The voltage obtained on the capacitor is vct qtc and

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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: Q=C·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 capacitor is 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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