Pretty much all aeroplanes (including little aeroplanes) will phugoid to some extent, although since it's invariably a nuisance mode, you'd hope that it'll be well damped.
Classical theory, with a bit of crunching, should give you a phugoid period in seconds of about 0.85 of the trimmed speed in knots. In practice this is hardly ever the case and the period is usually rather faster - as you've observed.
I'm not sure I've ever seen a rigorous study of what causes the phugoid in light aeroplanes, but in my experience it's usually elasticity and inertia in the pitch control circuit. In particular long and reasonably thin elevator / stabilator cables can usually give quite a marked and lightly damped phugoid.
G