经过射频上变频后 IQ 为什么反了？

数学原理

superheterodyne_transmitter

设数字域信号为 ，经过中频上变频，DAC 发射信号为 频域表示为

经过射频的上变频，最终发射信号表示为

（未完待续……）

仿真(MATLAB)

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close all; clear; clc;

%% System Parameters
fs = 24.576e3;       % 24.576MHz
fc = 10;             % 10kHz
f_if = 50;           % 50kHz
f_rf1 = 450;         % 450kHz
f_rf2 = 550;         % 550kHz

N = 2 ^ 20;
t = 0: 1/fs : 500;   % 500s
f = (-N/2 : N/2-1) * (fs/N);

%% Digital Baseband Signal
i = cos(2 * pi * fc * t);
q = 0.5 * sin(2 * pi * fc * t);
s = i + 1j * q;

S = 10 * log10(fftshift(fft(s, N)));

% Plot Digital Baseband Signal
figure;
subplot(2, 2, 1);
plot(t(1:32768), real(s(1:32768)));
title('Digital Baseband Signal - Real Part');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2, 2, 3);
plot(t(1:32768), imag(s(1:32768)));
title('Digital Baseband Signal - Imaginary Part');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2, 2, 2);
plot(f, real(S));
title('Digital Baseband Signal Spectrum - Real Part');
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');

subplot(2, 2, 4);
plot(f, imag(S));
title('Digital Baseband Signal Spectrum - Imaginary Part');
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');

%% Digital to IF Conversion
s_if = real(s .* (cos(2 * pi * f_if * t) + 1j * sin(2 * pi * f_if * t)));
S_if = 10 * log10(fftshift(fft(s_if, N)));

% Plot IF Signal
figure;
subplot(2, 1, 1);
plot(t(1:32768), s_if(1:32768));
title('Intermediate Frequency (IF) Signal Waveform');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2, 1, 2);
plot(f, real(S_if));
title('IF Signal Spectrum');
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');

%% IF to RF Conversion
s_rf1 = s_if .* cos(2 * pi * f_rf1 * t);
S_rf1 = 10 * log10(fftshift(fft(s_rf1, N)));
s_rf2 = s_if .* cos(2 * pi * f_rf2 * t);
S_rf2 = 10 * log10(fftshift(fft(s_rf2, N)));

% Plot RF Signals
figure;
subplot(2, 2, 1);
plot(t(1:32768), s_rf1(1:32768));
title(['RF Signal @ ', num2str(f_rf1), 'kHz - Waveform']);
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2, 2, 3);
plot(f, real(S_rf1));
title(['RF Signal @ ', num2str(f_rf1), 'kHz - Spectrum']);
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');

subplot(2, 2, 2);
plot(t(1:32768), s_rf2(1:32768));
title(['RF Signal @ ', num2str(f_rf2), 'kHz - Waveform']);
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2, 2, 4);
plot(f, real(S_rf2));
title(['RF Signal @ ', num2str(f_rf2), 'kHz - Spectrum']);
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');