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An oscillator is a nonrotating device which generates a signal at a frequency determined by the circuit constants. In this Section the operation of the Hartley and Colpitts RF oscillators, which generate sinusoidal waveforms, and the multi vibrator, which generates a nonsinusoidal waveform, will be discussed.
THE HARTLEY OSCILLATOR
Figs. 1 and 2 show two alternate hall-cycles in the operation of a transistorized version of the Hartley oscillator.
This oscillator is widely used in commercial electronic equipment as well as in such household equipment as television and radio receivers.
Identification of Components
The circuit components and their functions are listed below.
The manner in which these functions are accomplished-in other words, how the circuit operates-will be discussed later in the Section.
R1-Base-biasing and voltage-divider resistor.
R3-Emitter stabilizing resistor.
R4-Collector load resistor.
C1-Feedback coupling capacitor.
C2-Emitter filter capacitor.
C3-Output coupling and blocking capacitor.
C4-Oscillating tank capacitor.
T1 -Oscillating tank inductor and output inductor.
M1-Battery power supply.
Identification of Currents
The following electron currents are at work in this circuit, and it is necessary that their movements be understood before the operation of the circuit as a whole can be comprehended.
1. Voltage-divider current, used for base biasing ( dotted green).
2. Base-emitter biasing current (solid green).
3. Collector-emitter current (in both solid and dotted red).
4. Oscillating tank current (solid blue).
5. Feedback current (also in solid blue).
6. Replenishment current for support of the oscillation ( dotted blue).
7. Output current in transformer secondary ( also in solid blue).
Circuit Operation - Static Conditions
Fig. 1 has been labeled the negative half-cycle of operation, because during this half-cycle the feedback current flows down ward through R1 and creates a more negative voltage at the upper end of this resistor. This voltage is applied directly to the base of the transistor as part of the base-biasing voltage.
Conversely, Fig. 2 is labeled the positive half-cycle, because the feedback current flows upward through R1, creating a less negative voltage at the upper end of this resistor.
A single battery, M1, provides electron current for both main current paths through any three-element transistor. These current paths are from base to emitter, and from collector to emitter. The complete path of the base-emitter current, in solid green, includes a trip upward through battery M1 and out through its negative terminal, then to the left, and upward through R2 to the base of the transistor. From the base, the current goes to the emitter within the transistor, and then downward through stabilizing resistor R3 to the common ground point. From here it has free access to re-enter the positive terminal of the battery.
This base-emitter current is frequently referred to as the "biasing" current of a transistor, because a small change in its amount will normally cause a much larger change in the amount of collector-emitter current flowing through the transistor.
The base-emitter current normally is not much more than a few microamperes, and it is regulated by the difference in the voltages at the base and emitter. This voltage difference is frequently no more than a tenth of a volt. The origins of these element voltages will be discussed as the other currents are described.
The complete path of the voltage-divider current (in dotted green) is from the negative terminal of battery M1, upward through resistor R2 and downward through R1 to common ground, where it has a ready return access to the positive terminal of the battery. Normally, R1 will be considerably smaller than R2 in value, so that most of the battery voltage will be "dropped" across R2. The voltage measured at the top of R1 is the biasing voltage, which is applied to the base of the transistor.
We might assume some typical values as follows:
Let R1 = 1,000 ohms
R2 = 5,000 ohms
Then, the voltage-divider current could be calculated from Ohm's law as follows:
-6V 5000+ 1000
= -1 milliampere
The voltage across R1 would then be: E1 = ffi1
= .001 X 1000
= 1 volt and would have a negative value at the top of R1.
The voltage across R2 would be: E2= IR2
= .001 X 5,000
The complete path of the collector-emitter current (in solid red, and usually referred to as the collector current) is from the negative terminal of battery M1, then upward through collector load resistor R4, through the transistor from collector to emitter, and downward through emitter stabilizing or swamping resistor R3 to the common-ground connection. From here it is free to return to the grounded positive terminal of the battery.
The directions in which the two transistor currents flow are of course dictated by the nature of the transistor itself.
The one used in this circuit is a PNP, as indicated by the emitter arrow pointing toward the base. This is a universal symbol, and the two electron currents always flow into the emitter in the direction opposite to that in which the arrow is pointing.
The battery must necessarily be connected so that its polarity will support the electron-flow directions dictated by the construction of the transistor itself. With this or any PNP transistor, both the base and collector must be connected to a negative biasing voltage.
