A tuned-collector oscillator has a fixed inductance of 70 μH and has to be tunable over the frequency band...

Question

A tuned-collector oscillator has a fixed inductance of 70 μH and has to be tunable over the frequency band of 500 kHz to 1000 kHz. Find the range of variable capacitor.

SnapAndSolve AI · Accepted Answer

The resonant frequency of an LC circuit is given by the formula:

f = 1 / (2π√(LC))

Where:

f is the frequency in hertz (Hz)
L is the inductance in henrys (H)
C is the capacitance in farads (F)

Given:

L = 70 μH = 70 x 10^-6 H
f_min = 500 kHz = 500 x 10³ Hz
f_max = 1000 kHz = 1000 x 10³ Hz

For f_min:

C_max = 1 / (4π²f_min²L)

C_max = 1 / (4π²(500 x 10³)² x 70 x 10^-6)

C_max ≈ 1.45 x 10^-12 F

For f_max:

C_min = 1 / (4π²f_max²L)

C_min = 1 / (4π²(1000 x 10³)² x 70 x 10^-6)

C_min ≈ 3.63 x 10^-13 F

Therefore, the range of the variable capacitor is approximately 0.363 pF to 1.45 pF.

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A tuned-collector oscillator has a fixed inductance of 70 μH and has to be tunable over the frequency band...

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