The Hall Effect

In 1879, E.H. Hall observed that a small voltage is generated across a conductor carrying current in an external magnetic field. The Hall voltage was very small with typical conductors, and little use was made of this effect. However, with the development of semiconductors, lager values of Hall voltage can be generated. The semiconductor material indium arsenide (In As) is generally used. As illustrated in Fig.13-14, the InAs element inserted in the magnetic field can generate 60 mV with B equal to 10 KG and an I of 100 mA. The applied flux must be perpendicular to the direction of current. With current in the direction of the length of conductor, the generated voltage is developed across the which.

The amount of Hall voltage v/H is directly proportional to the value of flux density B. This means that gauss meter in Fig.13-15 uses an InAs probe in the magnetic field to generate a proportional Hall voltage v/H. This value of v/H is then read by the meter, which is calibrated in gauss. The original calibration is made in terms of a reference magnet with a specified flux density.

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Norton's Theorem

Named after E,L. Norton, a scientist with bell telephone Laboratories Norton’s theorem is used for simplifying a network in terms of current instead of voltages. In many cases, analyzing the division of currents may be easier than voltage analysis. For current analysis, therefore, Norton’s theorem can be used to reduce a network to a simple parallel circuit, with a current source. The idea of a current source is that it supplies a total line current to be divided among parallel branches, corresponding to voltage source applying a total voltage to be divided among series components. This comparison is illustrated in Fig.10-7.

EXAMPLE OF A CURRENT SOURCE

A source of electric energy supplying voltage is often shown with a series resistance which represents the internal resistance of the source, as in Fig.10-7a. This method corresponds to showing an actual voltage source, such as a battery for dc circuits. However, the source may be represented also as a current with a parallel resistance, as in Fig.10-7b. Just as a voltage source is rated at, say, 10V , a current source may be rated at 2 A . For the purpose of analyzing parallel branches, the concept of a current source may be more convenient than a voltage source.
If the current I in Fig. 10-7is a 2-A source, it supplies 2A no matter what is connected across the output terminals A and B. Without anything connected across A and B, all 2 A flows through the shunt R. When a load resistance R/L is connected across A and B, then the 2-A I divides according to the current division rules for parallel branches.
Remember the parallel current divide inversely to branch resistance but directly with conductance. For this reason it may be preferable to consider the current source shunted by the conductance G, as shown in Fig. 10-7c. we can always convert between resistance and conductance, because 1/R in ohms is equal to G in siemens.
The symbol for a current source is a circle with an arrow inside, as shown inFig.10-7b and c, to shown the direction of current . This direction must be the same as the current produced by the polarity of the corresponding voltage source.
Remember that a source produce electron flow out from the negative terminal.
An important difference between voltage and current sources is that a current source is killed by making it open, compared with short-circuiting a voltage source. Opening a current source kills its ability to supply current without affecting any parallel branches. A voltage source is short-circuited to kill its ability to supply voltage without affecting any series components.

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Millman's Theorem

Millman’s theorem provides a shortcut for finding the common voltage across any number of parallel branches with different voltage sources. A typical example is shown in fig. 10-16 For all the branches, the ends at point Y are connected to chassis ground. Furthermore, the opposite ends of all the branches are also connected to the point X. The voltage V/x y, therefore, is the common voltage across all the branches.











Finding the value of V/x y gives the net effect of the all source in determining the voltage at X with respect to chassis ground. To calculate this voltage
 v/x y=V1/R1 + V2/R2 + V3/R3 ……etc
1/R1 + 1/R2 +1/R3
This formula is derived from converting the voltage source to current sources and combining the results. The numerator with V/R terms is the sum of the parallel current sources. The denominator with 1/R terms is the sum of the parallel conductances. The net V/x y then is the form of I/G or 1*R, which is in units of voltage.
CALCULATING V/XY
For the values in Fig.10-16,
Vxy =32/4 + 0/2 – 8/4
1/4 + 1/2 + 1/4
=8 + 0 -2
1
Vxy=6 V
Note the branches 3, V3 is considered negative because it world make point X negative. However, all the resistances are positive. The positive answer for Vxy means that point X is positive with respect to Y.
In branch 2, V2 is zero because this branch has no voltage source however, R2 is still used in the denominator.
This method can be used for any number of branches, but they must all be in parallel, without any series resistance between the branches. In a branch with several resistance, they can be combined as one Rt. When a branch has more than one voltage source, they can be combined algebraically for one Vt. Read More!

