The common Gunn diode oscillator (circuit diagrams) illustrates how negative resistance oscillators work. The diode D has voltage controlled ("N" type) negative resistance and the voltage source V b biases it into its negative resistance region where its differential resistance is d v / d i = − − r . The choke RFC prevents AC current from flowing through the bias source. R is the equivalent resistance due to damping and losses in the series tuned circuit L C , plus any load resistance. Analyzing the AC circuit with Kirchhoff's Voltage Law gives a differential equation for i ( t ) , the AC current d 2 i d t 2 + R − − r L d i d t + 1 L C i = 0 Solving this equation gives a solution of the form i ( t ) = i 0 e α α t cos ⁡ ⁡ ( ω ω t + ϕ ϕ ) where α α = r − − R 2 L ω ω = 1 L C − − ( r − − R 2 L ) 2 This shows that the current through the circuit, i ( t ) , varies with time about the DC Q point, I bias . When started from a nonzero initial current i ( t ) = i 0 the current oscillates sinusoidally at the resonant frequency ω of the tuned circuit, with amplitude either constant, increasing, or decreasing exponentially, depending on the value of α. Whether the circuit can sustain steady oscillations depends on the balance between R and r , the positive and negative resistance in the circuit: