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476 ^ Principles of Electronics
Fig. 18.
10V – 0.7V 9.3V
1 kΩ 1 kΩ = 9.3 mA
∴ Minimum β = ( ) 9.3 mA 0.48 mA
C sat B
I
I
( ii ) IB = BB^ BE B
V V
R
1V – 0.7V 0.3V
2.7 kΩ 2.7 kΩ = 0.111 mA ∴ IC = β IB = 50 × 0.111 = 5.55 mA Since the collector current is less than saturation current (= 9.3 mA), the transistor will not be saturated.
1 8 .1 0 M u l t i v i b r at o r s
An electronic circuit that generates square waves (or other non-sinusoidals such as rectangular, saw-tooth waves) is known as a *multivibrator.
Fig. 18.
A multivibrator is a switching circuit which depends for operation on positive feedback. It is basically a two-stage amplifier with output of one fedback to the input of the other as shown in Fig. 18.10.
- The name multivibrator is derived from the fact that a square wave actually consists of a large number of (fourier series analysis) sinusoidals of different frequencies.
Solid-Sta te Switching Circuits 477
Fig. 18.
The circuit operates in two states ( viz ON and OFF) controlled by circuit conditions. Each ampli- fier stage supplies feedback to the other in such a manner that will drive the transistor of one stage to saturation (ON state) and the other to cut off (OFF state).
After a certain time controlled by circuit con- ditions, the action is reversed i.e. saturated stage is driven to cut off and the cut off stage is driven to saturation. The output can be taken across ei- ther stage and may be rectangular or square wave depending upon the circuit conditions.
Fig. 18.10 shows the block diagram of a multivibrator. It is a two-stage amplifier with 100% positive feedback. Suppose output is taken across the transistor Q 2. At any particular instant, one transistor is ON and conducts IC ( sat ) while the other is OFF. Suppose Q 2 is ON and Q 1 is OFF. The collector current in Q 2 will be I (^) C ( sat ) as shown in Fig. 18.11. This condition will prevail for a time ( bc in this case) determined by circuit conditions. After this time, transistor Q 2 is cut off and Q 1 is turned ON. The collector current in Q 2 is now I (^) CEO as shown. The circuit will stay in this condition for a time de. Again Q 2 is turned ON and Q 1 is driven to cut off. In this way, the output will be a square wave.
1 8 .1 1 Ty p e s o f M u l t i v i b r at o r s
A multivibrator is basically a two-stage amplifier with output of one fedback to the input of the other. At any particular instant, one transistor is ON and the other is OFF. After a certain time depending upon the circuit components, the stages reverse their conditions – the conducting stage suddenly cuts off and the non-conducting stage suddenly starts to conduct. The two possible states of a multivibrator are : ON O F F First State Q 1 Q 2 Second State Q 2 Q 1 Depending upon the manner in which the two stages interchange their states, the multivibrators are classified as :
( i ) Astable or free running multivibrator ( ii ) Monostable or one-shot multivibrator ( iii ) Bi-stable or flip-flop multivibrator Fig. 18.12 shows the input/output relations for the three types of multivibrators. ( i ) The astable or free running multivibrator alternates automatically between the two states and remains in each for a time dependent upon the circuit constants. Thus it is just an oscillator since it requires no external pulse for its operation. Of course, it does require a source of d.c. power. Because it continuously produces the square-wave output, it is often referred to as a free running multivibrator.
( ii ) The monostable or one-shot multivibrator has one state stable and one quasi-stable ( i.e. half-stable) state. The application of input pulse triggers the circuit into its quasi-stable state, in which it remains for a period determined by circuit constants. After this period of time, the circuit returns to its initial stable state, the process is repeated upon the application of each trigger pulse. Since the monostable multivibrator produces a single output pulse for each input trigger pulse, it is generally called one-shot multivibrator.
Solid-Sta te Switching Circuits 479
Fig. 18.