Alternating Current Application

Figure 16-1 shows the out put from an voltage generator, with the reversals between positive and negative polarities and the variations in amplitude. In Fig. 16-1a, the wave from shown simulates an ac voltage as it would appear on the screen of an oscilloscope, which is an important test instrument for ac voltages. The oscilloscope shows a picture of any as voltage connected to its input terminals, while indicting the amplitude. The details of how to use the oscilloscope for ac voltage measurements are explained in App. D. “Using the oscilloscope”.
In Fig.16-1b the Read More!

Oscillator

An oscillator is a circuit that produces a repetitive waveform on its output with only the dc supply voltage as an input.A repetitive input signal is not required.The output voltage can be either sinusoidal or nonsinusoidal depending on the type of oscillator.

The basic concept of an oscillator is illustrated in figure(a).Essentially an oscillator converts electrical energy in the form of dc to electrical energy in the form of ac.A basics sinusoidal oscillator consists of an amplifier for gain( either discrete transistor or op-amp ) and a positive feedback circuit that produces phase shift and provides attenuation,as shown in figure(b).

The basic oscillator concept showing three common types of output waveforms sine wave,square wave and sawtooth.

Oscillator Principles:

Positive Feedback:

Positive feedback is characterized by the condition wherein a portion of the output voltage of an amplifier is fed back to the input with no net phase shift,resulting in a reinforcement of the output signal.This basic idea is illustrated in figure.As you can see the in phase feedback voltage Vf is amplified to produce the output voltage which in turn produces the feedback voltage.That is,a loop is created in which the signal sustains itself and a continous sinusoidal output is produced.This phenomenon is called oscillation.

Conditions for Oscillation:

Two conditions are required for a sustained state of oscillation.

1.The phase shift around the feedback loop must be zero degree.

2.The voltage gain Acl,around the closed feedback loop (loop gain) must equal 1 (unity).

The voltage gain around the closed feedback loop(Acl) ia the product of the amplifier gain (Av) and the attenuation (B) of the feedback circuit.

Acl=Av.b

For example,if the amplifier has a gain of 100,the feedback circuit must have a attenuation of 0.01 to make the loop gain equal to 1( that is Av.B=100*0.01=1).These conditions of oscillation are illustrated in figure.

Start-Up Conditions:

So far,you have seen what it takes for an oscillator to produce a continous sine wave output.Now let's examine the requirements for the oscillation to start when the dc supply voltage is turned on.As you know,the unity-gain condition must be met for oscillation to be sustained.For oscillation to begin,the voltage gain around the positive feesback loop must be greater than 1 ,so that the amplitude of the output can be build up to a desired level.The gain must then decrease to 1 so that the output stays at the desired level

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Operational Amplifier

The standard operational amplifier (op-amp) symbol is shown in figure(a).It has two input terminals,the inverting input(-) and the noninverting input(+) and an output terminal.The typical op-amp operates with two dc supply voltages,one positive and the other negative as shown in figure(b).Usually these dcvoltage terminals are left off the schematic symbol for simplicity but are always understood to be there.Some typical op-amp IC packages are shown in figure(c).

The Ideal Op-Amp:

To illustrate what an op-amp is.Let's consider its ideal characteristics.A practical op-amp of course,falls short of these ideal standards,but it is much easier to understand and analyze the device from an ideal point of view.

First,the ideal op-amp has infinite voltage gain and infinite bandwidth.Also it has an infinite input impedence(open),so that it does not load the driving source.Finally,it has a zero output impedence.These characteristics are illustrated in figure.The input voltage Vin appears between the two input terminals and the output voltage is AvVin as indicated by the internal voltage source symbol.The concept of infinite input impedence is a particularly valuable analysis tool for the various op-amp configuration,which will be discussed.

The practical Op-Amp:

Although modern integrated circuit (IC) op-amps approach parameter values that can be treated as ideal in many cases,the ideal device can never be made.

Any device has limitations,peak-to-peak output voltage,for example,is usually limited to slightly lass than the two supply voltages.Output current is also limited by internal restrictions such as power dissipation and component ratings.

