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.

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Free download of Dell Inspiron User Manual. 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. 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. 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.

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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.

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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. The result is a rectangular raster of closely spaced lines which cover the entire face of the tube and impart a uniform intensity to the screen.

When the video signal is applied to the electron gun, it modulates the intensity of the beam and thus forms the TV picture. Imagine that a cathode-ray tube is placed in J a constant longitudinal magnetic field, the axis of the tube coinciding with the direction of the magnetic field.

A magnetic field of the type here con- sidered is obtained through the use of a long solenoid, the tube being placed within the coil. Inspection of Fig.

The Y axis represents the axis of the cathode-ray tube. The origin is the point at which the electrons emerge from the anode. The velocity of the origin is v , the initial transverse velocity due to the mutual repulsion of the electrons being VoX. It is now shown that the resulting motion is a helix, as illustrated. The electronic motion can most easily be analyzed by resolving the velocity into two components, vv and v9t along and transverse to the magnetic field, respectively.

Since the force is perpendicular to B, there is no accelera- tion in the Y direction. A force eBvt normal to the path will exist, resulting from the transverse velocity.

This accounts for the appear- ance of a broad, faintly illuminated area instead of a bright point on the screen. However, the period, or the time to trace out the path, is independent of vex, and so the period will be the same for all electrons. If, then, the distance from the anode to the screen is made equal to one pitch, all the electrons will be brought back to the Y axis the point 0' in Fig.

Under these conditions an image of the anode hole will be observed on the screen. As the field is increased from zero, the smudge on the screen resulting from the defocused beam will contract and will become a tiny sharp spot the image of the anode hole when a critical value of the field is reached.

This critical field is that which makes the pitch of the helical path just equal to the anode-screen distance, as discussed above. By continuing to increase Sec. Electronic path the strength of the field beyond this critical value, the pitch of the helix decreases, and the electrons travel through more than one complete revolution.

The electrons then strike the screen at various points, so that a defocused spot is again visible. A magnetic field strength will ultimately be reached at which the electrons make two complete revolutions in their path from the anode to the screen, and once again the spot will be focused on the screen.

This process may be continued, numerous foci being obtainable. In fact, the current rating of the solenoid is the factor that generally furnishes a practical limitation to the order of the focus. The foregoing considerations may be generalized in the following way: If the screen is perpendicular to the Y axis at a distance L from the point of emergence of the electron beam from the anode, then, for an anode-cathode potential equal to Va, the electron beam will come to a focus at the center of the screen provided that L is an integral multiple of p.

This is a justifiable assumption. A Short Focusing Coil The method described above of employing a longitudinal magnetic field over the entire length of a commercial tube is not too practical. Hence, in a commercial tube, a short coil is wound around Because of the fringing of the magnetic lines of flux, a radial component of B exists in addition to the component along the tube axis. Hence there are now two components of force on the electron, one due to the axial component of velocity and the radial component of the field, and the second due to the radial component of the velocity and the axial component of the field.

The analysis is complicated, 8 but it can be seen qualitatively that the motion will be a rotation about the axis of the tube and, if conditions are correct, the electron on leaving the region of the coil may be turned sufficiently so as to move in a line toward the center of the screen. A rough adjustment of the focus is obtained by positioning the coil properly along the neck of the tube. The fine adjustment of focus is made by con- trolling the coil current. In other words, the electron will move in a direction parallel to the fields with a constant acceleration.

If the fields arc chosen as in Fig. Consequently, the resulting path is helical with a pitch that changes with the time. That is, the distance traveled along the Y axis per revolution increases with each revolution. The time for an electron to reach its maximum height above the XZ plane 6.

The position of the electron at this time c. The velocity components of the electron at this time Solution a. As discussed above, the path is a helix of variable pitch. The acceleration is downward, and for the coordinate system of Fig. The particle will then reverse its K-directed motion.

