An Explanation of how the "Mystery Crystal Radio" Works
By Ben H. Tongue
Two assumptions made in the analysis: They are that the distributed capacity between the two coil windings may be represented by one lumped capacitor, Cc, connected between the center of one winding to the center of the other. See Fig. B. The other is that the magnetic coupling between the primary and secondary windings is very high. This assumption is close to reality for the bifilar wound portion of the transformer, provided the capacity coupling is not too high. The magnetic coupling between the bifilar-ed parts and the end windings is not as close as that between the bifilar-ed parts. This does not affect the validity of the analysis. Keep in mind that in transformers with unity coupling, the ratio of the voltage on any winding to any other is directly proportional to the number of turns on each winding. This also applies to a portion of one winding. (Just use the number of turns in that portion.) Figures A through E show the inductive circuit through various changes as the following reduction and simplification proceeds.
Simplification and reduction of the circuit of the Mystery crystal set using the "Broad" non-earthy antenna connection:
The physical circuit of the Mystery set is shown in Fig. 1 with the antenna connected to the non-earthy side of the primary. The black dots on the windings show the start of each winding, assuming that they are both wound in the same direction.
Figure 2 shows a coupling capacitor Cc, between the two windings. It represents the parallel combination of two distributed capacitances: One is formed of the dielectric of the wire insulation between the bifilar-ed primary and secondary coil turns. The other is also between the primary and secondary coil turns, but in this case, there are three dielectrics in series. They are: (1) The dielectric of the insulation on, say, the primary winding that is in contact with the coil form. (2) The dielectric of the coil form between the primary and secondary windings. (3) The dielectric of the insulation on the secondary winding that is in contact with the coil form. Cc is in a series circuit with the antenna and ground.
Fig. 3 shows Cc shifted up to the antenna and out of the way. No change in performance will result.
The top and bottom leads of the secondary are connected (each 12.5 turns from the center), to the corresponding points on the primary (12.5 turns up and down from the center). This is shown in Fig. 4. Since the points that are connected together have the same AC voltage on them, no current will flow through their connection and the circuit operation will be undisturbed.
Figure 5 shows the resulting equivalent circuit from the connections made in #4. Since all portions of the winding are assumed to be unity-coupled to each other, performance will not change if the tuning capacitor C1 is connected as shown in Fig. 6, as long as its value is changed appropriately. C1 is connected across 50 turns of the inductor. C2 is connected across 37.5 turns. The inductances of a unity coupled 1:1 transformer are directly proportional to the square of the number of turns. The number of turns across which C2 is connected is 3/4 of the number of turns turns across which C1 is connected, therefore, the inductance across which C2 is connected will be 9/16 the inductance across which C1 is connected. C2 must be increased from the the value of C1 to 16/9 of C1 for the circuit to work the same as before the transformation. The bottom portion of the coil in Fig. 6 can be eliminated since nothing is connected to it.
The final result is the equivalent circuit shown in Fig. 7. Here we see a conventional crystal set circuit with the antenna-ground components connected directly across the full tank, with isolation from full antenna resistive loading supplied by the capacitor Cc. The detector load is tapped in at 2/3 of the tank voltage to reduce its resistive loading effect on the tuned circuit. That's it for the non-earthy "Broad" antenna connection.
Simplification and reduction of the circuit of the Mystery crystal set using the "Selective" earthy connection.
Figures 8 through 14 show the simplification and reduction of this circuit. It proceeds in an manner similar to the one for the "Broad" connection. Now look at Fig. 14. The value of Cc is unchanged from that in Fig. 7. C3 will have to be somewhat larger than C2 was for the circuit to work the same. The antenna-ground components and Cc are now connected across only 1/3 of the tank instead of the full tank. The detector load is still tapped in at 2/3 of the tank voltage. That's it for the earthy "Selective" antenna connection.
What might the value of the magnetic coupling coefficient between the bifilar-ed portion of the windings be?
To think about this, consider: Mentally unwind the bifilar portion of the coil from the coil form, but imagine the two wires are still in the same relative positions to each other. Stretch them out. The ends of one wire are the terminals of one winding of a transformer and the ends of the other winding, the terminals of the other. Now you have two parallel wires closely spaced and several tens of feet long. The spacing (from the wire insulation) between them is maybe 0.005". It should seem obvious that the magnetic coupling between them could not get much greater (without ferrite cores), no matter what one does with the wires. It can, however become greater when the bifilar wire is wound on a form. The reason is that places a primary wire on each side of every secondary wire and vice-versa, providing more magnetic coupling between the windings than when the wires are stretched out.
