  In a neuron with hyperpolarization activated current ($I_h$), the correct
input frequency leads to an enhancement of the output response. This behavior
is known as resonance and is well described by the neuronal impedance. In a
simple neuron model we derive equations for the neuron's resonance and we link
its frequency and existence with the biophysical properties of $I_h$. For a
small voltage change, the component of the ratio of current change to voltage
change ($dI/dV$) due to the voltage-dependent conductance change ($dg/dV$) is
known as derivative conductance ($G_h^{Der}$). We show that both $G_h^{Der}$
and the current activation kinetics (characterized by the activation time
constant $\tau_h$) are mainly responsible for controlling the frequency and
existence of resonance. The increment of both factors ($G_h^{Der}$ and
$\tau_h$) greatly contributes to the appearance of resonance. We also
demonstrate that resonance is voltage dependent due to the voltage dependence
of $G_h^{Der}$. Our results have important implications and can be used to
predict and explain resonance properties of neurons with the $I_h$ current.
