questions about mixer

i would like to ask is it possible to design a simple single transistor mixer with all the three ports well-matched.

Yes, is possible to design this kind of mixer, but is rarely implemented.
In this case is preferable to use a BJT instead of a FET. BJT due to its impedances is easier to be matched.
The most critical is the input matching circuit, that should not only match the RF source to BJT base-emitter junction, but must also provide an IF short circuit to the device.
If the IF frequency is much lower than the RF, this short can be realized via the bias-circuit elements. As long as the IF short is realized effectively, the only other critical function of the input matching network is impedance matching at the RF frequency and, if possible, at the LO frequency.

thanks alot .
btw i would like to ask why need an IF short circuit?
to provide a good isolation for IF to RF?!

Yes, this is the only way to get isolation for this kind of mixer.