Consider the circuit in Figure 4.66. The voltage source and the current source are the sum of a DC-level and an AC-perturbation: v = V + Δv i= I + Δi such that V = 30 V (DC), I = 10 A (DC), Δv = 100 mV (AC), Δi = 50 mA (AC). The resistors have the following values: R1 = R2 = 1/2 . The nonlinear element Z0 has the characteristic: i0 = v0 + v0^2. Find, by incremental analysis, the DC and AC components of the output voltage v0. (Remark: You can assume in your analysis that the nonlinear element is behaving as a passive element, i.e., is consuming power.)

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    \$\begingroup\$ hey, welcome. This is your homework, but you forgot to ask a question for us. So, there's nothing we can answer here. We'll not do your homework! \$\endgroup\$ Nov 18 at 0:16
  • \$\begingroup\$ peachykun, I've no clue what incremental analysis is in your class, but I0 is 30 amps, Z0 is 1/6 Ohm, the change in v0 is 1/7th the change in v and 1/14th the change in i. Work it out. \$\endgroup\$
    – jonk
    Nov 18 at 3:20
  • \$\begingroup\$ @jonk what methode should i use? node method by setting the small signal to zero? \$\endgroup\$
    – peachykun
    Nov 18 at 10:09
  • \$\begingroup\$ @peachykun You don't need to use anything like nodal. You can. But don't need to. Just convert \$i\$ and \$R_1\$ from norton to Thevenin, sum that voltage with \$v\$ and that resistance with \$R_2\$ and work out \$i_0\$. You are given \$i_0\$ as a function of \$v_0\$. Set them equal to each other and solve for \$v_0\$. You have the DC now. It should be easy to see the rest from there. \$\endgroup\$
    – jonk
    Nov 18 at 17:14