Table of Contents

Transistor Switch and PWM

A transistor switch can connect and disconnect a load very quickly. If the switch is periodically on and off, the load sees an average voltage.

For an ideal switch with supply voltage \(U_{\rm dc}\):

\[ \begin{align*} \overline{u}_{\rm L} = \frac{1}{T}\int_0^T u_{\rm L}(t)\,{\rm d}t = \frac{T_{\rm on}}{T}U_{\rm dc}. \end{align*} \]

The duty cycle is

\[ \begin{align*} d=\frac{T_{\rm on}}{T}. \end{align*} \]

Thus

\[ \begin{align*} \boxed{ \overline{u}_{\rm L}=dU_{\rm dc} } \end{align*} \]

This is the basic idea of pulse-width modulation (PWM). Applications to motor drivers and power stages are continued in Block 14.

2.8 Applications for bipolar junction transistors

2.8.1 Darlington-Transistor

The Darlington circuit or the Darlington transistor (as a discrete element) is a simple construction, which makes it possible to control the output voltage $U_{\rm BE}$ with a considerably lower base current $I_\rm B$. In the simulation is the Darlington circuit compared to a simple bipolar junction transistor. Details can be found in Wikipedia under Darlington circuit.

2.8.2 Internal life of an operational amplifier

The operational amplifier as an “almost ideal” differential voltage amplifier represents a central component of electronic circuit technology from the next chapter on. In the chapter basics to amplifiers - feedback an ideal differential voltage amplifier was already used. In the simulation, the core of the differential voltage amplifier is simplified. Accordingly, there is no differential voltage at the input, but a small sinusoidal voltage. This is first applied to the base of the first bipolar junction transistor, which is a high-impedance input amplifier stage. The current $I_\rm C$ regulated by this in turn leads to a base of another bipolar junction transistor and then to the output amplifier stage. In the simulation, this setup achieves a differential gain of about $A_\rm D=10'000'000$. In real differential amplifiers, this is more in the range $A_\rm D ≈100'000$. Details can be found in Wikipedia under operational amplifier.

2.9 Applications for Field-Effect Transistors

2.9.1 NOT Gate

Just about all consumer electronics products have field-effect transistors at their core. In detail, this is based on CMOS technology (CMOS: Complementary metal-oxide-semiconductor) is used. The MOSFETs on the ground side and the MOSFETs on the power supply side behave in opposite ways, i.e. complementary. The simulation shows the simplest gate, the NOT gate. Another gate was considered in an introductory way.

2.9.2 Reverse Polarity Protection

Many chips (such as microcontrollers) can be destroyed by an incorrectly polarized power supply. Battery-powered electronics should have an active protection circuit for this. A diode is not practical for the power supply (why?). Instead, a MOSFET can be used, which does not pass negative voltages. Details are well explained on the page of Lothar Miller.

2.9.3 Level Converter

During electronics development, several integrated circuits (e.g. intelligent light sensor, microcontroller, intelligent LED) may require different voltage levels. This can lead to problems especially during data exchange if logic High has to be in a certain voltage range. This problem can be solved by a level converter. The level converter (also logic level converter, level shifter) enables the bidirectional connection of digital connections of different voltage levels, e.g. $5 ~\rm V$ to $3.3 ~\rm V$.

For the level converter, any N-channel enhancement MOSFET whose threshold voltage is below $1.8...2.0 ~\rm V$ can be used. This limit is due to the minimum logic level of $2.0 ~\rm V$ for logic high. For simplicity, “logic level enhancement mode MOSFET” is used, which is just optimized for the logic voltage of $3.3 ~\rm V$.

The way it works is well explained on Wikipedia and can be derived with simulation.