Fig. 18.
bias on Q 2 and its collector current starts decreasing. As the collector of Q 2 is connected to the base of Q 1 through C 2 , therefore, base of Q 1 becomes more nega- tive i.e. Q 1 is more forward biased. This further in- creases the collector current in Q 1 and causes a further decrease of collector current in Q 2. This series of ac- tions is repeated until the circuit drives Q 1 to satura- tion and Q 2 to cut off. These actions occur very rap- idly and may be considered practically instantaneous. The output of Q 1 (ON state) is approximately zero and that of Q 2 (OFF state) is approximately V (^) CC. This is shown by ab in Fig. 18.14.
When Q 1 is at saturation and Q 2 is cut off, the full voltage V (^) CC appears across R (^) 1 and voltage across R (^) 4 will be zero. The charges developed across C (^) 1 and C 2 are sufficient to maintain the satura- tion and cut off conditions at Q 1 and Q 2 respectively. This condition is represented by time interval bc in Fig. 18.14. However, the capacitors will not retain the charges indefinitely but will discharge through their respective circuits. The discharge path for C 1 , with plate L negative and Q 1 conducting, is LAQ (^) 1 V (^) CCR (^) 2 M as shown in Fig. 18.15 ( i ).
The discharge path for C (^) 2 , with plate K negative and Q 2 cut off, is KBR 4 R 3 J as shown in Fig. 18.15 ( ii ). As the resistance of the discharge path for C (^) 1 is lower than that of C 2 , therefore, C 1 will discharge more rapidly. As C 1 discharges, the base bias at Q 2 becomes less positive and at a time determined by R (^) 2 and C 1 , forward bias is re-established at Q 2. This causes the collector current to start in Q 2. The increas- ing positive potential at collector of Q 2 is applied to the base of Q 1 through the capacitor C 2. Hence the base of Q 1 will become more positive i.e. Q (^) 1 is reverse biased. The decrease in collector current in Q 1 sends a negative voltage to the base of Q 2 through C 1 , thereby causing further increase in the collector current of Q 2. With this set of actions taking place, Q 2 is quickly driven to saturation and Q 1 to cut off. This condition is represented by cd in Fig. 18.14. The period of time during which Q 2 remains at saturation and Q 1 at cut off is determined by C 2 and R (^) 3.
480 ^ Principles of Electronics
Fig. 18. ON or OFF time. The time for which either transistor remains ON or OFF is given by : ON time for Q 1 (or OFF time for Q 2 ) is T 1 = 0.694 R 2 C 1 OFF time for Q 1 (or ON time for Q 2 ) is T 2 = 0.694 R 3 C 2 Total time period of the square wave is T = T 1 + T 2 = 0.694 ( R (^) 2 C 1 + R (^) 3 C 2 ) As R (^) 2 = R (^) 3 = R and C (^) 1 = C 2 = C , ∴ T = 0.694 ( RC + RC ) j 1.4 RC seconds Frequency of the square wave is f =
T RC
g; (^) Hz
It may be noted that in these expressions, R is in ohms and C in farad. Example 18.4. In the astable multivibrator shown in Fig. 18.13, R 2 = R 3 = 10 k Ω and C 1 = C 2 = 0.01 μF. Determine the time period and frequency of the square wave.
Solution. Here R = 10 kΩ = 10 4 Ω; C = 0.01 μF = 10 −^8 F Time period of the square wave is T = 1.4 RC = 1.4 × 104 × 10 −^8 second = 1.4 × 10 −^4 second = 1.4 × 10 −^4 × 103 m sec = 0.14 m sec Frequency of the square wave is f = 1 Hz = 1 4 Hz T in second (^) 1.4 × 10 − = 7 × 103 Hz = 7 kHz
1 8 .1 3 Tr a n s i s t o r M o n o s t a b l e M u l t i v i b r at o r
A multivibrator in which one transistor is always conducting (i.e. in the ON state) and the other is non-conducting (i.e. in the OFF state) is called a monostable multivibrator.
