The PI-1, 5, 10, and 100 series Integrators are passive resistor-capacitor integrators with standard RC time constants of 1, 5, 10 or 100 microseconds. They are available with standard connector types such as N-type (shown) or other styles can be specified. The unit and its idealized circuit (which is based on the AFWL RCI-1B integrator) is shown below:

The transfer function of the Integrator is implicit in the differential equation:

where Q is the charge on the capacitor. The integrator is designed to drive a >1 megohm, <10 pf load impedance. The voltage out is essentially the voltage across the capacitor, Q/C, which is calculated by solving (integrating) the differential equation for Q(t). This is most conveniently done by Laplace transforms, which yield the transfer function in the frequency domain:

where s = j = Laplace operator. The transfer function is an integrator for sinusoidal inputs with frequencies large compared to 1/2RC ; or for transient inputs for times small compared to RC. Typical performance of the PI-100 integrating a 5ms square pulse is shown below. This pulse is integrated with an error of 2.5% over the 5ms duration.

SPECIFICATIONS