The base-emitter, collector-emitter, and voltage-divider cur rents described in the foregoing are "static" currents, in the sense that they flow continuously, whether an oscillation exists in the tank circuit or not. If no oscillation or feedback currents existed, these three currents would all be "pure" DC, with no fluctuations in value. However, if the circuit is properly connected, an oscillating current will spring into existence in the tuned tank circuit as soon as power is applied from the battery.
Through the mechanics of the feedback connection, the collector current through the transistor will be increased or de creased in such a fashion that it will in turn support or replenish the oscillation of electrons in the tank current. The circuit is then said to be operating under "dynamic" conditions, during which all the additional currents for accomplishing the oscillation and replenishing it come into existence along with the cur rents for accomplishing the feedback or filtering action at the emitter and for delivering an output current to the next stage. Additionally, the two currents through the transistor become pulsating rather than pure DC. Let us examine the interrelationships between these currents.
Operation Under Dynamic Conditions
As soon as power is applied to the transistor circuit, a small amount of electron current (solid green) will begin flowing through the transistor, from base to emitter, and immediately cause a much larger current to flow from collector to emitter.
The latter current, in both solid and dotted red, initially is drawn both through load resistor R4 and also from the left plate of coupling capacitor C3.
Capacitor action is always such that when a certain number of electrons are drawn away from one plate, an equal number will be drawn onto the opposite plate from the external circuit.
That is what happens here; the current being drawn onto the right plate of capacitor C3 is shown in dotted red lines. Its complete path is from ground, into the center tap and through the upper half of the transformer primary to the coupling capacitor.
As this current is drawn through part of the transformer, what is known as autotransformer action occurs throughout the entire primary winding. In any inductor, the fundamental electrical action is such that the inductor opposes any change in the amount of current flowing through it. Another way of saying this is that an inductor will try to keep at a constant value the current flowing through it.
We can visualize this fundamental inductor action by looking at the current being drawn upward through the upper half of the winding. During the first half-cycle depicted by Fig. 1, this current is flowing upward at an increasing rate. In so doing, it induces a second current (in dotted blue) to flow downward through the entire primary winding, also at an in creasing rate. Because of its downward flow during the first half-cycle, the induced current delivers electrons to the lower plate of tank capacitor C4 and builds up a negative charge, or voltage, there.
This negative voltage drives electron current through the feedback line to the left plate of coupling capacitor C1, and this action in turn drives an equal amount of electron current downward, through biasing-and-driving resistor R1. This makes the voltage at the top of R1 more negative and, in effect, in creases the "forward bias" at the base of the transistor, thereby driving more electron current from the base through the emitter than would normally flow under static conditions.
Action within the transistor will always be such that a small increase in the base-emitter current is accompanied by a large increase in collector-emitter current. Notice the cumulative nature of all the dynamic conditions described so far during the first half-cycle of Fig. 1: The initial surge of electron current (both solid and dotted red) into the collector caused autotransformer action within the primary winding, and the latter action placed a negative voltage on the lower plate of tank capacitor C4. The resulting feedback current through resistor R1 developed a voltage across it of such polarity as to increase the base-emitter current and to further increase the current entering the collector terminal.
Two independent circuit actions now occur and prevent these cumulative increases in both currents from continuing in definitely. As the collector-emitter current increases, the volt age it develops across emitter resistor R3 will also increase.
(This voltage will be negative at the top of R3.)
As the negative voltage at the top of R3 increases due to this increased collector current, the voltage-bias conditions between the base and emitter are affected adversely. In any PNP transistor, the voltage at the base must always be slightly more negative than the voltage at the emitter, in order for electron current to flow from base to emitter. Thus, the rise in collector current eventually reduces the base-emitter cur rent which, in turn, reduces the amount of collector-emitter current flowing through the transistor.
This particular set of cumulative actions eventually reduces the collector-emitter current, bringing us to the conditions shown in Fig. 2. This is the logical moment to discuss the second in dependent action, which operates to keep the collector-emitter current from increasing indefinitely. This is the action of the tuned tank circuit, consisting of capacitor C4 and the primary winding of transformer T1. This tank is tuned to be resonant at the desired frequency of oscillation; and once the lower plate of C4 has been charged to its initial negative voltage, an oscillation of electrons between inductor and capacitor will automatically begin. During the second half-cycle shown in Fig. 2, the electrons initially stored on the lower plate of C4 will flow upward through the primary winding of trans former T1, until at the end of this half-cycle practically all of them will have been delivered to the upper plate of C4, placing a negative voltage on it and a positive voltage ( a deficiency of electrons) on the lower plate.
This positive voltage on the lower plate of C4 reverses the flow direction of the feedback current, shown in solid blue.
