Hearing the radio by touching a jack plug

Question

Here is what happened to me a few days ago:

I own an amplified speaker with a jack plug. Usually, when I touch the jack plug with my finger I hear a "hum" sound. On this specific day, on a specific location, I heard the radio (repeating the experiment with other people, it is always the same radio channel.)

How can you explain this phenomenon?

My understanding of radio frequency modulation/demodulation is very poor, but I understand that when you receive the radio-waves, you get all the radio channels at once and you need to demodulate it before you can hear the radio of your choice. So, what acted as a demodulator in this situation?

Answer 1

Here is a circuit having four "components" that can act as a radio receiver. When each component is optimized, reception can be too loud to bear:

^{simulate this circuit – Schematic created using CircuitLab}

In your scenario:

• YOU are the antenna, connected to the jack tip
• In the amplified speaker, there exists a semiconductor junction serving as D1
• Needless to say, there is a speaker serving as SPKR1
• A path to ground must exists - the amplified speaker requires a DC source that is likely grounded via the power plug. If your amplified speaker were powered by a battery, then a ground is not present, and any radio signals would not be detected.

You are not a wonderful antenna. So this scenario likely occurs only if a radio station's transmitting antenna is nearby. This would also account for you hearing ONE station that dominates stations further away.

^{simulate this circuit}

In the amplifier of an amplified speaker, hundreds of semiconductor junctions exist, each of which is capable of non-linear operation - a key requirement of this kind of radio. It is likely that one junction, perhaps in a transistor nearest the input jack serves as D1...the audio it produces is amplified by the remaining part of the amplifier.
You mention hum as well. In this case, you also act as a kind of antenna, transferring local electric fields into the input jack. However, in this case there is no radio carrier wave and a non-linear element like D1 is NOT required. The electric field at the input jack is amplified directly.

Answer 2

This is typically "transmodulation" or "crossmodulation" for some ...

Suppose the amplifier input characteristic is :

Vs: = a0 + a1 * vg + a2 * vg ^ 2 + a3 * vg ^ 3. For a diode ... exp (vg) can also be used...

(for example: a0 = 1; a1 = 1; a2 = 1; a3 = 1)

Suppose the signal (picked up by the finger) at the input of the amplifier (very bad) is:

vg: = sin (x) + sin (y) * sin (z);

x = 50 is the frequency of the local network,

y = 1000000 is the carrier of the "received" signal,

z = 1000 is the modulation of the carrier (the useful information);

Calculating then the spectrum of signal generated by the non linear function :

The "received signal" is therefore (sorry for the length ...) = -. 500 * sin (998950) -. 500 * sin (1001050) +. 500 * sin (1000950) +. 125 * cos (1998000) -. 250 * cos (2000) -. 250 * cos (2000000) +. 125 * cos (2002000) + 1.53 * cos (999000) -. 250 * sin (150) + 2.50 * sin (50) -. 375 * sin (2000050 ) +. 375 * sin (1950) -. 375 * sin (2050) +. 375 * sin (1999950) +. 313e-1 * cos (2997000) -. 313e-1 * cos (3003000) -. 500 * cos (100) + 1.75-.188 * sin (1997950) +. 188 * sin (2002050) -. 188 * sin (2001950) -. 938e-1 * cos (997000) -. 938e-1 * cos (2999000) + .375 * cos (1000900) +. 375 * cos (1001100) +. 938e-1 * cos (1003000) +. 938e-1 * cos (3001000) +. 188 * sin (1998050) -. 375 * cos (998900 ) -. 375 * cos (999100) -1.53 ​​* cos (1001000) +. 500 * sin (999050).

In this result; only usefull the values ​​in the sines between 20 Hz and 20 kHz !!!

There are therefore only two signals centered on 100 Hz and 2000 Hz.

So you hear the distorted "50 Hz" ... and the carrier information centered on "2000 Hz" and not 1000 Hz, so also distorted but audible.