Block 13 — Transistor Fundamentals

Learning objectives

90-minute plan

• Warm-up (10 min):
  • Where do transistors occur in a robot controller?
  • Recall from Block 11: pn junctions and diode behavior.
  • Recall from Block 12: diodes are useful, but they cannot actively control a load current.

• Core concepts (55 min):
  • Introductory example: transistors inside logic circuits.
  • Transistor as controlled valve: control circuit and load circuit.
  • BJT terminals, npn/pnp structure, and sign conventions.
  • BJT current gain, characteristic curves, and operating regions.
  • Switching times as a bridge to transistor applications.
  • FET and MOSFET operating principle.
  • MOSFET channel formation, body diode, and MOSFET types.
  • BJT versus MOSFET as switching element.

• Practice (20 min):
  • Calculate collector current from base current and current gain.
  • Decide whether a BJT is likely in cutoff, active region, or saturation.
  • Estimate MOSFET conduction losses with \(R_{\rm DS(on)}\).
  • Compare BJT and MOSFET control losses.

• Wrap-up (5 min):
  • Summary: BJT is current-controlled in the simple model; MOSFET is voltage-controlled in the simple model.
  • Preview: transistor applications such as low-side switches, high-side switches, PWM, relay drivers, and H-bridges are continued in Block 14.

Conceptual overview

Core content

From diode to transistor

A variable resistor can be developed from the diode.
A diode has two terminals and one pn junction, as we have seen in Block11. It can conduct or block depending on the applied voltage.
Therefore, there is only one path on which the current is dependent on the voltage on this path

With this controlled transition resistor (“transfer resistor” or better transistor) this gets a bit more extreenally controlled:

1. A transistor has at least three terminals.
2. One terminal is used to control the current path between the other two terminals.

Bipolar junction transistor: structure and terminals

A bipolar junction transistor (BJT) has three doped regions and three terminals.

• Emitter \(E\): emits charge carriers (either holes or electrons) into the transistor.
• Base \(B\): thin control region.
• Collector \(C\): collects charge carriers.

There are two basic BJT types:

• npn transistor: n-p-n layer sequence,
• pnp transistor: p-n-p layer sequence.

Depending on the layer sequence (or “direction of the diodes”), PNP or NPN transistors result, represented by different circuit symbols with three terminals (see figure 1). In both transistor variants, charge carriers are emitted from the emitter terminal (E) toward the collector terminal (C) if a suitable current flows through the base terminal (B). In simplified terms, the negative charge carriers of the n-doped sides could represent a current through an NPN structure if negative charge carriers were also present in the P-doped layer. The current $I_\rm C$ flowing with it in the technical current direction is illustrated in the circuit symbol by the arrow direction at the emitter. In the NPN transistor, the current $I_\rm C$ flows from the collector to the emitter. Since positive charge carriers enable conductivity in the PNP transistor, the technical current direction here points from the emitter to the collector, and the arrow on the emitter points towards the collector. The direction of the arrow is similar to the direction of the diode or the PN junction.

Correct connection and normal operation of an npn transistor

For an npn transistor in normal active operation, the base-emitter junction is forward-biased and the collector-base junction is reverse-biased.

\[ \begin{align*} U_{\rm BE} &> 0, & U_{\rm CE} &> 0, & U_{\rm CB} &> 0. \end{align*} \]

With the reference arrows commonly used in this course:

\[ \begin{align*} I_{\rm B}>0, \qquad I_{\rm C}>0, \qquad I_{\rm E}<0. \end{align*} \]

Kirchhoff's current law gives

\[ \begin{align*} I_{\rm B}+I_{\rm C}+I_{\rm E}=0. \end{align*} \]

Using current magnitudes:

\[ \begin{align*} |I_{\rm E}|=I_{\rm B}+I_{\rm C}. \end{align*} \]

How the npn transistor controls current

Here, the figures in figure 2 shall be described:

1. Figure: The physics of controlling the BJT takes place in the narrow P-layer in the middle.
   The following figures 2. - 6. refer to the highlighted section.
2. Figure - Situation $U_{\rm CE}=0~{\rm V}, U_{\rm BE}=0 ~\rm V$:
   In this picture the unpowered transistor is shown. In it the free charge carriers (electrons in green, holes in red) and the junction layers between base and emitter, and base and collector in yellow. Only the junction layer shows the stationary charge carriers with their sign. As shown in the band model, the stationary charge carriers are present everywhere in both doped regions.
   