Electrons are now drawn from the left plate of C1 along the feedback line, toward the tuned tank. This in turn draws electron current upward through resistor R1 and creates a small positive voltage at its upper terminal. The small positive voltage partially neutralizes the permanent negative voltage which exists at this point because of the flow through R2 and R1 of the voltage-divider current shown in dotted green. The algebraic or instantaneous sum of these two voltages across R1--one a fixed negative voltage and the other a voltage which is constantly changing from negative to positive and back again constitutes the complete biasing voltage present at the base of the transistor.
The voltage at the bottom of the tank circuit reaches its most positive value at the same moment the base-emitter current reaches its minimum value, and the collector-emitter current will in turn be reduced to its minimum value. This reduction is indicated in Fig. 2 by the absence of a dotted red line passing through the transistor. Electron current flowing up ward through the load resistor R4 will be temporarily diverted onto the left plate of capacitor C3 during this second half-cycle, since it is unable to enter the collector terminal. This action accounts for the reversal in flow direction of the support cur rent shown in dotted red. It now flows away from the right plate of capacitor C3 and downward, through the upper half of the transformer primary winding, to ground.
This replenishment current again supports the oscillation of the tank current during this half-cycle, by inducing in the entire primary winding a current which will again be in phase with the tank current. This induced current ( dotted blue in Fig. 2) flows upward through the inductor. Being in phase with the tank current, it is therefore able to replenish the inevitable losses which occur in any oscillation, and thus permit the oscillation to continue indefinitely.
There are three main sources of loss which exist for this particular tank-circuit oscillation. The resistive wire losses within the inductor winding are inherent in any tank circuit.
They cause a small percentage of electrons to drop out of oscillation during each half-cycle, so that the number which reach one capacitor plate at the end of any particular half-cycle is never quite as large as the number which left the other capacitor plate at the beginning of the half-cycle.
The electron current, which we call the feedback current and which is driven up and down through the biasing resistor R1 represents another source of loss to the tank-circuit oscillation. Consequently, it is always desirable to keep this feedback current as small as possible. This might be accomplished by making resistor R1 as large as possible. However, the overriding considerations in the choice of resistor values for both R1 and R2 are first, the amount of base-emitter current which the transistor requires for normal operation, and secondly, the amount of normal biasing voltage which should be provided to the base.
The third source of loss to the tank circuit is the support of the output current flowing in the secondary winding of transformer T1. This output current, shown in solid blue, flows up and down at the radio frequency generated in the tank circuit.
THE COLPITTS OSCILLATOR
Figs. 3 and 4 show two successive half-cycles in the operation of a transistorized Colpitts oscillator. The circuit components and their functions are:
R1-Voltage divider or biasing resistor.
R2-Voltage divider or biasing resistor.
R3-Emitter stabilizing resistor.
R4-Collector load resistor.
C1-Filtering or bypass capacitor.
C2-Output coupling and blocking capacitor.
C3 and C4-Voltage-dividing capacitors in tuned tank circuit.
M1-Battery power supply.
Identification of Currents
The following electron currents are at work in this typical oscillator circuit, and a thorough understanding of their movements is essential to an understanding of circuit operation, as well as to an ability to troubleshoot and repair the circuit or to modify its design or adapt it to various applications:
1. Voltage-divider current (dotted green).
2. Base-emitter current (solid green).
3. Collector-emitter current (solid red).
4. Oscillator tank current (solid blue).
5. Feedback current to the emitter ( also in solid blue) .
6. Output current in transformer secondary (also in solid blue).
7. Support current which supports the tank oscillation ( dotted red).
8. Base-emitter filter current (solid green).
Fig. 3. Operation of the Colpitt's oscillator-negative half-cycle.
The first three are static currents, or DC, and they will flow whenever power is applied to the circuit, whether an oscillation exists in the tuned tank circuit or not. The remaining currents are directly associated with the oscillating tank currents, and are consequently known as "dynamic" currents.
Details of Operation
The transistor base is brought to its desired bias voltage by voltage divider R1-R2 across battery M1. The voltage divider current (dotted green) flows continuously in a clock wise direction around a closed circuit consisting of R1, R2 and M1. This clockwise flow is of course dictated by the polarity of the battery, since electrons must always leave a battery at its negative terminal and re-enter it at the positive terminal.
Normally, R2 will be somewhat larger in resistance than R1, so that most of the battery or applied voltage is "dropped" across R2. The voltage at the junction of these two resistors is also the voltage applied to the transistor base.
The base-emitter current (in solid green in both circuit diagrams) flows around the closed path that begins at the negative terminal of the power supply ( which in this circuit is connected to ground). This current flows upward through stabilizing resistor R3 and through the transistor, from emitter to base, then downward through resistor R2, and to the right where it re-enters the battery at its positive terminal.
