# Why in a voltage driven parallel RLC circuit (at resonance), the current of the inductor has a DC component?

I'm refreshing my knowledge on LC/RLC circuits, and an interesting thing came up that puzzled me.

I'm doing simulation on parallel a RLC circuit (in LTSpice), which is driven with a sine voltage source, at the resonating frequency of the LC tank. The puzzling part is that the current flowing out of the voltage source, as well as the current flowing through the inductor (90 degrees out of phase of corse) have a DC value of Vout,max/R. For the component values that I've chosen - L=100u ; C=10n ; R=100R, the output current of the voltage source has a DC value of 100mA, as well as the current through the inductor. The current through the capacitor, and through the output load resistor swing ±100mA.

Here is a picture of the simulation output : The same thing happens if I try to simulate just the LC tank. The output current of the voltage source has a DC value of 100mA (with an extremely small AC waveform), and the current of the inductor has a 100mA DC value : What's the reason behind this ? Regards!

• You know you are using 1p as a resistor value, which I think in LTspice works out to 1E-12 ohms? I just want to make sure you want that.
– jonk
Aug 15, 2016 at 20:41
• I'm using the 1p resistors in order to see the current (in the direction I want) which is flowing. The 1p resistors are there only for that reason Aug 15, 2016 at 20:50
• Yes, I thought so. I just wanted to make sure we were both on the same page about it.
– jonk
Aug 15, 2016 at 20:50
• Yeah. LTSpice drives me nuts while showing the output current of a voltage source with a 180degrees phase shift, and I can rotate the resistor any way I like :-) Aug 15, 2016 at 20:52
• It's a transient, initiated when the sine wave input is switched on. If you wait for steady state it will disappear.
– Chu
Aug 16, 2016 at 6:41

Just so we are on the same page... You have your resonant tank (which might be closer to 159155Hz) in parallel with a resistor of $100\Omega$. That pretty much means $\infty$ for the tank, leaving the $100\Omega$ resistor. So the DC current from the source isn't surprising. Removing the resistor just leaves the tank. But since it is $\infty\Omega$ at resonance, again it is no surprise that there is then zero DC current. I'm guessing that you already know this stuff. The only reason I'm bringing it up is to make it clear that we both see the same thing here.

So... You are probably using the transient analysis and not allowing enough time to go by. Have you considered running the analysis for, say, 5ms? (The time delay will need to be about the same with and without the resistor.)

• Hi jonk! Thanks for the quick answer! (I rounded the resonant frequency to 160kHz, didn't want to write too many numbers) Can you elaborate, why is the DC component of the current form the source not surprising ? Has this something to do with the fact that the current through the inductor needs time to reach steady state? I think that you miss read about the instance when I remove the load resistor from the picture, there still IS a DC component to the output current of the source, exactly Vo,max/Zo (100mA in this case) Aug 15, 2016 at 21:15
• You are spot on about the second point, I'm currently running the simulation (transient) with a stop time of 10s. I'm seeing that the DC value of the inductor current and the output current of the source are dropping to zero! Why is this ? Energy needs time to be stored in the inductor or ? What is the time-constant of the DC value of the current then? Aug 15, 2016 at 21:15
• @aleks: Look at damping factors in en.wikipedia.org/wiki/RLC_circuit and see if that helps a little.
– jonk
Aug 15, 2016 at 21:23
• I just did a simulation on the lone LC tank only. The DC value of the current again drops, and judging by eye, with the same rate as when I simulated the RLC circuit. So, the time-constant must be related only to the reactive parts of the circuit, right? I'm still puzzled from where does this time lag come from? What is the physical reasoning behind it ? Regards! Aug 15, 2016 at 21:24
• See: Section 8.3 of: ee.nthu.edu.tw/~sdyang/Courses/Circuits/Ch08_Std.pdf
– jonk
Aug 15, 2016 at 21:27