# MILLMAN HALKIAS EBOOK

Millman and Halkias · Electronic Devices and Circuits. Millman and Halkias · Integrated Electronics: Analog and Digital Circuits and Systems. Miliman and Taub. Millman Halkias Integrated Electronics. Topics electronics Identifier MillmanHalkiasIntegratedElectronics. Identifier-arkark://t7wm5sz7b. Electronics by Jecob Millman & C. Halkias download link: Free Pdf download. electronics by "ebook integrated electronics by millman halkias. myavr.info

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## Noughts And Crosses Comprehension Questions

The solution of this problem is given by the well-known expressions for the velocity and displacement, viz.

It is to be emphasized that, if the acceleration of the particle is not a con- stant but depends upon the time, Eqs. Equations follow directly from Eqs. The applied voltage is zero at the, instant the elec- tron is released, and it increases linearly from zero to 10 V in 0,1 Msec.

If the opposite plate is positive, what speed will the electron attain in 50 nsec? Where will it be at the end of this time? With what speed will the electron strike the positive plate? Solution Assume that the plates are oriented with respect to a cartesian system of axes as illustrated in Fig. The magnitude of the electric field intensity is a. Conversion factors and prefixes are given in Appendix B.

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Equation shows that an electron that has "fallen" through a certain difference of potential V in going from point xa to point x has acquired a specific value of kinetic energy and velocity, independent of the form of the variation of the field distribution between these points and dependent only upon the magnitude of the potential difference V.

This law is known to be valid even if the field is multidimensional. This result is extremely impor- tant in electronic devices.

Stated in its most genera] form, Eq. By definition, the potential energy between two points equals the potential multiplied by the charge in question.

Thus the left-hand side of Eq. The right-hand side repre- sents the drop in kinetic energy from A to B. Thus Eq. If the particle is an electron, then — e must be substituted for q. If the electron starts at rest, its final speed v, as given by Eq. Despite this tremen- dous speed, the electron possesses very little kinetic energy, because of its minute mass. It must be emphasized that Eq. If the electron does not have zero initial velocity or if the particle involved is not an electron, the more general formula [Eq.

For a discussion of the energies involved in electronic devices, even the erg is much too large a unit. This statement is not to be construed to mean that only minute amounts of energy can be obtained from electron devices. It is true that each electron possesses a tiny amount of energy, but as previously pointed out Sec.

A unit of work or energy, called the electron volt eV , is defined as follows: The name electron volt arises from the fact that, if an electron falls through a potential of one volt, its kinetic energy will increase by the decrease in potential energy, or by eV - 1. The abbreviations MeV and BeV are used to designate 1 million and 1 billion electron volts, respectively.

In the general case, where the field may vary with the distance, this equation is no longer true, and the correct result is obtained by differentiating Eq. We obtain dV ax The minus sign shows that the electric field is directed from the region of higher potential to the region of lower potential.

It will again be assumed that the electric field between the plates is uniform. Hence the component of velocity in the Z direction remains constant. Since the initial velocity in this direction is assumed to be zero, the motion must take place entirely in one plane, the plane of the paper.

For a similar reason, the velocity along the X axis remains constant and equal to vox. These equations indi- cate that in the region between the plates the electron is accelerated upward, the velocity component vv varying from point to point, whereas the velocity component vx remains unchanged in the passage of the electron between the plates.

The path of the particle with respect to the point is readily determined by combining Eqs. The electrons are to emerge at the point B in time 4. What is the distance AB? What angle does the electron beam make with the horizontal? The bullet will travel in a parabolic path, first rising because of the muzzle velocity of the gun and then falling because of the downward attrac- tive force of the earth.

The source of the charged particles is called an electron gun, or an ion gun. The initial electron velocity is found using Eq. The hot cathode A' emits electrons whieh are accelerated toward the anode by the potential Va.

Those electrons which are not collected by the anode pass through the tiny anode hole and strike the end of the glass envelope. Thus the positions where the electrons strike the screen are made visible to the eye. The displacement D of the electrons is deter- mined by the potential Vd assumed constant applied between the delecting plates, as shown. The velocity vox with which the electrons emerge from the anode hole is given by Eq.

