Question 8.PE.2: To investigate the astable multivibrator using (a) the 741 o...
To investigate the astable multivibrator using (a) the 741 operational amplifier ic, (b) the 555 timer ic, (c) the 7414 Schmitt trigger ic
For this exercise you will need the following components and equipment:
1 – 741 ic (operational amplifier)
1 – 555 ic (timer)
1 – 74LS14 ic (hex inverting Schmitt trigger)
1 – ±15 V dc supply
1 – +5 V dc supply
1 – set of components for the 741 circuit:
resistors 1 × 100 kΩ, 1 × 10 kΩ, 1 × 1 kΩ
potentiometer 1 × 5 kΩ
capacitor 1 × 0.1 μF
1 – set of components for the 555 circuit:
resistors 2 × 4.7 kΩ
capacitors 1 × 0.01 μF, 1 × 0.1 μF
1 – set of components for the 7414 circuit:
resistor 1 ÷ 1 kΩ
capacitor 1 ÷ 0.1 μF
1 – double-beam cathode ray oscilloscope
Procedure (a): using the 741 operational amplifier
1 Connect up the circuit of Figure 8.11. The pin connection diagram for the 741 ic is shown in Figure 8.4.
2 Sketch, on graph paper, the waveform of the voltages across the capacitor C_{1} and at the output, which should resemble those shown in Figure 8.12. Make sure that you show clearly the voltage and time values.
3 Measure (using the oscilloscope) the periodic time of the output waveform and hence calculate its frequency.
4 Modify the circuit to that of Figure 8.13 and show that a variation in frequency can be achieved. Measure this variation (maximum to minimum).
Conclusions
If you now work through the following exercise, it should help your understanding of the action of this form of astable.
Important points
• From the circuit (Figure 8.11), notice the positive feedback from the output, through the potential divider R_{2} and R_{3} to the non-inverting (+) input.
• For a supply voltage V_{S} of ±15 V, the maximum (saturated) output from the amplifier (V_{Osat}) will be about ±13 V.
• The fraction of the output voltage fed back (β) is given by
\beta=\frac{R_{3}}{R_{2}+R_{3}}=\frac{1 \mathrm{k} \Omega}{11\mathrm{k} \Omega}=0.091 \mathrm{k} \Omega• The expected voltage at the non-inverting input for the saturated output will be given therefore by
β × ± V_{s}
which, for the above values, gives
0.091 × ±13 V or ±1.18 V
Copy out the following statements, selecting the correct word from within the square brackets and filling in the spaces with values or names as appropriate
1 Assume that the output is at its maximum positive value, that is, the output
voltage = + V_{Osat} = + ــــــــــــ.
This positive voltage charges up the capacitor (C_{1}) through the ـــــــــــ ( ).
2 As C_{1} charges up positively, the voltage at the ـــــــــــ input [rises/falls] until after a time t = t_{1} when it becomes more [positive /negative] than the voltage at the ــــــــــ input.
The amplifier output will now swing rapidly [negative/positive] to a value of ـــــــــ V, helped by the action of [positive/negative] feedback.
3 This [negative/positive] voltage will again charge up the ـــــــــ ( ) through the ـــــــــ ( ), until the input becomes more [positive/negative] than the ـــــــــ input, at which point (t – t_2), the amplifier output voltage switches back to a [positive/negative] saturated value (= ـــــــــ V).
4 The theoretical value of the frequency (f) of the output waveform, also known as pulse repetition frequency (prf), is given by f = 1/T, where
T=2 C_{1} R_{1} \log _{e}\left(1+\frac{2 R_{3}}{R_{2}}\right)(f in hertz, T in seconds, C in farads, R in ohms, and e the base of Naperian logarithms).
Compare the theoretical and measured values and account for any differences.
5 For the circuit modification shown in Figure 8.13 calculate the theoretical frequency range possible.
Note. You will need to take into account the value of RV_1 that is in series with R_2 and R_3 respectively.
Procedure (b): using the 555 timer
1 Connect up the circuit of Figure 8.14. The pin connection diagram for the 555 ic is shown in Figure 8.15.
2 Sketch, on graph paper, the waveform of the voltages across the capacitor C_1 and at the output, which should resemble those shown in Figure 8.16. Make sure that you show clearly the voltage and time values.
3 Measure (using the oscilloscope) the periodic time of the output waveform and hence calculate its frequency.
Conclusions
Important points
• At switch-on, the capacitor is uncharged and the output (at pin 3) will
be high (approximately +V_{CC}).
• Capacitor C_1 charges up towards the supply voltage +V_{CC} with a time constant of CxR seconds, where
• C = C_1 (farads) and R = (R_1 + R_2) (ohms)
• When the voltage across C_1 (pin 6) reaches an upper threshold value of \frac{2}{3} V_{CC} (at time t_1 in Figure 8.16) the output goes low (approximately 0 V).
• Capacitor C_1 then discharges through R_2 (time constant C_1R_2) until its voltage reaches the lower threshold of \frac{1}{3} V_{CC} (at time t_2). At this point, the output switches back to its high level.
• Using a supply voltage (V_{CC}) of +5 V provides a TTL-compatible output (pin 3).
Calculate the following values.
(a) Time 7º for which the output is high (called the Mark) is given by
T_1 = 0.7 (R_1 + R_2) C_1
(R_1 and R_2 in ohms, C_1 in farads, T_1 in seconds.
Calculate T_1
(b) Time T_2 for which the output is low (called the Space) is given by
T_2 = 0.7 R_2 C_1
Calculate T_2
(c) Periodic time, T = T_1 + T_2 = 0.7 (R_1 + 2R_2) C_1, and
frequency, (f) = 1/T
(T in seconds, f in hertz).
Calculate f.
(d) The mark-space ratio is found from
\begin{aligned}\frac{\text { time for the mark }}{\text { time for the space }}=\frac{T_{1}}{T_{2}}&=\frac{0.7\left(R_{1}+R_{2}\right) C_{1}}{0.7 R_{2} C_{1}} \\&=\frac{R_{1}+R_{2}}{R_{2}}\end{aligned}Calculate the mark-space ratio.
(e) The duty cycle is found from
\begin{aligned}&\frac{\text { Time for the mark (the 'on' time) }}{\text { Time for mark and space (the total time) }} \\&=\frac{0.7\left(R_{1}+R_{2}\right) C_{1}}{0.7\left(R_{1}+2 R_{2}\right)C_{1}}=\frac{R_{1}+R_{2}}{R_{1}+2 R_{2}}\end{aligned}Procedure (c): using the 7414 Schmitt trigger
1 Connect up the circuit in Figure 8.17. The pin connection diagram for the 7414 ic is shown in Figure 8.7.
2 Measure the frequency of the output waveform.
