Unijunction Relaxation Oscillator

Operation of the Unijunction Transistor:

When battery V_BB is turned on, the capacitor C charges through resistor R₁. During the charging period the voltage across the capacitor rises in an exponential manner until it reaches the peak point voltage. At this instant of time the UJT switches to its low resistance conducting mode and the capacitor is discharged between E and B₁. As the capacitor voltage flies back to zero, the emitter ceases to conduct and the UJT is switched off. The next cycle then begins allowing the capacitor C to charge again. The frequency of the output saw tooth wave can be varied by changing the value of R₁ since this control the time constant (R₁C) of the capacitor charging circuit.

V_C = V_BB(1 - e^-t/R₁C)

The discharge of the capacitor occurs when V_C is equal to the peak point voltage ηV_BB.

ηV_BB = V_BB(1 - e^-t/R₁C)

η = 1 - e^-t/R₁C

e^-t/R₁C = 1 - η

t = R₁Clog_e1/(1 - η)

t = 2.3R₁Clog₁₀1/(1 - η)