  The recently proposed Josephson traveling-wave parametric amplifier (JTWPA)
based on a ladder transmission line consisting of radio-frequency SQUIDs and
exploiting three-wave mixing (3WM), has great potential in achieving both a
gain of 20 dB and a flat bandwidth of at least 4 GHz. To realize this concept
in practical amplifiers we model the advanced JTWPA circuit with periodic
modulation of the circuit parameters (engineered dispersion loadings), which
allow the basic mixing process, i.e., $\omega_s=\omega_p-\omega_i$, where
$\omega_s$, $\omega_p$, and $\omega_i$ are the signal, the pump, and the idler
frequencies, respectively, and efficiently suppress propagation of unwanted
higher tones including $\omega_{2p}=2\omega_p$, $\omega_{p+s}=\omega_p
+\omega_s$, $\omega_{p+i} = \omega_p + \omega_i$, etc. The engineered
dispersion loadings allow achieving sufficiently wide $3$ dB-bandwidth from $3$
GHz to $9$ GHz combined with a reasonably small ripple ($\pm2$ dB) in the
gain-versus-frequency dependence.