The path is a straight line from the point of emergence M at the edge of the plates to the point P' on the screen, since this region is field-free. The straight-line path in the region from the deflecting plates to the screen is, of course, tangent to the parabola at the point M. The slope of the line at this point, and so at every point between M and P', is [from Eq. Consequently, a cathode-ray tube may be used as a linear-voltage indicating device.

The electrostatic-deflection sensitivity of a cathode-ray tube is defined as Furthermore, the sensitivity varies inversely with the accelerating potential Va. The idealization made in connection with the foregoing development, viz. Consequently, the effect of fringing of the electric field may be enough to necessitate correc- tions amounting to as much as 40 percent in the results obtained from an application of Eq.

Typical measured values of sensitivity are 1.

These plates are referred to as the vertical-deflection and horizontal-deflection plates because the tube is ori- ented in space so that the potentials applied to these plates result in vertical and horizontal deflections, respectively. The reason for having two sets of plates is now discussed. Suppose that the sawtooth waveform of Fig. Since this voltage is used to sweep the electron beam across the screen, it is called a sweep voltage.

The electrons are deflected Vertical-deflection plates Horizontal- deflection plates Vertical signal voltage v. Horizontal sawtooth voltage Electron beam Ftg.

Time linearly with time in the horizontal direction for a time T. Then the beam returns to its starting point on the screen very quickly as the sawtooth voltage rapidly falls to its initial value at the end of each period. If a sinusoidal voltage is impressed across the vertical-deflection plates when, simultaneously, the sweep voltage is impressed across the horizontal- deflection plates, the sinusoidal voltage, which of itself would give rise to a vertical line, will now be spread out and will appear as a sinusoidal trace on the screen.

The pattern will appear stationary only if the time T is equal to, or is some multiple of, the time for one cycle of the wave on the vertical plates. It is then necessary that the frequency of the sweep circuit be adjusted to synchronize with the frequency of the applied signal.

Actually, of course, the voltage impressed on the vertical plates may have any waveform. Consequently, a system of this type provides an almost inertialess oscilloscope for viewing arbitrary waveshapes. This is one of the most common uses for cathode-ray tubes.

If a nonrepeating sweep voltage is applied to the horizontal plates, it is possible to study transients on the screen. This requires a system for synchronizing the sweep with the start of the transient. The sensitivity is greatly increased by means of a high-gain amplifier interposed between the input signal and the deflection plates. The electron gun is a complicated structure which allows for acceler- ating the electrons through a large potential, for varying the intensity of the beam, and for focusing the electrons into a tiny spot.

Controls are also pro- vided for positioning the beam as desired on the screen. The quantity m is known as the rest mass, or the electrostatic mass, of the particle, and is a constant, independent of the velocity. From Eqs.

By defining the quantity vx as the velocity that would result if the relativistic variation in mass were neglected, i. That it does so is seen by applying the binomial expansion to Eq.

This equation also serves as a criterion to determine whether the simple classical expression or the more formidable relativistic one must be used in any particular case.

For example, Swc. For an electron, the potential difference through which the particle must fall in order to attain a velocity of 0. Thus, if an electron falls through a potential in excess of about 3 kV, the relativistic corrections should be applied. If the particle under question is not an elec- tron, the value of the nonrelativistic velocity is first calculated. If this is greater than 0.

In cases where the speed is not too great, the simplified expression may be used. The accelerating potential in high-voltage cathode-ray tubes is sufficiently high to require that relativistic corrections be made in order to calculate the velocity and mass of the particle. Other devices employing potentials that are high enough to require these corrections are x-ray tubes, the cyclotron, and other particle-accelerating machines. Unless specifically stated otherwise, nonrelativistic conditions are assumed in what follows.

If I and B are not perpendicular to each other, only the component of I perpendicular to B contributes to the force.

## Herculles Library | mail.deporteschiclana.es-Page:290

Some caution must be exercised with regard to the meaning of Fig. If the particle under consideration is a positive ion, then I is to be taken along the direction of its motion. This is so because the conventional direction of the current is taken in the direction of flow of positive charge.

If the current 's due to the flow of electrons, the direction of I is to be taken as opposite to the direction of the motion of the electrons. Other conversion factors are given in Appendix B. To sum- marize: T-8 Pertaining to the determination of the magnitude of the force fm on a charged particle in a magnetic field.

