# Bi-SQUID Versus dc SQUID in Flux-Driven Traveling-Wave Parametric Amplifier
## 3 Increase in Dynamic Range Using bi-SQUID Cells
As follows from the numerical simulation (see [21]), this current always flows through the third junction in the same direction independently of the transport current direction; however, on different paths through the other circuit elements, there is a dependence on the transport current direction and therefore it changes distribution of the transport current between the main junctions J1 and J2. These two possible paths of the current \(I_{3}\) are shown in Figure 4b by the red lines and red arrows for the positive transport current and by the green lines and arrows for the negative transport current. In both cases, the current \(I_{3}\) provides a decrease in the current flowing through that junction which is responsible for nonlinearity in the relation between the phase drop \(\Delta\varphi\) and the transport current \(i_{b}\) (i.e., for nonlinearity of the dipole inductance of the cell). As an example, Figure 5 shows phase drops \(\Delta\varphi\) on both dc SQUID (green line) and bi-SQUID (blue line) having the same critical current \(I_{c}\) of the basic junctions, J1 and J2, and the same normalized geometric inductance \(l=0.5\) versus the transport current \(i_{b}=I_{b}/I_{c}\) created by both the signal and idler waves. The same dc magnetic flux \(\Phi_{dc}=\Phi_{0}/3\) is applied to both devices to the set operation point. In bi-SQUID, the normalized critical current of the third junction \(i_{c3}\equiv I_{c3}/I_{c}=2\). The presented dependences evidence the appreciable increase in the linearity range when using bi-SQUID cells and hence the increase in the dynamic range of the flux-driven JTWPA. Quantitative characterization of the linearity domain increase can be conducted by considering the 1 dB compression points of the power gain. Figures 6 and 7 present the calculated 1 dB compression points as a function of the applied dc bias flux \(\varphi_{dc}=2\pi\Phi_{dc}/\Phi_{0}\), setting the operation point for both the dc SQUID cell and the bi-SQUID cell at the same values, \(l=1\) and \(l=0.75\), of the normalized cell inductances. It is evidenced that dynamic range of the flux-driven JTWPA can be increased by two to three times when using bi-SQUID cells. Figure 4: After [21]. (**a**) Josephson phases and currents through the junctions J1 and J2 described by two points in sinusoid on the current-phase plane when some dc magnetic flux is applied to the cell, dc SQUID or bi-SQUID, inducing counterclockwise circular screening supercurrent, and bias current is absent. The red and green arrows show directions of displacement of the points at positive (red color) and negative (green color) bias current. (**b**) Paths of the current flowing through the additional junction in bi-SQUID at positive (red lines and red arrows) and negative (green lines and arrows) bias currents. The junctions J1 and J2 are on the left and right sides, respectively, and J3 is above them. Figure 5: After [21]. Phase drops on both dc SQUID (green line) and bi-SQUID (blue line) with \(i_{\text{c3}}=2\) and same value \(l=0.5\) of the normalized geometric inductance versus transport current. The same dc magnetic flux \(\Phi_{dc}=\Phi_{0}/3\) is applied to both devices.