Checked how the envelope detector works by the traditional theory in about 1925

I checked how the envelope detector which used a diode worked to decode AM modulated E/M wave.

I knew that figures followings were the theory established in about 1925 when the crystal radio was invented in USA. I think it was great invention in those days and I respect it for the inventor. Because it changed the method of human's communication.

According to the envelope decoder theory, I configured the circuit in the LTspice,

and checked how it worked.

Unfortunately, outcome from my LTspice is in the negative.

See the figure above. 

Blue line is AM modulated input RF E/M wave.

The rate of AM modulation is 100% here.

Green line is output on the envelope detector.

Apparently, AM signal is not decorded to AF signal.

Frequency spectrum indicates AM modulated signal there on expected HF frequency.

I gave Bios voltage 2V to the diode 1N914, then AM signal was decorded to AF sine wave as the green line showed.

The decoding process seems to improved.

As many people know, this bias voltage makes the diode work better and that shot-key diode can get better result rather than switching diode 1N914.

The magnitude gain of switching diode decreases on AF frequency range, and it passes RF frequency almost pass through.

This is caused by the AC characteristics of the diode.

Beside, the diode detector on the IF amp stage similar to this circuit but it is not the same. 

In the Crystal radio, the impedance at the input of the diode is very high. [1]

In the IF stage, the impedance of it is lower than that.

I'm happy if you check these works OK or not.

Please let me know your advice. 

This figure is very famous explanation of the crystal radio in Japan. 

(Ref. from a famous free dictionary in internet.)

However, I'm afraid this work may not be different from the actual principle or the real works of the radio.

After a diode AM demodulator, a condenser such as 0.001uF to 0.02uF passes RF signal (Green area) is fed to grand. So, it should be written as only base band AF signal without green indication.

And a diode characteristics on RF frequency doesn't behave as a rectifier.

It behaves as a kind of frequency convertor between Carrier frequency and base band modulated sidebands (USB and LSB).

 i.e. 

A diode converts RF AM frequency to AF base band signal.

It is not working as Envelope detector or Peak detector.

(Pretty girl on the picture is "Ms. Mayuyu Watanabe" of AKB48.)

This is the LTspice simulation result of the crystal diode.

This works is different from the traditional theory of so called "Envelope detector" or "Peak detector."

Harmonics frequencies of the demodulated base band signals are be able to calculate by Taylor series math operation.  

By using the formula by Shockley's ideal diode. i=Is*(exp(K*v)-1), current of the diode calculated. 

AM modulated RF signal can be written by "v" = (1+x(t))*A*sin(ω*t).

As the differential math operation of "i=Is*(exp(K*v)-1)" becomes "di/dv=K*Is*(exp(K*v)-1)",  "d^2i/dv^2=K^2*Is*(exp(K*v)-1)", "d^3i/dv^3=K^3*Is*(exp(K*v)-1)" and so on. 

Here, K << 1 . This is the reason why the harmonics frequencies of the demodulated base band AF signals degrees for 2nd, 3rd, ... Nth differential math operation.

Please read the precise description as following analysis.

Related document:

[1] I designed 1 shot-key diode crystal radio

http://ji1nzl-official.blogspot.jp/2015/06/i-designed-1-shotkey-diode-radio.html

[2] A simulation example of 1 shot-key diode "crystal radio" by LTspice4

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