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

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KVS TGT WET (Work Experience Teacher) 23 Dec 2018 Official Paper
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  1. \(\rm TR=\sqrt{\frac{fr(min)}{fr(max)} } \)
  2. \(\rm TR=\sqrt{\frac{fr(max)}{fr(min)} } \)
  3. \(\rm TR=\frac{f^2_r(max)}{f^2_r(min)} \)
  4. \(\rm TR=\frac{fr(min)}{fr(max)} \)

Answer (Detailed Solution Below)

Option 3 : \(\rm TR=\frac{f^2_r(max)}{f^2_r(min)} \)
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Detailed Solution

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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

F4 Vinanti Engineering 21.12.22 D8

  • Fig A shows a simple tank circuit for fmax whereas fig B shows the tank circuit with two capacitances for fmin
  • Cvar 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

T= Tunning ratio

TR = \(C_{Max} \over C_{min}\)

=( \(f_{max} \over f _{min}\))2

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