commonly used pulse compression signal, it has been widely used in the field of high-resolution radar.

Matlab is a mathematical software launched by MathWorks in the United States in the mid-1980s. Its excellent numerical calculation and data visualization capabilities quickly made it stand out among similar software. Matlab has developed into a powerful large-scale software with multiple disciplines and multiple working platforms. This paper uses Matlab software to establish a simulation model of linear frequency modulation signals in DDS systems , which is of reference significance for understanding linear frequency modulation signals and realizing linear frequency modulation signals in FPGA.

Block Diagram Design of DDS Linear Frequency Modulation Signal Generator

Figure 1 Basic principles of DDS technology

1 Basic Principles of DDS Technology

The basic model is shown in Figure 1, which mainly consists of a clock frequency source fclk, a phase accumulator, a waveform memory (ROM), a digital/analog converter (D/A), and a low-pass filter (LPF). The frequency expression of the output signal waveform is:

(1) In the formula, fclk is the reference clock frequency, ΔΦ is the phase increment, and N is the number of bits in the phase accumulator. As long as N is large enough, DDS can obtain very small frequency intervals. To change the frequency of the output signal of DDS , just change ΔΦ. When the reference clock frequency is given, the frequency of the output signal depends on the frequency control word, the frequency resolution depends on the number of bits in the accumulator, the phase resolution depends on the number of bits in the ROM address, and the amplitude quantization depends on the data word length of the ROM and the number of bits in the D/A converter.

2 Implementation block diagram of linear frequency modulation signal

Figure 2 Schematic diagram of software programming to achieve linear frequency modulation signal

The most common modulation signal of pulse compression radar is linear frequency modulation signal, and matched filter is used to compress the pulse during reception. Its mathematical expression is as follows:

In the formula, fe is the carrier frequency, K=B/T is the frequency modulation slope, so the instantaneous frequency of the signal is.

The corresponding quantitative formula is as follows (this formula is the principle formula implemented in Figure 2):

Where N is the number of bits of the phase accumulator, Kc is the frequency control word, and K is the frequency modulation slope in the above formula.

The DDS principle block diagram shown in FIG1 is used to realize a fixed-frequency sine wave signal. By changing ΔΦ in real time according to formula (3), a linear frequency modulation signal can be generated.

The frequency accumulator outputs an instantaneous frequency that grows strictly linearly. In practice, the output of the phase accumulator is addressed after phase truncation, which introduces a certain phase error. Although this error will affect the linearity of the linear frequency modulation signal, the frequency modulation slope is the second derivative of the phase, and the phase truncation error itself is very small, so the impact on the frequency modulation linearity is even smaller. In the Matlab implementation of this article, the truncation problem is not considered for the time being and can be ignored. 3 Matlab software modeling to realize linear frequency modulation signal

This program is written in accordance with the above software programming to implement the schematic diagram of linear frequency modulation signal. It is written in the form of .m file. The following is the source program for implementation:

%Accumulator implementation of frequency modulation signal

clear all;clc % Clear all variables and clear the screen

M=2^11; %Number of sampling points

a(1:1:M)=0; %The value of the frequency accumulator

b(1:1:M)=0; %The value of the phase accumulator

y(1:1:M)=0; %Output waveform data

K=400; % FM slope

Kc=10; % initial frequency control word

N=10; %Amplitude quantization bit number

L=24; %Number of bits in the phase accumulator

%The following paragraph implements the frequency accumulator

a(1)=0.5*K; % Initial frequency step

for i=2:1:M

a(i)=a(i-1)+K;

end

%The following paragraph implements the phase accumulator

b(1)=Kc+a(1); % initial phase value

for i=2:1:M

b(i)=b(i-1)+(Kc+a(i));

end

%The following section implements the lookup table ROM and performs amplitude quantization

for i=1:1:M

y(i)=floor(2^N*cos(2*pi/(2^L)*b(i)));

end

% Draw the corresponding graph in the following paragraph

figure(1);plot(y);axis([0 M,-2^N-100 2^N+100]);

figure(2);freqz(y)

In the above program, there are many variables, including frequency modulation slope K, frequency control word Kc, amplitude quantization bit N and phase accumulator bit L, etc. Modifying different variable values ​​can obtain different linear frequency modulation signals. The specific implementation should be set according to actual needs. 4 Experimental results

According to the above program, the frequency modulation slope is 400, the frequency control word is 10, the amplitude quantization is 10 bits (matched with the D/A used), and the phase accumulator is 24 bits. The waveform of the linear frequency modulation signal and the corresponding amplitude-frequency response obtained by Matlab simulation are shown in Figures 3 and 4 .

Figure 4 Amplitude-frequency characteristic curve for Figure 3

Conclusion

The principle and method of generating linear frequency modulation signals described in this article have good scalability. Modifying the content of the frequency accumulator can realize various other frequency modulation signals. As linear frequency modulation signals are widely used in high-resolution radar systems, it is of practical significance to correctly understand the principle and method of generating linear frequency modulation signals. In practical applications, dedicated DDS chips or FPGAs are mainly used to realize linear frequency modulation signals (each with its own advantages and disadvantages). This article verifies this solution based on the good programmability of Matlab software. The simulation results prove the feasibility of this solution well, and the expected solution design and demonstration are completed.