   
3. Figure - Situation $U_{\rm CE}=0~{\rm V}, 0~{\rm V}<U_{\rm BE}<0.6~\rm V$:
   First, consider a small, positive voltage $U_{\rm BE}$. This provides holes in the base with current $I_\rm B$. This operates the PN junction between the base and emitter in the forward direction. In the figure, it is indicated with black circles that the injected holes compensate some stationary negative charge carriers in both junction layers. Electrons also flow through the emitter into the n-region, which attenuates the junction on the other side.
4. Figure - Situation $U_{\rm CE}=0~{\rm V}, U_{\rm BE}>0.6 \rm V$:
   When the forward voltage of the PN junction between the base and emitter is exceeded, the injected holes and electrons cancel the bottom junction. In the simulation below, it can be seen that the circuitry of the transistor is such that in the diode circuit (which is not physically correct), the diode between the base and emitter becomes conductive.
   
   
5. Figure - Situation $U_{\rm CE}>0~{\rm V}, U_{\rm BE}>0.6~\rm V$:
   Now with this voltage at the base, the working circuit, i.e. a voltage $U_{\rm BE}>0$ should be present at the output. In the real system, the base is very small compared to the mean free path length of the electrons (“path to recombination with a hole”). This changes the situation at the upper PN junction. In a classical diode, no electrons are present in the P-doped region. However, the electrons present here can cross the base and compensate for the stationary positive charge carriers in the upper junction. The holes injected into the base in turn compensate for the stationary negative charge carriers. Thus, this junction layer is also removed. This is possible as long as enough holes are injected into the base.
6. Figure - Situation $U_{\rm CE}>0~{\rm V}, U_{\rm BE}>0.6~\rm V$:
   Thus, in the NPN bipolar junction transistor, both holes (to remove the junction layers) and electrons (as the “main agents” responsible for charge transport, the so-called majority carrier charges) contribute to the conductivity. This is where the name bipolar junction transistor comes from.

Current gain of the BJT

In the active region, a small base current controls a larger collector current. The base current flows over a diode between base and emitter (depict as arrot in the symbol).

\[ \begin{align*} \boxed{ I_{\rm C}\approx B I_{\rm B} } \end{align*} \]

The factor \(B\) is the DC current gain:

\[ \begin{align*} B=\frac{I_{\rm C}}{I_{\rm B}}. \end{align*} \]

For small changes around an operating point, the small-signal current gain is

\[ \begin{align*} h_{\rm FE} = \beta = \frac{\Delta I_{\rm C}}{\Delta I_{\rm B}} = \frac{i_{\rm C}}{i_{\rm B}} \approx B. \end{align*} \]

BJT characteristic curves and differential quantities

A transistor is nonlinear. Therefore we describe it by characteristic curves.

Important BJT characteristics are:

• Input characteristic: \(I_{\rm B}(U_{\rm BE})\)
  The base-emitter path behaves approximately like a diode.
• Control characteristic: \(I_{\rm C}(I_{\rm B})\)
  This shows the current gain.
• Output characteristic: \(I_{\rm C}(U_{\rm CE})\) for different values of \(I_{\rm B}\).

Important parameters around an operating point are

\[ \begin{align*} r_{\rm BE} &= \frac{\Delta U_{\rm BE}}{\Delta I_{\rm B}} = \frac{u_{\rm BE}}{i_{\rm B}}, \\[4pt] r_{\rm CE} &= \frac{\Delta U_{\rm CE}}{\Delta I_{\rm C}} = \frac{u_{\rm CE}}{i_{\rm C}}. \end{align*} \]

BJT operating regions

A BJT operates mainly in three different regions.

Switching view

For a BJT used as a switch:

• off: cutoff region,
• on: saturation region.

