# Devices and Power Electronic Circuits in PE Power Exam

Welcome to our PE preparation guide on Devices and Power Electronic Circuits in the PE Power exam. As you prepare for the NCEES® PE Power exam, developing a solid foundation of power electronic circuits is essential.

With the NCEES® exam guidelines and course roadmap in mind, we will walk you through the intricacies of diodes, transistors, thyristors, and inverters, providing a clear understanding of how these devices function in real-world engineering scenarios.

This study guide will delve into the fundamental concepts, working principles, and applications of power electronic components that play a crucial role in modern power systems. Let’s dive deep into the details.

## Introduction to Power Electronic Devices

To help you in smooth takeoff for mastering devices and power electronic circuits in the PE power exam, we will start with the basics involving some characteristics of the power electronics systems and their critical components. Let’s have a quick look at some vital concepts and components.

### Semiconductor Diodes

Diodes are semiconductor devices with two terminals that allow current to flow in only one direction. They are fundamental components in power electronics because they can rectify AC signals into DC, protect circuits from reverse voltage, and serve as switches in various applications.

#### How are Diodes Made?

The manufacturing of diodes involves several key steps:

**Crystal Growth**– The process begins with the growth of single-crystal ingots of semiconductor material, usually silicon (Si) or germanium (Ge). The crystal orientation determines the diode’s properties. The next step is the doping of P and N-type semiconductors that together create a diode (PN – Junction)**Doping**– To create p-type and n-type semiconductors, the ingots are doped with specific impurities. Doping introduces atoms with excess or fewer valence electrons than the semiconductor material, altering its electrical behavior.**P-type Semiconductor Formation**– Doping silicon with elements such as boron (B) creates a p-type semiconductor. Boron has three valence electrons, and when it replaces some silicon atoms in the crystal lattice, it forms “holes” in the structure. These holes act as positive charge carriers.**N-type Semiconductor Formation**– Doping silicon with elements like phosphorus (P) creates an n-type semiconductor. Phosphorus has five valence electrons, and when it substitutes some silicon atoms, it introduces excess electrons into the lattice, which act as negative charge carriers.**P-N Junction Formation**– By combining a p-type semiconductor with an n-type semiconductor, a p-n junction is formed. At the junction, the excess electrons from the n-side diffuse to the p-side, and the holes from the p-side diffuse to the n-side. This diffusion creates the depletion zone, which contains immobile charged ions.

#### Diode Operation – Forward and Reverse Bias

The behavior of a diode is determined by its biasing conditions:

**Forward Bias **– The diode becomes forward-biased when a positive voltage is applied to the anode (the p-side) and a negative voltage to the cathode (the n-side). This reduces the width of the depletion zone, lowering the barrier potential. As a result, current can flow effortlessly from the anode to the cathode, and the diode behaves like a closed switch, allowing current to pass through.

**Reverse Bias **– When a negative voltage is applied to the anode and a positive voltage to the cathode, the diode becomes reverse-biased. This widens the depletion zone, increasing the barrier potential. Under reverse bias, the diode acts like an open switch, and only a small leakage current (reverse saturation current) flows through it.

#### What is the Dynamic Resistance of a Diode?

The dynamic resistance of a diode refers to the incremental resistance exhibited by the diode when conducting in forward bias or blocking in reverse bias (contributing voltage drop to break the barrier, which is 0.7 V for a silicon diode).

It is a small-signal resistance representing the change in voltage concerning the change in current across the diode. In other words, it measures how the diode’s voltage changes for a given change in current. The dynamic resistance can be calculated using the formula:

**Dynamic Resistance (rd) = ΔV / ΔI**

Where ΔV is the change in voltage across the diode, and ΔI is the corresponding change in current flowing through the diode. This resistance is not a constant value but varies with the operating point of the diode and the diode’s characteristics. Generally, the dynamic resistance is lower at higher and lower currents due to the nonlinearity of the diode’s current-voltage relations.

