Single Tuned Circuit:

Consider the Single Tuned Circuit in Fig. 10.21. A tank circuit (i.e. a parallel resonant circuit) on the secondary side is inductively coupled to coil (1) which is excited by a source, υ_i. Let R_s be the source resistance and R₁,R₂ be the resistances of coils, 1 and 2, respectively. Also let L₁,L₂ be the self inductances of the coils, 1 and 2, respectively.

Let

with the assumption that R_s >> R₁ >> jωL_1. The mesh equations for the circuit shown Rs in Fig. 10.21 are

or

The output voltage

The voltage transfer function, or voltage amplification, is given by

When the secondary side is tuned, i.e. when the value of the frequency ω is such that ωL₂ = 1/ωC, or at resonance frequency ω_r, the amplification is given by

the current i₂ at resonance

Thus, it can be observed that the output voltage, current and amplification depends on the mutual inductance M at resonance frequency, when M = K√L₁L₂. The maximum output voltage or the maximum amplification depends on M. To get the condition for maximum output voltage, make dυ_o/dM = 0.

From which,

or

From the above value of M, we can calculate the maximum output voltage. Thus

or the maximum amplification is given by

The variation of the amplification factor or output voltage with the coefficient of coupling of Single Tuned Circuit is shown in Fig. 10.22.