Bistable multivibrator – has two stable states ; the circuit can remain in either stable state indefinitely and moves to the other stable state ONLY when appropriately triggered.
The Feedback Loop –
Bistability can be obtained by connecting an amplifier in a positive-feedback loop having a loop gain greater than unity as shown in the following figure which consists of an op-amp and a resistive voltage divider in the positive-feedback loop.
Assume the electrical noise that is inevitably present which causes a small positive increment in the voltage v+.
The incremental signal will be amplified by the large open-loop gain A of the op amp resulting in much greater signal in the op-amp’s output voltage vo.
Notice that the feedback factor β = R1/(R1+R2) which feed the fraction of the output signal back to the positive input terminal of the op amp. If loop gain βA is greater than unity, the fed-back signal will be greater than the original increment in v+.
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The regenerative process continues until eventually the op amp saturates with its output voltage at the positive saturation level, L+
The voltage at the positive input terminal becomes L+R1/(R1+R2) which is positive and thus keeps the op amp in positive saturation.
So, what’s happening for a negative increment ?
We thus conclude the circuit has two stable states, one with the op amp in positive saturation and the other with the op amp in negative saturation.
Transfer Characteristics of the Bistable Circuit –
Refer to the circuit we know that there are two circuit nodes that are connected to ground can serve as an input terminal.
One possible external input configuration is shown in the follows,
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Here an input vIapplied to the inverting input terminal of the op amp. As vI is increased from 0V there is nothing happens until vI reaches a value equal to v+ ( βL+, L+ is one of the two possible levels )
As vI begins to exceed this value, a NET negative voltage develops between the input terminals of the op amp and this voltage is amplified by the open-loop gain of the op amp which makes vo goes negative.
Finally, the voltage divider in turn causes v+ to go negative, thus increasing the net negative input to the op amp and keeping the regenerative process going.
Let’s consider what happens as vI is decreased. Here we see that the circuit remains in the negative-saturation state until vI goes negative to the point that it equals βL-……..
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As vI goes below this value,…….
The complete transfer characteristics indicates the circuit changes state at different values of vI , depending upon whether vI is increasing or decreasing ⇒ hysteresis.
The width of the hysteresis is the difference between the high threshold VTH and the low threshold VTL.
Since the bistable circuit switches from the positive state to negative state as vI is increased past the positive threshold VTH, the circuit is said to be inverting.
Triggering the Bistable Circuit –
According to the last figure, we know that if the circuit is in the L+ state it can be switched to the L- state by applying an input vI of value greater than VTH ≡ βL+.
Such an input causes a net negative voltage to appear between the input terminals of the op amp, which initiates the regenerative cycle that culminates in the circuit switching to the L- stable state.
The input signal vI is thus referred to as a trigger signal ( trigger ).
The Bistable Circuit as a Memory Element –
Notice that for input voltages in the range VTL < vI < VTH the output can be either L+ or L- , depending on the state that the circuit is already in.
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Thus for this input range, the output is determined by the previous value of the trigger signal.
⇒ The circuit exhibits memory.
Note that we also call the bistable circuit as a Schmitt trigger.
A Bistable Circuit with Non-inverting Transfer Characteristics –
By applying a trigger signal vI to the terminal of R1, we can obtain a bistable circuit with non-inverting transfer characteristics.
By employing superposition, we can express v+ in terms of vI and vo as
Here we know for positive stable state vo = L+ , positive values vI make v+remain in positive values.
However, for negative vI we can trigger the circuit into the L -state by letting v+ decrease below zero.
Thus, the low threshold VTL can be obtained by substituting v0 = L+ , v+ = 0 and vI = VTLinto the above equation, which results in
So, what’s going to happen for VTH ?
The Bistable Circuit as a Comparator –
Recall that we use comparators in some analog-circuit building blocks such as in analog-to-digital ( A/D ) converters. Note that we may think comparators have only a single threshold value as shown in the following figures.
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However, it can be very useful to add hysteresis to a comparator in many applications. In other words, we obtain TWO threshold values, VTL and VTHsymmetrically placed around the desired reference level as shown in figure (b).
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Let’s see what happen if we got interference in a circuit as shown in the following figure.
The signal might cross the zero axis a number of times around each of the zero-crossing points. The comparator would thus change state a number of times at each of the zero crossings, which it can lead to malfunctions.
However, if we have an idea of the expected peak-to-peak amplitude of the interference, the problem can be solved by introducing hysteresis of appropriate width in the comparator characteristics.
In other words, if the input signal is increasing in magnitude, the comparator with hysteresis will remain in the low state until the input level exceeds the high threshold VTH and vice versa.
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We can also employ limiter circuits to obtain more precise output levels as illustrated in the following figures.
Generation of Square Waveforms using Astable Multivibrators
- A square waveform can be generated by arranging for a bistable multivibrator to switch states periodically, which we can connect the bistable multivibrator with an RC circuit in a feedback loop as shown in the following figure.
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Operation of the Astable Multivibrator
- Let’s firstly investigate the operation of the following circuit.
Since we obtain a positive feedback configuration, we may assume the output of the bistable multivibrator be one of the possible levels, say L+.
Capacitor C will start to charge toward this level through resistor R. Thus the voltage at v- will rise exponentially toward L+ with a time constant τ = CR and the voltage at v+ = βL+.
