Bipolar Junction Transistors (BJTs)

Overview

Bipolar junction transistors (BJTs) are 3 legged active semiconductor devices. They behave as a current-amplifier, amplifying a small base-emitter (BE) current into a larger collector-emitter (CE) current.

It was the first type of transistor to ever be mass produced.

Types

BJTs come in two flavours, NPN or PNP. They both have three terminals, the collector (C), the base (B) and the emitter (E).

The differences between the NPN and PNP transistor types are analogous to the N-Channel and P-Channel MOSFET types.

Schematic Symbols

The schematic symbols for NPN and PNP transistors are shown below:

Notice that the collector and emitter have been flipped for the PNP (compared to the NPN), this is how they are normally drawn on schematics.

The arrow is always on the emitter leg of the BJT. To differentiate between the two, the arrow on the NPN points away from the transistor, the arrow on a PNP points towards the transistor.

Sometimes you will see the transistors drawn without the circles around them, they represent exactly the same thing as the symbols above.

How They Work

BJTs are made from a hunk of silicon. They are either a thin slice of P-type semiconductor sandwiched between two layers of N-type semiconductor (NPN) or the reverse, a thin slice of N-type semiconductor sandwiched between two layers of P-type semiconductor (PNP).

The bipolar part of their name comes from the fact they conduct by using both majority and minority charge carriers.

Important Parameters

Beta And Gain (B, hfe)

The gain of a BJT is the ratio between the base current and the collector current (hence it is a current gain), typically when measured with the BJT in a common-emitter configuration. There are few different gains and symbols used, so it’s important to know what exact gain is being talked about:

• \(\beta\): DC (large-signal) gain
• \(H_{fe}\) (or \(h_{FE}\)): DC (large-signal) gain, part of the H-parameter (Hybrid parameter) model (same as \(\beta\)). Also sometimes written as \(h_{21}\)
• \(h_{fe}\): Small-signal gain, part of the H-parameter model

All of them depend somewhat other parameters such as collector current and temperature, but typically the gain is treated as a constant. The main thing to remember is to not expect the current gain to equal an exact number, even between the same BJT transistor from the same manufacturing batch.

$$ I_C = \beta I_B $$

The \(FE\) part of the two H-parameter gains represents:

• \(F\): The Forward current amplification
• \(E\): As measured with the BJT in the common-Emitter configuration

Temperature has a major influence on the gain of a BJT.

Early Voltage (Va)

The Early Voltage is normally denoted with \(V_A\).

As \(V_{CE}\) on a BJT increases, the reverse-bias on the \(V_CB\) junction increases (this is just a PN junction in reverse bias under typical operation). This increases the depletion region of this junction, which reduces the effective width of the base. Because the saturation current is inversely proportional to the effective width of the base, an increase in \(V_{CE}\) results in an increase in \(I_C\).

The effect of the collector-emitter current on collector current is given by the following equation:

\begin{align} I_C = I_{C(sat)} ( 1 + \frac{V_{CE}}{V_A} ) \end{align}

Miller Capacitance

TODO: Add notes here

Thermal Voltage

The thermal voltage of a BJT transistor is the voltage across a PN junction caused by the temperature of the junction.

\begin{align} V_T = \frac{kT}{q} \end{align}

where:
\(k\) is Boltzmann's constant in Joules per Kelvin, which is \(1.38\times 10^{-23}JK^{-1}\)
\(T\) is the temperature of the junction, in Kelvin \(K\)
\(q\) is the charge on a electron in Coulombs, which is \(1.6\times 10^{-19}C\)

At a room temperature of \(22^{\circ}C\), \(V_T\) is approximately \(25mV\). \(25mV\) is a good enough approximation for the thermal voltage in many scenarios without taking the actual junction temperature into account. The thermal voltage is used in the hybrid-pi model of the BJT transistor.

BJT Transistor Models

Ebers-Moll Transistor Model

TODO: Add info here

Hybrid-Pi Transistor Model

The hybrid-pi model is a well-used model for approximating the small-signal behaviour of transistors at low frequencies. There are a few variants of the hybrid-pi model, the simplest being the small-signal linearized version.

Small-Signal Linearized Hybrid-Pi Model

The small-signal linearized hybrid-pi model is a simplification of the complete hybrid-pi model.

