Analysis of the Tuggle Front EndThis
article analyzes the Tuggle tuner, of common use in
high-performance DX crystal sets. An equivalent circuit for the antenna-ground
system with the tuner connected is shown in Fig. 1 below. It must be recognized
that there is some stray capacitance of the rotor and frame of the two-gang
variable capacitor to ground. This should be shown as a fixed capacitor across
the bottom variable capacitor. Its presence will reduce the maximum frequency
to which the circuit will tune. However, in the present analysis this stray
capacitance is neglected.
The
mesh current is described by:
_{} …(1) _{}
where: _{} _{} _{} _{} _{} or: _{} Then, I = I_{MAX} when: _{} This is, when: _{} …(2) which is satisfied at certain radian frequency w_{r}. At this frequency, the L-C tank circuit behaves
as an equivalent inductance
_{} Usually, L is much greater than L_{a}
for antennas used in crystal set work. Then, _{} Equation (2) can be written as: _{} We can then write:
_{} After some algebraic manipulation we obtain: _{} …(3) The equivalent capacitance resonating with L
is: _{} Clearly, C_{eq}>C. Following is a numerical example illustrating
the use of the above results. Let C be a variable capacitance with C_{MIN}
= 20 pF and C_{MAX} = 475 pF. Let also C_{a} be 200 pF. Then, C_{eq} varies between
C_{eqMIN} = 38.18 pF and C_{eqMAX }= 615.74 pF. If we wish to tune the MW broadcast band
starting at 530 kHz, then the required inductance L will be: _{} _{} The circuit will tune up to: _{}
_{} If we use for C a variable capacitance with C_{MIN}
= 20 pF and C_{MAX} = 365 pF, then C_{eqMIN} = 38.18 pF and C_{eqMAX}
= 494.20 pF, giving for the required inductance L a value of 182.46 uH. The
circuit will tune up to f_{MAX} = 1.906 MHz. Acknowledgements: Special thanks are given to Ben Tongue for
his comments on the manuscript and for encouraging further
mathematical analysis of the circuit regarding bandwidth variation with
frequency, which will be done shortly.
Ramon Vargas Patron
Lima-Peru,
_{} _{}
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