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The loose coupler is an early example of a crystal receiver. The primary of this "radio transformer" is the largest of the two coils. The secondary smaller coil is usually where the crystal detector is connected.
There is a slider on top that adjusts the turns of the big coil. The antenna is connected to the slider. One end of the coil is connected to ground. The slider is adjusted to the desired station. The antenna required for a crystal radio has capacitance that resonates the coil to a particular frequency.
The secondary has taps on the coil which sets the wave band. The crystal detector in the lower part of the picture is connected to the tap switch end of the secondary of the coil. The bottom of the coil goes to ground. The earphone goes in series with the crystal detector and ground.
When the secondary coil is slid into the primary coil lots of signal will appear in the earphones with a properly adjusted crystal detector. With a high degree of coupling the signal is very broad and several strong stations will be heard at once. When the coupling is decreased or "loose coupled" the volume drops, but with adjustment made only a single station is heard. It is desirable to couple the primary to the secondary as loosely as possible and still hear the station.
One can connect a variable capacitor across the primary and secondary to get some fine tuning accomplished.
I made my loose coupler out of poplar and hemlock wood. The coil forms were made out of cardboard mailing tubes that are available at stores that sell shipping and packing materials. The forms were dipped in very hot paraffin wax to seal out moisture and maintain a high Q factor. The windings were made on a lathe spinning the form very slowly.
The picture of the original 1920's loose coupler had double cotton covered wire instead of enameled wire on it. The windings with double cotton covered wire gives higher Q factor due to reduced capacity between turns.
My loose coupler performs very well with a 75 foot antenna. It covers a frequency range of 1000 meters to about 150 meters.
This loose coupler was used on the 160 meter ham band as the receiver for a contact of another AM ham radio station near by.