Resistance-Capacitance (RC) Circuit Characteristics [PHOTOFACT Television Course (1949)]

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The elements in a cathode-ray or picture tube provide an emitter or source of electrons, a means of forming an electron beam and accelerating its speed, and a phosphor surfaced screen which will fluoresce or glow when bombarded by the stream of electrons. They also provide for the movement of the beam horizontally and vertically to form a frame of light, or raster, on the face of the picture tube.

The voltage or current waveforms which are required for deflecting the electron beam are obtained from sweep generators which are followed by special wave-shaping circuits. The sweep generators are triggered by the synchronizing pulses which are clipped from the transmitted signal. This makes possible the synchronization of the sweep circuits in the receiver with those of the transmitter. The formation of certain waveshapes is required in order to obtain a linear sweep. This waveshape may be a sawtooth, as is required for electrostatic deflection, or a more complex voltage waveform used to obtain a sawtooth current flow in magnetic deflection coils. Some circuits are designed to pass a waveform with a minimum of distortion, while others are designed to effect great distortion when generating, amplifying, or passing a waveform. The behavior of these distortion circuits can best be understood by studying a charging or discharging capacitor in series with a resistor.

It is elemental in radio theory that when electrons flow through a resistor, a voltage or IR drop is developed across that resistor.

The value of voltage developed by a current flowing through a resistance is found by applying Ohm's law: E = I x R where E is in volts, I in amperes, and R in ohms.

A further study of fundamentals reveals that a capacitor is capable of storing or holding a charge of electrons. When charged, one plate contains more free electrons than the opposite plate; when the capacitor is completely discharged, both plates contain the same number of free electrons. The difference in number of electrons is a measure of the charge that exists across the capacitor. When the accumulation of electrons on one plate exceeds the accumulation on the other plate, a potential difference exists across the terminals of the capacitor, and this potential will continue to increase until it equals, for practical purposes, the applied or charging voltage. The value of voltage developed by a charging capacitor is computed by applying the following equation:

E=Q c

... where Q is in coulombs, C in farads, and E in volts. One coulomb is the quantity of electrical charge transferred if one ampere flows for one second.

R-C CIRCUIT CHARGING: A capacitance and a resistance employed in a voltage divider circuit, as shown in Figure 43, develop a pressure or potential across their respective terminals.

Fig. 43. Resistor-Capacitor Charging Curve

This circuit is commonly known as an R-C circuit, to which both Kirchoff's and Ohm's laws apply. Referring to the graphs and diagram in Figure 43, the voltage divider AB of the circuit diagram is shown in various time positions on the graph after closing the switch.

As time progresses, the voltage E_c on the capacitor gradually increases, while the voltage developed across the resistor E_r gradually decreases.

When the switch is closed, electrons are displaced from the upper plate of the capacitor, thus developing a positive charge causing electrons to be attracted to the lower plate through the resistor. This flow of electrons is the current that charges the capacitor. At the instant the current begins to flow, no charge is present on the capacitor, as seen at point "a" on the graph; therefore, the applied voltage E across the divider must all appear as a voltage drop across the resistor. The initial charge current, therefore, must be equal to E. R In recalling Kirchoff's law, it states that the sum of the voltages in a closed circuit is equal to zero. Likewise, the sum of the voltage drops in a closed circuit must equal the applied voltage. Therefore, if 100 volts is applied to an R-C circuit, this entire voltage appears across the resistor at the time the switch closes. The graph shows that at the instant the switch is closed, the entire applied voltage appears across R, while the voltage across C is zero.

However, the current flowing in the circuit soon charges the capacitor a small amount, and a voltage will appear across this capacitor.

See position ''b'' of the voltage divider plotted on the graph. Note: Ee is now 20 volts and Er is 80 volts, the sum of the two being equal to the applied voltage. As time elapses, Ee be comes greater and Er smaller, as will be noted at the time points "b", "c", "d", "e", and "f". Actually, the capacitor voltage becomes a re-active voltage, or back pressure (opposite in polarity and opposed to the applied potential). This causes the charging current to decrease and the IR drop across the resistance to fall, resulting in the capacitor charging at a slower rate.

