The hysteresis it's used whenever you're dealing with slow slope signals (reading a shunt voltage, a delay circuit and so on). If you're not using hysteresis (different high/low thresholds), each time the input signal it's reaching that single threshold, the opamp output quickly toggles.. then the opamp might consider it just reaches the "down" threshold and toggle it's output again.. and that leads to very quick oscillations.
1) why did you use 2 OPamps? could you please explain it's working in brief?
The first opamp toggles its output with a frequency of 1Hz (one second HIGH, one second LOW). When its output is HIGH, the diode D2 keeps the C2 fully charged so the output of the second opamp will be permanently in LOW state (thus no output oscillations).
When the output of the first opamp is LOW, the D2 diode is not conducting so the second opamp will freely oscillate (buzzing).
The D1 diode has a similar behaviour (inhibits first opamp oscillations).
Regarding the way an opamp oscillator works:
The IN+ input could have only two values (the hysteresis resistors being equal and Vref~Vcc/2): 1/4 * Vcc (when opamp output is LOW) and 3/4 * Vcc (when output is HIGH).
Let's say the capacitor C is discharged at the begining. That means the IN- has a voltage level of zero (GND). Regardless the opamp output state, the IN+ voltage is greater than IN- so the opamp output switches to HIGH. Now the capacitor starts to charge through R1. When it reaches the HIGH threshold (3/4 * Vcc), IN- becomes greater than IN+ so opamp output switches to LOW. Now the capacitor starts discharging through R1 until it reaches the LOW threshold (1/4 * Vcc).
The entire cycle then repeats indefinitely.
i have seen some circuits in which a resistor is connected between the output and inverting input of opamp(negative feedback) . In all the circuits that you have provided , has a Vref on non-inverting terminal , what if i choose Vref on inverting terminal of opamp?
For a regular hysteresis comparator, it doesn't matter where you apply the input signal or Vref (to IN- or IN+) as long as you're using the hysteresis network between the output and IN+.
If you apply the input signal at the IN+ input, the HIGH/LOW thresholds are dynamically changed during input signal voltage variations while the IN- remains steady (Vref).
For the oscillator above, it's better to use IN- for the capacitor as to not interfere with the hysteresis network.
Any resistor between output and IN- acts like a negative feedback and it just slows down the commutation process of the comparator. An ideal comparator has an infinite gain, to toggle its output in no time.
- - - Updated - - -
About the one-BJT oscillator.. you need a phase-shift network for that (RC/LC) but you better use a two BJT oscillator (if you ran out of opamps!):
To periodically inhibit its oscillations, just put a diode toward one of BJTs base.