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# Transistor Biasing Calculations

## Terminal Voltage:

❶Above a particular electric field, known as the dielectric strength E ds , the dielectric in a capacitor becomes conductive.

## Electromotive Force:

Aging is fastest near the beginning of life of the component, and the device stabilizes over time. In contrast with ceramic capacitors, this occurs towards the end of life of the component. It can usually be taken as a broadly linear function but can be noticeably non-linear at the temperature extremes. The temperature coefficient can be either positive or negative, sometimes even amongst different samples of the same type.

In other words, the spread in the range of temperature coefficients can encompass zero. Capacitors, especially ceramic capacitors, and older designs such as paper capacitors, can absorb sound waves resulting in a microphonic effect. Vibration moves the plates, causing the capacitance to vary, in turn inducing AC current.

Some dielectrics also generate piezoelectricity. The resulting interference is especially problematic in audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, the varying electric field between the capacitor plates exerts a physical force, moving them as a speaker.

This can generate audible sound, but drains energy and stresses the dielectric and the electrolyte, if any. Current reversal occurs when the current changes direction. Voltage reversal is the change of polarity in a circuit. Reversal is generally described as the percentage of the maximum rated voltage that reverses polarity. In DC circuits and pulsed circuits, current and voltage reversal are affected by the damping of the system. Voltage reversal is encountered in RLC circuits that are underdamped.

The current and voltage reverse direction, forming a harmonic oscillator between the inductance and capacitance. The current and voltage tends to oscillate and may reverse direction several times, with each peak being lower than the previous, until the system reaches an equilibrium. This is often referred to as ringing. In comparison, critically damped or overdamped systems usually do not experience a voltage reversal.

Reversal is also encountered in AC circuits, where the peak current is equal in each direction. For maximum life, capacitors usually need to be able to handle the maximum amount of reversal that a system may experience. Reversal creates excess electric fields in the dielectric, causes excess heating of both the dielectric and the conductors, and can dramatically shorten the life expectancy of the capacitor. Reversal ratings often affect the design considerations for the capacitor, from the choice of dielectric materials and voltage ratings to the types of internal connections used.

Capacitors made with any type of dielectric material show some level of " dielectric absorption " or "soakage". On discharging a capacitor and disconnecting it, after a short time it may develop a voltage due to hysteresis in the dielectric. This effect is objectionable in applications such as precision sample and hold circuits or timing circuits. The level of absorption depends on many factors, from design considerations to charging time, since the absorption is a time-dependent process.

However, the primary factor is the type of dielectric material. Capacitors such as tantalum electrolytic or polysulfone film exhibit relatively high absorption, while polystyrene or Teflon allow very small levels of absorption. Any capacitor containing over 10 joules of energy is generally considered hazardous, while 50 joules or higher is potentially lethal. A capacitor may regain anywhere from 0. Leakage is equivalent to a resistor in parallel with the capacitor.

Constant exposure to heat can cause dielectric breakdown and excessive leakage, a problem often seen in older vacuum tube circuits, particularly where oiled paper and foil capacitors were used.

In many vacuum tube circuits, interstage coupling capacitors are used to conduct a varying signal from the plate of one tube to the grid circuit of the next stage. A leaky capacitor can cause the grid circuit voltage to be raised from its normal bias setting, causing excessive current or signal distortion in the downstream tube. In power amplifiers this can cause the plates to glow red, or current limiting resistors to overheat, even fail.

Similar considerations apply to component fabricated solid-state transistor amplifiers, but owing to lower heat production and the use of modern polyester dielectric barriers this once-common problem has become relatively rare. Aluminum electrolytic capacitors are conditioned when manufactured by applying a voltage sufficient to initiate the proper internal chemical state. This state is maintained by regular use of the equipment.

If a system using electrolytic capacitors is unused for a long period of time it can lose its conditioning. Sometimes they fail with a short circuit when next operated. Practical capacitors are available commercially in many different forms.

The type of internal dielectric, the structure of the plates and the device packaging all strongly affect the characteristics of the capacitor, and its applications.

