On a basic gas furnace and air conditioning system the thermostat control circuit is a simple design. The transformer steps the line voltage down to 24 VAC. When you are checking this circuit the volt meter needs to be set up for AC not DC. The primary side of the transformer should have an input of 120 VAC. The secondary terminals should have an output of 24-28 VAC. If you do not have 120 VAC between the 2 primary terminals you will not have an output voltage. If you do have input voltage between the primary terminals and 0 volts between the secondary terminals the transformer has failed. This indicates an issue in the 24 V circuit that must be addressed. Otherwise the new transformer will fail as soon as power is applied. One of the secondary terminals on the transformer will be connected to one side of all of the operating devices such as contactors, relays, circuit boards. The other secondary terminal supplies the R terminal on the thermostat. The thermostat acts like a switch to turn everything on for operation.

When you have a call for heat the thermostat closes a switch connecting R from the transformer to W on the thermostat. This sends power through all the safety switches to the circuit board to start the fan and to the gas valve to light the burners. Common practice is to connect the red thermostat wire to R and the white thermostat wire to W. The circuit board has a time delay built in to allow the burner to start generating heat before starting the fan. When the thermostat reaches temperature and shuts off the gas valve another time delay is initiated to allow the fan to run and cool down the furnace. This is why we do not recommend aftermarket circuit boards. The timing has been determined by the manufacturer for optimum life and efficiency of the furnace and the algorithm is proprietary to the equipment manufacturer. Using a true OEM board can prevent premature failure of your equipment.