  In this note we describe Josephson parametric amplifier (JPA) matching
networks based on Legendre polynomials. These networks typically exhibit lower
ripple and gentler roll-off than Chebyshev networks with similar parameters,
and can be viewed as bridging the gap between Butterworth and Chebyshev ones.
We tabulate prototype coefficients for parametric amplifiers based on Legendre
polynomials with a range of gain and ripple parameters, and for a range of
network orders. We also use this opportunity to further illustrate the
synthesis of these networks based on methods from previous work, and synthesize
a prototype JPA with 20dB gain at a center frequency of 5GHz with a bandwidth
of 500MHz.