Above approximately 1 microfarad electrolytic capacitors are usually used because of their small size and low cost compared with other types, unless their relatively poor stability, life and polarised nature make them unsuitable. Very high capacity supercapacitors use a porous carbon-based electrode material. Most capacitors have a dielectric spacer, which increases their capacitance compared to air or a vacuum. In order to maximise the charge that a capacitor can hold, the dielectric material needs to have as high a permittivity as possible, while also having as high a breakdown voltage as possible.

The dielectric also needs to have as low a loss with frequency as possible. However, low value capacitors are available with a vacuum between their plates to allow extremely high voltage operation and low losses.

Variable capacitors with their plates open to the atmosphere were commonly used in radio tuning circuits. Later designs use polymer foil dielectric between the moving and stationary plates, with no significant air space between the plates. Several solid dielectrics are available, including paper , plastic , glass , mica and ceramic.

Paper was used extensively in older capacitors and offers relatively high voltage performance. However, paper absorbs moisture, and has been largely replaced by plastic film capacitors.

Most of the plastic films now used offer better stability and ageing performance than such older dielectrics such as oiled paper, which makes them useful in timer circuits, although they may be limited to relatively low operating temperatures and frequencies, because of the limitations of the plastic film being used. Large plastic film capacitors are used extensively in suppression circuits, motor start circuits, and power factor correction circuits. Ceramic capacitors are generally small, cheap and useful for high frequency applications, although their capacitance varies strongly with voltage and temperature and they age poorly.

They can also suffer from the piezoelectric effect. Ceramic capacitors are broadly categorized as class 1 dielectrics , which have predictable variation of capacitance with temperature or class 2 dielectrics , which can operate at higher voltage. Modern multilayer ceramics are usually quite small, but some types have inherently wide value tolerances, microphonic issues, and are usually physically brittle.

Glass and mica capacitors are extremely reliable, stable and tolerant to high temperatures and voltages, but are too expensive for most mainstream applications. Electrolytic capacitors and supercapacitors are used to store small and larger amounts of energy, respectively, ceramic capacitors are often used in resonators , and parasitic capacitance occurs in circuits wherever the simple conductor-insulator-conductor structure is formed unintentionally by the configuration of the circuit layout.

Electrolytic capacitors use an aluminum or tantalum plate with an oxide dielectric layer. The second electrode is a liquid electrolyte , connected to the circuit by another foil plate.

Electrolytic capacitors offer very high capacitance but suffer from poor tolerances, high instability, gradual loss of capacitance especially when subjected to heat, and high leakage current. Poor quality capacitors may leak electrolyte, which is harmful to printed circuit boards. The conductivity of the electrolyte drops at low temperatures, which increases equivalent series resistance. While widely used for power-supply conditioning, poor high-frequency characteristics make them unsuitable for many applications.

Electrolytic capacitors suffer from self-degradation if unused for a period around a year , and when full power is applied may short circuit, permanently damaging the capacitor and usually blowing a fuse or causing failure of rectifier diodes. For example, in older equipment, this may cause arcing in rectifier tubes.

They can be restored before use by gradually applying the operating voltage, often performed on antique vacuum tube equipment over a period of thirty minutes by using a variable transformer to supply AC power. The use of this technique may be less satisfactory for some solid state equipment, which may be damaged by operation below its normal power range, requiring that the power supply first be isolated from the consuming circuits.

Such remedies may not be applicable to modern high-frequency power supplies as these produce full output voltage even with reduced input. Tantalum capacitors offer better frequency and temperature characteristics than aluminum, but higher dielectric absorption and leakage. A feedthrough capacitor is a component that, while not serving as its main use, has capacitance and is used to conduct signals through a conductive sheet.

Several other types of capacitor are available for specialist applications. Supercapacitors store large amounts of energy. Alternating current capacitors are specifically designed to work on line mains voltage AC power circuits. They are commonly used in electric motor circuits and are often designed to handle large currents, so they tend to be physically large.

They also are designed with direct current breakdown voltages of at least five times the maximum AC voltage. The dielectric constant for a number of very useful dielectrics changes as a function of the applied electrical field, for example ferroelectric materials, so the capacitance for these devices is more complex.

