How NPN Transistors (BJTs) Work: Explained with Calculations

In the previous tutorial we took a good look at the standard Bipolar Junction Transistors, which is often referred to as the BJT.

We learned that it actually comes in two main types which are known as the NPN configuration, standing for Negative-Positive-Negative, and the PNP configuration which means Positive-Negative-Positive.

So basically we have two different types of BJTs: the NPN BJT and the PNP BJT.

Out of these two types, the NPN Transistor is definitely the one that we use very often in our electronic projects.

We also learned that when it comes to the junctions of a bipolar transistor, there are three different ways we can bias them, we can use Common Base, Common Emitter, or Common Collector configurations.

In this tutorial we will investigate more about the bipolar junction transistors. Here we will be focusing on the “Common Emitter” configuration specifically using the Bipolar NPN Transistor (BJT).

We will also provide an example which will show how an NPN transistor is constructed, along with some detailed characteristics about how current flows through these BJTs. So let us get started!

Understanding the NPN Bipolar Junction Transistor Configuration

Referring to the diagram above, we can see that the Arrow is pointing outwards, which shows the location of the emitter terminal. And remember this arrow also shows how the conventional current flows “out” for a Bipolar NPN Transistor.

We have the construction details and the terminal voltages for this type of transistor displayed above as well.

Now when we talk about the voltage between the Base and Emitter, which we refer to as V_BE, it is important to note that it is positive at the Base and negative at the Emitter.

This is because, in the case of an NPN transistor we always find that the Base terminal is positive with respect to the Emitter terminal.

Also we need to keep in mind that the Collector supply voltage also has to be more positive compared to the Emitter (that is V_CE).

So in short, in order for a bipolar NPN transistor to function properly and correctly, we must ensure that the Collector terminal is always more positive compared to both the Base and the Emitter terminals.

As seen above in this configuration we connect the voltage sources to an NPN transistor, and everything is placed exactly as shown in the diagram.

We begin by connecting the Collector to the supply voltage V_CC through a load resistor R_L.

This resistor is quite significant since it does more than simply connect things; it also controls the maximum current that goes through the device, functioning as a protection.

Next, we will look at the transistor’s base. Here the base supply voltage V_B is connected to another resistor R_B.

This base resistor R_B performs a similar function by limiting the maximum current, but in this case it controls the current going into the base.

An NPN transistor functions by passing negative current carriers (electrons) via the base region. The movement of electrons is precisely what causes the “transistor action.”

What is interesting about this process is that these electrons bridge the gap between the Collector and Emitter circuits. This link between the input and output circuits is really the heart of what makes a transistor do its job so well.

In reality this connection is what enables the transistor to amplify since it allows the Base to direct the current traveling from the Collector to the Emitter, which is where the magic of amplification occurs.

So what we have here is a transistor which is actually a current-operated device. In other words it works based on the flow of current which is why it is commonly referred to as the “Beta model.”

Here is how it works: when the transistor is turned “fully ON,” a large amount of current, let us call it Ic, flows easily from the Collector to the Emitter.

But for this to happen, there has to be a small current, known as Ib, flowing into the Base of the transistor. This little current at the Base acts as a control, allowing us to switch the larger current on and off between collector to emitter.

Now here’s where things get interesting. In a bipolar NPN transistor, the relationship between the larger current (Ic) and the smaller Base current (Ib) is quite important.

This ratio which is called the DC Current Gain, is represented by the symbol hfe or more commonly, the Beta (β). To be precise, β is just a number that shows us how much larger Ic is compared to Ib.

And here’s an important fact: for standard BJTs, β can be pretty high, going up to around 200. This large ratio between the Collector current (Ic) and the Base current (Ib) is what makes the NPN transistor so effective as an amplifier.

When we use this NPN BJT in its active region, Ib serves as the input, whereas the Ic acts as the output, giving us a way to amplify signals. It is also worth noting that Beta (β) is just a ratio, so it does not have any units.

We have another important aspect of transistor behavior here, specifically about how current flows between the Collector and the Emitter.

This current gain, expressed as Ic/Ie, is what we call Alpha (α). Think of Alpha as a characteristic of the transistor itself, it is determined by how electrons move or “diffuse,” across the internal junction of the transistor.

