I would like to model a low pass filter in LTSpice, but my frequency response looks like a bandpass, similar to an RLC filter.
Is LTSpice incapable of simulating LC filters with an RC one?
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It looks like a low pass filter to me but with very high Q. That isn't a surprise because you have not restricted the Q of the circuit with either a load resistor or series resistor. The effect of high Q is that you get a massive resonant peak in the mid range that is fogging your eyes from seeing the truth. Look more closely and add some resistance.
Here's what your spectrum looks like on my reasonably-adequate-but-not-crazy-in-yer-face-sparkly website low-pass filter calculator with 0.1 Ω series resistance: -
As you can see, the peak goes off the scale (feature alert) but, if we lowered the Q by increasing the resistance to something like 100 Ω it looks a little more reasonable: -
To expand on the other two answers, here is what you are plotting:
As others have pointed out, your circuit is high-Q which will exhibit peaking. The Q is limited by LTspice's default series resistance of 1 mohm for the inductor.
The following example shows what happens when you use different resistor values (1k, 2k, 4k, 100k) to change the Q of the circuit using LTspice's
.step function. The green trace is when R1 = 1k, the cyan trace is when R1 = 100k. Using a resistor in series with the inductor, instead of a resistor in parallel with the capacitor, will also work.
In the future, you should refer to a guide on designing RLC filters. There are many books on the subject and also some good online calculators.
Online filter calculator
My favorite book: "Simplified Modern Filter Design", by Philip Geffe, is an old book (1963) with intuitive explanations that most filter books leave out. You may be able to find this in a university library.