For example, in charging such a capacitor the differential increase in voltage with charge is governed by:. This field polarizes the dielectric, which polarization, in the case of a ferroelectric, is a nonlinear S -shaped function of the electric field, which, in the case of a large area parallel plate device, translates into a capacitance that is a nonlinear function of the voltage.

Corresponding to the voltage-dependent capacitance, to charge the capacitor to voltage V an integral relation is found:. The nonlinear capacitance of a microscope probe scanned along a ferroelectric surface is used to study the domain structure of ferroelectric materials.

Another example of voltage dependent capacitance occurs in semiconductor devices such as semiconductor diodes , where the voltage dependence stems not from a change in dielectric constant but in a voltage dependence of the spacing between the charges on the two sides of the capacitor. Sze This effect is intentionally exploited in diode-like devices known as varicaps. If a capacitor is driven with a time-varying voltage that changes rapidly enough, at some frequency the polarization of the dielectric cannot follow the voltage.

As an example of the origin of this mechanism, the internal microscopic dipoles contributing to the dielectric constant cannot move instantly, and so as frequency of an applied alternating voltage increases, the dipole response is limited and the dielectric constant diminishes. A changing dielectric constant with frequency is referred to as dielectric dispersion , and is governed by dielectric relaxation processes, such as Debye relaxation.

Under transient conditions, the displacement field can be expressed as see electric susceptibility:. See, for example, linear response function. A Fourier transform in time then results in:. The capacitance, being proportional to the dielectric constant, also exhibits this frequency behavior.

Fourier transforming Gauss's law with this form for displacement field:. When a parallel-plate capacitor is filled with a dielectric, the measurement of dielectric properties of the medium is based upon the relation:. For practical purposes, when measurement errors are taken into account, often a measurement in terrestrial vacuum, or simply a calculation of C 0 , is sufficiently accurate. Using this measurement method, the dielectric constant may exhibit a resonance at certain frequencies corresponding to characteristic response frequencies excitation energies of contributors to the dielectric constant.

These resonances are the basis for a number of experimental techniques for detecting defects. The conductance method measures absorption as a function of frequency. Another example of frequency dependent capacitance occurs with MOS capacitors , where the slow generation of minority carriers means that at high frequencies the capacitance measures only the majority carrier response, while at low frequencies both types of carrier respond.

At optical frequencies, in semiconductors the dielectric constant exhibits structure related to the band structure of the solid. Sophisticated modulation spectroscopy measurement methods based upon modulating the crystal structure by pressure or by other stresses and observing the related changes in absorption or reflection of light have advanced our knowledge of these materials.

The arrangement of plates and dielectric has many variations in different styles depending on the desired ratings of the capacitor. For small values of capacitance microfarads and less , ceramic disks use metallic coatings, with wire leads bonded to the coating. Larger values can be made by multiple stacks of plates and disks. To reduce the series resistance and inductance for long plates, the plates and dielectric are staggered so that connection is made at the common edge of the rolled-up plates, not at the ends of the foil or metalized film strips that comprise the plates.

Modern paper or film dielectric capacitors are dipped in a hard thermoplastic. Large capacitors for high-voltage use may have the roll form compressed to fit into a rectangular metal case, with bolted terminals and bushings for connections. The dielectric in larger capacitors is often impregnated with a liquid to improve its properties.

Capacitors may have their connecting leads arranged in many configurations, for example axially or radially. Radial leads are rarely aligned along radii of the body's circle, so the term is conventional. The leads until bent are usually in planes parallel to that of the flat body of the capacitor, and extend in the same direction; they are often parallel as manufactured. Small, cheap discoidal ceramic capacitors have existed from the s onward, and remain in widespread use.

After the s, surface mount packages for capacitors have been widely used. These packages are extremely small and lack connecting leads, allowing them to be soldered directly onto the surface of printed circuit boards. Surface mount components avoid undesirable high-frequency effects due to the leads and simplify automated assembly, although manual handling is made difficult due to their small size.

Mechanically controlled variable capacitors allow the plate spacing to be adjusted, for example by rotating or sliding a set of movable plates into alignment with a set of stationary plates.

