A CEHB, a furnace and a method of constructing a furnace are disclosed. In one embodiment, the CEHB includes: (1) a fixed orifice configured to regulate air flow through a heat exchanger of the furnace, wherein a combustion air inducer induces the air flow and (2) a negative pressure channel including a negative channel supply port that communicates with an inlet of the combustion air inducer, a negative pressure port configured to connect to a negative input port of a pressure switch and bleed ports configured to reduce a pressure received through the negative channel supply port at the inlet to a targeted range at the negative pressure port, the pressure switch configured to monitor a combustion pressure through the heat exchanger.