<Dd> f o s c i l l a t i o n = 1 2 π R 2 R 3 (C 1 C 2 + C 1 C 3 + C 2 C 3) + R 1 R 3 (C 1 C 2 + C 1 C 3) + R 1 R 2 C 1 C 2 (\ displaystyle f_ (\ mathrm (oscillation)) = (\ frac (1) (2 \ pi (\ sqrt (R_ (2) R_ (3) (C_ (1) C_ (2) + C_ (1) C_ (3) + C_ (2) C_ (3)) + R_ (1) R_ (3) (C_ (1) C_ (2) + C_ (1) C_ (3)) + R_ (1) R_ (2) C_ (1) C_ (2)))))) </Dd> <P> The feedback resistor required to just sustain oscillation is: </P> <Dl> <Dd> R f b = 2 (R 1 + R 2 + R 3) + 2 R 1 R 3 R 2 + C 2 R 2 + C 2 R 3 + C 3 R 3 C 1 + 2 C 1 R 1 + C 1 R 2 + C 3 R 3 C 2 + 2 C 1 R 1 + 2 C 2 R 1 + C 1 R 2 + C 2 R 2 + C 2 R 3 C 3 + C 1 R 1 2 + C 3 R 1 R 3 C 2 R 2 + C 2 R 1 R 3 + C 1 R 1 2 C 3 R 2 + C 1 R 1 2 + C 1 R 1 R 2 + C 2 R 1 R 2 C 3 R 3 (\ displaystyle (\ begin (aligned) R_ (\ mathrm (fb)) = &2 (R_ (1) + R_ (2) + R_ (3)) + (\ frac (2R_ (1) R_ (3)) (R_ (2))) + (\ frac (C_ (2) R_ (2) + C_ (2) R_ (3) + C_ (3) R_ (3)) (C_ (1))) \ \ & + (\ frac (2C_ (1) R_ (1) + C_ (1) R_ (2) + C_ (3) R_ (3)) (C_ (2))) + (\ frac (2C_ (1) R_ (1) + 2C_ (2) R_ (1) + C_ (1) R_ (2) + C_ (2) R_ (2) + C_ (2) R_ (3)) (C_ (3))) \ \ & + (\ frac (C_ (1) R_ (1) ^ (2) + C_ (3) R_ (1) R_ (3)) (C_ (2) R_ (2))) + (\ frac (C_ (2) R_ (1) R_ (3) + C_ (1) R_ (1) ^ (2)) (C_ (3) R_ (2))) + (\ frac (C_ (1) R_ (1) ^ (2) + C_ (1) R_ (1) R_ (2) + C_ (2) R_ (1) R_ (2)) (C_ (3) R_ (3))) \ end (aligned))) </Dd> </Dl> <Dd> R f b = 2 (R 1 + R 2 + R 3) + 2 R 1 R 3 R 2 + C 2 R 2 + C 2 R 3 + C 3 R 3 C 1 + 2 C 1 R 1 + C 1 R 2 + C 3 R 3 C 2 + 2 C 1 R 1 + 2 C 2 R 1 + C 1 R 2 + C 2 R 2 + C 2 R 3 C 3 + C 1 R 1 2 + C 3 R 1 R 3 C 2 R 2 + C 2 R 1 R 3 + C 1 R 1 2 C 3 R 2 + C 1 R 1 2 + C 1 R 1 R 2 + C 2 R 1 R 2 C 3 R 3 (\ displaystyle (\ begin (aligned) R_ (\ mathrm (fb)) = &2 (R_ (1) + R_ (2) + R_ (3)) + (\ frac (2R_ (1) R_ (3)) (R_ (2))) + (\ frac (C_ (2) R_ (2) + C_ (2) R_ (3) + C_ (3) R_ (3)) (C_ (1))) \ \ & + (\ frac (2C_ (1) R_ (1) + C_ (1) R_ (2) + C_ (3) R_ (3)) (C_ (2))) + (\ frac (2C_ (1) R_ (1) + 2C_ (2) R_ (1) + C_ (1) R_ (2) + C_ (2) R_ (2) + C_ (2) R_ (3)) (C_ (3))) \ \ & + (\ frac (C_ (1) R_ (1) ^ (2) + C_ (3) R_ (1) R_ (3)) (C_ (2) R_ (2))) + (\ frac (C_ (2) R_ (1) R_ (3) + C_ (1) R_ (1) ^ (2)) (C_ (3) R_ (2))) + (\ frac (C_ (1) R_ (1) ^ (2) + C_ (1) R_ (1) R_ (2) + C_ (2) R_ (1) R_ (2)) (C_ (3) R_ (3))) \ end (aligned))) </Dd>

Circuit diagram of rc phase shift oscillator using op amp