# In this question, can i use node analysis method by assuming Δv and Δi is zero in the 1st step of incremental analysis? [closed]

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.)

• 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! Nov 18 at 0:16
• 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.
– jonk
Nov 18 at 3:20
• @jonk what methode should i use? node method by setting the small signal to zero? Nov 18 at 10:09
• @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.
– jonk
Nov 18 at 17:14