Analysis of the Tuggle Front End

This 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

rvargas@inictel.gob.pe

Lima-Peru, South America

March 14^th, 2004