The following discussion is about type of coupling involved to couple rf amplifier with the mixer. The coupling involved is impedance coupling in which Lm provides a shared mutual impedance between two stages and provides coupling.The higher the Lm higher is the mutual impedance and higher is bandwidth.
Now one requirement that needs to be fulfilled in Vhf tuner circuit is that the gain should remain constant at all frequencies of the entire vhf band(that need to be coupled). According to the figure L2//C2 and L3//C3 is not coupled directly so there is no transformer action between them. They are only linked via Lm.
So to make gain constant for whole passband and to achieve this special techniques are being employed and one of them is involving mutual inductance to manipulate the gain in predetermined way. The equivalent mutual inductance m is the sum total of various planned and unplanned coupling prevalent in the primary circuit.
The eq. mutual inductance m, seeks to maintains its value constant around every frequency of the vhf broadcast band. This is possible because m has two component one is fixed and other is variable with frequency. This variable component is higher at high frequency. This variable second component is subtracted from the fixed one so m is less at high frequencies and at lower frequencies vice versa making m a little high. So in both of these cases m has been observed to put its value apparently constant thus maintaing gain constant over the frequency range in demand.
The how does this is possible to maintain gain constant in the below circuit if the circuit is not mutually coupled..??