The current flowing out of the Emitter, called Ie, is actually a combination of a tiny amount of current from the Base and a much larger amount from the Collector.

Because of this, the Alpha value, which is the ratio of these currents, ends up being very close to 1. For a typical low-power signal transistor, Alpha usually sits between about 0.950 and 0.999.

This high value tells us that nearly all of the Emitter current comes from the Collector, with only a tiny portion coming from the Base.

Understanding the Relationship Between the α and β in a NPN Transistor

DC Current Gain = Output Current/Input Current = I_C/I_B

I_E = I_B + I_C …… (KCL), and I_C/I_E = α

Therefore: I_B = I_E – I_C

I_B = I_E – αI_E

I_B = I_E(1 – α)

I_B = I_E(1 – α)

∴ β = I_C/I_B = I_C/I_E(1 – α) = α/(1 – α)

When we combine the two expressions α and β, then we are able to derive two mathematical formulas which helps us to get the relationship between the various currents that may be flowing through the transistor, as shown below:

α = β/β + 1 or α = β(1 – α)

β = α/1 – α) or β = α(1 + β)

If α = 0.99, β = 0.99/0.01 = 99

The Beta (β) value of a transistor represents the ratio of collector current to base current. The value changes according on the type of transistor. For high-current power transistors, Beta is typically low, approximately 20.

But for high-frequency, low-power transistors, Beta can be substantially higher, typically exceeding 1000! Most common NPN transistors have a Beta value between 50 and 200.

If you need to know the actual Beta value, see the manufacturer’s data sheet.

We may now reorganize the Beta formula so that we concentrate on the collector current (Ic). If no current flows into the Base (Ib = 0), no current will pass through the Collector.

This is because multiplying Beta by zero yields zero current (β * 0 = 0).

Another important factor to remember is that as the base current grows, so does the collector current. So, the Base current may be thought of as a “control knob” for the Collector current.

One of the most essential characteristics of a Bipolar Junction Transistor (BJT) is that a low base current may regulate a much higher collector current.

This characteristic makes transistors extremely useful in amplifiers and other circuits. Let us now look at an example to understand how this works in practice.

Solving an NPN BJT Problem #1

Let say we have an NPN BJT having a DC current gain (Beta) value of 190. We want to calculate the base current Ib that is necessary for switching a resistive load of 5 mA.

I_B = I_C/β

= (5 * 10^-3)/190

= 0.0000263 Amp = 26 µA

As per the above calculations, the base current Ib = 26 µA

Here is an important point about Bipolar NPN Transistors. For current to flow through the transistor, we must have the Collector voltage (Vc) higher than the Emitter voltage (Ve).

It also needs to be positive with respect to the Emitter.

Another detail is the voltage drop between the Base and Emitter terminals. For silicon transistors, this drop is around 0.7V. This happens because the input of an NPN transistor behaves like a forward-biased diode.

So for the transistor to conduct, the Base voltage (Vbe) must be greater than this 0.7V. If it is not then the transistor will not conduct even if there is a Base current present.

I_B = (V_B – V_BE)/R_B

In the above formula the Ib indicates the base current, Vb represents the base bias voltage, Vbe denotes the base-emitter volt drop (0.7v) and Rb refers to the base input resistor.

If we increase Ib, then the Vbe also increases slowly to 0.7V, but the Ic only increases exponentially.

Solving an NPN BJT Problem #2

In this problem we have an NPN BJT which specifies a DC base bias voltage Vb of 9 V and an input base resistor Rb of 120 kΩ. So we want to calculate the base current Ib of the transistor.

I_B = (V_B – V_BE)/R_B

= (9 – 0.7)/120000

= 0.0000691 = 69 µA

As per the above calculations, the base current Ib = 69 µA

Understanding the BJT Common Emitter Configuration

Bipolar NPN Transistors can be quite versatile. Not only can we use them as switches to turn a load current fully “ON” or “OFF” but they can be also used to amplify signals. This amplification happens when they operate in their active region.

Here is exactly how it works: we apply a small AC signal to the Base, and also by keeping the Emitter grounded. This allows the transistor to amplify the signal.

