  Molecular communication is an emerging paradigm for systems that rely on the
release of molecules as information carriers. Communication via molecular
diffusion is a popular strategy that is ubiquitous in nature and very fast over
distances on the order of a micron or less. Existing closed-form analysis of
the diffusion channel impulse response generally assumes that the transmitter
is a point source. In this paper, channel impulse responses are derived for
spherical transmitters with either a passive or absorbing receiver. The derived
channel impulse responses are in closed-form for a one-dimensional environment
and can be found via numerical integration for a three-dimensional environment.
The point transmitter assumption (PTA) is formally defined so that its accuracy
can be measured in comparison to the derived spherical transmitter impulse
responses. The spherical transmitter model is much more accurate than the PTA
when the distance between a transmitter and its receiver is small relative to
the size of the transmitter. The derived results are verified via microscopic
particle-based simulations using the molecular communication simulation
platform AcCoRD (Actor-based Communication via Reaction-Diffusion). A spherical
transmitter variation where molecules are released from the surface of a solid
sphere is also considered via simulation.
