The basic UJT relaxation oscillator circuit is as shown in figure. in this circuit the capacitor c1 is charged through potentiometer R1, until the emitter voltage reaches Vp at which time UJT turns ON and discharges C1 through R2. when the emitter voltage reaches a value of about 2v, the UJT stops conducting and the cycle repeats. the charging time for capacitor C1 depends on the value of the capacitor C1 depends on the value of the potentiometer R1. the period of oscillations T is independent of the supply voltage Vcc and temperature and it is given by,

T = $\frac{1}{f}$ = $R_1$ $c_1$ loge [$\frac{1}{1-\eta}]$

T = $\frac{1}{f}$ $\approx$ 2.3 $R_1$ $c_1$ logio [$\frac{1}{1-\eta}]$

where $\eta$ = intrinsic stand off ratio

$\eta$ = 0.63

The waveform for the basic relaxation oscillator is shown. if the o/p pulses are used for triggering the SCR, resistance R2 should be made sufficiently small so that the voltage drop across R2 due to leakage current. when UJT is OFF, it will not trigger the SCR. The total energy dissipated in R2 in parallel with the gate to cathode resistance is approximately equal to the energy stored in the capacitor C1 at the time the UHT is switched ON. there is minimum amount of energy required for reliable turn ON of the SCR.

stored energy = $\frac{1}{2}$ C1 $\eta^2$ $Vcc^2$

and this stored energy should be greater than or equal to minimum energy to turn on SCR. once the value of C1 is decided, R1 can be calculated from the following equation.

T = $R_1$ $C_1$ loge [$\frac{1}{1-\eta}]$