This charging action continues until the capacitor is almost fully charged. At this time, the voltage across R must be near zero, and the charging current is practically zero. Theoretically, a capacitor never fully charges, and some minute voltage will always appear across the resistor. However, if the switch is closed long enough, an almost steady state condition is reached and the capacitor is considered fully charged for all practical purposes.

Charging a capacitor electrically can be likened to inflating a flat tire where a current of air first rushes into the inner tube and gradually tapers off as the tire becomes inflated.

The current of air flowing into the tire from the compressor sometimes rings a bell. At first the bell rings in rapid succession, but gradually slows up as the tire builds up a back pressure.

Fig. 44. Resistor-Capacitor Discharging Curve

R-C CIRCUIT DISCHARGE: Suppose that, just before point "f" on the charging curve, the charging switch is thrown open and the discharging switch closed, as shown in Figure 44.

Note that the capacitor voltage reached a value of 99 volts. This value would have been slightly higher if the charging circuit had been left closed for a longer period of time. In Figure 44, the battery switch is open and a short circuit path is switched across the divider.

The 99 volts of potential energy stored by the capacitor now becomes an applied voltage of the discharge circuit and will cause a current to flow around the circuit. The discharge current will be opposite in direction to the charging current, developing an IR drop across the resistor. The voltage drop across the resistor, due to the discharge current, will be opposite in polarity to that developed by the charging current. The discharge curve will vary exponentially in exactly the same manner as the charge curve, but will be diminishing in value.

During discharge, the capacitor voltage is shown dropping from its initial value, and, representing the applied voltage of the discharge circuit, will be equal to the voltage drop across the resistor (Kirchoff's Law). Seeing that the capacitor voltage now represents the applied voltage of the discharge circuit, Ee and Er will slowly approach zero together. (The plotted charging curve is not linear throughout.

However, the initial charge portion of the curve, Figure 43, is practically straight up to 40 volts, and it is this portion of the curve that we will be more concerned with in television sweep circuits because of this linearity. This is the most important point of the discussion and should be borne in min for future reference.) Also note that the capacitor voltage does not reverse in polarity during the charge and discharge cycle. This is not true in the case of the resistor voltage because the current actually reverses its direction between the charge and discharge period.

Fig. 45. R-C Time Constants

TIME CONSTANTS OF AN R-C CIRCUIT: The diagram in Figure 45 shows an R-C circuit connected across an applied voltage. The time required to charge the capacitor to 63.2% of the applied voltage is known as the time constant of the circuit. The value of this time constant in seconds is equal to the product of the circuit resistance in ohms and the capacity in farads, and may be found by using any of the following relations:

1. R (in ohms) x C (in farads) = t (in seconds)

2. R (in megohms) x C (in microfarads) = t (in seconds)

3. R (in ohms) x C (in microfarads) = t (in microseconds)

4. R (in megohms) x C (in micro-microfarads) =t (in microseconds)

EXAMPLE: A 0.1 microfarad capacitor in series with a 100K ohm resistor will take .01 of a second or 10,000 microseconds to reach 63.2% of the applied voltage.

Referring to Figure 45, a .01 mfd. capacitor is in series with a 10 k-ohm (.01 megohm) resistor.

Now, we find from the above table that multiplying microfarads by megohms will give an R-C time constant of .0001 seconds or 100 microseconds for this circuit.

Therefore, we interpret from the time constant that when 100 microseconds has elapsed since switching on, 63.2% of the applied voltage is across the capacitor and 36.8% across the resistor.

The applied voltage being 100 volts, the capacitor charge will be approximately 63 volts and the IR drop across the resistance, due to the charging current, will be approximately 37 volts.

In twice the R-C time, or 200 microseconds, 63.2% of the remaining 37 volts is added to the original 63.2% charge, making approximately 86 volts across the capacitor and 14 volts drop across the resistor.

