A B737-300 flight crew declared an emergency and returned to their departure airport following the loss of multiple auto flight capabilities accompanied by a report of smoke in the cabin by the flight attendants.

Narrative

Everything was normal until rotation when the Flight Director disappeared and the Auto Pilot Disconnect horn and warning light activated. While cleaning up the aircraft the Master Caution; Mach Trim and Yaw Damper lights illuminated. We were now VMC above a cloud layer and started to complete the Mach Trim Failure Checklist. A Flight Attendant then called to report smoke and fumes in the cabin.We donned our oxygen masks and completed the memory items for smoke in the cabin and cockpit. I was the pilot flying and flew the aircraft for the return approach and landing. The Captain declared an emergency; communicated with the flight attendants about the condition of the cabin and passengers; completed the Smoke Removal Checklist; and set up the aircraft for the return to our departure airport. The autopilot and Flight Director were not available. Upon landing; the Fire Department escorted us back to the gate. The passengers were deplaned and the aircraft was turned over to Maintenance. A preliminary inspection turned up a damaged inverter in the E&E compartment.