In saturation, the collector-emitter voltage is small, often approximated by

\[ \begin{align*} U_{\rm CE,sat}\approx 0.1\ldots 0.3~{\rm V}. \end{align*} \]

The conduction loss of a saturated BJT switch is approximately

\[ \begin{align*} P_{\rm on,BJT} \approx U_{\rm CE,sat}I_{\rm C}. \end{align*} \]

The control loss at the base is approximately

\[ \begin{align*} P_{\rm ctrl,BJT} \approx U_{\rm BE}I_{\rm B}. \end{align*} \]

Switching times of a BJT

Real transistor switching is not instantaneous.

Typical time intervals are:

During switching, both current and voltage can be significant at the same time.
Therefore switching losses occur during turn-on and turn-off.

\[ \begin{align*} p(t)=u_{\rm CE}(t) \cdot i_{\rm C}(t). \end{align*} \]

Field-effect transistor: basic idea

A field-effect transistor controls current by an electric field.

For a MOSFET:

• gate \(G\): control terminal,
• source \(S\): reference terminal for \(U_{\rm GS}\),
• drain \(D\): load current terminal,
• bulk \(B\): semiconductor body, often internally connected to source in discrete MOSFETs.

The name MOSFET means:

\[ \begin{align*} \text{Metal-Oxide-Semiconductor Field-Effect Transistor}. \end{align*} \]

MOSFET structure and channel formation

The gate is separated from the semiconductor by a thin oxide layer. Therefore the gate behaves approximately like one plate of a capacitor.

For an n-channel enhancement MOSFET:

• at \(U_{\rm GS}=0\), no conductive channel exists,
• when \(U_{\rm GS}\) becomes large enough, electrons form a channel,
• then drain current \(I_{\rm D}\) can flow.

The threshold voltage \(U_{\rm GS(th)}\) indicates when a small channel just begins to form.

Body diode of a MOSFET

In a discrete power MOSFET, the bulk is often internally connected to the source. Together with the drain region, this creates an internal pn junction. This is the body diode.

MOSFET output characteristics

The drain current $I_{\rm D}$ depends on

• the drain-source voltage $U_{\rm DS}$, and
• the gate-source voltage $U_{\rm GS}$.

A MOSFET has several operating regions.
Their names can be confusing because they are not identical to the BJT names.

When a MOSFET is fully switched on, the drain-source path behaves approximately like a small resistance:

\[ \begin{align*} U_{\rm DS}\approx R_{\rm DS(on)} \cdot I_{\rm D}. \end{align*} \]

The conduction loss is

\[ \begin{align*} \boxed{ P_{\rm on,MOS} = R_{\rm DS(on)} \cdot I_{\rm D}^2 } \end{align*} \]

MOSFET types

MOSFETs can be classified by channel type and by whether they are normally off or normally on.

In many mechatronic power circuits, the most common device is the n-channel enhancement MOSFET.

BJT versus MOSFET as a switch

Exercises

Common pitfalls

• Thinking a BJT is just two diodes: The thin base region makes transistor action possible. Two separate diodes do not behave like a transistor.
• Forgetting the base-emitter diode: The BJT input characteristic resembles a diode. For silicon, \(U_{\rm BE}\) is often around \(0.6\ldots0.7~{\rm V}\), depending on current and temperature.
• Treating \(B\) as an exact constant: The current gain can vary strongly. Robust switching circuits are not designed with a typical \(B\) only.
• Confusing active region and saturation: In the active region, \(I_{\rm C}\approx B I_{\rm B}\). In saturation, the load circuit limits \(I_{\rm C}\).
• Using MOSFET threshold voltage as full-on voltage: \(U_{\rm GS(th)}\) is not sufficient for low conduction loss.
• Confusing MOSFET saturation with BJT saturation: A fully switched-on MOSFET is usually in the linear or ohmic region, not in the MOSFET saturation region.
• Forgetting the MOSFET body diode: A real power MOSFET is not an ideal bidirectional switch.
• Ignoring MOSFET gate charge: The stationary gate current is nearly zero, but fast switching still requires charging and discharging the gate capacitance.
• Mixing voltage polarities for pnp and p-channel devices: Their useful operating polarities are reversed compared with npn and n-channel devices.
• Ignoring power dissipation: Both BJTs and MOSFETs convert electrical energy into heat during conduction and switching.

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