The point P' in space at which the reversal takes place is obtained by con- sidering the projection of the path in the XZ plane since the Y coordinate U already known. The angle 8 in Fig. The magnetic field is directed along the - 1' axis, and tho electric field is directed along the -Xaxis. Any force due to the magnetic field is always normal to B, and Sec. Thus there is no component of force along the Y direction, and the Y component of acceleration is zero.

It is desired to investigate the path of an electron starting at rest at the origin. The initial magnetic force is zero, since the velocity is zero. As soon as the electron is in motion, the magnetic force will no longer be zero. Clearly, the electric and magnetic forces interact with one another.

In fact, the analysis cannot be carried along further, profitably, in this qualitative fashion. The arguments given above do, how- ever, indicate the manner in which the electron starts on its path. This path will now be shown to be a cycloid. To determine the path of the electron quantitatively, the force equations must be set up. The force due to the magnetic field is found as follows: Since B is in the Y direction, no force will be exerted on the electron due to vy.

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Because of vx , the force is eBvx in the --Z direc- tion, as can be verified by the direction rule of Sec. Similarly, the force due to v, is eBvt in the —X direction.

Substituting this expression for vx in Eq. Path Equations are the parametric equations of a com- mon cycloid, defined as the path generated by a point on the circumference of a circle of radius Q which rolls along a straight line, the Z axia.

This is illustrated in Fig. The dark curve is the locus of the point P. The reference line CC is drawn through the center of the generating circle parallel to the X axis. Since the circle rolls on the Z axis, then OC represents the length of the circumference that has already come in contact with the Z axis. This length is evidently equal to the arc PC and equals Qd. The angle 8 gives the number of radians through which the circle has rotated.

The physical interpretation of the symbols introduced above merely as abbreviations is as follows: Q represents the radius of the rolling circle. From these interpretations and from Fig. Also, the distance along the Z axis between cusps is equal to the circumference of the rolling circle, or 2vQ.

At each cusp the speed of the electron is zero, since at this point the velocity is reversing its direction Fig. This is also seen from the fact that each cusp is along the Z axis, and hence at the same potential.

Therefore the electron has gained no energy from the electric field, and its speed must again be zero. If an initial velocity exists that is directed parallel to the magnetic field, the projection of the path on the XZ plane will still be a cycloid but the particle will now have a constant velocity normal to the plane. This path The electric force is eS along the --X direction Fig.

This discussion gives another interpretation to u. It represents that velocity with which an electron may be injected into perpendicular electric and magnetic fields and suffer no deflection, the net force being zero. Note that this velocity u is independent of the charge or mass of the ions. The length I of the deflecting plates along the tube axis is 2.

Solution Choose the system of coordinate axes illustrated in Fig.

In this chapter we begin with a review of the basic atomic properties of

Then f. Thus If Q' - Q, the path is called a common cycloid, illustrated in Fig. If Q' is less than Q, the path is called a aviate cycloid, 6 and has blunted cusps, as indicated in Fig. These high-energy positive ions are then allowed to bombard some substances, which become radioactive and generally disintegrate. Because of this, the cyclotron has popularly become known as an atom smasher.

The basic principles upon which the cyclotron operates are best under- stood with the aid of Fig. The essential elements are the "dees," the Rolling circle Angular velocity to Fig. The trocholdal paths of electrons in perpendicular electric and magnetic fields. A moving positive ion released near the center of the dees will be acceler- ated in a semicircle by the action of the magnetic field and will reappear at point 1 at the edge of dee I.

Assume that dee II is negative at this instant with respect to dee I. Then the ion will be accelerated from point 1 to point 2 across the gap, and will gain an amount of energy corresponding to the poten- tial difference between these two points. Once the ion passes inside the metal dee II, the electric field is zero, and the magnetic field causes it to move in the semicircle from point 2 to point 3. If the frequency of the applied ac poten- tial is such that the potential has reversed in the time necessary for the ion to Dees Particle orbit schematic Fig.

