# LC Resonance circuit : output voltage

What I understand(FACTS) :

In for example a LC resonance circuit the output can many times greater than the input voltage. At resonance the impedance of the inductor is the same as the impedance of the capacitor.

At the resonance frequence Xl=Xc

What I fail to understand

If the impedance's are equal, how can the output voltage be larger than the input voltage? Although not correct, you would almost start to reason that the output voltage is half the input voltage(voltage divider). Where the output voltage is the voltage across the capacitor.

It seems so counter intuitive.

Why is the voltage higher at the output? What is a intuitive way of explaining why the output voltage is higher than the input voltage. Or is it one of those circuit where it only starts to make sense when you deriver the transfer function.

• first, define where in your circuit your "output voltage" is being measured. Then mathematically (with an equation) define what you meant when you said "the impedances must be equal". Being exact here makes a difference! – Marcus Müller Oct 30 '18 at 20:51
• The impedances aren't equal they are complex conjugates at resonance. Big difference – sstobbe Oct 30 '18 at 20:59
• In the circuit you show, the voltage across C at resonance is not just large, it is infinite. Or equivalently: without any R, the peak voltage across C will be higher on each cycle, ramping upwards without limit. – wbeaty Oct 31 '18 at 0:59