Characteristics of a practical op-amp are very high voltage gain,very high input impedence,very low output impedence and wide bandwidth.Three of these are lebelled in figure:

.

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Bipolar Junction Transistor ( BJT )

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The bipolar junction transistor is constructed with three doped semiconductor regions separated by two pn junctions.The three regions are emitter,base and collector.There are two types of bipolar junction transistors.

One type consists of two n regions separated by p region called npn.
Second type consists of two p regions separated by n region called pnp.


fig.1 ( npn )
fig.2 ( pnp )

The pn junction joining the base and emitter regions called base-emitter junction.Also the pn junction joining the base collector regions called base-collector junction.The three leads are connected to these regions and named as E, B and C for emitter ,base and collector respectively.
The base region is lightly doped and thin,emitter is heavily doped and collector is moderaftely doped.
The bipolar term is for both holes and electrons as carriers in transistor.

Transistor Operation:

To operate the transistor properly as an amplifier, The two pn juctions must be correctly biased with proper dc voltage.For npn and pnp both the BE base-emitter junction is forward biased and BC base-collector junction is reverse biased known as forward-reverse bias.
Let's examine what happen when BE and BC junctions in npn transistor are forward-reverse biased.The forward bias for BE junction narrows the BE depletion region and reverse bias for BC junction widens the BC depletion region. Read More!

P Type Semiconductors

When the trivalent impurity atoms like aluminium (Al), boron (B), indium (In) and gallium (Ga) having three valence electrons are added to silicon,after forming covalent bond one hole remains in silicon which need fourth electrons.As much as impurities atoms added more holes are produced called majority carriers.
The number of holes can be controled by impurites atoms added to silicon.The majority of current carriers is P-type material.There are also some free electrons produced when electron holes are thermally treated.These electrons are the minority carriers in p-type material. Read More!

N Type Semiconductors

Doping:

The conductivity of silicon and germenium can be drastically increased by the controlled addition of impurities to the intrinsic (pure) semiconductor material. This process, called doping, increases the number of current carriers (electrons or holes).

N Type Semiconductor:

To increase the number of conduction band electrons , pentavalent impurity atoms like arsenic (As), phosphorus (P), bismith(Bi) and antimony (Sb) are added.
Each pentavalent atom leaves an extra free conduction electron after combining with the silicon atom forming covalent bond.As pentavalent atom gives an electron so called donar atom.
The number of conduction electrons can be controled by the impurities ato added to silicon.

Most of current carriers are electron,silicon doped with pentavalent atoms is an n-type semiconductor material.The electrons are called majority carriers.There are also some holes when electrons are paired when thermally processed.These holes are called minority carriers. Read More!

CAPACITORS

Capacitors store energy in an electric field. The electric field is created by displacing positive and negative charges such that they tend to attract each other.

In electric circuits, capacitors are used to store energy for flash lamps, to provide a tuning mechanism for radios, and to perform various other useful tasks.


This device consists of two metallic surfaces or plates separated by a dielectric.Ideally , the perfect dielectric is insulator,so that it prevents charge flow inside the capacitor.

When a voltage source is attached to a capacitor an electric field is created between the plates. This field holds the energy supplied by the source to move the charges.so

A capacitor stores energy in an electric field produced by displaced charge on the plates.Mathematically,

q= C v where the proportionality constant C is called the capacitance,defined as

C= q/v

Capacitance is measured in farads(F),named in the honour of English experimentalist Michael Faraday(1791-1867).

TYPES OF CAPACITORS:
Capacitors come in a wide variety of shapes and sizes.Particular families are categorized according to the type of dielectric material.some capacitors often consist of thin ceramic disks with metal coatings on the plat surfaces to from the plates.
Larger capacitances are achieved by rolling sheets of metal foil and flexible dielectric into a tubular shape.The dielectric is usually a plastic film such as mylar.


For,
Air variable capacitor's capacitance is 10-500 pF, voltage is 500 and RC is Infinity.
Ceramic disk capacitor's capacitance is 5 pF-50 nF, voltage is 600-1000 and RC is 1000.
Plastic film capacitor's capacitance is 1 nF-5 uF, voltage is 100-600 and RC is 100,00.
Electrolytic capacitor's capacitance is 1 uF-1 F, voltage is 6-250 and RC is 50-500.



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