Phase-locked loop (PLL) is a commonly used frequency and phase tracking algorithm, which is widely used in signal demodulation, AC grid connection and other fields. This article introduces the principle of the all-digital phase-locked loop, and then provides verilog implementation and simulation.
PLL lock principle
The structure of the phase-locked loop is shown in the figure below, which is mainly composed of a phase detector, a loop filter, a voltage-controlled oscillator, etc.
Among them, the phase detector is a multiplier, and the reference signal ui u_i is setui, home signal uo u_ouoBoth are sinusoidal signals
ui ( t ) = cos ( ω 1 t + φ 1 ) u_i(t)=cos(\omega_1 t+\varphi_1)ui(t)=cos ( oh1t+Phi1)
uo ( t ) = cos ( ω 2 t + ϕ 2 ) u_o(t)=cos(\omega_2 t+\varphi_2)uo(t)=cos ( oh2t+Phi2)
According to the product and difference formula, ui u_iuigive uo u_ouoThe product of will contain ω 1 + ω 2 \omega_1+\omega_2oh1+oh2Sum ω 1 − ω 2 \omega_1-\omega_2oh1−oh2Two frequency components, after LF low-pass filtering, only the difference frequency signal of the two remains
uc = cos [ ( ω 1 − ω 2 ) t + ( φ 1 − φ 2 ) ] = cos [ 2 π ( f 1 − f 2 ) t + ( φ 1 − φ 2 ) ] \begin{aligned} u_c&=cos[(\omega_1-\omega_2)t+(\varphi_1-\varphi_2)]\\ &=cos[2\pi(f_1 -f_2)t+(\varphi_1-\varphi_2)] \end{aligned}uc=cos [( oh1−oh2)t+( f1−Phi2)]=cos[2π(f1−f2)t+( f1−Phi2)]
使用 f 2 = f 0 + K 0 u c f_2=f_0+K_0 u_c f2=f0+K0ucPhase locking can be accomplished by controlling the frequency of the voltage-controlled oscillator (digital generally generated by DDS technology).
Suppose the input signal is relative to the reference frequency f 0 f_0f0existΔ f \Delta fΔ f frequency deviation, then the two signals will have a fixed phase deviationΔ φ \Delta \varphiΔ φ , the following relations
Δ f = K 0 cos ( Δ φ ) \Delta f=K_0cos(\Delta \varphi)f _=K0cos ( Δ φ ) Of course, we should also pay attention to the Δ φ \Delta \varphi
hereThe sign of Δφ cannot be determined.
verilog implementation
The main program of the PLL module is as follows
/*
* file : ADPLL.v
* author : 今朝无言
* lab : WHU-EIS-LMSWE
* date : 2023-08-03
* version : v1.0
* description : 锁相环
* Copyright © 2023 WHU-EIS-LMSWE, All Rights Reserved.
*/
module ADPLL(
input clk,
input rst_n,
input signed [15:0] A, //参考信号
input signed [15:0] B, //本地信号
output signed [15:0] df //频偏
);
parameter CLK_FREQ = 1_000_000; //采样频率
reg signed [15:0] df = 16'd0;
//-----------------------multi---------------------------------
reg signed [31:0] multi = 32'd0;
always @(posedge clk) begin
if(~rst_n) begin
multi <= 32'd0;
end
else begin
multi <= A*B;
end
end
//------------------------FIR---------------------------------
wire signed [15:0] multi_filt [1:3];
localparam FIR_N = 20; //FIR阶数
wire [16*(FIR_N+1)-1:0] FIR_params;
FIR_params_0d1 FIR_params_inst(
.params (FIR_params)
);
wire clk_div10;
wire clk_div100;
clkdiv #(.N(10)) clkdiv10(
.clk_in (clk),
.clk_out (clk_div10)
);
clkdiv #(.N(100)) clkdiv100(
