common emitter configuration

Common emitter mode :

The common emitter configuration with input and output supply is shown in figure in which emitter is common. Here, the input current is \(I_B\) and input base-emitter voltage \(V_{BE}\). However, the output current \(I_C\) with output voltage i.e. collector emitter voltage \(V_{CE}\) as shown in figure:

Input current=\(I_B\)

Output current=\(I_C\)

Now, current amplification factor in CE mode is denoted by \(\beta\) and is defined by,

Amplification factor (\(\beta\))=\(\frac{Output current}{Input current}\) $$\beta=\frac{I_C}{I_B}$$ $$I_C=\beta I_B$$The value of \(\beta\) is very large as \(I_B<<I_C\).Also,

Relationship between the \(\alpha\) and \(\beta\):

We have for normal transistor operation,

$$I_E=I_B+I_C$$

$$\frac{I_E}{I_B}=\frac{I_B}{I_C}+1$$

$$\frac{1}{\alpha}=\frac{1}{\beta}+1$$

$$\frac{1}{\alpha}=\frac{1+\beta}{\beta}$$

$$\alpha=\frac{\beta}{1+\beta}$$Also,

$$\beta=\frac{I_C}{I_B}$$

$$I_C=\beta I_B$$

$$\alpha I_E=\beta I_B$$

$$I_E=\frac{\beta}{\alpha} I_B$$

$$I_E=\frac{\beta}{\frac{\beta}{1+\beta}} I_B$$

$$I_E=(1+\beta) I_B$$Also,

$$\frac{1}{\beta}=\frac{1}{\alpha}-1$$

$$\frac{1}{\beta}=\frac{1-\alpha}{\alpha}$$

$$\beta=\frac{\alpha}{1-\alpha}$$Also,

$$I_C=\alpha I_E=\beta I_B$$

$$I_C=\biggl(\frac{ \beta}{1+\beta}\biggr) I_E$$and

$$I_C=\biggl(\frac{\alpha}{1-\alpha}\biggr)I_B$$

Leakage current:

Even when base is open there is flow of small amount of current through collector to emitter. This is due to reverse bias. Collector –base junction due to flow of minority charge carrier, this is called as leakage current. This leakage current in C.E. mode is denoted by \(I_{CEO}\) and it is the current from collector to emitter region when base is open. This leakage current is extremely temperature dependent. When, E\B base is closed then total collector current is,

$$I_C=\beta I_B+I_{ICO}$$

$$I_C=\beta I_B+(1+\beta) I_{CBO}$$

Thermal Runway:

We have the expression for collector current (\(I_C\)) in CE made is given by,

$$I_C=\beta I_B+(1+\beta) I_{CBO}\dotsm(1)$$

This (1) relation show that the leakage current (\(I_(CBO)\)) is multiplied by the factor\( (1+\beta)\) which consequently changes the collector current (\(I_C\)). The leakage current is extremely temperature dependent. The sight increase in leakage current in \(I_{CBO}\) is multiplied by the factor \beta or (1+\beta) and hence the collector current increases rapidly. As a result, the collector power dissipation increases. This increases the temperature of collector region thereby increasing leakage current. If this phenomena and the value of collector current \(I_C\) exceeds the certain safe limiting value by damaging the transistor permanently. This condition is called as thermal runway.

Current stabilization is needed to avoid the transistor from thermal runway.

Characteristics of C-E mode :

• Input characteristics:

It is the variation of input current (\(I_B\)) with input voltage (\(V_{BE}\)) of constant output voltage (\(V_{CE}\)) is called as input characteristics. The input characteristics is below figure:

In this characteristics input current doesn’t flow through transistor when the input voltage exceed the knee voltage (\(V_K\)).When \(v_{BE}\) exceeds \(V_k\) large current flow through the base region. This is similar to forward characteristics of P-N junction diode. This characteristics also help to find the forward resistance of the transistor and is given by reciprocal of slope of forward characteristics.

i.e. Input resistance(\(R_{in}\))=\(\frac{1}{slope}=\frac{1}{\frac{\Delta I_B}{\Delta V_{BE}}}=\frac {\Delta V_{BE}}{\Delta I_B}\) at constant \(V_{CE}\)

(2) Output characteristics:

It is the variation of output collector current (\(I_C\)) with output voltage (\(V_{BE}\)) for constant input base current. It is shown is above figure.

From the output characteristics, it is seen that when \(V_{CE}\) increases from zero \(I_C\) increases sharply to a certain value and its saturates as a result at most constant collector current flows through transistor circuit for large increase in output voltage \(V_{CE}\) junction breakdown occurs due to the reverse biasing and large collector current flows through the circuit. This gives the breakdown region.

When \(I_B=0\) a leakage current \(I{CEO}\) small flows through collector current to emitter region. Thus, the main collector current (due to majority charge carrier) is almost zero.So that the transistor in switch condition. This region is called as cut off region.

When \(V_{CE}\) is very small (Ideally zero). Collector current increases shortly to a certain level( saturation level) due to flow of majority charge carrier from emitter to base is reversed by collector.In this region the transistor works.

The output characteristic also helps to find the output resistance of transistor,

i.e.$$R_{out=}\frac{1}{slope}=\frac{1}{\frac{\Delta I_C}{\Delta V_{CE}}}$$

$$R_{out}=\frac{\Delta V_{CE}}{\Delta I_C}$$

(3)Transfer characteristics:

It is the variation of collector current with base current at constant collector to emitter voltage (\(V_{CE}\)). The transfer characteristics is shown in figure above.

The transfer characteristics in C-E mode is straight line with slope equal to that of amplification factor(\(\beta\)) and intercept is equal to that of leakage current ((\(I_{CEO}\)) i.e.$$I_C=\beta I_B+I_{CEO}$$ Where $$\beta=\frac{\Delta I_C}{\Delta I_B}$$ \(I_{CEO}=\beta\)

In this way we can study the all characteristics of common emitter configuration.

References:

(1)Theraja, B.L. Basic Electronics. N.p.: S.Chand, n.d. Print.

(2)C.L.Arora. Refresher Course in Physics. Vol. II and III. N.p.: S.Chand, 2006. Print.

(3)Malvino. Electronic Principles. N.p.: Tata McGraw-Hill, n.d. Print.

(4)N.Nelkon and P.Parker. Advanced Level Physics. 5th ed. N.p.: Arnold Heinemann, n.d. Print.

(5)Priti Bhakta Adhikari,Diya Nidhi Chaatkuli, Ishowr Prasad Koirala. A Textbook of Physics (2nd Year). N.p.: Sukunda Pustak Bhawan, 2070. Print.