  24 February 2009
Author: Giorgos Lazaridis
BJT Transistor theory

How BJT transistors work
Inside a transistor

A BJT (Bipolar Junction Transistor) transistor has inside two similar semiconductive materials, and between them there is a third semiconductive material of different type. So, if the two similar materials are P and the middle one is N, then we have a P-N-P or PNP transistor. Similarly, if the two materials are N and the middle one is P, then we have a N-P-N material or NPN.

Each transistor has 3 leads which we call base, collector and emitter, and we use the symbols b, c and e respectively. Each lead is connected to one of the 3 materials inside, with the base being connected to the middle one. The symbol of the transistor has an arrow on the emitter. If the transistor is a PNP, then the arrow points to the base of the transistor, otherwise it points to the output. You can always remember that the arrow points at the N material. These are the symbols: Transistor operation

We will now explain the operation for the transistor, using an NPN type. The same operation applies for the PNP transistors as well, but with currents and voltage sources reversed.

With no power applied to the transistor areas, there are two depletion zones between the two P-N contacts. Suppose now that we connect a power source between the base and the collector in reverse-bias, with the positive of the source connected to the collector and the negative to the base. The depletion zone of the P-N contact between the base and the collector will be widened. Moreover, a slight current will flow withing this contact (due to impurities). This current is the reverse contact current and we will use the symbol ICBO: Now suppose that we connect another voltage supply between the emitter and the base in forward bias, with the positive of the source connected to the base and the negative connected to the emitter. The depletion zone between the emitter and the base will be shortened, and current (electrons) will flow when the voltage exceeds a specific level. This level depends on the material that the transistor is made of. Germanium (Ge) is the material that was originally used to make transistor, and later Silicon (Si) was used. For Germanium, the voltage is around 0.3 volts (0.27 @ 25oC), and for Silicon the voltage is around 0.7 volts (0.71 @ 25oC). Some of the electrons that go through the e-b depletion zone, will re-connect with holes in the base. This is the base current and we will use the IB symbol for reference. In real life, this current is at the scale of micro-amperes (μA or uA): But most of the electrons will flow through the base (due to spilling) and will be directed to the collector. When these electrons reach the depletion area between the base and the collector, they will experience a force from the electric field which exists in this zone, and the electrons will pass through the depletion zone. The electrons will then re-connect with holes in the collector. The re-connected holes will be replaced with holes coming from the base-collector power supply (VCC). The movement of these holes equals to a movement of electrons in the opposite direction, from the collector to the supply. In other words, the current that flows to the emitter will be divided into the small base current and the larger collector current:

IE = IB + IC

Generally, the number of electrons that arrive at the collector is the 99% of the total electrons, and the rest 1% causes the base current.

At the collector, except the electrons that come from the emitter, there is also the reverse current from the base-collector contact that we saw before. Both currents flow at the same direction, so they are added:

IC' = IC + ICBO

The following drawing shows how the electrons and holes flow within the transistor: This is generally what happens inside a transistor when voltage is applied. The purpose of this theory is to explain how can someone use the transistor to design an amplifier or a switch, so we will not go into many details. It is enough to know this basic operation.

The hybrid parameters [h]

The hybrid parameters are values that characterize the operation of a transistor, such as the amplification factor, the resistance and others. They are used to calculate and properly use the transistor in a circuit. Most of the the hybrid parameter values are given in the datasheet by the manufacturer. You do not need to learn everything about hybrid parameters to design a transistor circuit, but it is good to know that they exist. Here is a quick reference:

The hybrid parameters for Common Emitter (CE) connection

Here is the first set of hybrid parameters for a transistor connected with Common Emitter. For now you do not have to worry about the type of connection. We will discuss them thoroughly in the next chapters.

hie - input impedance

The first hybrid parameter that we will see is the hie. This parameter is defined by the result of the division of the VBE by IB:

hie = VBE / IB

This parameters defines the input resistance of a transistor, when the output is short-circuited (VCE=0).

hfe - Current Gain

This is the most important parameter and is extensively used when calculating a transistor amplifier. This is actually the only parameter you need to know to begin designing amplifiers. The equation for this parameter is the following:

hfe = IC / IB

When we have the output of the transistor short-circuited (VCE=0), hfe defines the current gain of the transistor in common emitter (CE) connection. Using this parameter we can calculate the output current (IC) from the input current (IB):

IC = IB x hfe

This explains why this parameter is so useful. A BJT transistor has typical current amplification from 30 to 800, while a Darlington pair transistor can have an amplification factor of 10.000 or more. Another symbol for the hfe is the Greek letter β (spelled "Beta").

hre - Dynamic transfer ratio reverse voltage

This parameter is calculated with this equation:

hre = VBE / VCE

If the input of the transistor is open (IB=0) then this parameter gives the voltage gain when the transistor is connected with common emitter (CE).

hoe - Output Conductivity

This parameter is defined with the input open (IB=0) and the transistor connected in common emitter (CE) connection. The equation is:

hoe = IC / VCE

With the above conditions, this parameter defines the conductivity of the output. So, the impedance of the output can be defined as follows:

ro = 1 / hoe = VCE / IC

The hybrid parameters for Common Base(CB) connection
hfb - Current Gain

Like in Common Emitter connection, in Common Base connection there is a current gain ratio which is defined by the manufacturer with the hfb parameter. In this type of connection, the current amplification is almost 1 which means that no practical amplification occurs. hfb is also symbolized with the Greek letter α (Alpha).

0.9 < α < 1

The formula to calculate this parameter is the following:

-hfb = IC / IE

The hybrid parameters for Common Collector(CC) connection
hfc - Current Gain

As you understand, the current gain is the most important parameter in every type of connection. Same applies for the common collector connection. The equation is as follows:

-hfc = IE / IB

An alternative symbol for hfc is the Greek letter γ (Gama).

Static and Dynamic operation

As we saw above, the hybrid parameters begin with the letter h, and then a pointer follows to define which parameter we are talking about. If the pointer is written with lowercase letters, then this parameter refers to dynamic transistor operation. We call dynamic operation when the transistor operates with AC voltage, like for example in an audio amplifiers. If the pointer of the h parameter is written with capital letters, then the parameter refers to static transistor operation. The transistor operates statically if there is only DC voltage, like for example in a transistor relay driver.

The current gain parameters have almost the same values in both static and dynamic operation. So, we can safely say that hFE is almost equal to hfe. Generally:

hfe ≈ hFE (hfe ≠ hFE)
hfb ≈ hFB (hfb ≠ hFB)
hfc ≈ hFC (hfc ≠ hFC)

For static operation, the alternative Greek letters can be used as well, with the pointer 0 or dc:

hFE = β0 = βdc
hFB = α0 = αdc
hFC = γ0 = γdc

Hybrid parameters are unstable

One of the most common problems that a circuit designer faces when using transistors, is the fact that the h parameters are very sensitive to temperature changes. The most annoying thing about this is that the current gain changes dramatically. In common emitter connection for example, hfe can increase by 60% if the temperature climbs form 25 to 100 degrees. Take also into account that a transistor dissipates power in the form of heat, so temperature increment is something common that happens all the time.

Another problem with hybrid parameters is that even between completely identical transistors, they may vary dramatically. You may have two transistors with the same code from the same manufacturer (completely identical) and yet one transistor may have hfe 150 and the other 300 (real measurement)! Within the next pages, we will see how can a designer work around with these problems.

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