# How to determine the variation in Q point given some resistor tolerances

In Microelectronics 4ed (Neamen), in page 157 Ex 3.8 they ask to find how Id and Vd would vary acording to some variation in the resistors. They don't explain how to do this in the book so i thought using partial derivatives on Id(R1,R2) with respect to R1 and R2 and see how the function behaves in the scope that they are asking me. Then evaluate Id acordingly. I couldn't arrive to the answer through this method because the derivatives weren't that friendly.

One could arrive to the answer graphing with matlab or using LTspice but i think there should be an easier way to do this. So that is my question, is there an easier way to arrive to the answer? How?

Ex 3.8: (a) Consider the circuit shown in Figure 3.33. The transistor parameters are VT P = −0.40 V and Kp = 30μA/V2. Design the circuit such that IDQ = 60μA and VSDQ = 2.5 V. (b) Determine the variation in Q-point values if the VT P and Kp parameters vary by ±5 percent. (Ans. (a) RS = 19.77 k, RD = 38.57 k; (b) 58.2 ≤ IDQ ≤ 61.08μA, 2.437 ≤ VSDQ ≤ 2.605 V

• Please show us how far you got working on this yourself. Show us the equations that you came up with and explain why they "weren't that friendly". – Elliot Alderson May 5 at 1:44