How to capture both channels of the radio broadcast band?

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To all those who said NO.
Please try it out - it is quite a simple setup.
I have one made in the late 70's, it still works fine today.
Then your circuit is magic, because you can't recover the signal from a DSB suppressed carrier signal without reinserting the carrier.
 
Then your circuit is magic, because you can't recover the signal from a DSB suppressed carrier signal without reinserting the carrier.
There is a feed to the centre tap of the last coil; I'd guess that is inserting a carrier that is mixed back in with the coupled signal to the winding?
 
According to the article about the Grundig, they amplify and double the 19KHz tone - so no PLL, and pretty crude
 
There is no magic. The confusion is because one tends to look at only the DSB/SC of the L-R at 38 KHz.
The Disc output has L+R, and the DSB of L-R all together.
The L+R adds up with the modulated L-R resulting in a 38 KHz AM with 2L and 2R as the top and bottom envelopes.
One can see it very clearly in an oscilloscope that the Disc output is a 38 KHz AM that does not have a symmetric envelope.
Another point to be noted is (though it is not part of this debate), even if the FM is weak, Stereo reception is possible since the 19 KHz pilot plays no role.
 
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