.clk_in (clk),
.clk_out (clk_div100)
);
//低通滤波 多级低通滤波,中间穿插下采样
FIR_filter #(.N(FIR_N + 1))
FIR_filter_inst1(
.clk (clk),
.rst_n (rst_n),
.filter_params (FIR_params),
.data_in (multi[31:16]),
.data_out (multi_filt[1])
);
//低通滤波
FIR_filter #(.N(FIR_N + 1))
FIR_filter_inst2(
.clk (clk_div10),
.rst_n (rst_n),
.filter_params (FIR_params),
.data_in (multi_filt[1]),
.data_out (multi_filt[2])
);
//低通滤波
FIR_filter #(.N(FIR_N + 1))
FIR_filter_inst3(
.clk (clk_div100),
.rst_n (rst_n),
.filter_params (FIR_params),
.data_in (multi_filt[2]),
.data_out (multi_filt[3])
);
//---------------------control---------------------------------
always @(posedge clk_div100) begin
df <= multi_filt[3]; // df=K*multi_filt,此处省略鉴相灵敏度K,外部请自行设置合理的K值s
end
endmodule
The low-pass filter and its parameter code are as follows
/*
* file : FIR_filter.v
* author : 今朝无言
* lab : WHU-EIS-LMSWE
* date : 2023-07-03
* version : v1.0
* description : FIR 滤波器
*/
module FIR_filter(
input clk,
input rst_n,
input [16*N-1:0] filter_params,
input signed [15:0] data_in,
output reg signed [15:0] data_out
);
parameter N = 32; //滤波器参数个数
parameter div_N = 16; //sum结果除 2^div_N,作为 filter 的输出
//FIR 滤波器参数
reg signed [15:0] b[0:N-1];
integer m;
always @(*) begin
for(m=0; m<N; m=m+1) begin
b[m] <= filter_params[(m << 4) +: 16];
end
end
reg signed [15:0] shift_reg[0:N-1];
integer i;
always @(posedge clk) begin
if(~rst_n) begin
for(i=N-1; i>=0; i=i-1) begin
shift_reg[i] <= 16'd0;
end
end
else begin
for(i=N-1; i>0; i=i-1) begin
shift_reg[i] <= shift_reg[i-1];
end
shift_reg[0] <= data_in;
end
end
reg signed [31:0] multi[0:N-1];
integer j;
always @(*) begin
for(j=0; j<N; j=j+1) begin
multi[j] <= shift_reg[j] * b[j];
//这里可以考虑使用multiplier IP核,使用LUT搭建(而这里直接乘使用的是DSP资源,一般的FPGA芯片只有几百个)
end
end
reg signed [47:0] sum;
integer k;
always @(*) begin
sum = 0;
for(k=0; k<N; k=k+1) begin
sum = sum + multi[k];
end
end
always @(posedge clk) begin
data_out <= sum[47-div_N : 32-div_N];
end
endmodule
/*
* file : FIR_params.v
* author : 今朝无言
* lab : WHU-EIS-LMSWE
* date : 2023-08-04
* version : v1.0
* description : FIR 滤波器 lowpass N=20 fc=0.1 fs
*/
module FIR_params_0d1(
output [335:0] params
);
assign params[15:0] = 16'h0000;
assign params[31:16] = 16'h0057;
assign params[47:32] = 16'h0131;
assign params[63:48] = 16'h0302;
assign params[79:64] = 16'h0616;
assign params[95:80] = 16'h0A6D;
assign params[111:96] = 16'h0FA8;
assign params[127:112] = 16'h1518;
assign params[143:128] = 16'h19E1;
assign params[159:144] = 16'h1D28;
assign params[175:160] = 16'h1E53;
assign params[191:176] = 16'h1D28;
assign params[207:192] = 16'h19E1;
assign params[223:208] = 16'h1518;
assign params[239:224] = 16'h0FA8;
assign params[255:240] = 16'h0A6D;
assign params[271:256] = 16'h0616;
assign params[287:272] = 16'h0302;
assign params[303:288] = 16'h0131;
assign params[319:304] = 16'h0057;
assign params[335:320] = 16'h0000;
endmodule
For this part of the FIR filter, please refer to my previous blog post.
