**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 R_{1},R_{2} be the resistances of coils, 1 and 2, respectively. Also let L_{1},L_{2} be the self inductances of the coils, 1 and 2, respectively.

Let

with the assumption that R_{s} >> R_{1 }>> 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 ωL_{2} = 1/ωC, or at resonance frequency ω_{r}, the amplification is given by

the current i_{2} 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√L_{1}L_{2}. 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.