The closed loop around which this base-emitter current flows obviously includes the three circuit elements consisting of R2, R3, and M1. But it also includes the semiconductor junction between the base and the emitter within the transistor. The external voltages applied to these two elements really determine how much of this base-emitter current can flow through the transistor and, consequently, around the entire loop. Normally, the base-emitter current will range from perhaps 100 micro-amperes, down to only a few microamperes.
The third of the three static currents in this circuit is the collector-emitter current, which flows continuously around its own closed loop in a clockwise direction. This current flow (shown in solid red) begins at the negative terminal of the battery. From here, the path is through ground to the lower end of emitter resistor R3 and upward through it to the emitter.
The electrons enter the transistor at the emitter and exit at the collector, then flow downward through collector load resistor R4 and enter the positive terminal of the battery.
The fact that an NPN transistor is used here determines the directions of both of the currents which actually flow through the transistor. The emitter arrow points away from the base in an NPN transistor, and you will recall that the electron currents through a transistor always How against the direction of the emitter arrow.
The amount of collector-emitter electron current which flows around the closed loop discussed previously is determined almost entirely by conditions within the transistor, rather than by the particular voltage value applied to the collector. The over riding condition within the transistor is the amount of base emitter current flowing. The fluctuations in this small current control the fluctuations in the much larger collector-emitter current. This phenomenon will be discussed in considerably more detail later.
Operation Under Dynamic Conditions
The manner in which an oscillation is set up in the tank circuit can be visualized by referring to Fig. 3, which is labeled the negative half-cycle of operation. As soon as power is ap plied to the circuit, the base-emitter current (in solid green) will flow through the transistor in the direction shown. As explained in connection with Figs. 1-8 and 1-9 of Section 1, the quantity of electrons within the base at any instant directly affects and controls the quantity of electrons which can flow through the base between emitter and collector-in other words, the amount of collector-emitter current which can flow.
The initial surge of collector-emitter current delivers electrons to the upper terminal of load resistor R4, and also onto the left plate of coupling capacitor C2. By normal capacitor action, these electrons cannot enter one side of a capacitor unless an equal number are driven away from the opposite side. The electrons which are driven away (dotted red) flow down into the tuned tank and set up the oscillation of electrons shown in solid blue. Once any voltage or current unbalance is applied to a resonant tank circuit, electrons will be set in oscillation between the tank capacitor (s) and tank inductor.
This oscillation, even if unsupported, will continue for many cycles-depending on the strength of the initial disturbance and on the Q, or quality, of the tank circuit.
Fig. 4 shows a second half-cycle of this tank-circuit oscillation occurring. Electrons now flow downward through the trans former primary, which acts as the necessary inductor for the tank circuit. As a result of this flow, electrons are removed from the upper plate of capacitor C3 and eventually delivered to the lower plate of C4. The current flows downward throughout this entire second, or positive, half-cycle, with maximum volt age (indicated by minus signs on the lower plate of C4 and plus signs on the upper plate of C3) occurring across the tank at the end of the half-cycle.
How Feedback is Accomplished
Feedback is accomplished in this oscillator by connecting the emitter to the point between C3 and C4. These two tank capacitors constitute a capacitive voltage divider. The two voltages across them are in series, and they add to equal the total voltage existing across the tank circuit at any instant. The portion of the total tank voltage across C4 is applied directly to the emitter as the feedback voltage. It is perhaps easier to visualize this feedback voltage if you also visualize the feed back current which must flow in conjunction with it. This current (in solid blue), flows to the left and downward through emitter resistor R3 during the negative half-cycle of Fig. 3, adding a small amount of negative voltage to the positive volt age already existing at the emitter. The latter is produced by the upward flow of the base-emitter and collector-emitter currents through resistor R3. Thus, the effect of the feedback voltage, during the negative half-cycle of Fig. 3, is to slightly reduce the positive voltage at the emitter and thereby increase the amount of base-emitter current.
This small increase in base-emitter current causes a much larger increase in the collector-emitter current. The extra collector current delivers more electrons onto the left plate of coupling capacitor C2, and in turn adds electrons ( dotted red) to those being driven down into the tuned tank circuit.
Since the electrons in dotted red arrive at the tank circuit in the appropriate phase (meaning at the appropriate time) to support or reinforce the oscillation of electrons within the tank, the feedback is said to be "regenerative." In Fig. 4 the total voltage across the tuned tank circuit is positive, as indicated by plus signs on the upper plates of tank capacitors C3 and C4. The fraction of the total tank voltage across C4 now draws electrons upward through emitter resistor R3, and also adds a small increment of positive voltage to the positive voltage already existing at the top of R3 since the top of R3 is connected directly to the emitter, the positive voltage already at the emitter increases slightly and thereby reduces the base emitter current.