Here is an approach for determining the coupling coefficient of a bifilar winding: Construct a bifilar wound coil that has about the same inductance as the bifilar-ed wires in a standard Mystery" set. This inductance calculates out to be 57 uH. No wire of the gage originally used was available, so the largest bonded bifilar wire I had available was used. It was made by MWS Wire and consisted of two #30 ga. film insulated wires bonded together. Its cross section measures 0.012x0.024". Twenty turns were wound on an available 3 1/2" styrene coil form since a 3" diameter coil form, as used in the original Mystery set was not available. The winding length came out to be a very small 0.475" because of the small wire size. This is much less than that in the original Mystery set but, tough, that wire is all that was available. The leads from the coil were still bifilar-ed, 10" long ends.
Several resonance measurements were then taken using a Q meter. The first was with one winding connected to the inductance terminals of the Q meter, the other winding being open circuited (Loc), at several frequencies from 0.515 to 2.36 MHz. The indicated capacitance readings on the Q meter were noted. The other was with the same winding still connected to the inductance terminals of the Q meter but with the other winding shorted (Lsc), at frequencies from 3.0 to 11.0 MHz. Again, the indicated Q meter capacitance readings were noted. At frequency extremes these readings will be distorted by the presence of distributed capacitance between the two windings, 1020 pF in this case. The conventional Mystery set would have considerably less capacitance between the windings because of the much thicker insulation on the wires. Note: The capacitance between the windings cannot be determined at RF by the use of a Q meter. It can be measured by the use of an RLC bridge operating at 1 kHz or a DVM having a capacitance measuring function (if it operates at about 1 kHz).
Over the frequency range of 0.515 to 1.71 MHz, Loc was calculated to be: 66.5 +/- 2.5 uH. Over the frequency range of 3 to 7 MHz, Lsc was calculated at: 2.01 +/- 0.06 uH. A derivation results in the following relation for the coupling coefficient between two identical magnetically coupled inductors: k=sqrt(1-Lsc/Loc). The calculated coupling coefficient between the two bifilar-ed windings is 0.984, which I consider very close to unity.
The bifilar wire was re-wound on the same form, but spaced to cover a 1" length. The coupling coefficient came out at 0.966 and the distributed capacitance: 895 pF. Another coil was then wound from the same piece of wire on a 1.5" diameter polypropylene form. The winding was slightly space wound and had a length of 1.5 ". Coupling coefficient: 0.983 and distributed capacity coupling: 945 pF.
Of course, manufactured, bonded, bifilar wire is not recommended for use in a Mystery set. Usually two independent, insulated wires are wound close spaced. This practical case results in substantially less distributed capacitance than when using bonded wires.
The beauty if the Mystery set is that it provides an antenna decoupling capacitor (Cc) (made from the distributed capacity between the bifilar-ed windings), along with the effect of two different points for its connection to the tank; all without any specific physical capacitor or taps on the inductor. Further, the diode is effectively tapped 1/3 down on the tank for improved selectivity. The only downside to this arrangement is some loss caused by the probable relatively low Q of Cc.
When using the "Broad" antenna connection, the antenna-ground components are connected through Cc across the full tank. This arrangement puts a relatively large amount of antenna resistive loading on the tank. The loading results in as reduced selectivity, but stronger signal strength than one gets in the "Selective position. See Fig. 7.
When using the "Selective" antenna connection, the antenna-ground components are connected through Cc across only 1/3 of the tank coil turns. This results in a reduction to about 1/9 of the resistive loading by the antenna on the tank, compared to the loading in the "Broad" connection. See Fig. 14. This reduced loading increases the loaded circuit Q, and hence selectivity. The ratio of unloaded to loaded Q is reduced, thus reducing sensitivity.
For practical purposes the 'leakage inductance' between that part of the primary that is bifilar wound with the secondary is very low. To the extent that it is not zero, it and the leakage inductance between the outer turns of the primary and the inner bifilar-ed 25 turns can be considered to be an added "leakage inductance" in series with C2 in Fig. 7; and in series with C3 in Fig. 14. The main effect of this leakage inductance, compared to having none, is to somewhat lower the highest frequency than can be tuned. The low end of the tuning range will be extended a small amount.
#19 Published 08/11/01; Revised 12/29/2002