# Parallel RLC circuit doesn't produce expected results in Multisim

I am trying to create AC from DC. My device is based on the transient response of a parallel RLC circuit:

simulate this circuit – Schematic created using CircuitLab

If there is some energy stored in the capacitor or the inductor and $$\ R_{1}>\sqrt{\frac{L_{1}}{4C_{}1}}\$$ then the circuit will oscillate with a angular frequency of $$\ \sqrt{\frac{1}{L_{1}C_{1}}-\frac{1}{4R_{1}^{2}C_{1}^{2}}}\$$ with a damping constant of $$\\frac{1}{2R_{1}C_{1}}\$$

Here is the circuit I want to test in Multisim:

simulate this circuit

Since the input of an op-amp has a very big resistance $$\ R_{1}>\sqrt{\frac{L_{1}}{4C_{}1}}\$$, but when I try to simulate it in Multisim I don't see the expected waveform:

What am I doing wrong?

Your upper circuit appears to be powering the TL081 op-amp from a 1 volt supply via a 100 ohm resistor. This of course would never work. Also, you need to have the inductor biased at mid-rail to prevent the op-amp's input common mode range half-wave rectifying the resulting sinewave but, having said all of that, it should show signs of working in your simulation because the power rail problem is fixed.

So, try looking at the voltage across the inductor instead of the op-amp output to see if that gives a clue as to what is happening. If no-luck there, remove the op-amp and see that your circuit works with a decaying sinewave across the inductor. Also check that your switch's on-resistance isn't defaulted to some ludicrously high value.

Maybe also try using the .IC command to set the initial voltage on the capacitor to 10 volts. You would see something very similar to this: -

I've added a series resistor to the coil to demonstrate what sort of values cause a low/moderate decay.

I don't know Multisim but the numbers below indicate to me that you did a full transient analysis for 48 seconds and, if that is true then, after that length of time the waveform could have died out completely (given that it's meant to be 50 Hz): -

Like I said, I don't know Multisim and this could be a red-herring.

• if the output resistance is infinite the oscillation never dies and the opamp has a input resistance close to infinity... Mar 25, 2023 at 16:01
• Even ideal models of op-amps have some real-world characteristics and, as far as I know, you can also implicitly add series resistance to an inductor without it showing on the schematic. All those things could tail-off the sinewave. Mar 25, 2023 at 16:06

The simulation is rather accurate. If you put that circuit together from real components, it would behave the same.

Something needs to be pumping energy into the capacitor or inductor periodically to deal with losses. As it stands, the simulation starts with no energy in the resonator, so the amplitude is zero. Since, presumably, you want a continuous oscillation and not just one that decays to nothing, you'll need those elements in an oscillator circuit.

Or, if you actually want to generate low frequency AC, then magic sinewaves do that nicely :) The "trick" is that even those are "just" multi-pulse repeating PWM waveforms, they have many lower harmonics with zero amplitude, so low-pass filtering them into a sine wave is much easier than with "plain" PWM.