Inputs (independent variables) to the model are:

• Small-signal base-emitter voltage \(v_\pi\)
• Small-signal collector-emitter voltage \(v_{CE}\)

From this the model calculates the following outputs (dependent variables):

• Small-signal base current \(i_B\)
• Small-signal collector current \(i_C\)

The transconductance \(g_m\) can be calculated with:

\begin{align} g_m &= \frac{i_C}{v_{BE}} & \text{when $v_{CE} = 0$} \\ &= \frac{I_C}{V_T} \end{align}

where:
\(I_C\) is the DC bias collector current (not the small-signal collector current) \(V_T\) is the thermal voltage

Circuit Design Basics With BJTs

The current through the base pin (\(I_b\)) and the current through the collector pin (\(I_c\)) always sums to give the current through the emitter pin (\(I_e\)).

$$ I_e = I_b + I_c $$

Because the collector current is usually much larger than the base current, for most scenarios you can treat the collector and emitter current as equal.

$$ I_e \approx I_c $$

As a general rule, NPN transistors are useful for connecting things to ground. PNP transistors are useful for connecting things to your power rail.

NPNs require a small positive base-emitter voltage to create a current which flows into the base. This current, multiplied by the gain of the transistor, determines the collector-to-emitter current (well, to be technically correct, the maximum collector current). Because of this, a NPN transistor will only conduct when both the base and collector have a higher voltage than the emitter.

A PNP transistor will only conduct when both the base and collector have a negative voltage w.r.t the emitter.

High And Low-side Switching With BJTs

NPN transistors are good for low-side switching. You can connect the collector to the negative end of the load, the emitter to ground, and control the base with a digital low/high signal through a resistor (low/ground base signal = load off, high base signal = load on).

However, NPN transistors cannot be used as a simple high-side switch, as the emitter rises to the high-side load voltage. To keep the NPN transistor in saturation, this would mean the base voltage would need to be higher than the high-side load voltage, which is not usually viable (charge-pumps are sometimes used to overcome this, but more commonly seen when using N-channel MOSFETs as high-side switches). Normally you would want to use a PNP transistor for high-side switching.

BJT Circuits

Common Collector Amplifier

The BJT common-collector amplifier is one of the three basic single-stage BJT amplifier topologies. The common collector amplifier topology is also known as a emitter follower amplifier.

The output voltage is almost equal to the input voltage, except for an approximately \(0.7V\) diode drop. This means that the amplifier has a voltage gain of almost unity (1), or \(0dB\).

$$ v_{out} = v_{in} - 0.7V $$

Here is a graph of \(v_{in}\) vs. \(v_{out}\) for the above circuit:

Common-Base Amplifier

The BJT common-base (a.k.a. grounded-base, and sometimes just abbreviated to CB or GB) amplifier is one of the three basic single-stage BJT amplifier topologies. The base of the BJT is connected to ground and shared with the output signal, hence the “common-base”. The input signal is fed to the emitter and the output comes from the collector. It is not as popular in discrete low-frequency circuits as the common-collector or common-emitter BJT amplifiers.

A basic schematic of a common-base NPN BJT amplifier is shown below, excluding DC biasing components:

Note that the above circuit is not realistic because it does not show the DC biasing componentry, however it is useful to illustrate the basic principle of the amplifier. The following schematic shows a common-base amplifier with the DC biasing component included:

Input Resistance

The small-signal input resistance of the common-base BJT amplifier is equal to:

\begin{align} r_{in} &= \frac{v_{in}}{i_{in}} \\ &= \frac{v_e}{i_e} \\ &= \frac{i_e \cdot (r'e\,||\,R_E)}{i_e} &\text{Replacing $v_e$} \\ &= r'e\,||\,R_E &\text{$i_e$'s cancel out} \end{align}

Basic BJT Amplifier Topology Summary

Constant-Current Sink

BJTs can be configured to sink a relatively constant amount of current which is independent on the output-side voltage. This can be a useful way of driving an LED from a microcontroller with a constant current, no matter what voltage source is used to drive the LED. BJT current sinks and sources are good for simple, cheap situations in where high precision is not the name of the game. If you want high precision, you’re best bet is to build a current-sink from an op-amp.

The above schematic was designed to drive the LED with 10mA of current when the BJT was driven from a microcontroller running at \(+3.3V\). Since \(+3.3V\) is applied to the base of the NPN transistor, the transistor will always turn on just enough so that the voltage at the emitter is \(0.7V\) less, e.g.

$$ V_e = V_b - 0.7V $$

Since we know the emitter voltage is going to be \(+2.6V\), we can choose the right resistor, \(R_1\) to get the LED current we desire (remember that the current out of the emitter is pretty much equal to the current into the collector).

$$ R_1 = \frac{V_e}{I_{LED}} $$

So if we want a LED current of 10mA, that means we need \(R1 = 260\Omega\). The closest E12 value is \(270\Omega\).

Notice how the LED current is independent of the \(+12V\). The \(+12V\) can change to say, \(+9V\) and the LED current will still be \(10mA\). The current draw from the microcontroller into the base of the transistor will be very low (somewhere around \(100uA\)).