Transistor action will always be such that a small decrease in base-emitter current will cause a much greater decrease in collector-emitter current. When the collector current de creases, the support current between capacitor C2 and the tank circuit now reverses direction and flows upward, away from the tank and toward capacitor C2. Again, this flow direction supports the oscillation in the tuned tank. Thus, we see that both the increases and decreases in collector current de liver reinforcing impulses to the oscillation in the tuned tank.
Since emitter resistor R3 is not bypassed by a filter capacitor, degeneration will occur as a result of the changes in collector current. Degeneration is synonymous with loss of amplification.
To see how it occurs, we need to consider the voltage changes produced at the top of R3 by the variations in collector-emitter current flowing through it.
Three electron currents flow independently through resistor Rthe base-emitter, collector-emitter, and feedback currents.
The effects of the feedback current on the collector-emitter current have already been discussed, and need not be re considered here. Although the base-emitter current changes in value from half-cycle to half-cycle, the amount-in comparison with the changes in collector-emitter current-is insignificant.
Consequently, voltage changes generated by these current changes across R3 are so negligible that they may be disregarded.
This brings us to the collector-emitter current (frequently referred to in many books as the collector current). At the start of the negative half-cycle of Fig. 3, the collector current will have been reduced to its minimum; and as a result of its flow through R3, a small component of positive voltage will exist at the top of R3. At the end of this half-cycle, a much larger collector current will be flowing, and hence a much larger positive voltage will exist at the top of R3 and also at the emitter.
This larger positive voltage, at the emitter of an NPN transistor, has an adverse effect on the bias conditions existing be tween base and emitter. The end result is to reduce the base emitter current. This is contrary to the effect of the feedback current and voltage, which at the end of the same negative half-cycle will increase the base-emitter current.
The feedback voltage developed across resistor R3 is in reality the signal, or driving, voltage for the whole transistor circuit. Whenever a feedback voltage and the resulting transistor current are out of phase with each other, then degeneration is said to be occurring.
Degeneration also occurs during the positive half-cycle of Fig. 4. At the end of this half-cycle, the feedback voltage across R3 is positive, reducing the two currents through the transistor and R3. The latter flows upward through R3, reducing the positive voltage across this resistor and thus partially counteracting the increase in positive voltage caused by the feedback. This is degeneration; and as stated before, its effect is to lower the amplification from that which the circuit would normally deliver.
Resistor R2 and the battery are bypassed ( or filtered) by capacitor C1, so that degeneration does not occur in this part of the circuit. The fluctuations in base-emitter current through R2 would normally change the voltage at the base of the transistor, and these voltage changes would affect the amount of base-emitter current. As an example, the increase in base emitter current indicated in Fig. 3 would normally cause a greater voltage drop across R2 which would lower the positive voltage at the top of R2. Since this voltage is applied directly to the base of the transistor, less base-emitter current would flow.
This would be degeneration, which is avoided by having filter capacitor C1 in the circuit. It, along with R2, constitutes a conventional long time-constant circuit. In Fig. 3, excess electrons flowing through the transistor from emitter to base (the base-emitter current) will accumulate on the upper plate of capacitor C1 and drive an equal number away from the lower plate. This is the filtering current and is shown in solid green. On the positive half-cycle of Fig. 4, when the base emitter current is reduced, the excess electrons driven onto the upper plate of C1 will now drain off, through resistor R2, to the positive terminal of the power supply or battery.
As long as this filtering is permitted, the base-emitter cur rent will be fairly pure or constant direct current during its passage through R2 and the battery. For the remainder of its journey through resistor R3 and the transistor, it is pulsating DC. Since the base-emitter current through R2 is pure DC, the voltage it develops across R2 will be constant, and the voltage applied to the base will be steady from one half-cycle to the next.
Normal transformer action between the primary and secondary windings of T1 induces an output current in the secondary, as shown in solid blue in Figs. 3 and 4. This output current normally is used to develop the driving voltage for succeeding amplifier stages.
THE FREE-RUNNING MULTIVIBRATOR
Figs. 5 and 6 show two successive half-cycles in the operating of a typical transistorized multivibrator circuit. The title "free-running"· is applied to any multivibrator which oscillates continuously. Such a multivibrator is said to be "bistable"--as opposed to a one-shot, or "monostable," multivibrator where each cycle of oscillation must be initiated by a separate trigger pulse.