With the frequency of the accelerating voltage properly adjusted to this "resonance" value, the ion continues to receive pulses of energy corresponding to this difference of potential again and again.

Thus, after each half revolution, the ion gains energy from the electric field, resulting, of course, in an increased velocity. The radius of each semi- circle is then larger than the preceding one, in accordance with Eq. EXAMPLE Suppose that the oscillator that supplies the power to the dees of a given cyclotron imparts 50, eV to heavy hydrogen atoms deuterons , each of atomic number 1 and atomic weight 2. Calculate the magnetic field intensity, the frequency of the oscillator, and the time it will take for an ion introduced at the center of the chamber to emerge at the rim of the dee with an energy of 5 million electron volts 5 MeV.

Assume that the radius of the last semicircle is 15 in. The frequency of the oscillator must be equal to the reciprocal of the time of revolution of the ion. This is, from Eq.

That, is, the ion must make 50 complete revolutions in order to gain the full energy. Thus, from Eq. Also, the design of a kV oscillator for these high frequencies and the method of coupling it to the dees present some difficulties, since the dees are in a vacuum-tight chamber.

Further, means must be provided for introducing the ions into the region at the center of the dees and also for removing the high- energy particles from the chamber, if desired, or for directing them against a target. This results in a great saving in weight and expense.

The dees of the cyclotron are replaced by a single-cavity resonator. Electrons and protons have been accelerated to the order of a billion electron volts Bev in synchro- trons. The defocusing of the beam limits the number of allow- able cycles. These radioactive elements are of the utmost importance to physicists, since they permit a glimpse into the consti- tution of nuclei.

They are likewise of extreme importance in medical research, since they offer a substitute for radium. Radioactive substances can be fol- lowed through any physical or chemical changes by observing their emitted radiations.

This "tracer," or u tagged-atom," technique is used in industry, medicine, physiology, and biology. Thus, if electrons were used in a cyclotron, their angular velocity would decrease as their energy increased, and they would soon fall out of step with the high-fre- quency field. For this reason electrons are not introduced into the cyclotron. For positive ions whose mass is several thousand times that of the elec- tron, the relativistic correction becomes appreciable when energies of a few tens of millions of electron volts are reached.

For greater energies than these, the ions will start to make their trip through the dees at a slower rate and Blip behind in phase with respect to the electric field. This difficulty is overcome in the synchrocyclotron, or f-m cyclotron, by decreasing the frequency of the oscillator frequency modulation in accordance with the decrease in the angu- lar velocity of the ion.

With such an f-m cyclotron, deuterons, a particles, and protons have been accelerated to several hundred million electron volts.

Such an instrument is called a synchrotron. The particles are injected from a gun, which gives them a velocity approaching that of light. The vacuum chamber is built in the form of a doughnut instead of the cyclotron pillbox.

Millman, J. Goedicke, E.

Busch, Physik. Cosslett, V. James, G. Van Nostrand Com- pany, Inc. Livingston, M. The Cyclotron, I, J. Particle Accelerators, Advan. Brobeck, W. Lawrence, K. MaeKenzie, E. McMillan, R. Serber, D. Sewell, K. Simpson, and R. Blewett, G. Green, and L. Courant, E. Livingston, and H.

The Strong-focusing Syn- chrotron:Thus the total charge per second passing any area, which, by definition, is the current in amperes, is. Hence, nominally, zero current results. Far from the junction the minority carriers are equal to their thermal-equilibrium values pno and npo, as is also the situation in Fig.

Crosses are powerful and do not give Noughts a fair chance in life. There is more than one way to explain this phenomenon - explain in terms of capacitor dimensions, or in terms Basic Electronics Chapter 2, 3A test T5, T6 Basic Electrical Principles and the Functions of Components Figures in this course book are reproduced with the permission of the American Radio Relay League.