Low cost variable capacitors squeeze together alternating layers of aluminum and plastic with a screw. Electrical control of capacitance is achievable with varactors or varicaps , which are reverse-biased semiconductor diodes whose depletion region width varies with applied voltage. They are used in phase-locked loops , amongst other applications. Most capacitors have numbers printed on their bodies to indicate their electrical characteristics. Additionally, the capacitor may be labeled with its working voltage , temperature and other relevant characteristics.

The working voltage of a capacitor is nominally the highest voltage that may be applied across it without undue risk of breaking down the dielectric layer. The notation to state a capacitor's value in a circuit diagram varies. A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary battery , or like other types of rechargeable energy storage system.

This prevents loss of information in volatile memory. A capacitor can facilitate conversion of kinetic energy of charged particles into electric energy and store it. There is an intermediate solution: Supercapacitors , which can accept and deliver charge much faster than batteries, and tolerate many more charge and discharge cycles than rechargeable batteries. They are however 10 times larger than conventional batteries for a given charge. On the other hand, it has been shown that the amount of charge stored in the dielectric layer of the thin film capacitor can be equal or can even exceed the amount of charge stored on its plates.

In car audio systems, large capacitors store energy for the amplifier to use on demand. Also for a flash tube a capacitor is used to hold the high voltage. In the s, John Atanasoff applied the principle of energy storage in capacitors to construct dynamic digital memories for the first binary computers that used electron tubes for logic.

Groups of large, specially constructed, low-inductance high-voltage capacitors capacitor banks are used to supply huge pulses of current for many pulsed power applications.

These include electromagnetic forming , Marx generators , pulsed lasers especially TEA lasers , pulse forming networks , radar , fusion research, and particle accelerators.

Large capacitor banks reservoir are used as energy sources for the exploding-bridgewire detonators or slapper detonators in nuclear weapons and other specialty weapons.

Experimental work is under way using banks of capacitors as power sources for electromagnetic armour and electromagnetic railguns and coilguns. Reservoir capacitors are used in power supplies where they smooth the output of a full or half wave rectifier. This restores the AC gain since the capacitor is a short for AC signals. The DC emitter current still experiences degeneration in the emitter resistor, thus, stabilizing the DC current.

Cbypass is required to prevent AC gain reduction. What value should the bypass capacitor be? That depends on the lowest frequency to be amplified. For radio frequencies Cbpass would be small.

For an audio amplifier extending down to 20Hz it will be large. The capacitor should be designed to accommodate the lowest frequency being amplified.

The capacitor for an audio amplifier covering 20Hz to 20kHz would be:. Note that the internal emitter resistance r EE is not bypassed by the bypass capacitor. Stable emitter bias requires a low voltage base bias supply, Figure below. Voltage Divider bias replaces base battery with voltage divider. Draw the voltage divider without assigning values.

Break the divider loose from the base. The base of the transistor is the load. The Thevenin equivalent resistance is the resistance from load point arrow with the battery V CC reduced to 0 ground. In other words, R1 R2. The Thevenin equivalent voltage is the open circuit voltage load removed. This calculation is by the voltage divider ratio method.

R1 is obtained by eliminating R2 from the pair of equations for Rth and Vth. The equation of R1 is in terms of known quantities Rth, Vth, Vcc. Note that Rth is R B , the bias resistor from the emitter-bias design. The equation for R2 is in terms of R1 and Rth. Emitter-bias example converted to voltage divider bias. R1 is a standard value of K. The closest standard value for R2 corresponding to This does not change I E enough for us to calculate it.

Calculate the bias resistors for the cascode amplifier in Figure below. V B2 is the bias voltage for the common emitter stage. V B1 is a fairly high voltage at It will be 10V after accounting for the voltage drop across R B1.

We desire a 1mA emitter current. Bias for a cascode amplifier. Convert the base bias resistors for the cascode amplifier to voltage divider bias resistors driven by the V CC of 20V.

Published under the terms and conditions of the Design Science License. Collector-Feedback Bias Variations in bias due to temperature and beta may be reduced by moving the V BB end of the base-bias resistor to the collector as in Figure below. Emitter-Bias Inserting a resistor R E in the emitter circuit as in Figure below causes degeneration , also known as negative feedback. This work would increase the potential energy of the charge and thus increase its electric potential.