482 ^ Principles of Electronics
With Q 1 at saturation and Q 2 at cut off, the circuit will come back to the original stage ( i.e. Q 2 at saturation and Q 1 at cut off) after some time as explained in the following discussion. The capacitor C (^) 1 (charged to approximately V (^) CC ) discharges through the path R (^) 2 V (^) CC Q 1. As C 1 discharges, it sends a voltage to the base of Q 2 to make it less positive. This goes on until a point is reached when forward bias is re-established on Q 2 and collector current starts to flow in Q 2. The step by step events already explained occur and Q 2 is quickly driven to saturation and Q 1 to cut off. This is the stable state for the circuit and it remains in this condition until another pulse causes the circuit to switch over the states.
1 8 .1 4 Tr a n s i s t o r B i s t a b l e M u l t i v i b r at o r
A multivibrator which has both the states stable is called a bistable multivibrator.
The bistable multivibrator has both the states stable. It will remain in whichever state it happens to be until a trigger pulse causes it to switch to the other state. For instance, suppose at any particular instant, transistor Q 1 is conducting and transistor Q 2 is at cut off. If left to itself, the bistable multivibrator will stay in this position forever. However, if an external pulse is applied to the circuit in such a way that Q 1 is cut off and Q 2 is turned on, the circuit will stay in the new position. Another trigger pulse is then required to switch the circuit back to its original state. Circuit details. Fig. 18.17 shows the circuit of a typical transistor bistable multivibrator. It consists of two identical CE amplifier stages with output of one fed to the input of the other. The feedback is coupled through resistors ( R (^) 2 , R (^) 3 ) shunted by capacitors C (^) 1 and C 2. The main purpose of capacitors C (^) 1 and C (^) 2 is to improve the switching characteristics of the circuit by passing the high frequency components of the square wave. This allows fast rise and fall times and hence distortionless square wave output. The output can be taken across either transistor.
Fig. 18.
Operation. When VCC is applied, one transistor will start conducting slightly ahead of the other due to some differences in the characteristics of the transistors. This will drive one transistor to
Solid-Sta te Switching Circuits 483
saturation and the other to cut off in a manner described for the astable multivibrator. Assume that Q 1 is turned ON and Q 2 is cut OFF. If left to itself, the circuit will stay in this condition. In order to switch the multivibrator to its other state, a trigger pulse must be applied. A negative pulse applied to the base of Q 1 through C 3 will cut it off or a positive pulse applied to the base of Q 2 through C 4 will cause it to conduct.
Suppose a negative pulse of sufficient magnitude is applied to the base of Q 1 through C (^) 3. This will reduce the forward bias on Q 1 and cause a decrease in its collector current and an increase in collector voltage. The rising collector voltage is coupled to the base of Q 2 where it forward biases the base-emitter junction of Q 2. This will cause an increase in its collector current and decrease in collector voltage. The decreasing collector voltage is applied to the base of Q 1 where it further reverse biases the base-emitter junction of Q 1 to decrease its collector current. With this set of actions taking place, Q 2 is quickly driven to saturation and Q 1 to cut off. The circuit will now remain stable in this state until a negative trigger pulse at Q 2 (or a positive trigger pulse at Q 1 ) changes this state.
1 8 .1 5 Di f f e r e n t i at i n g Ci r c u i t
A circuit in which output voltage is directly proportional to the derivative of the input is known as a differentiating circuit.
Output ∝ d dt
(Input)
A differentiating circuit is a simple RC series circuit with output taken across the resistor R. The circuit is suitably designed so that output is proportional to the derivative of the input. Thus if a d.c. or constant input is applied to such a circuit, the output will be zero. It is because the derivative of a constant is zero.
Fig. 18.
Fig. 18.18 shows a typical differentiating circuit. The output across R will be the derivative of the input. It is important to note that merely using voltage across R does not make the circuit a differentiator; it is also necessary to set the proper circuit values. In order to achieve good differen- tiation, the following two conditions should be satisfied :
( i ) The time constant RC of the circuit should be much smaller than the time period of the input wave.
( ii ) The value of XC should be 10 or more times larger than R at the operating frequency. Fulfilled these conditions, the output across R in Fig. 18.18 will be the derivative of the input. Let ei be the input alternating voltage and let i be the resulting alternating current. The charge q on the capacitor at any instant is q = C ec
Now i = ( )^ (^ c )
dq (^) d d q C e dt dt dt