Identification of Components
This circuit is composed of the following components:
R1--Voltage-divider and collector load resistor for XL
R2--Voltage-divider and filter resistor.
R3--Voltage-divider and base biasing resistor for X2.
R4--Voltage-divider and collector load resistor for X2.
R5--Voltage-divider and filter resistor.
R6--Voltage-divider and base-biasing resistor for X1.
R7--Emitter stabilizing resistor for both transistors.
C1-Coupling capacitor between X1 collector and X2 base.
C2-Coupling capacitor between X2 collector and X1 base.
C3-Emitter bypass capacitor for both transistors.
M1-12-volt battery power supply.
Identification of Currents
At least ten electron currents flow in this circuit. Once their movements and significance are thoroughly understood, their associated voltages likewise become easy to understand. These ten electron currents are:
1. Voltage-divider current, which provides "bias" voltages for the collector of transistor X1 and the base of X2 (solid red).
2. Collector-emitter current for transistor X1 (dotted red).
3. Base-emitter current for transistor X2 (also in dotted red).
4. Voltage-divider current, which provides "bias" voltage to the collector of transistor X2 and the base of X1 (solid green).
5. Collector-emitter current for transistor X2 (dotted green).
6. Base-emitter current for transistor X1 ( also in dotted green).
7. The instantaneous pulsation of current, which flows at the beginning of the first half-cycle and cuts off all cur rent flow through transistor X2 (solid blue).
8. The instantaneous pulsation of current which flows at the beginning of the second half-cycle and cuts off all current flow through transistor X1 (dotted blue) .
9. The long time-constant discharge current flowing between capacitor C1 and resistor R2 ( also in dotted blue) .
10. The long time-constant discharge current flowing between capacitor C2 and resistor RS ( also in solid blue).
Details of Operation
As soon as power is applied to this circuit, the two voltage divider currents shown in solid red and solid green, respectively, will begin to flow. The flow directions of both currents are as shown in Figs. 5 and 6. The path of the first current (in solid red) is upward from the negative terminal of battery M1, through resistors R1, R2, and R3 to the common ground connection. The path of the second current (in solid green) is upward from the battery, and through resistors R4, RS, and R6 to ground.
These electron flow directions tell us that the voltage at the left end of resistor R2 (collector voltage of X1) must be more negative than the voltage at the right end of R2, because electrons inevitably flow from more negative to less negative areas.
Fig. 7 shows the relationships between the two collector and two base voltages. At the beginning of the first half-cycle, transistor X1 starts to conduct electrons from collector to emitter. This collector-emitter current (dotted red in Fig. 5) follows the expected path for a PNP transistor. This is up ward from the negative terminal of M1, through resistor R1, into the collector and out the emitter of X1, then down through common emitter stabilizing resistor R7 to ground. Here it has ready return access to the positive terminal of battery, which is connected to ground.
The fact that two currents are now flowing side by side upward through R1 causes a greater voltage drop across R1 than before. Since the voltage at the battery end of R1 is fixed at -12 volts, the voltage at the top of R1 must become less negative.
As a rough example, the voltage at the collector of X1 (line 1 of Fig. 7) is shown increasing abruptly from -8 to - 4 volts.
As soon as this voltage begins to change ( at the start of the first half-cycle), the voltage at the base of transistor X2 also begins to go in the positive direction because of coupling capacitor C1. This action quickly cuts off the flow of base-emitter current through transistor X2, because in a PNP transistor the base must be less negative than the emitter in order for this current to flow. And since the base-emitter current is the "biasing" current which causes or permits the other current to flow between collector and emitter, both currents through transistor X2 are cut off immediately at the first half-cycle.
Now only one current will be flowing upward through resistor R4 instead of two. As a result, the smaller voltage drop across R4 causes the negative voltage at the upper terminal of R4 to become more negative.
This increase in negative voltage at the collector of X2 is passed to the base of X1 via coupling capacitor C2. A more negative base voltage on any PNP transistor acts to increase the base-emitter biasing current, and also the collector-emitter current. The rise in collector-emitter current through X1 further raises the voltage at the collector of X1, making the collector voltage still less negative and in turn contributing further to the positive voltage at the base of X2.
All the events described in the foregoing are cumulative and occur at the very beginning of the first half-cycle, so that as transistor X1 goes from zero to full conduction, X2 goes from full conduction to zero, or "cutoff." At the start of the second half-cycle, the opposite sequence will occur- X1, which is conducting, will end up cut off, and X2 will go into full conduction. This sequence is initiated by the discharge action which has been occurring between capacitor C1 and resistor R2 throughout the entire first half-cycle.
