when a diode is operated inthe reverse biased condition, the width of the depletion region increases as voltage that is applied increases. Varying the width of the depletion region is equivalent to varying the plate separation of a very small capacitor such that the relationship between junction capacitance & applied reverse voltage will look something like that presented in figure below. The typical variation of capacitance supplied by a varactor is from about 50pF to 10pF as the reverse voltage goes up from 2V to 20V. The symbol used for a varactor diode has been shown above.

### Varactor diodes

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### Transistor operating configurations

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There are 3 basic circuit configurations that are used for transistor amplifiers. These 3 circuit configurations depend upon which one connection among the 3 transistor connections is made common to both the input and the output. In the case of bipolar junction transistors, the configurations are referred to as common emitter, common collector or emitter follower, & common base, as shown in diagram below.

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### Analogue instruments

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All analogue electrical indicating instruments need 3 essential devices these devices are briefly discussed below:

1- A

A mechanical force is generated by the current or voltage which causes the pointer to have some deflecition from its 0 position.

2- A

The controlling force works in opposition to the deflecting force & ensures that the deflection being shown on the meter is always the same for a given measured quantity. It also pr events the pointer always going to maximum level of deflection. There are 2 main types of controlling devices, which includes spring control & gravity control.

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1- A

**deflecting or operating device**.A mechanical force is generated by the current or voltage which causes the pointer to have some deflecition from its 0 position.

2- A

**controlling device**.The controlling force works in opposition to the deflecting force & ensures that the deflection being shown on the meter is always the same for a given measured quantity. It also pr events the pointer always going to maximum level of deflection. There are 2 main types of controlling devices, which includes spring control & gravity control.

### The superposition theorem

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This tutorial is superposition theorem. The superposition theorem states:

‘In any network which is made up of linear resistances & containing more than 1 source of e.m.f., the resultantcurrent flowing in any branch is the algebraic sum of the currents that would flow in that branch if eachsource was considered separately, all other sourcesbeing replaced at that time by their respective internal resistances.’

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‘In any network which is made up of linear resistances & containing more than 1 source of e.m.f., the resultantcurrent flowing in any branch is the algebraic sum of the currents that would flow in that branch if eachsource was considered separately, all other sourcesbeing replaced at that time by their respective internal resistances.’

### Delta and star connections

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The network presented below in Figure 34.1-a) containing 3 impedances Z A, ZB and ZC is said to be Ï€-connected.such network can be redrawn as drawn in Figure 34.1(b),where the arrangement is said to be as delta-connectedor mesh-connected.

The network drawn in Fig 34.2-a, containing of 3 impedances, Z1, Z2 and Z3, is referred to beT-connected. This network can be redrawn as drawn in Figure 34.2(b), where the arrangement is referred to as star-connected.

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The network drawn in Fig 34.2-a, containing of 3 impedances, Z1, Z2 and Z3, is referred to beT-connected. This network can be redrawn as drawn in Figure 34.2(b), where the arrangement is referred to as star-connected.

### Current and voltage relationships

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Figure 44.3 below presents us a voltage source VS supplied to the input terminals of an infinite line, or a line terminated in its characteristic impedance, so that a current IS flows into the line.At a point, say, one km down the line let the current be I1. The current I1 will not have the same magnitude as IS because of line attenuation; also I1 willlag IS by some angle Î². The ratio IS/I1 is therefore aphasor quantity. Let the current a further onekm down theline be I2, & so on, as demonstrated in Figure 44.3 below. Each unit-length of line can be considered as a section of a repetitive network. The attenuationis in the form of a logarithmic decay &

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### Advanced Electronics formulas

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Below is the List of Advanced Electronics formulas:

- Comlex numbers formulas
- LR-C network formula
- LR-CR formulas
- Advanced Electronics Determinants
- Delta star formula
- Star delta formula
- Impedance matching formula
- Formulas for R-L-C series circuits
- Fourier series formulas
- Field theory Formulas
- Harmonic Analysis Formulas
- Formulas for Hysteresis and Eddy current

### Shunts and multipliers

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An

**ammeter**, which is used for measuring current, offers a low level resistance (ideally 0) & must be connected in series with the circuit.

A

**voltmeter**, which is used for measuring p.d., offers a high level of resistance (ideally I has infinite) & must be connected in parallel with the part of the circuit whose p.d. is required. There is no difference between the basic instrument used to measure current and voltage because both make of use a milliamp meter as their basic part. This is a sensitive instrument which gives f.s.d. for currents of just a few milli amperes. When an ammeter is needed to measure currents of having large magnitudes, a proportion of the current is diverted through a low-value resistance connected in parallel with the meter. Such a diverting type of resistor is referred to as**shunt**.### Moving-iron instrument

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There are two types of moving iron instrument which are discussed below briefly

**Attraction type**

Figure (a) below demonstrates an

**attraction type**of moving-iron instrument is When current flows in the solenoid, a pivoted soft-iron disc is attracted towards the solenoid & themovement causes a pointer to have some movement across a scale.### Electrical Engineering Formulas (principles and technology)

A.C Theory: all Formulas for a.c circuits

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### Passive networks and reciprocity theorem

**The ABCD parameters for a 2-port network are:**

*V*1 =

*AV*2 −

*BI*2 (28)

