I recommend you plot the theoretical Bode plot, using a model of the capacitor that includes the series resistance. The measurements may be exactly what you should expect them to be. If you don't already know how to do that, then this could be a good learning opportunity. If you don't want to learn the math, you could at least plot these in a spice package such as LTSpice.
Anyway, I just did a quick and dirty experiement with a low-pass filter from a 33-Ohm resistor and 4.7 uF capacitor. It also shows deviations from what you might expect for the Bode plot if the resistor and capacitor were ideal, but we will see that a model that includes the ESR of the capacitor will predict the measurements pretty well.
Case 1: 4.7 uF electrolytic capacitor (Xicon, 35V, purchased at Radio Shack a decade ago I would guess) with measured (using a cheap transistor-checker) capacitance of 4.32 uF and ESR 2.6 Ohms. The first image is the measured Bode plot (from a Picoscope) where I am applying no DC bias across the capacitor.
Applying a 1V DC bias (using 0.1V peak-to-peak AC) did change things a little, but not dramatically, as shown in the second image.
Now, the theory (including the ESR) says I should measure the following phase shown in the third image.
This is close enough to the measurement that I would say the measurement is expected.
EDIT: if you want to understand qualitatively what is going on, consider what happens when the frequency is high enough that the ESR of the capacitor is much larger than its reactance. At these high frequencies, a resistor of value ESR is a reasonable model for the electrolytic capacitor. So the simple voltage divider equation should give you the gain at high frequencies (and is why the measurements look like they will asymptote to a fixed gain, instead of continuing to fall off at 20 dB / decade). Likewise, the phase should be close to zero. Of course, as the frequency gets higher, other effects (inductance of component leads, capacitance of the resistor, etc) may also play a role.
Case 2: a 4.7 uF film capacitor (a Panasonic metalized polyester 100V job that is quite large!). The fourth image shows the measured Bode plot
Closer to the ideal theory, since the ESR is apparently lower. The cheap tester says this film cap has an ESR of 0.3 Ohms (spec on the cap is < 0.34 Ohms at 1 kHz), but a theoretical plot with 0.05 Ohms is closer to the measurements. I think I believe the scope more than the tester, though. The last plot is the theoretical phase assuming 0.05 Ohm ESR.
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Jason
PS: sorry fo the mess with the images. I tried to make them inline (first with thumbnails) but am not the best user of this forum! Also, I didn't bother to show the theoretical amplitude Bode plots; they also are consistent with the measurements.