Line 2 of Fig. 7 shows the voltage at the base of transistor X2 throughout the entire cycle. This waveform, during the first half-cycle, resembles an "exponential" discharge or charging curve and is actually the result of several actions to be described later. There is one significant fact about any free-running multi vibrator, whether it uses vacuum tubes or transistors as the switching devices: when one begins to conduct electrons, it changes the bias voltage on the other and thereby cuts it off.
The latter will remain cut off until an RC discharge action can take place. After the discharge has been completed, the device which was cut off will begin to conduct again, initiating a new half-cycle. The duration of each half-cycle is therefore regulated by the values of resistors and capacitors being discharged.
It is evident from Figs. 5 and 6 that transistor X1 con ducts its two currents during the first half-cycle only, and that transistor X2 conducts its two currents during the second half-cycle only. The base-emitter current for X1 (dotted green in Fig. 5) may be considered an offshoot of the voltage divider current (solid green) which flows continuously through divider resistors R4, R5, and R6. The base-emitter current, which is the "biasing" current for X1, enters the base and exits from the emitter (normal flow direction for the PNP transistor). It then flows downward, through stabilizing resistor R7, to ground. From here it can re-enter the grounded positive terminal of battery M1. This current will flow only when the base of X1 is more negative than the emitter.
The base-emitter current of X2 ( dotted red in Fig. 6) may be looked on as an offshoot of the other voltage-divider current which flows continuously through R1, R2, and R3. The former enters the base of X1 and exits from the emitter, then flows down through R7 to ground. Like its companion current in the other transistor, the base-emitter current through X2 can flow only when the base of X2 is more negative than the emitter. This mandatory set of conditions is implied by the descriptive term "forward bias." The Instantaneous Current Pulses Figs. 5 and 6 show two currents which are best described as instantaneous pulses of current. It is necessary to under stand the movements of both in order to understand how each transistor is turned on or cut off. Let us consider the actions which occur at the start of the first half-cycle. You have already seen how the X1 collector voltage becomes less negative when collector current begins its flow. The extra electrons necessary to make up this increased current cannot be drawn immediately through resistor R1, but must be taken from the left plate of coupling capacitor C1. This can occur only if an equal number of electrons are drawn onto the right plate. These electrons must be drawn upward through resistor R3; there is no other circuit component through which they can possibly come.
In flowing upward through R3, this electron current (in solid blue) inevitably is associated with a voltage which is positive at the top of R3, because electrons flow away from negative voltage areas and toward positive-voltage areas. This electron flow is of course opposite to the continuously downward flow of the voltage-divider current (in solid red). Thus, during the first half-cycle, two currents are flowing in opposite directions through the same resistor, R3, and developing two components of voltage which are opposite in polarity across it. The voltage at the base of X2, at any instant, is the algebraic sum of these two voltages. At the start of the first half-cycle, the positive voltage clearly predominates. This can only mean that the instantaneous current pulse which is shown in solid blue, and which is equal to the change in collector current being drawn into X1, is much larger than the voltage-divider cur rent flowing downward through R3.
The discharging action between capacitor C1 and resistor R2 is a difficult one to visualize. It begins at the start of the first half-cycle and continues throughout the half-cycle. The electron current that actually does the discharging has been shown in dotted blue, to differentiate it from the instantaneous current, in solid blue, moving to the left along the capacitive path represented by C2. The path of this discharge current is from the right plate, through resistor R2, to the left plate of C2.
It can be looked upon as an equalizing current, which must flow to correct or redistribute the unbalance of electric charge between the two plates of capacitor C2. It flows at what is called an exponential rate, a term derived from higher mathematics and beyond the scope of this guide. For our purposes, it describes a discharge process which begins at a high rate and continues at a decreasing rate to zero. Theoretically, no quantity can ever be decreased to zero by this system, because, during each unit of time a certain percentage of the quantity that existed at the beginning of the unit of time will be discharged. Hence, some fraction of the original quantity, however small, will always exist. Practically, five time periods are sufficient for charge redistribution to occur between a capacitor and resistor.
An exponential discharge curve is shown in the first half cycle of Line 2, Fig. 7. This portion of the curve actually represents the intrinsic voltage at the base of X1. However, it also resembles the quantity of discharge current flowing be tween C1 and R2 during the same half-cycle-namely, a large current to start with, and decreasing exponentially throughout the entire half-cycle.