## Millman Halkias Integrated Electronics

This concept is very useful in many later applications. By definition, the current density, denoted by the symbol J, is the current per unit area of the conducting medium.

That is, assuming a uniform current distribution, "i where J is in amperes per square meter, and A is the cross-sectional area in meters of the conductor. This becomes, by Eq.

This derivation is independent of the form of the conducting medium. Consequently, Fig. It may represent equally well a portion of a gaseous-discharge tube or a volume element in the space-charge cloud of a vacuum tube or a semiconductor.

Furthermore, neither p nor v need be constant, but may vary from point to point in space or may vary with time. Numerous occasions arise later in the text when reference ia made to Eq. Consider an electron to be placed in the region of the magnetic field. If the initial velocity of the particle is along the lines of the magnetic flux, there is no force acting on the particle, in accordance with the rule associated with Eq.

Hence a particle whose initial velocity has no component normal to a uniform magnetic field will continue to move with constant speed along the lines of flux.

Now consider an electron moving with a speed v to enter a constant uniform magnetic field normally, aa shown in Fig. Since the force fm is perpendicular to v and so to the motion at every instant, no work is done on the electron.

This means that its kinetic energy is not increased, and so its speed remains unchanged. Further, since v and B are each constant in magnitude, then fm is constant in magnitude and perpendicular to the direction of motion of the particle. This type of force results in motion in a circular path with constant speed. It is analogous to the problem of a mass tied to a rope and twirled around with constant speed. The force which is the tension in the rope remains constant in magnitude and is always directed toward the center of the circle, and so is normal to the motion.

Further, the period and the angular velocity are inde- pendent of speed or radius. This means, of course, that faster-moving particles will traverse larger circles in the same time that a slower particle moves in its smaller circle.

This very important result is the basis of operation of numer- ous devices, for example, the cyclotron and magnetic-focusing apparatus. Assume that the tube axis is so oriented that it is normal to the field, the strength of which is 0.

The anode potential is V; the anode- screen distance is 20 cm Fig. Solution According to Eq. From Eq. This example indicates that the earth's magnetic field can have a large effect on the position of the cathode-beam spot in a low-voltage cathode-ray tube. If Fig.

This figure is not drawn to scale.

I -U the anode voltage is higher than the value used in this example, or if the tube is not oriented normal to the field, the deflection will be less than that calculated. In any event, this calculation indicates the advisability of carefully shielding a cathode-ray tube from stray magnetic fields.

However, since it is not feasible to use a field extending over the entire length of the tube, a short coil furnishing a transverse field in a limited region is employed, as shown in Fig. The magnetic field is taken as pointing out of the paper, and the beam is deflected upward.

It is assumed that the magnetic field intensity B is uniform in the restricted region shown and is zero outside of this area. Hence the electron moves in a straight line from the cathode to the boundary of the magnetic field. In the region of the uniform magnetic field the electron experiences a force of magnitude eBv, where v is the speed. The path OM will be the arc of a circle whose center is at Q.

It is observed that this quantity is independent of B. This condition is analogous to the electric case for which the electrostatic sensitivity is independent of the deflecting potential. However, in the electric case, the sensitivity varies inversely with the anode voltage, whereas it here varies inversely with the square root of the anode voltage.

Because the sensitivity increases with L, the deflecting coils are placed as far down the neck of the tube as possible, usually directly after the accelerating anode. Deflection in a Television Tube A modern TV tube has a screen diameter comparable with the length of the tube neck.

Under these cir- cumstances it is found that the deflection is no longer proportional to B Prob. If the magnetic-deflection coil is driven by a sawtooth current waveform Fig. For such wide-angle deflection tubes, special linearity- correcting networks must be added. A TV tube has two sets of magnetic-deflection coils mounted around the neck at right angles to each other, corresponding to the two sets of plates in the oscilloscope tube of Fig.

Sweep currents are applied to both coils, with the horizontal signal much higher in frequency than that of the vertical sweep. Sponsored Read more Show Draw a noughts and crosses grid on the board, and number each box from 1 to 9: Now, divide the children into two teams, and label the teams "noughts" or "crosses". This tests your knowledge of the book 'Noughts and Crosses': what is the other name for a nought?

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