As the positive test charge moves through the external circuit from the positive terminal to the negative terminal, it decreases its electric potential energy and thus is at low potential by the time it returns to the negative terminal.

If a 12 volt battery is used in the circuit, then every coulomb of charge is gaining 12 joules of potential energy as it moves through the battery. And similarly, every coulomb of charge loses 12 joules of electric potential energy as it passes through the external circuit.

The loss of this electric potential energy in the external circuit results in a gain in light energy, thermal energy and other forms of non-electrical energy. With a clear understanding of electric potential difference, the role of an electrochemical cell or collection of cells i.

The cells simply supply the energy to do work upon the charge to move it from the negative terminal to the positive terminal. By providing energy to the charge, the cell is capable of maintaining an electric potential difference across the two ends of the external circuit.

Once the charge has reached the high potential terminal, it will naturally flow through the wires to the low potential terminal. The movement of charge through an electric circuit is analogous to the movement of water at a water park or the movement of roller coaster cars at an amusement park. In each analogy, work must be done on the water or the roller coaster cars to move it from a location of low gravitational potential to a location of high gravitational potential.

Once the water or the roller coaster cars reach high gravitational potential, they naturally move downward back to the low potential location. For a water ride or a roller coaster ride, the task of lifting the water or coaster cars to high potential requires energy.

The energy is supplied by a motor-driven water pump or a motor-driven chain. In a battery-powered electric circuit, the cells serve the role of the charge pump to supply energy to the charge to lift it from the low potential position through the cell to the high potential position. It is often convenient to speak of an electric circuit such as the simple circuit discussed here as having two parts - an internal circuit and an external circuit.

The internal circuit is the part of the circuit where energy is being supplied to the charge. For the simple battery-powered circuit that we have been referring to, the portion of the circuit containing the electrochemical cells is the internal circuit. The external circuit is the part of the circuit where charge is moving outside the cells through the wires on its path from the high potential terminal to the low potential terminal.

The movement of charge through the internal circuit requires energy since it is an uphill movement in a direction that is against the electric field. The movement of charge through the external circuit is natural since it is a movement in the direction of the electric field.

When at the positive terminal of an electrochemical cell, a positive test charge is at a high electric pressure in the same manner that water at a water park is at a high water pressure after being pumped to the top of a water slide. Being under high electric pressure, a positive test charge spontaneously and naturally moves through the external circuit to the low pressure, low potential location.

As a positive test charge moves through the external circuit, it encounters a variety of types of circuit elements. Each circuit element serves as an energy-transforming device. Light bulbs, motors, and heating elements such as in toasters and hair dryers are examples of energy-transforming devices.

In each of these devices, the electrical potential energy of the charge is transformed into other useful and non-useful forms. For instance, in a light bulb, the electric potential energy of the charge is transformed into light energy a useful form and thermal energy a non-useful form. The moving charge is doing work upon the light bulb to produce two different forms of energy.

By doing so, the moving charge is losing its electric potential energy. Upon leaving the circuit element, the charge is less energized. The location just prior to entering the light bulb or any circuit element is a high electric potential location; and the location just after leaving the light bulb or any circuit element is a low electric potential location.

Referring to the diagram above, locations A and B are high potential locations and locations C and D are low potential locations. The loss in electric potential while passing through a circuit element is often referred to as a voltage drop.

By the time that the positive test charge has returned to the negative terminal, it is at 0 volts and is ready to be re-energized and pumped back up to the high voltage, positive terminal.

An electric potential diagram is a convenient tool for representing the electric potential differences between various locations in an electric circuit. Two simple circuits and their corresponding electric potential diagrams are shown below. In Circuit A, there is a 1.

In Circuit B, there is a 6-volt battery four 1. In each case, the negative terminal of the battery is the 0 volt location. The positive terminal of the battery has an electric potential that is equal to the voltage rating of the battery.

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Feb 28,  · EDIT: Note that your "Terminal Voltage Formula" assumes that the battery is producing a current that flows out of its positive terminal. In that case the internal resistance causes a voltage drop in the direction of the current flow, and so decreases the voltage that you see at the battery terminals.

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