A tank circuit in a radio transmitter is a series RCL circuit connected to an antenna?
a asked:
A tank circuit in a radio transmitter is a series RCL circuit connected to an antenna. The antenna broadcasts radio signals at the resonant frequency of the tank circuit. Suppose that a certain tank circuit in a shortwave radio transmitter has a fixed capacitance of 2.4 x 10-11 F and a variable inductance. If the antenna is intended to broadcast radio signals ranging in frequency from 3.8 MHz to 9.1 MHz, find the (a) minimum and (b) maximum inductance of the tank circuit.
A tank circuit in a radio transmitter is a series RCL circuit connected to an antenna. The antenna broadcasts radio signals at the resonant frequency of the tank circuit. Suppose that a certain tank circuit in a shortwave radio transmitter has a fixed capacitance of 2.4 x 10-11 F and a variable inductance. If the antenna is intended to broadcast radio signals ranging in frequency from 3.8 MHz to 9.1 MHz, find the (a) minimum and (b) maximum inductance of the tank circuit.
The resonant frequency “f” of a tank circuit is:
2*π*f = 1/sqrt(L*C)
(2*π*f)^2 = 1/(L*C)
L = 1/[ (2*π*f)^2 * C ]
At 3.8MHz:
L = 1/[ (2*π*3.8*10^6)^2 * 2.4*10^-11 ] = 73.1*10^-6 H = 73.1 μH
This is the maximum inductance. The minimum inductance is needed at the maximum tuned frequency.
At 9.1MHz:
L = 1/[ (2*π*9.1*10^6)^2 * 2.4*10^-11 ] = 12.7*10^-6 H = 12.7 μH