Look, this is the principle analysis of modulation and demodulation! Simulation documents attached

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Modulation and demodulation are very common technologies in communication , In fact, this technology will also be used in weak signal acquisition , So what's the matter with modulation and demodulation ？

Modulation and demodulation , Its principle can be summarized in four words ： Spectrum shift .

1. Let's first establish the concept of intuitive application , Take AM modulation as an example , Understand the function and result of modulation and demodulation , Then we will analyze it from the principle .

example 1： Weak signal amplification .

If there is a signal X = sin(2πt)+ 1; It contains a 1V DC component of , Time domain 、 The frequency domain waveform is shown in the figure below .

If you want to amplify the original signal directly , Then the DC signal contained in it will also be directly amplified , The subsequent circuit may mainly deal with the amplified DC signal , It will even enter the nonlinear region , Affect the normal operation of subsequent circuits .

We can add a DC blocking capacitor , Or high pass circuit , To suppress this DC , And then in the AC amplification , However, this disadvantage is for signals with a certain bandwidth , While removing DC components , It also removes some useful low-frequency signals , Hurt the enemy 1000 Since the loss 800, This is what we don't want to see .

Modulation and demodulation gives a solution , The idea is to use a high-frequency signal to modulate the original signal we collected , Move the spectrum of the original signal to high frequency , after AC After zooming in , Then move the spectrum back , Achieve the purpose of amplification , Kill two birds with one stone .

Now we use a high frequency signal to modulate the original signal , The process is to use the frequency as Fc High frequency signal of Xc Take the original signal X, This high frequency Fc The frequency of the signal is much higher than that of the original signal .

As can be seen from the figure below , The modulated signal is expressed in Fc As carrier , The spectrum was moved to high frequency , We can now zoom it in . If low-frequency interference is introduced into the circuit , At this time, the DC isolation capacitor can be used , Because at this time, the low-frequency DC and the target signal frequency band （Fc±B） Has been separated , Direct the incoming DC , There will be no impact .

Modulated ->AC Zoom in -> The signal after straightening , Then demodulate , That is, after the spectrum is moved again , Back to the original frequency band , Although it has increased （2Fc±B） The ingredients of , As long as it is low-pass filtered to remove the new high-frequency part , You can realize the original intention of amplification .

2. Principle analysis .

Set the target signal to X = cos(2πB*t), Its frequency is B, Modulation signal Xc=cos(2πFc*t), Its frequency is Fc.

After the two are modulated

Vm = X*Xc = cos(2πB*t)*cos(2πFc*t) = 0.5cos(2π(Fc+B)t)+ 0.5cos(2π(Fc-B)t),( High school knowledge , Don't say that previous knowledge is useless ), We observe Vm The frequency band of the signal in is Fc+B And Fc-B.

Yes Vm Conduct A times AC After zooming in , The low-frequency part can be filtered out with a direct isolation capacitor or high pass . And then to Vm Demodulate , That is, multiply the modulation signal Xc, Get the output Vo, The demodulation process is :

Vo = Vm * Xc = A*[0.5cos(2π(Fc+B)t) + 0.5cos(2π(Fc-B)t) ] * cos(2πFc*t) = 0.25A[cos(2π(2Fc+B)t) + cos(2π(2Fc-B)t) + 2cos(2πB*t)]

Vo It contains both high frequency and original frequency band , After low-pass , You can get the amplified signal .

The modulation and demodulation process is summarized as follows ：

3. Matlab Simulation

The simulated original signal is (AC1V+DC1V)&1Hz The AC signal of

The frequency used is 30Hz The carrier of is adjusted to the back , The frequency is moved to 30Hz±1Hz Location. , On the 5 Zoom in , Look at the time domain waveform after modulation and amplification , Its amplitude is smaller than the original signal .

Then demodulate the signal , Move the spectrum again . original (AC1V+DC1V)&1Hz The signal of , Becomes... At low frequencies 1Hz&(0.25*5*2)=2.5V, The results are consistent with the previous theoretical analysis .

The waveform after low-pass filtering is as follows ：

The above is the principle of modulation and demodulation .