By momentarily considering this RC combination isolated from all other circuit components, it will be fairly simple to visualize the discharge action. When the left plate of C1 is made more positive than the right plate, electrons will flow, or "discharge," through resistor R2 in the direction shown in Fig. 5. This discharge will continue until there is no longer any charge unbalance between the plates, meaning there is no voltage across the capacitor. However, this RC combination is not isolated from the rest of the circuit. Instead, across resistor R2, there is a permanent, or fixed, voltage difference caused by the flow of voltage-divider current (in solid red). This permanent voltage difference also exists across the capacitor plates, making the left plate more negative than the right.
This permanent voltage across C1 is momentarily upset or modified by the sudden change in collector voltage at the start of the first half-cycle. The collector voltage moves abruptly in the positive direction by an amount assumed to be 4 volts, or from -8 to -4 volts. If the voltage on the right plate of C1, as well as at the base of transistor X2, was assumed to be -1 volt before, it must now increase in the positive direction by the same 4 volts, to a new instantaneous value of +3 volts.
This positive peak value of the X2 base voltage (Line 2, Fig. 7) will cut off both currents through X2, and they will remain cut off until the base can again be made more negative than the emitter (which does not occur until the end of the first half-cycle) . To sum these actions up, the total current through resistor R2 always flows from left to right. The instant before the first half-cycle begins, the total current consists exclusively of the voltage-divider current (in solid red). The amount is determined by the Ohm's-law relationship between the combined series resistances of R2 and R3 and the -8 volts at the collector of X1.
The instant before the first half-cycle ends, and while X1 is still conducting, the total current through R2 again consists exclusively of the voltage-divider current shown in solid red. Its amount has changed, however, because the voltage at the collector of X1 has dropped from -8 to -4 volts. This would indicate that the voltage-divider current has been reduced by exactly one-half.
This change in amount of current during the first half-cycle might be looked on as an exponential reduction in the current flowing from left to right. Such a reduction must occur because, the instant before the first half-cycle starts, the voltage difference across R4 is 7 volts ( -8 volts at the left end and -1 volt at the right end), whereas the instant before this half cycle ends, this voltage difference is only 3 volts ( -4 volts at the left end and -1 volt at the right end, after the capacitor discharge) .
The Second Half Cycle
How current conduction is initiated through X2 at the start of the second half-cycle has already been discussed. The expected series of cumulative actions occurs almost instantaneously. As the collector voltage of X2 begins to rise from -8 to -4 volts, it raises the base voltage at X1 in the positive direction, cutting off both currents through X1. In turn, the X1 collector voltage is driven from -4 to -8 volts. This tends to drive the base of X2 even more negative, and quickly leads to full electron conduction through X2.
The base voltages cannot be driven as far negative as they can be positive. This is due to the "forward bias" condition of each transistor. As soon as the base of any PNP transistor becomes more negative than the emitter, electrons flow very freely from base to emitter. The reason is that the diode junction, N to P, has very little resistance in the so-called "forward" direction. Another way of saying this is that the forward-biased junction "short-circuits" the base resistors. This does not occur when the base-emitter junctions are reverse-biased. In Fig. 6, for example, the instantaneous current (in solid blue) flows downward exclusively through R3 as long as the base is less negative than the emitter. The moment the base becomes more negative, this current pulse is largely diverted through the much lower resistance path represented by the diode junction and resistor R7.
In Fig. 5, the instantaneous pulse current (in dotted blue) flows exclusively through R6 until the diode junction between base and emitter becomes forward-biased and offers a much lower resistance path.
Resistor R7 serves to prevent thermal runaway of either transistor. Both transistor currents must flow downward through R7 to ground, and this continuing current flow keeps both emitters at a small negative voltage. Thermal runaway is an undesirable, cumulative condition whereby an overheated transistor begins to conduct larger quantities of both currents, and the increased conduction further aggravates the overheated condition. With an emitter stabilizing resistor such as R7 in the circuit, any runaway current condition is quickly checked by the resulting increase in negative voltage at both emitters because an increase in negative voltage at a PNP emitter will reduce or cut off the currents through the transistor. Thus, a stabilizing resistor automatically prevents thermal runaway.
Relatively little has been said about the instantaneous pulse current, (in dotted blue) which flows through C2 and R6 and "turns off" the currents through X1; nor about the long time constant discharge current (in solid blue) which flows between C2 and R5 and eventually turns the transistor currents back on again. The movements of these currents are associated with the voltages shown in Lines 3 and 4 of Fig. 7. Observe that the square wave of voltage generated at the collector of X2 is exactly a half-cycle out of phase with the collector voltage of X1. Also, the exponential voltage waveforms at the two bases are exactly a half-cycle out of phase with each other.
Because of the similarity in physical action between the pulse currents and the exponential discharge currents for the two transistors, there is no need to discuss this set of currents their action is the same as for the set already discussed.