*I*1 =

*CV*2 −

*DI*2 (29)

Figure shown below shows a two-port network whose terminals RS are short-circuited with an input voltage

*V*across terminals PQ. Then*V*2 in the above equations is 0 and the equations become:*V*=−

*BI*2 (31)

and

*I*1 =−*DI*2 (32)### ABCD Parameters

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The

**two-port network**has a pair of input terminals, shown as PQ in Figure below, & a pair of output terminals, shown as RS in the diagram below. When a voltage

*V*1 is supplied to terminals PQ, the input & output currents,

*I*1 and

*I*2, flow & an output voltage

*V*2 is produced.There are therefore

**4 variable quantities**

*V*1,

*I*1,

*V*2 and

*I*2 for a two-port network. If the elements are supposed to be linear, then there are a number of ways in which we can write the relationships. One such way is termed

**ABCD parameters**which we consider in this tutorial; there are others few parameters, such as

*z*-,

*y*-,

*h*- and

*g*- parameters that are not discussed here.

### General equation for a complex waveform

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The instantaneous value of a complex voltage wave

*v*performing in a linear circuit may be demonstrated by the general equation written below.

### Balance conditions for an a.c. bridge

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**The majority of famously knoen a.c. bridges are categorized as four-arm bridges & contain an arrangement of 4 impedances (in complex form,**

*Z*=

*R*+ or -

*jX*) as presented in diagram 27.1. As with the d.c. Wheat-stone bridge circuit, an a.c. bridge is understood to be ‘balanced’ when the current through the detector is 0 (i.e. when there is no current flowing b/w B and D of Figure 27.1). If the current through the detector is 0, then the current

*I*1 flowing

### Motor power controller

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**A**

**motor power controlle**r can be constructed from 4 discrete power MOSFETs that are joined connected as shown in the diagram below:

The 4 power MOSFETs constitute a bridge. The control input switches on the transistors in pairs. Either Q1 or Q4 are on or Q2 and Q3 are on.This switches the current through the motor in just one direction or the other, functioning as a reversing switch.

### LOW SCALE INTEGRATION

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Low scale integration is a simple way from making a single transistor to putting several transistors on the same chip and linking them into straightforward circuit modules. The fact that the transistors are all on the same chip implies that their characteristics (e.g. gain) are the same. This removes the requirement of match transistors while building a circuit from various individual devices.

The very simple CMOS logic ICs are representative examples of LSI. The figure shown below is the circuit of an inverter.

### SWITCHED CAPACITOR FILTERS

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The principle circuit of a switched capacitor filter has been demonstrated in the figure 25.5 shown below The basic low-pass filter is made up of 2 capacitors, along with CMOS switches that are turned on alternately by a built-in clock oscillator. The clock runs at more than a few tens of kilohertz.

The switch C1 samples the input voltage when the 1st switch is closed & the 2nd switch is open. This voltage may be +ve or -ve depending on the phase of the input signal at that instant. An instant later the switches change state & the charge on C1 is equalized with the charge on C2, which came from the preceding sampling.

### PHASE LOCKED LOOP

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The main function of a PLL is to lock on to an input logical signal of any given frequency, even when the signals are distorted, or they are coming from a noisy background, & signal is mixed with some other signals having different frequencies. The essential components of a PLL are shown in the diagram below. The first stage is the phase detector. It receives 2 logic-level signals, one at the input to the PLL and the other fed back from its output.

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### Differential Amplifier

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The differential amplifier (shown in fig below) is also referred to as along-tailed pair. A differential amplifier contains 2 inputs namely, vIN1 and vIN2. This amplifier is used as amplifier in order to amplify the voltage difference between its inputs. When it does this, we say that it is operating in the differential mode.

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### DARLINGTON PAIR

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The construction of Darlington pair consists of 2 BJTs connected as shown below in the figure. The emitter current of Q1 becomes the base current of Q2 transistor. The current gain of the pair will be equal to the product of the current gains of the individual transistors.

### BYPASS CAPACITOR

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The application of an emitter resistor (R4) provides improved stability but it also gives reduced gain. When needed, we can restore the gain by wiring a high-value capacitor across R4.This keeps the emitter voltage substantially constant. Without the use of capacitor, the voltage at the emitter rises and falls with the signal. And hence it will provide negative feedback.

Lets take an example, as iB rises (tending to increase vBE),iC rises, and the emitter voltage goes up. This tends to decrease vBE, which decreases iC and resists the rise in emitter voltage. Different way of analyzing this is to say that the capacitor shunts the signal at the emitter through to the ground. This is the foremost reason why C3 is called a bypass capacitor. With this capacitor inplace, the voltage gain of the amplifier is about 280.The lower cut-off point is raised to 130 Hz, so bandwidth is somewhat reduced.

### FERROMAGNETISM

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Ferro-magnetism is very commonly used type of magnetism. Ferromagnetism is found on the Bar magnets, compass needles, and the coating on magnetic hard disks. It is a fine property of iron, cobalt, and compounds of these few other metals which includes nickel, chromium and magnesium. All these stated materials shows ferromagnetic properties because the spins of the electrons cancel out much less than in other materials. Groups of spinning electrons align readily with an external magnetic field, thus forming magnetic domains. This alignment is permanent so that the material becomes magnetized, & remains so, even when we remove the external field.

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