#### Equivalent Circuits of Transistors, Physics tutorial

Bipolar Junction Transistor:

Three elements of two-junction transistor are given below:

i) The emitter that gives off, or emits, current carriers (electrons or holes)

ii) The base that controls flow of current carriers and

iii) The collector that collects current carriers.

Transistors are categorized as either NPN or PNP according to arrangement of their N and P materials. Basic construction and chemical treatment is involved by their names, "NPN" or "PNP." NPN transistor is produced by introducing the thin region of P-type material between two regions of N-type material. On where as PNP transistor is produced by introducing thin region of N-type material between two regions of P-type material. Transistors formed in this manner have two PN junctions, one PN junction is between emitter and base; other PN junction is between collector and base. Two junctions share one section of semiconductor material so that transistor truly comprises of three elements. As majority and minority current carriers are different for N and P materials, it stands to reason that internal operation of NPN and PNP transistors will also be different.

The Transistor Models:

There are essentially three possible ways to connect the Bipolar Transistor within the electronic circuit with each method of connection responding differently to input signal as static characteristics of transistor differ with each circuit arrangement.

• Common Base Configuration - has Voltage Gain but no Current Gain.
• Common Emitter Configuration - has both Current and Voltage Gain.
• Common Collector Configuration - has Current Gain but no Voltage Gain.

The Common Base Configuration:

In Common Base or Grounded Base configuration, BASE connection is common to both input signal and output signal with input signal being applied between base and emitter terminals. Corresponding output signal is taken from between base and collector terminals as shown with base terminal grounded or joined to fixed reference voltage point. Input current flowing in emitter is fairly large as its sum of both base current and collector current respectively thus, collector current output is less than emitter current input resulting in the Current Gain for this type of circuit of less than 1, or in other words it attenuates signal.

The Common Base Amplifier Circuit: This kind of amplifier configuration is non-inverting voltage amplifier circuit, in that signal voltages Vin and Vout are In-Phase. This kind of arrangement is not very common due to unusually high voltage gain characteristics. Its Output characteristics represent that of forward biased diode while Input characteristics represent that of the illuminated photo-diode. Also this kind of configuration has a high ratio of Output to Input resistance or more importantly Load resistance (RL) to Input resistance (Rin) giving it value of Resistance Gain. Then Voltage Gain for the common base can thus be given as:

AV = IC x RLIe x Rin = α x RLRin

Common Base circuit is usually only utilized in single stage amplifier circuits like microphone pre-amplifier or RF radio amplifiers because of its very good high frequency response.

The Common Emitter Configuration:

In Common Emitter or Grounded Emitter configuration, input signal is applied between base, whereas output is taken from between collector and emitter as shown. This kind of configuration is most commonly utilized circuit for transistor based amplifiers and that represents normal method of connection. Common emitter amplifier configuration produces highest current and power gain of all three bipolar transistor configurations. This is chiefly due to input impedance is low as it is joined to a forward-biased junction, while output impedance is high as it is taken from reverse-biased junction.

Common Emitter Amplifier Circuit: In this kind of configuration, current flowing out of transistor should be equal to currents flowing in transistor as emitter current is given as Ie = Ic + Ib. Also, as the load resistance (RL) is connected in series with the collector, Current gain of the Common Emitter Transistor Amplifier is quite large as it is ratio of Ic/Ib and is given symbol of Beta, (β). As relationship between these three currents is determined by transistor itself, any small change in base current will result in the large change in collector current. Then, small changes in base current will therefore control current in Emitter/Collector circuit.

By combining expressions for both Alpha, α and Beta, β mathematical relationship between the parameters and thus current gain of the amplifier can be given as:

IE = IC + IB, α =IC/IE and β= IC/IB

α= β/(β+1), β= α/(1- α)

Where: IC is current flowing into collector terminal, IB is current flowing into base terminal and IE is current flowing out of emitter terminal.

This kind of bipolar transistor configuration has greater input impedance, Current and Power gain than that of common Base configuration but its Voltage gain is much lower. Common emitter is inverting amplifier circuit resulting in output signal being 180o out of phase with input voltage signal.

Common Collector Configuration:

In Common Collector or Grounded Collector configuration, collector is now common and input signal is joined to Base, whereas output is taken from Emitter load. This kind of configuration is usually called as a Voltage Follower or Emitter Follower circuit. Emitter follower configuration is very helpful for impedance matching applications due to very high input impedance, in region of hundreds of thousands of Ohms, and it has comparatively low output impedance.

