The two states of circuit are only stable for a limited time and the circuit switches between them with the output alternating between positive and negative saturation values.
Analysis of this circuit starts with the assumption that at time t=0 the output has just switched to state 1, and the transition would have occurred.
An op-amp Astable multivibrator is also called as free running oscillator. The basic principle of generation of square wave is to force an op-amp to operate in the saturation region (±Vsat).
A fraction β =R2/(R1+R2) of the output is feedback to the positive input terminal of op-amp. The charge in the capacitor increases & decreases upto a threshold value called ±βVsat. The charge in the capacitor triggers the op-amp to stay either at +Vsat or –Vsat.
Asymmetrical square wave can also be generated with the help of Zener diodes. Astable multi vibrator do not require a external trigger pulse for its operation & output toggles from one state to another and does not contain a stable state.
Astable multi vibrator is mainly used in timing applications & waveforms generators.
1. The expression of fo is obtained from the charging period t1 & t2 of capacitor as T=2RCln (R1+2R2)/R1
2. To simplify the above expression, the value of R1 & R2 should be taken as R2 = 1.16R Such that fo simplifies to fo =1/2RC.
3. Assume the value of R1 and find R2.
4. Assume the value of C & Determine R from fo =1/2R C
5. Calculate the threshold point from βVSATl = R1lVTl/ R1-R2 l/βVSATl w h e r e β is the feedback ratio.
A multivibrator which has only one stable and the other is quasi stable state is called as Monostable multivibrator or one-short multivibrator. This circuit is useful for generating signal output pulse of adjustable time duration in response to a triggering signal. The width of the output pulse depends only on the external components connected to the op-amp. Usually a negative trigger pulse is given to make the output switch to other state. But, it then return to its stable state after a time interval determining by circuit components. The pulse width T can be given as T = 0.69RC. For Monostable operation the triggering pulse width Tp should be less then T, the pulse width of Monostable multivibrator. This circuit is also called as time delay circuit or gating circuit.
1. Calculating β from expression
2. The value of R and C from the pulse width time expression.
3. Triggering pulse width Tp must be much smaller than T. Tp < T.
This signal generator gives two waveforms: a triangle-wave and a square- wave. The central component of this circuit is the integrator capacitor CI. Basically we are interested in performing two functions on CI: charge it, discharge it - repeat indefinitely. The output waveforms are shown here and it is apparent that a square wave generator followed by an integrator acts as a triangular wave generator.
The triangle peaks and period may not accurately meet +/-10V swing at 100 us. The main reason is that current source and thresholds are derived from Zener diodes - not exactly the most accurate reference.
A triangle wave implies that the circuit generates a linear voltage ramp. One way to achieve this goal is by charging discharging CI with a constant current. The Op Amp Integrator provides for this.
Connect RI to VN and With V- held at the virtual ground (0V), a constant current flows from V- to VN.
Iin = VN / RI.
CI integrates Iin creating a positive linear ramp at Vo. The ramp is linear because Vo changes proportionally to the time elapsed ΔT.
ΔVo = - VN / (CI ∙ RI) ∙ ΔT
Ramp Down Connect RI to VP and constant current flows from VP to V-,
Iin = - VP / RI.
Now Vo ramps down linearly ΔVo = - VP / (CI ∙ RI) ∙ ΔT
Ramp Up:ΔVo/ΔT= -VN/(CIRI)
Ramp Down:ΔVo /ΔT = - VP / ( CI∙RI )
These equations show the parameters available to control the ramp up / down speeds. Asymmetrical voltage swings are got by including a reference voltage VREF to the comparator's negative input.
Vth- = VREF ∙ (R1+R2)/R2 -VP ∙ R1 / R2
When do we switch from charging to discharging CI? Basically, there is a need to pick two levels - an upper and a lower threshold - to define the bounds of the triangle wave. The circuit ramps up or down, reversing at the upper and lower thresholds.
· With one leg of RI at VN, the output ramps up until the Upper Threshold (Vth+ ) is reached. Then RI is switched from VN to VP.
· With one leg of RI at VP, the output ramps down until the Lower Threshold (Vth- ) is reached. Then RI is switched from VP to VN.
An Op Amp Comparator with two thresholds. Produce circuit changes in output state from VN to VP (or vice-versa) depending on the upper Vth+ and lower Vth- thresholds.
Vth- = -VP ∙ R1 / R2
o When Vin > Vth+, the output switches to VP, the POSITIVE output state.
o When Vin < Vth-, the output switches to VN, the NEGATIVE output state.
Zener diodes D1 and D2 set the positive and negative output levels:
VP=VfD1+VZD2 VN = VfD2 + VZD1.
These output levels do double duty - they set the comparator thresholds, and set the voltage levels for the next stage - the integrator.