2.9.4 Voltage Doubler/Inverter

As a power supply for electronics, $5 ~\rm V$ or $3.3 ~\rm V$ is often used. In the following chapter, we will see that a bipolar power supply is often used for operational amplifier circuits. To be able to generate $-5 ~\rm V$ at low currents from a $5 ~\rm V$ supply, charge pumps are often used. One such can be seen in the simulation. In the oscilloscope (in the simulation below), the voltage $U_{\rm C1}$ is displayed at the input capacitor $C1$ and $U_{\rm C2}$ at the storage capacitor C1. This circuit can be found, for example, in IC ICL7660 (Renesas), LMC7660 (TI), TC7660 (Microchip) integrated. Details on how it works can be found in this video, for example.

Study Questions:

2.9.5 Voltage Inverter in the Microcontroller

In some microcontrollers, a negative voltage is required internally (e.g. for operational amplifiers). Since this voltage is not supplied externally, the microcontroller must provide it via an internal circuit. The simulation shows a circuit that can be integrated into a microcontroller in this way. The ring oscillator generates a high-frequency clock signal, which drives an inverter stage (logical NOT gate). The charge can then be shoveled down via the two capacitors in such a way that the capacitor provides a negative voltage at the output. For more information, see Wikipedia under charge pump and “Inside the 8087's substrate bias circuit”.

2.9.6 H-Bridge

In many applications, current and voltage must be controlled independently of each other. This is the case, for example, with a motor (= ohmic-inductive load). There, the current is essentially proportional to the torque and the voltage to the speed. If voltage and current are to be output bipolar (or in the application: Torque and speed are to be controlled in both directions), a four-quadrant controller made of transistors is suitable. In modern integrated circuits, these are made of MOSFETs, directly equipped with the MOSFET driver, and several four-quadrant controllers can be found next to each other (e.g. the stepper motor driver DRV8835). Details can be found on Wikipedia under four-quadrant actuators.

2.9.7 MOSFET as Substitution for Diodes

Diodes always show a voltage drop given by the forward voltage. To circumvent this issue a MOSFET can be used.
The following example shows one way to cope with it, when two voltage sources should be combined (e.g. a rechargeable battery with $U_1$ and a nonrechargable buffer battery with $U_2$):

Often the rightside one can be simplified and the disadvantages can be avoided by using integrated circuits (like LTC4417)

2.9.8 Other MOSFET Applications

MOSFETs are not only used for pure switching of currents. Further applications are also:

  1. as a display element in TFT screens (TFT ... Thin Film Transistor).
  2. as memory element e.g. in SD cards Floating Gate Transistor, or also new approaches, like Ferroelectric_Random_Access_Memory)
  3. as an integrated “upstream” element for power bipolar junction transistors, especially in the Bipolar_transistor_with_insulated_gate_electrode (IGBT)
  4. as a chemical sensor for various materials (see Chemical_sensitive_field_effect_transistor)
  5. as a link between photonics/optoelectronics and classical electronics

Exercises

Exercise 2.8.1 Current/Voltage/Power limitations

Imagine you work at the company “mechatronics and robotics” and you try to build an IoT device for vehicles.
This device shall use the power of the $12 ~\rm V$-battery of the vehicle to send regular information over Wifi. The Wifi IC needs $3.3 ~\rm V$ supply voltage and drains up to $800 ~\rm mA$ when sending signals.

To get the supply voltage a linear regulator shall be used. In detail, you want to use the LM317 regulator. A linear regulator acts as a regulated shunt resistor, which regulates its voltage drop to have a fixed output value. The output value can be regulated with a voltage divider.

  1. Investigate the LM317 datasheet in order to find out, whether the LM317 is suitable for the operating conditions:
    1. input voltage $V_{\rm I,max}=14 ~\rm V$,
    2. output voltage $V_{\rm O} =3.3 ~\rm V$ and
    3. output current $I_{\rm O} =0.8 ~\rm A$.
  2. When the linear regulator acts as a shunt resistor, how can the power loss $P_{\rm loss}$ be calculated?
  3. With the power loss $P_{\rm loss}$ the temperature of the IC will rise. The power loss takes place within the junction. This creates a temperature drop $T_{\rm Jx}$ between the junction and surrounding. The IC will get soldered onto a PCB, and therefore the temperature drop $T_{\rm JB}$ between junction and board is most important. These temperature drop can be calculated by: $\Delta T_{\rm JB}= T_{\rm J} - T_{\rm B} =R_{\theta \rm JB}\cdot P_{\rm loss}$, where $R_{\theta \rm JB}$ is the junction-to-board thermal resistance.
    1. Search for the thermal information of the LM317 in the datasheet and calculate the maximum temperatures of the junction $T_{\rm J}$, when the temperature of the board $T_{\rm B}$ is $30 ~\rm °C$.
    2. Which package of the IC can be used, when the operating virtual junction temperature $T_\rm J$ in the recommended operating conditions shall not be exceeded?