simulation
The simulation test code is as follows
`timescale 100ns/1ns
module PLL_tb();
reg clk_1M = 1'b1;
always #5 begin
clk_1M <= ~clk_1M;
end
reg rst_n = 1'b1;
//---------------------参考信号A-------------------------------
wire [15:0] A_out_tmp;
wire signed [15:0] A_out; //参考信号
localparam f0 = 24'd10_000;
localparam df = -24'd9; //频率偏差
DDS #(
.Freq(1_000_000)
)
DDS_inst1(
.clk (clk_1M),
.rst_n (rst_n),
.fout (f0+df),
.phase0 (16'd0),
.sin_out (A_out_tmp)
);
assign A_out = A_out_tmp - 16'd32768;
//---------------------本地信号B-------------------------------
wire [15:0] B_out_tmp;
wire signed [15:0] B_out;
wire signed [23:0] df2; //控制本地信号的频偏
DDS #(
.Freq (1_000_000)
)
DDS_inst2(
.clk (clk_1M),
.rst_n (rst_n),
.fout (f0+df2),
.phase0 (16'd0),
.sin_out (B_out_tmp)
);
assign B_out = B_out_tmp - 16'd32768;
//-----------------------PLL---------------------------------
wire signed [15:0] df_PLL;
ADPLL #(
.Freq (1_000_000)
)
PLL_inst(
.clk (clk_1M),
.rst_n (rst_n),
.A (A_out), //参考信号
.B (B_out), //本地信号
.df (df_PLL) //频偏
);
assign df2 = df_PLL/64;
//-----------------------tb---------------------------------
initial begin
rst_n <= 1'b0;
#5000;
rst_n <= 1'b1;
#100;
#1000000;
$stop;
end
endmodule
The DDS code is as follows
/*
* file : DDS.v
* author : 今朝无言
* Lab : WHU-EIS-LMSWE
* date : 2023-05-17
* version : v1.0
* description : 根据给定频率输出正弦信号
* Copyright © 2023 WHU-EIS-LMSWE, All Rights Reserved.
*/
module DDS(
input clk,
input rst_n,
input [23:0] fout, //输出正弦波的频率 1k-10M 要24位
input [15:0] phase0, //初相
output [15:0] sin_out
);
parameter Freq = 100_000_000; //clk频率,Hz
//-----------------相位累加器-----------------------
reg [47:0] int_f_16 = 48'd0; //相位累加器,x-16定点数
wire [55:0] dphi_16; //相位步进
//dphi*Freq=fout*T, T=65536
assign dphi_16 = (fout << 32)/Freq;
always @(posedge clk or negedge rst_n) begin
if(~rst_n) begin
int_f_16 <= 48'd0;
end
else begin
int_f_16 <= int_f_16 + dphi_16;
end
end
//-----------------正弦查找表-----------------------
wire [15:0] phase;
sin_gen sin_gen_inst(
.clk (clk),
.phase (phase), //相位
.sin_out (sin_out)
);
assign phase = phase0 + (int_f_16 >> 16);
endmodule
The corresponding sine lookup table is as follows (this module uses linear interpolation method, which reduces the quantization error by two orders of magnitude with only a small increase in resource consumption; this part can also be found in my previous blog post)
/*
* file : sin_gen.v
* author : 今朝无言
* Lab : WHU-EIS-LMSWE
* date : 2023-05-17
* version : v1.0
* description : 根据给定相位输出正弦信号
* Copyright © 2023 WHU-EIS-LMSWE, All Rights Reserved.
*/
module sin_gen(
input clk,
input [15:0] phase, //相位,0~65535对应[0~2pi)
output [15:0] sin_out
);
//---------------------正弦查找表-------------------------
wire [7:0] addr1;
wire [7:0] addr2;
wire [15:0] sin_dat1;
wire [15:0] sin_dat2;
//sin rom, 16bit, 256 depth
sin_rom sin_rom_inst1(
.clka (clk),
.addra (addr1),
.douta (sin_dat1)
);
sin_rom sin_rom_inst2(
.clka (clk),
.addra (addr2),
.douta (sin_dat2)
);
//-----------线性插值获取更精确的相位分辨率-------------------
assign addr1 = (phase>>8);
assign addr2 = (phase>>8)+1;
wire [15:0] phase1;
wire [15:0] phase2;
assign phase1 = addr1<<8;
assign phase2 = addr2<<8;
reg [15:0] phase_d0;
reg [15:0] phase_d1; //由于rom数据2拍后才给出,因此phase需要与之同步
reg [15:0] phase1_d0;
reg [15:0] phase1_d1;
always @(posedge clk) begin
phase_d0 <= phase;
phase_d1 <= phase_d0;
phase1_d0 <= phase1;
phase1_d1 <= phase1_d0;
end
wire [31:0] multi;
assign multi = (sin_dat2 > sin_dat1)?
(sin_dat2 - sin_dat1)*(phase_d1 - phase1_d1) :
(sin_dat1 - sin_dat2)*(phase_d1 - phase1_d1);
assign sin_out = (sin_dat2 > sin_dat1)?
sin_dat1 + (multi >> 8) : sin_dat1 - (multi >> 8);
endmodule
The simulation results are as follows