Common Collector Amplifier Circuit: In common collector configuration load resistance is situated in series with emitter so its current is equal to that of emitter current. As emitter current is combination of collector and base currents combined load resistance in this kind of amplifier configuration also have both collector current and input current of base flowing through it. Then current gain of circuit is given as:

IE= IC+ IB, Ai = IE/IB= (IC + IB)/IB, Ai =( IC/IB) + 1, Ai= β+1

This kind of bipolar transistor configuration is the non-inverting amplifier circuit in that signal voltages of Vin and are Vout In-Phase. It has voltage gain which is always less than 1 (unity). Load resistance of common collector amplifier configuration receives both base and collector currents giving large current gain (as with Common Emitter configuration) thus, giving good current amplification with very little voltage gain.

NPN Transistor:

An NPN (Negative-Positive-Negative) type and PNP (Positive-Negative-Positive) type, with the most generally utilized transistor type being NPN Transistor. The transistor junctions can be biased in one of three different ways - Common Base, Common Emitter and Common Collector.

An NPN Transistor Configuration:

The transistor is a current operated device and that large current (IC) flows freely through device between collector and emitter terminals. Though, this just happens when the small biasing current (IB) is flowing into base terminal of transistor therefore allowing base to serve as sort of current control input. Ratio of the two currents (IC/IB) is known as DC Current Gain of device and is given symbol of Beta, (β). Beta has no units as it is ratio. Current gain from emitter to collector terminal, IC/IE, is known as Alpha, (α), and is function of transistor itself. As emitter current IE is product of very small base current to very large collector current the value of parameter α is very close to unity, and for typical low-power signal transistor this value ranges from about 0.950 to 0.999

α and β Relationships:

DC Current Gain= Output Current/Input Current= IC/IB

β= IC/IB α= IC/IE

IE= IC+ IB

VCE= VCB+ VBE

By combining two parameters α and β we can create two mathematical expressions which give relationship between different currents flowing in transistor.

α= β/β+1 β= α/1- α

The equation for Beta can also be re-arranged to make IC as subject, and with zero base current (IB = 0) resultant collector current IC will also be zero, (β x 0). Also when base current is high corresponding collector current will also be high resulting in base current controlling collector current. One of the most significant properties of Bipolar Junction Transistor is that small base current can control a much larger collector current.

The Common Emitter Configuration:

If appropriate DC biasing voltage is firstly applied to transistors Base terminal therefore allowing it to always operate within linear active region, inverting amplifier circuit known as a Common Emitter Amplifier is produced.

One such Common Emitter Amplifier configuration is known as Class A Amplifier. Class A Amplifier operation is one where transistors Base terminal is biased in such a manner that transistor is always operating halfway between cut-off and saturation points, thereby letting transistor amplifier to correctly reproduce positive and negative halves of AC input signal superimposed on DC Biasing voltage. Without this Bias Voltage only positive half of input waveform would be amplified. This kind of amplifier has several applications but is usually utilized in audio circuits like pre- amplifier and power amplifier stages.

Emitter current IE is sum of collector current, IC and base current, IB, added together IE = IC + IB for common emitter configuration.

By using output characteristics curves and also Ohm´s Law, current flowing through load resistor, (RL), is equivalent to collector current, IC entering transistor that in-turn corresponds to supply voltage, (VCC) minus voltage drop between collector and emitter terminals, (VCE) and is given as:

Collector Current, IC= (VCC- VC )/RL

Also, Load Line can be drawn directly onto graph of curves above from point of Saturation when VCE = 0 to point of Cut-off when IC = 0 giving Operating or Q-point of transistor. These two points are computed as:

When VCE=0, IC= VCC- 0 RL, IC= VCC/RL

When IC= 0, 0= VCC- VCE/RL, VCC= VCE.

PNP Transistor:

PNP Transistor is exact opposite to NPN Transistor device. Essentially, in this kind of transistor construction two diodes are reversed with respect to NPN type, with arrow, that also defines Emitter terminal this time pointing inwards in transistor symbol. Also, all polarities are reversed that means that PNP Transistors sink current as opposed to NPN transistor which sources current. Then PNP Transistors use the small output base current and negative base voltage to control much larger emitter-collector current. Construction of PNP transistor comprises of two P-type semiconductor materials either side of N-type material.

