脉冲积分鉴相(相敏检波)法原理

T
T 2 A sin (ω0t 4
+θ0
)dt
=
−
A ω0
cos (ω0t
+θ0
)
T 2
T 4
=
−A ω0
⎡⎢⎣cos ⎛⎜⎝ω0T
2
+θ0
⎞⎟⎠ − cos ⎛⎜⎝ω0T
4
+θ0
⎞⎟⎠⎤⎥⎦
ω0 =2π
⎯c⎯osα⎯−cos⎯β =−⎯2sin⎯αT +⎯β sin⎯α −⎯β →
2
2
( ) ( ) ( ) Q
=
−
2 AT π
sin
(θ0
)
二、波形图
sin(ω0t+θ0) I:0oCLK Q:90oCLK sin(ω0t+θ0)
I:0oCLK/Q:90oCLK I:0oCLK/Q:90oCLK
+ I(θ0) /Q(θ0)
-
三、仿真结果 Matlab 程序
clear all; close all; %===================== A0=1; f0=100; %100Hz T=1/f0; w0=2*pi*f0; tIP=0:T/1000:T/2; tIN=T/2:T/1000:T; tQP=T/4:T/1000:3*T/4; tQN=[0:T/1000:T/4,3*T/4+T/1000:T/1000:T]; t=0:T/1000:T; vt=A0*sin(w0*t); for k=0:360;
vtQ=vtQP-vtQN; K=k+1; I(K)=sum(vtI) /1000; Q(K)=sum(vtQ) /1000; end %============================== figure(1); kk=(0:360);%*1001/361; h=plot(kk,I,'r'); set(h,'linewidth',3); hold on; h = plot(kk,Q,'black');%r'); set(h,'linewidth',3) A=(I(1).^2+Q(1).^2).^0.5; %vt=A*vt; plot(t*360/T,vt) hold off; grid; axis([0 365 -1.1 1.1]); xlabel('³õÏà(¶È)'); ylabel('¼øÏàµçѹ');
=
−
AT 2π
⎡⎣−2 sin
3π 4 +θ0
sin
π 4
⎤ ⎦
=
2 AT 2π
cos
θ0
+π
4
二、波形图
sin(ω0t+θ0) I:0oCLK I':0oCLK' Q:90oCLK Q':90oCLK'
sin(ω0t+θ0)
I':0oCLK' /Q':90oCLK'
I(θ0) / Q(θ0)
三、仿真结果
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单 π 4 脉冲积分鉴相（相敏检波）法原理一、公式推导：来自∫ I =T 4
0
A sin (ω0t
+θ0 )dt
=
−
A ω0
cos (ω0t
+θ0
)
T 4
0
=
2A ω0
cos
(ω0t
+θ0 )
T T
2
=
2A ω0
⎢⎣⎡cos (ω0T
+θ0 ) − cos ⎜⎝⎛ω0T
2
+θ0
⎟⎠⎞⎥⎦⎤
ω0 =2π
⎯⎯⎯T
⎯,ω0T⎯=2π⎯→
I
=
2A ω0
⎡⎣cos (θ0
)
+
cos (θ0
)⎤⎦
=
2 AT π
cos (θ0
)
∫ ∫ ∫ Q =
3T T
4
A
sin
(ω0t
T 4
=
−
2A ω0
⎡⎢⎣cos ⎛⎜⎝ 3ω0T
4
+θ0
⎞⎟⎠ − cos ⎛⎜⎝ω0T
4
+θ0
⎞⎟⎠⎤⎥⎦
ω0 =2π
⎯⎯⎯T
⎯,ω0T⎯=2π⎯→
( ) ( ) Q
=
−
2A ω0
⎡⎣cos
3π 2 +θ0
− cos π 2 +θ0
⎤ ⎦
=
−
2 AT 2π
⎡⎣sin
(θ0
)
+
sin (θ0
)⎤⎦
Matlab 程序
clear all; close all; %============================ A0=1; f0=100; %100Hz T=1/f0; w0=2*pi*f0; tI=0:T/1000:T/4; tQ=T/4:T/1000:T/2; t=0:T/1000:T; vt=A0*sin(w0*t); for k=0:360;
双 π 4 脉冲积分鉴相（相敏检波）法原理
一、公式推导：
∫ ∫ ∫ ∫ I =
T 0
2
A
sin
(ω0t
+
θ0
)dt
−
T T
A sin (ω0t +θ0 )dt
=
2
T 0
A sin (ω0t
+θ0
)dt
−2
T T
A sin (ω0t
2
+θ0
)dt
∫ =
−2
T T
A sin (ω0t
2
+θ0 )dt
=
Silta=k*pi/180; %23Degree Ns=length(Silta); vtIP=A0*sin(w0*tIP+Silta); vtIN=A0*sin(w0*tIN+Silta); vtI=vtIP-vtIN; vtQP=A0*sin(w0*tQP+Silta); vtQN=A0*sin(w0*tQN+Silta);
−A ω0
⎡⎢⎣cos ⎛⎜⎝ω0T
4
+ θ0
⎞⎟⎠
−
cos
(θ0
)
⎤ ⎥⎦
ω0 =2π
⎯c⎯osα⎯−cos⎯β =−⎯2sin⎯αT +⎯β sin⎯α −⎯β →
2
2
( ) ( ) ( ) I
=
−
AT 2π
⎣⎡−2 sin
π 4 +θ0
sin
π 4
⎤ ⎦
=
2 AT 2π
sin
θ0
+π
4
∫ Q =
Silta=k*pi/180; %23Degree Ns=length(Silta); vtI=A0*sin(w0*tI+Silta); vtQ=A0*sin(w0*tQ+Silta); K=k+1; I(K)=sum(vtI) /1000; Q(K)=sum(vtQ) /1000; end
%============================= figure(1); kk=(0:360);%*1001/361; h=plot(kk,I,'r'); set(h,'linewidth',3); hold on; h = plot(kk,Q,'black');%r'); set(h,'linewidth',3) A=(I(1).^2+Q(1).^2).^0.5; %vt=A*vt; plot(t*360/T,vt) hold off; grid; axis([0 365 -1.1 1.1]); xlabel('³õÏà(¶È)'); ylabel('¼øÏàµçѹ');
+
θ0
)dt
−
4
T 0
4
A
sin
(ω0t
+
θ0
)dt
−
T 3T
A sin (ω0t +θ0 )dt
4
∫ ∫ ∫ = 2
3T T
4
A
sin
(ω0t
+
θ0
)dt
−
4
T 0
A sin (ω0t
+θ0 )dt
=
2
( 3T
T 4 A sin ω0t 4
+θ0
)dt
=
−
2A ω0
cos
(ω0t
+θ0 )
3T 4