Analog systems and applications — lecture-XVII.

## Regions of operations in BJT, leakage current, Lecture-XVII.

This article belongs to a series of lectures on analog electronics, the paper goes by the name “Analog Systems and Applications” for the physics honors degree class. All lectures of this series will be found here. This is the 17th lecture of the series. The lecture was delivered on 20th March 2018.

In our last two lectures (find’em here) we discussed in all detail the bipolar transistors and some of their characteristics in various configurations. There we briefly mentioned the BJT operate in various regions such as the active, cut-off and the saturation region. Today we will discuss that aspect a little more into our wit.

## Regions of operations in transistors.

There are two junctions in a BJT, that we have already mentioned in earlier instances, they are the Collector-Base and the Emitter-Base junctions. This is the reason the BJTs are known as bipolar devices. In contrast the FET or field effect transistors which are another type of 3-terminal transistors are uni-polar devices operating either with only P-type or only N-type regions, in their construction. (Therefore the FET have only one type of free carriers, either holes or electrons). In addition BJTs are current controlled devices while FETs are voltage controlled devices.

Accordingly BJTs can be biased in four ways. Each junction can be biased in two ways, either in a forward fashion or a reverse fashion. This leads to 4 different regions of operations for a BJT (of which we will discuss 3).

### (i) Active region

• The emitter junction (Emitter-Base component in the circuit) is forward biased and the collector junction (Collector-Base component in the circuit) is reverse biased.
• In such a niche the transistors get numerous applications. It is also known as the “linear region”.
• In this region the transistor behaves like an amplifier.
• The active region lies between the saturation region and the cut-off region which we will discuss in brief presently, and in more details later.
• In this region or state “collector current (IC)” is β times the “base current (IB)” where β is “current amplification factor” which we have discussed in our last two lectures. (linked again) With β = ΔIC/ΔIB, IC = βIB.

### (ii) Saturation region

• The transistor has its emitter (Emitter-Base part) and collector junctions (Collector-Base part) both forward biased.
• Thus transistor behave like a closed switch (i.e. ON). Its like collector and emitter are shorted.
• IC and IE are maximum in this mode of operation. IC = IE.

### (iii) Cut-off region

• The transistor has its both junctions (CB = Collector-Base and EB = Emitter-Base) “reverse biased”.
• The transistor behaves like an open switch, (OFF). Its like collector and emitter are both open.
• All currents (IC, IE and IB ) are zero in this mode of operation. IC = IE = IB = 0.

## Leakage current

Now we will discuss the effect of leakage current to the expressions we already have for collector current.

### Common-Base configuration.

The two diagrams below show the common-base configuration using either a npn or a pnp type transistor.

A common-base configuration with npn type transistor.

A common-base configuration with pnp type transistor.

• Lets consider a npn transistor (as shown above in one of the diagram) in the common-base configuration, where the emitter is forward biased (the emitter N represented by arrow is connected to battery -).
• The electrons from -ve terminal repel the electrons from the emitter. Current flows through emitter and base to the collector. This contributes to collector current. VCB is kept constant.
• Input current is (IE) and output current is (IC). α is the current amplification factor. Its defined as the ratio of the change in the collector current (ΔIC) to the change in the emitter current (ΔIC) when collector voltage (VCB) is kept constant. So α = (ΔIC/ΔIE) VCB = constant.

### Collector current

There are 3 currents that are flowing

(i) Emitter current: due to foward bias.

(ii) Base current: due to electron-hole generation.

(iii) Leakage current: as Collector-Base junction is reverse biased (its due to minority carriers and we have discussed this along with reverse saturation current, here, see under reverse bias heading).

If IE is the emitter current, αIE reaches the collector terminal. So, IE = αIE + Ileakage. If emtter-base voltage (VEB) is zero, the leakage current is small, its denoted as ICBO, where CBO stands for collector-base current with output open.

So, IC = αIE + ICBO but IE = IC + IB, this means: IC = α(IC + IB) + ICBO. So, IC (1-α) =αIB + ICBO and we get;

$\boxed{I_C = \Big( \frac{\alpha}{1-\alpha}\Big)I_B + \frac{I_{CBO}}{1-\alpha} }$.

We have already discussed the characteristics of the common-base configuration.

• It provides voltage gain, but no current gain.
• VEB = constant ⇒ small change in VEB makes good deal of change in IE. IE is independent of VCB.
• VCB drives IC only at low voltages if VEB is kept constant.
• Input resistance: $\boxed{r_i = \eta = \Big(\frac{\Delta V_{EB}}{\Delta I_{E}}\Big)_{V_{CB}=constant} }$. η is low and this point (ii) above.
• Output resistance $\boxed{r_o = \Big(\frac{\Delta V_{CB}}{\Delta I_{C}}\Big)_{I_E=constant} }$. r0 is very high, this large change in VCB impacts IC a little.
• Has good stability against temperature.
• Used in high frequency application.