Exercise 2.10.1 beta factor on BJT

  1. A bipolar junction transistor shows with a load the collector current $I_\rm C = 398 ~\rm mA$ and the base current $I_\rm B= 2 ~\rm mA$. What is the value of the current gain $\beta$?
  2. A quite common BJT is the BC847, which can be bought from multiple suppliers. Given the datasheet from BC847 - Nexperia, what is the needed base current $I_\rm B$, when a collector current of $I_\rm C=2 ~\rm mA$ shall be driven? Calculate $I_\rm B$ for all 3 groups of BC847 transistors in the datasheet.

Exercise 2.10.2 Voltage calculation

Given is the circuit shown in the simulation below.

  1. For the first situation the base current is given with $I_ \rm B=50 ~\rm µA$, and the current gain $\beta=150$.
    Calculate the voltage drop $U_\rm L$ on the load $R_\rm L$ and $U_{\rm CE}$.
  2. For the second situation, the base current of $I_\rm B=250 ~\rm µA$ is needed.
    1. In order to do so: calculate first $U_{\rm BE}$ of the first situation. $U_{\rm BE}$ is assumed to be constant.
    2. Calculate the correct value of $R$.
    3. Run the simulation and set $R$ to the calculated value. Try to measure $\beta$. Why is it not $150$ anymore?

Exercise 2.10.3 Low Side Switch and High Side Switch

Given is the circuit shown in the simulation below. The transistor is called either a “High Side Switch” or a “Low Side Switch”, depending on the voltage which is directly connected to it. In the depicted circuits each transistor drives a load resistor of $10 ~\Omega$. The input to the base/gate is a logic signal with $0 ~\rm V$ and $5 ~\rm V$ as a voltage level.

  1. Explain the advantages of the MOSFET compared to the BJT based on this application.
  2. Change the voltage $VCC$ from $5 ~\rm V$ to $15 ~\rm V$, with the switch on the lower left corner. Are the transistors still able to switch in all configurations?
  3. How can the problem be solved? Try to combine the BJT low-side switch as a driver with the FET high-side switch.

Exercise 2.10.4 Simple Temperature Detector

Given is the circuit shown in the simulation below. $R_2$ is an NTC resistor, which is used to detect the rise over a threshold temperature.

  1. At first, the series resistor in front of the LED has to be calculated. For this, the voltage drop $U_{\rm CE}$ of the BJT can be neglected. The given LED lights are bright for about $10 ~\rm mA$ (lighting starts for about $1 ~\rm mA$). The supply voltage is $U_\rm S=5.0 ~\rm V$ and the forward voltage of the LED is $U_{\rm LED}=1.7 ~\rm V$.
    1. What is the ideal value of $R_ \rm D$?
    2. The value in the simulation is not correct. Which effect does this have?
  2. At second, the system shall be designed for a temperature threshold of $T_0=50 ~\rm °C$.
    1. The $R(T)$-characteristic the NTC $R_2$ is shown in the diagram below. What is the value of $R_2(T_0)$?
    2. The BJT is conducting for $U_{\rm BC}=0.6 ~\rm V$. What is the correct value for $R_1$?

electrical_engineering_and_electronics_2:diagramtemperaturesensor.svg

Learning questions

for self-study

with answers

Looking at the picture above, which of the following statement(s) is/are correct?
Which statement(s) about bipolar junction transistors is/are correct?
Which statement(s) about MOSFETs is/are correct?
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Further reading