jQuery fullcalendar send custom parameter and refresh calendar with JSON

try this:

$(document).ready(function () {
    $('#calendar').fullCalendar({
        events: {
            url: '/myfeed',
            data: function () { // a function that returns an object
                return {
                    personId: $('#personDropDown').val(),
                };

            }
        });


    $('#personDropDown').change(function () {
        $('#calendar').fullCalendar('refetchEvents');
    });

});