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Unformatted text preview: y. R1 R3 C L R2 R4 Fig. 11.1.2: LC resonant circuit Unattenuated oscillation in this instance can however only be obtained if the
resonant circuit does not have any ohmic resistance. In practice, it is therefore
necessary to use an amplifier, which compensates for the attenuation resulting from
the resistance. In Fig. 11.1.2, an operational amplifier is used to illustrate the
principles of the circuit.
In order to obtain a value for the frequency of an LC resonant circuit, the time
varying charge Q on the capacitor is examined. The following applies in the case of a
plate capacitor with capacity C and voltage V:
At any given time t, a variable charge q(t) is obtained, which provides a variable
voltage v(t). © Festo Didactic GmbH & Co. KG • FP 1110 157 11. Physical fundamentals The derivation of this charge according to time, dq/dt, determines the current i(t),
which flows through the coil with inductance L. The voltage obtained on the
vC(t) = q(t)/C
and the voltage on the coil
vL = L di/dt = L d2q/dt2
The equation for oscillation is
vC + vL = L d2q/dt2 + q/C = 0
If this equati...
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This note was uploaded on 11/01/2012 for the course CHEMICAL 102 taught by Professor Jamesrodriguez during the Spring '12 term at Universidad Politécnica de Cartagena.
- Spring '12