For a given range of frequencies, the required capacitance Tuning Ratio (TR) can be calculated as:

The correct answer is option 1): \(\rm TR=\frac{f^2_r(max)}{f^2_r(min)} \)

Concept:

• The capacitance tuning ratio is calculated for a tank circuit with a single inductor and multiple capacitors
• This arrangement is used for achieving a wide range of resonant frequency

• Fig A shows a simple tank circuit for f_max whereas fig B shows the tank circuit with two capacitances for f_min
• C_var is the variable part of the tuning-condenser capacitance (maximum minus minimum)
• The ratio of capacitance values needed to cover a specific range of resonant frequencies is equal (ideally) to the square root of the frequency ratio

TR = Tunning ratio

T_R = \(C_{Max} \over C_{min}\)

=( \(f_{max} \over f _{min}\))²