Does drag increase with increasing bypass ratio in turbofan engines?

Does drag increase as the bypass ratio increases in turbofan engines? Is there an analytical expression describing the increase in drag related to an increase in the fan duct diameter? How else might one consider this effect?

• To me the bypass path seems to be a lower drag path than it would if it were going through the compressor, so it would (maybe I'm completely wrong) that increasing the bypass ratio wouldn't increase the drag vs the same size duct and a lower bypass ratio. – Ron Beyer Jul 4 '16 at 3:51

According to this 1975 NASA report on the effects of turbofan engine bypass ratio, the drag does increase for increasing bypass ratios. In the report, they use the following drag coefficient equation: $$C_{D,prop}=C_{D,nacelle}\cdot \frac{A_{nacelle}}{S} = \frac{D_{nacelle}}{\rho_\infty A_{nacelle}} \cdot \frac{A_{nacelle}}{S}$$ As shown below, the nacelle drag coefficient initially increases for increasing bypass ratio.
Since $\frac{A_{nacelle}}{S}$ also increases with bypass ratio, the propulsion system drag will increase as well. So drag is closely related to the frontal area of the engine.