PNP Transistors require negative (-ve) voltage at Collector terminal with flow of current through emitter-collector terminals being Holes as opposed to Electrons for NPN types. As movement of holes across depletion layer tends to be slower than for electrons, PNP transistors are usually slower than their equivalent NPN counterparts when operating.

Base current or Collector current is same as those utilized for equivalent NPN transistor and is given as. IE= IC + IB

IC = βIB

IB = IC

Transistor As A Switch:

When utilized as AC signal amplifier, transistors Base biasing voltage is applied so that it operates in its Active region and linear part of output characteristics curves are utilized. If circuit uses Transistor as Switch, then biasing is arranged to operate in output characteristics curves in areas called as Saturation and Cut-off regions.

Pink shaded area at bottom represents Cut-off region. Here operating conditions of transistor are zero input base current (IB), zero output collector current (IC) and maximum collector voltage (VCE) that results in large depletion layer and no current flows through device. Transistor is switched Fully-OFF. Lighter blue area to left signifies Saturation region. Here transistor will be biased so that maximum amount of base current is applied, resulting in maximum collector current flow and minimum collector emitter voltage that results in depletion layer being as small as possible and maximum current flows through device. Transistor is switched Fully-ON.

With inductive loads like relays or solenoids flywheel diode is placed across load to dissipate back EMF produced by inductive load when transistor switches OFF and so protect transistor from damage. If load is of a very high current or voltage nature, like motors, heaters etc, then load current can be controlled by appropriate relay.

Circuit resembles that of Common Emitter circuit. Difference this time is that to operate transistor as a switch transistor requires to be turned either completely OFF (Cut-off) or completely ON (Saturated). The ideal transistor switch would have infinite resistance when turned OFF resulting in zero current flow and zero resistance when turned ON, resulting in maximum current flow. When turned OFF, small leakage currents flow through transistor and when completely ON device has low resistance value causing small saturation voltage (VCE) across it. In both Cut-off and Saturation regions power dissipated by transistor is at its minimum. By varying Base-Emitter voltage VBE, Base current is modified and which in turn manages amount of Collector current flowing through transistor. When maximum Collector current flows transistor is said to be saturated. Value of Base resistor finds how much input voltage is needed and corresponding Base current to switch transistor completely ON.

Important Parameters

Input Impedance, Zi:

For input side, input impedance is defined by Ohm's law as the following:

Zi = Vi/Ii(v)

If input signal is changed, current can be calculated using same level of input impedance. For small-signal analysis, once input impedance has been determined same numerical value can be utilized for changing levels of applied signal.

Output Impedance, Zo:

Output impedance is naturally defined as output set of terminals, but way in which it is stated is quite different from that of input impedance. Output impedance is determined at output terminals looking back in system with applied signal set to zero.

Z0 = V0/I0

Voltage Gain:

Voltage Gain, One of the most significant characteristics of the amplifier is small signal ac voltage gain as determined by

Av = V0/Vi

The re Transistor Model:

The re model uses a diode and controlled current source to duplicate behavior of the transistor in region of interest. Current-controlled current source is one where parameters of current source are controlled by current elsewhere in network. In fact, in general:

BJT transistor amplifiers are referred to as current-current controlled devices.

Common Base Configuration:

Common-base pnp transistor has been inserted within two-port structure. The re model for transistor has been placed between same four terminals. The model is chosen in such a way as to estimate behavior of device that it is replacing in operating region of interest. Result achieved with model in place must be relative close to those attained with actual transistor. One junction of the operating transistor is forward-biased while other is reversed-biased. Forward-biased junction will behave much like diode. For base-to-emitter junction of transistor, diode equivalent between same two terminals appears to be quite suitable. Recall that:

IC ≈ IB as desired from IC = IB for range of values of VCE

Current source establishes fact that IC = αIe, with controlling current Ie appearing in input side of equivalent circuit. We have therefore established equivalent at input and output terminals with current-controlled source, giving link between two.

The input impedance Zi for common-base configuration of transistor is simply re. That is:

[Zi = re]CB

For output impedance, if we set signal to zero, then Ie = 0.4, and IC = αIe = α (0A), resulting in open-circuit equivalent of output terminals. Result is that for model

[Z0 = ∞Ω].

Output resistance of common-base configuration is determined by slope of characteristic lines of output characteristics.

Voltage gain will now be determined for network

V0 = -I0RL = -(-IC)RL = αIeRL

AV = V0/Vi = αIeRL/Iere

For the current gain, and

Ai = I0/Ii - -IC/Ie - αIe/Ie

[Ai - α ≈ -1]CB

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