  We investigate the characteristics and noise performance of rf
Superconducting Quantum Interference Devices (SQUIDs) by solving the
corresponding Langevin equations numerically and optimizing the model
parameters with respect to noise energy. After introducing the basic concepts
of the numerical simulations, we give a detailed discussion of the performance
of the SQUID as a function of all relevant parameters. The best performance is
obtained in the crossover region between the dispersive and dissipative
regimes, characterized by an inductance parameter \beta_L'\equiv 2\pi L
I_0/\Phi_0\approx 1; L is the loop inductance, I_0 the critical current of the
Josephson junction, and \Phi_0 the flux quantum. In this regime, which is not
well explored by previous analytical approaches, the lowest (intrinsic) values
of noise energy are a factor of about 2 above previous estimates based on
analytical approaches. However, several other analytical predictions, such as
the inverse proportionality of the noise energy on the tank circuit quality
factor and the square of the coupling coefficient between the tank circuit and
the SQUID loop, could not be well reproduced. The optimized intrinsic noise
energy of the rf SQUID is superior to that of the dc SQUID at all temperatures.
Although for technologically achievable parameters this advantage shrinks,
particularly at low thermal fluctuation levels, we give an example for
realistic parameters that leads to a noise energy comparable to that of the dc
SQUID even in this regime.