Below are the simulation results for the above schematic, showing the LED current to be indeed \(10mA\). It works!

Using A Resistor Divider To Drive The Base

A resistor divider can simple way to drive the base of an NPN current-sink if you don’t need active control. This works well if the supply voltage is known and stable, as the current will fluctuate with supply voltage (if this is going to be an issue, consider using a Zener-based circuit to drive the base of the NPN BJT). Schematics of the design are shown below:

Design Procedure:

1. Choose the resistor-divider \(R_1\) and \(R_2\) to provide a voltage at the base of the transistor in the region of \(2.0-5.0\)V. I choose \(R_1 = 10k\Omega\) as this is a standard resistance, and then \(R_2 = 2.2k\Omega\) to give a \(V_B = 2.16V\).

2. Subtract \(0.7V\) of \(V_B\) to get \(V_E\). In this case, \(V_E = 1.46V\).

3. Size \(R_E\) to set the desired current of your current sink. Using Ohm’s Law, \(R_E = \frac{V_E}{I}\). In this case we wanted \(2mA\) to drive an LED, so:

   \begin{align} R_E &= \frac{1.46V}{2mA} \\ &= 730\Omega \\ &\approx 732 \, \text{(closest E96 value)} \end{align}

4. As a sanity check, make sure the output impedance of the resistor divider is much less than the input impedance looking into the base of the BJT (otherwise the resistor divider output will get significantly loaded and it’s output voltage will drop). That is:

   \begin{align} R_1 || R_2 &\ll \beta R_E \\ \frac{10k\Omega \cdot 2.2k\Omega}{10k\Omega + 2.2k\Omega} &\ll 100 \cdot 732\Omega \\ 1.80k\Omega &\ll 73.2k\Omega \end{align}

   The above equation holds true so this design should work as a good current sink ✅

Current Mirrors

A current mirror is a current-copying circuit in where one the current in one BJT is programmed via a resistor and is used to control the current in a second BJT which is used to drive the same current into a load. The current-mirrors shown below are built with BJTs, but other active transistors such as MOSFETs can also be used.

A basic PNP BJT-based current mirror is shown below:

Design Procedure:

1. Decide on the program current, \(I_P\). This will also be the current through the load. We’ll use this value later! For this example we’ll choose \(1mA\).

2. Find the voltage across \(R_1\), nothing that \(Q_1\) has a diode voltage drop of \(0.7V\) from emitter to base (with the emitter tied to \(V_{CC}\)), at that the base and collector of \(Q_1\) are tied together and hence at the same voltage:

   \begin{align} V_{R1} &= 12V - 0.7V \\ &= 11.3V \end{align}

3. Set the resistance of \(R_1\) using Ohm’s Law:

   \begin{align} R_1 &= \frac{V_{R1}}{I_P} \\ &= \frac{11.3V}{1mA} \\ &= 11.3k\Omega \end{align}

4. All done!

Common BJTs

The BC range of BJTs, including the BC547 and BC548 are very common, low-cost general purpose BJT transistors that you will encounter in hobbyist and professional electronics designs alike. They originated with the BC108 family of metal-cased transistors.

• BC547: Same as the BC548, but with a higher breakdown voltage.
• BC548: Common NPN transistor, used for switching and amplification purposes.
• BC549: Low noise version of the BC548.

Multiple-Collector And Multiple-Emitter BJTs

Multiple emitter and multiple collector BJTs are special types of BJTs which have more than one emitter or more than one collector.

In the case of a multiple collector BJT, the total collector current \(I_{C,tot}\,\) is set by the base current \(I_B\). If all the collectors are the same size (the silicon is physically the same size), then the current is equally split across all collectors.

The multiple-emitter BJT can be used to implement AND logic. The multiple-emitter BJT forms an integral part of the TTL AND input circuitry (e.g. the 7400 series of integrated circuits). They were introduced into digital logic design to replace the diodes of diode-transistor logic (DTL), with the advantage of a lower switching time and lower power dissipation.

Multiple emitter BJTs were also used in older (e.g. from the 1960’s) RAM. For example, Intel’s first IC, the 3101 (64 bits of RAM!), contains multiple emitter BJTs as part of the 2-state latch circuitry which holds one bit of information. One emitter is used to select which cell to read or write, while the other emitter is used to read or write the data. See an excellent tear-down of the IC on Ken Shirriff’s blog.

Reverse Active Mode

By utilizing the voltage regulation hysteresis behaviour of a BJT in reverse active mode, it can be used to create a simple single transistor LED blinker

External Resources

This is a great video on two not-so-common transistor biasing configurations.

The you are looking for a slice of history and some informative transistor information, check out the 1964 edition of the GE Transistor Manual.

References