200 microseconds = 2RC = 63 volts+ (63.2% x 37) = 86.4 volts.

This value may be found by following the Ee curve in Figure 45 . Theoretically, the capacitor never reaches a fully charged condition; but at the completion of 5 R-C seconds, approximately 99% displacement of voltage across the circuit has occurred and for all practical purposes, this is sufficient to be considered as full charge. Refer to chart in Figure 45.

DISCHARGE: The time required to discharge a capacitor is the same as that required in charging. Therefore, the time constant (R-C) is proportional to the time required to charge or discharge a capacitor.

Fig. 46. R-C Charge and Discharge Curves

In 1 R-C time of the discharge period, 36.8% of the original charge will remain in the capacitor. The charge and discharge curves are shown in Figure 46. Note the similarity; exponentially they are the same.

FORMATION OF SQUARE AND SAWTOOTH WAVES: If a source of DC voltage connected to a resistive load is switched on and off in equal alternate periods, the applied electrical pressure across the resistor will take the form of a symmetrical square-wave of voltage--see Figure 47.

Fig. 47. Square Waveforms

On the o the r hand, if the circuit is switched on and off in unequal alternate periods, the applied voltage to the load would appear as an asymmetrical square-wave--see Figure 47.

Therefore, by mechanically operating an on and-off switch, we are able to generate two types of voltage wave forms. They are:

1. Symmetrical square-wave of voltage.

2. Asymmetrical square-wave of voltage.

Now, if a fairly large capacitor is connected in series with the resistor, and a DC source of supply is switched on and off in equal time periods to produce an applied square-wave of voltage, the resistive and capacitive components of the circuit will produce the following wave-shapes.

1. The capacitor voltage, known as the "integrator" voltage, will appear as a back-to back sawtooth--see Figure 48.

Fig. 48. Application of Square Wave of Voltage to R-C Circuits

Fig. 49. Examples of Time Constants and their R-C Waveforms

2. The voltage drop across the resistor, known as the "differentiator" voltage , will appear as a partially distorted square-wave--see Figure 48.

NOTE: The polarity of the integrator voltage is unchanged during the charge and discharge period, while the differential voltage is driven in two directions: i.e., positive and negative.

By increasing or decreasing the value of the capacitor in the RC network, the integrator and differentiator voltage waveforms are changed, as shown in Figure 49.

Note that the output waveforms for the 100 microsecond circuit are similar to the ones shown in Figure 48. When the capacitor is in creased in value to give a time constant of 1000 microseconds, only a slight voltage is obtained across the capacitor, while the voltage across the resistor is distorted very little from the applied waveform. On the other hand, when the value of the capacitor is reduced to give a time constant of 10 microseconds, the voltage waveform across the capacitor is similar to the applied voltage, while the waveform across the resistor is differentiated a great amount, giving very sharp positive and negative peaks. Keeping in mind that the waveforms applied to each of the circuits in Figure 49 are identical as to frequency and amplitude, it can be seen that a square wave can be differentiated or integrated a variable amount to give the desired wave-shape by properly selecting the values in the RC circuit.

At this point we are interested in the integrator voltage; so, advancing still further in the study of wave-shapes and circuit analysis, let us refer to Figure 50. Here we have a circuit arrangement where a capacitor is permitted to charge through a l0K ohm resistor, and by throwing a switch the capacitor is discharged through a 1K ohm resistor. If the charge time is longer than the discharge time, for instance, let us say 10 times longer, the charge and the discharge voltage of the capacitor will take the form of a sawtooth of voltage. See Figure 51.

The slow charge and the rapid discharge effects can be clearly seen. To obtain linear horizontal and vertical scanning for building a frame or raster, it is necessary to generate and apply linear sawtooth waves to the deflection systems of the cathode-ray tube.

Fig. 50.

Fig. 51.

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Updated: Tuesday, 2021-11-16 12:07 PST