However we first need to apply a suitable DC “biasing” voltage to the Base. This keeps the transistor operating in its linear active region.

When we do this we create a type of amplifier, which we call as the “single-stage common emitter amplifier.”

This amplifier is inverting by nature, which means that it inverts the phase of the input signal across its output. One popular configuration for this amplifier is called a Class A Amplifier.

In a Class A Amplifier we bias the Base to keep the Base-emitter junction forward-biased. This keeps the transistor balanced, right between its cut-off and saturation points.

As a result the transistor can reproduce both the positive and negative halves of any AC input signal combined with the DC biasing voltage. This gives us a stable and an amplified output of the entire signal.

The “Bias Voltage” is important for full amplification. Without it, only one half of the input waveform would be amplified. This setup, called a common emitter amplifier configuration with an NPN transistor, is very versatile.

It is used in many applications, especially in audio circuits. For example this is popular in pre-amplifier and power amplifier stages in which the weak signals needs boosting.

Now with this common emitter configuration, we can also look at the Output Characteristics Curves. These curves show the relationship between the output Collector current (Ic) and the Collector-Emitter voltage (Vce).

They do this across different levels of Base current (Ib). These curves are useful for understanding how the transistor behaves under various conditions. They are especially helpful when we work with transistors that have the same Beta (β) value.

It is also possible for us to add a DC “Load Line” to the Output Characteristics Curves. This Load Line shows all the possible operating points as we adjust the Base current. To get the best amplification of an AC signal, we set an initial value for Vce.

This allows the output voltage to vary up and down smoothly. This setup is called the “Operating Point” or Quiescent Point, often shortened to the Q-point.

Understanding the Working of a Single BJT Common Emitter Amplifier Circuit

Analyzing the Output Characteristics Curves of a Typical BJT

The main point to focus on here is that, how V_CE impacts the collector current of the BJT, which we call I_C.

This effect is especially notable when VCE is above 1.0 volts.

At that point the I_C does not change much even if V_CE varies slightly. Instead it is stable, as if on an autopilot, with the base current I_B taking control.

In this state we can say the output circuit acts as a “Constant Current Source.”

Looking at the common emitter circuit we see that the emitter current IE is just the sum of I_C and I_B. So for our configuration we can express this simply as I_E = I_C + I_B.

Now referring to the above output characteristic curves of the circuit and applying Ohm’s Law to it, we observe that the current through the load resistor R_L equals the collector current I_C flowing into the transistor.

This current is determined by the supply voltage V_CC minus the voltage drop between the collector and emitter terminals V_CE. Thus, we can summarize this as shown below, with the formula:

Collector Current, I_C = (V_CC – V_CE)/R_L.

Now, we can sketch a straight line on the graph of those curves to show the Dynamic Load Line of our transistor.

We start this line from a point we call “Saturation” labeled as point A where V_CE is 0. Then we extend it to the point called “Cut-off,” labeled as point B where IC is 0. This straight line represents what’s known as the “Operating” or Q-point of the transistor.

When we connect these two points with the line, each point along it shows the “Active Region” of the transistor. Its like a map that shows where the action happens!

To place this load line accurately on the characteristic curves, we can perform some calculations. Here is how to work it out:

When we have: (V_CE = 0), I_C = (V_CC – 0)/R_L, I_C = V_CC/R_L

When we have: (I_C = 0), then 0 = (V_CC – V_CE)/R_L, V_CC = V_CE

Here’s what is interesting: we can use the collector or the output characteristics curves for common emitter NPN transistors to determine the collector current I_C.

This works if we know the values of V_CE and the base current I_B. We can also draw a load line on these curves to find a good operating point or Q-point.

We can adjust this Q-point by tweaking the base current. The slope of this load line is equal to the negative reciprocal of the load resistance which we can express as -1/R_L.

Now let’s break down how an NPN transistor works. It typically starts in an “OFF” state.

However if we apply a small input current and a positive voltage at its base (B) relative to its emitter (E), it switches “ON.”

When this happens, a much larger collector-emitter current flows through.

Remember that the NPN transistors operate best when V_C is much higher than V_E.

References:

Transistor Basics

NPN BJT Transistor