Low pass filter when the inductor is not ideal

[hanhan]

Hi,
Please help me about the low pass filter bellow? Thanks.

 

[johansen]

it is still a low pass filter even when R dominates, however the roll off is 20 db per decade instead of 40

 

[hanhan]

Thank you.
I am not sure why it is still a low pass filter. For example, consider input voltage has only a DC component and L is not ideal with internal resistance R, C is ideal.
At DC or zero frequency, XL = 0 and XC = ∞ then the circuit can be modeled as a DC voltage with internal impedance Zs in series with ZL.
Thus, the voltage across the load is:
VL = Vs*ZL/(R + ZL)
where Vs is DC input voltage.
Because R>>ZL => ZL/(R + ZL) ≈ 0 and VL ≈ 0.
This means that the circuit shorts DC components to ground and it is not a low pass filter.
Is my reasoning correct?

 

[MrAl]

Hi,


A low pass filter does not have to put out a voltage of 1 for an input voltage of 1 (at some frequency) to qualify as a low pass filter. There is such a thing as a low pass filter with attenuation. In this case we still have a LP filter but it also attenuates all frequencies to some degree as well as remains frequency selective for others. It may be considered to be not as good that way, but for some applications it may be just fine.

In the case of the inductor capacitor filter however, if the resistance is too high then the inductor is worthless. So in that case it would probably be better to replace the inductor with just a resistor. But even with a resistor we still have a LP filter, but now it's just a first order LP rather than a second order LP. If we include an inductor then that means we went through the trouble of buying an inductor so that we could have a second order filter, so we should make sure it has low enough series R to make it work that way. If we wanted a first order filter (resistor or high series resistance in the inductor) then we might as well not buy the inductor.

If the combined resistances are very low we might actually end up with something that looks like a combined low pass and band pass filter with the L and C. It's not perfect but it does look that way depending on the application requirements. The pseudo band pass response comes about because of the L and C causing a very high peak in the AC response for a certain frequency, even though in the pass band it might not look like a perfect band pass response.

After reading some of your questions and replies i think you would be happy if you were to start graphing some of these circuits, or at least starting to simulate them using some free software like LT Spice. You would gain a lot of understanding from that. If you want to calculate the response we could go into that and i dont think it would take too long for you to start to get accustomed to doing this. You could then graph the responses and see what you have there. Then you can answer some of these questions right away. I think you would find it rewarding either calculating or simulating.

 

[WTP Pepper]

Try using Thevenin's equivalent circuit theorm. It makes life so much simpler.