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Provided that v + > v , the op-amp will remain in its positive saturated state, then, until some external condition causes = v + v to become negative This condition is brought about at t = t0 by the trigger pulse vin , which brie y lowers the noninverting-terminal voltage by V volts If V is suf ciently large, the following condition will be satis ed: R2 v + = Vsat V < V R2 + R 3 (1550)
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and the op-amp will switch to the negative saturation state, as indicated in Figure 1557 The noninverting-terminal voltage may be expressed as a function of time for t > t0 , considering that vout has switched to Vsat at t = t0 and the diode now acts as an open circuit, since v is negative With the diode out of the picture, then, the R1 C circuit will discharge, causing v to drop from its initial voltage (V ) toward Vsat The circuit of Figure 1558 depicts the equivalent switching circuit, illustrating that the capacitor discharges from the initial value of vC (t0 ) = V toward the nal value, Vsat Recalling the analysis of transients in 5, we know that the capacitor voltage is given by the expression vC (t) = [vC (t0 ) + Vsat ]e (t t0 )/R1 C Vsat (1551)
Figure 1557 Op-amp monostable multivibrator and typical waveforms
t = t0
R1 C vC (t0) = V
Vsat
vC (t)
Figure 1558 Equivalent charging circuit for monostable multivibrator
15
Electronic Instrumentation and Measurements
As v becomes more negative, it eventually becomes smaller than v + Thus, when the condition vC (t) = [vC (0) + Vsat ]e (t t0 )/R1 C Vsat = v + (1552)
is met, the comparator will switch back to the positive saturation state, +Vsat , and remain in that state until a new trigger pulse is provided The value of the noninverting-terminal voltage during the time the output is in the negative saturated state is determined by the positive feedback circuit: v + = Vsat R2 R2 + R 3 (1553)
Clearly, the duration of the output pulse provided by the one-shot is determined by the time constant of the R1 C circuit, as well as by the value of the resistive voltage divider in the positive feedback network, as illustrated in Example 1514
EXAMPLE 1514 Analysis of Monostable Multivibrator (One-Shot)
Problem
Calculate the duration of the output pulse for the monostable multivibrator of Figure 1557
Solution
Known Quantities: Component values; diode offset voltage; supply saturation voltage Find: Duration of output pulse, T
100 k ; C = 7 F; V = 06 V; Vsat = 16 V t0 = 0 (see Figure 1557)
Schematics, Diagrams, Circuits, and Given Data: R1 = 20 k ; R2 = 670
; R3 =
Assumptions: A small pulse of amplitude V is applied to the input of the monostable at
Analysis: To compute the switching time of the circuit we need to determine when the
capacitor will charge to a voltage such that v = vC is equal to v + We use equation 1551 to compute the expression for the capacitor voltage: vC (t) = [vC (0) + Vsat ]e t/R1 C Vsat Note that vC (0) = 06 V because of the diode connected in parallel to the capacitor The noninverting terminal voltage is computed from: v + = Vsat R2 = 01065 V R2 + R 3
Setting the two above expressions equal to one another we obtain: 01065 = 166e 1064 10 or T = 1 158935 loge = 409 10 3 = 409 ms 1064 10 3 166
3 T
16
Part II
Electronics
Comments: In practice one rarely uses op-amps to build monostable multivibrators Integrated-circuit multivibrators are introduced next
Monostable multivibrators are usually employed in IC package form An IC one-shot can generate voltage pulses when triggered by a rising or a falling edge, that is, by a transition in either direction in the input voltage Thus, a one-shot IC offers the exibility of external selection of the type of transition that will cause a pulse to be generated: a rising edge (from low voltage to high, typically zero volts to some threshold level), or a falling edge (high-to-low transition) Various input connections are usually provided for selecting the preferred triggering mode, and the time constant is usually set by selection of an external RC circuit The output pulse that may be generated by the one-shot can also occur as a positive or a negative transition Figure 1559 shows the response of a one-shot to a triggering signal for the four conditions that may be attained with a typical one-shot
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