This situation will continue until the capacitor voltage reaches the positive threshold VTH at which point the bistable multivibrator will switch to the other stable state in which vo = L- and v+ = βL-.
And then the capacitor starts to discharge, and its voltage v- will decrease exponentially toward L-.
By this brief investigation, we realize the astable circuit oscillates and produces a square waveform at the output of the op amp.
But, how can we find out the period T of the square wave ? ( Recall the time constant RC ……. )
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We may simplify the circuit as an RC circuit as shown in the
Nevertheless, T1 can be calculated from
and Therefore,
force response natural response
−
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Note that here we also call the astable circuit has two quasi-stable states.
Generation of Triangular Waveforms –
We can obtain triangular waveforms by replacing the low-pass RC with an integrator as shown in the following figures.
The basic idea is that the integrator causes LINEAR charging /
discharging of the capacitor, which provides a triangular waveform.
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Let’s check how it operates, firstly we may assume the output of the bistable circuit be at L+, then we spot there will be a current L+/R flows into the resistor R and through capacitor C, which causes the output of the integrator to linearly decrease with a slope of –L+/CR.
This will continue until the output reaches the lower threshold VTL of the bistable circuit and makes the circuit switch states to L-. Note that at this moment the current through R and C will
reverse direction, and its value is |L-|/R. The output will start to increase linearly with a positive slope |L-|/RC until the output voltage reaches VTH.
So, we can find out T1 and T2, we know that Thus,
Similarly, we can have
CR
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Generation of a Standardized Pulse with Monostable Multivibrator
- The monostable multivibrator has one stable state in which it can remain indefinitely and a quasi-stable state to which it can be triggered and stays for a predetermined interval equal to the desired width of the output pulse.
We also called the monostable multivibrator as one shot.
Here the circuit comprises a clamping diode D1 is added across C1 , and a trigger circuit composed of C2, R4, and D2.
So, how it operates ? ( assume vAis L+ , vC is βL+ and vBis clamped to VD1 )
Trigger signal – negative triggering edge will be coupled to diode D2 via C2 and thus D2 conducts heavily and pulls node C down. If vC is below vB, the op amp will see a net negative input voltage and the output switch to L-.
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vC is now βL- and D2 cutoff which isolates the circuit from the trigger input terminal.
The negative voltage at A causes D1 to cut off, and C1 starts to discharge exponentially toward L- with a time constant C1R3.
The op-amp output switches back to L+ when vB goes below the voltage at node C ( βL- )
So we can calculate the duration T of the quasi-stable state with
By substituting vB(t) = βL- yields if VD1 << |L-|
Recovery period – the next trigger shall be activated until C1 has been recharged to VD1.
3
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Integrated-Circuit Timers –
The 555 Circuit
-Threshold
Trigger Discharge
The circuit comprises two comparators, an SR flip-flop, and a switch, transistor Q1. A resistive voltage divider consisting of three equal-valued resistors R1.
Note that the SR flip-flop are bistable circuits having complementary outputs.
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The figure shows a monostable multivibrator implemented using the 555 IC together with an external resistor R and an external
capacitor C.
In the stable state, the FF will be in the reset state and thus Q=0 and Q1 will be saturated, thus vC will be close to 0.
⇒ vo,comp1 = low
Also, vtrigger= high ⇒ vo,comp2 = low.
A negative input pulse is applied to the trigger input terminal to trigger the monostable multivibrator.
vtrigger= low which lower than VTL ⇒ vo,comp2 = high which sets the FF ⇒ turning off Q1 ⇒ capacitor C begins to charge up through resistor R and vC rises exponentially toward VCC.
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So, how does it return to the stable state ?
vC can be expressed as
Substituting vC = VTH = 2/3 VCC at t = T gives T= CR ln 3
An Astable Multivibrator Using the 555 IC – ) 1
( t/ RC
CC
C V e
v = − −
Here we employ a 555 IC and two external resistors RA and RB and an external capacitor C.
We may assume that firstly C is discharged and the FF is set, thus vo is high and Q1 is off. C will be charged up through the series combination of RA and RB. vC will rise exponentially toward VCC.
Firstly, vC will be higher than VTL but it doesn’t have any effect and vC continues to rise. When it is higher than VTH , vo,comp1= high which reset the FF and Q = 0, Q1 is turned on.
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It saturates Q1 and causes the common point of RA and RB near zero. Thus, C begins to discharge through RB and the collector of Q1 with the time constant CRB toward 0.
When vC reaches VTL, the output of comparator 2 goes high and sets the FF which turns off Q1 . Capacitor C begins to charge
through the series equivalent of RA and RB with the time constant C( RA + RB ).
How can we calculate the period T = TH + TL ? The exponential rise of vC can be described by
Substituting vC = VTH = 2/3VCC at t = TH and VTL = 1/3VCC results in TH = C( RA + RB ) ln2
How can we find out TL ?
) R t/C(R TL
CC CC
C V (V V )e A B
v = − − − +
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Nonlinear Waveform-Shaping Circuits
Diodes or transistors can be combined with resistors to synthesize two-port network having arbitrary nonlinear transfer characteristics.
The Breakpoint Method –
The desired nonlinear transfer characteristic is implemented as a piecewise linear curve.
Diodes are utilized as switches that turn on at the various
breakpoints of the transfer characteristic, which switch into the additional resistors that cause the transfer characteristic to change slope.