#### Applications of Diodes in Power Electronics

The application of power electronics heavily relies on Diodes as they are extensively used in power electronic circuits. Some of the critical applications include:

**Rectification**– Diodes are used in rectifiers to convert AC voltage into DC voltage, allowing devices to operate on DC power from AC sources like the main power supply.**Voltage Regulation**– Zener diodes, operating in the reverse breakdown region, are used as voltage regulators to maintain a stable output voltage. (In the following sections, zener diodes are discussed comprehensively with their critical use cases in a simulation of power electronics systems).**Power Supply Protection**– Diodes are protection devices to prevent reverse voltage polarity from damaging sensitive components.**Logic Gates in Integrated Circuits (ICs)**– Diodes are crucial components in implementing logical functions using diode-resistor logic (DRL) or diode-transistor logic (DTL) techniques. For instance:**AND Gate**– An AND gate can be constructed using two diodes in series. When both inputs are high (1), both diodes conduct and the output becomes high (1). If either or both inputs are low (0), at least one diode will be off, and the output remains low (0).**OR Gate**– An OR gate can be created using two diodes in parallel. When any input is high (1), the corresponding diode conducts, and the output becomes high (1). Only when both inputs are low (0) will both diodes be off, and the output remains low (0).

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### Transistors

Transistors are semiconductor devices with three terminals: the emitter, the base, and the collector. They are essential components for the amplification and switching application of power electronics.

**PNP Transistor**– In a PNP transistor, the base is a p-type semiconductor sandwiched between two n-type regions (the emitter and the collector). The emitter-base junction is forward-biased, while the base-collector junction is reverse-biased.**NPN Transistor**– In an NPN transistor, the base is an n-type semiconductor sandwiched between two p-type regions (the emitter and the collector). The emitter-base junction is forward-biased, while the base-collector junction is reverse-biased.

#### Transistor Current Formulas

The operation of transistors can be described using the following current formulas:

**Emitter Current (Ie) = Base Current (Ib) + Collector Current (Ic):**

The emitter current is the sum of the base and collector current.

**Collector Current (Ic) ≈ Emitter Current (Ie)**

When a transistor is active, and β (beta) is high. The collector current is approximately equal to the emitter current for transistors operating in the active mode with a high current gain (β).

### Power Transistors

Power transistors are specially designed to handle higher power and current levels. They are used in applications that require high-power switching and amplification. Power transistors typically have larger dimensions and are equipped with heat sinks to dissipate excess heat effectively.

The following parameters of transistors highly impact the characteristics of the power electronics systems.

**Maximum Collector Current (Ic)**– The maximum current that a power transistor can handle without damage.**Maximum Collector-Emitter Voltage (Vce)**– The maximum voltage applied across the collector-emitter terminals.**Power Dissipation Rating**– The transistor’s maximum power (P=IV) that it can handle without overheating.

### Thyristors

Thyristors are a type of semiconductor device with four layers of alternating p-type and n-type materials. They have three terminals: anode, cathode, and gate. Thyristors are extensively used in power electronics for high-power applications, where they can control large amounts of current with a small gate current.

Thyristors are Instrumental in the following applications of power electronics.

**Phase-Controlled Rectifiers **– Thyristors are employed in phase-controlled rectifiers to control the output voltage in DC power supplies and motor drives.

**Motor Control **– Thyristors are used in motor drives to regulate the speed of motors in industrial applications.

**Voltage Regulation **– Thyristors are used in voltage regulators to maintain a constant output voltage in power supplies.

### Devices and Power Electronic Circuits in PE Power Exam – Sample Problems

#### Problem 1: Diode Dynamic Resistance

A silicon diode is forward-biased with a voltage of 0.7V applied across it. The diode has a forward current of 10mA. Calculate the dynamic resistance of the diode at this operating point.

The formula gives the dynamic resistance (rd) of a diode:

rd = ΔV / ΔI

Where ΔV is the change in voltage, and ΔI is the change in current.

In this case, the diode voltage changes from 0V (reverse bias) to 0.7V (forward bias), and the current changes from 0A to 10mA.

ΔV = 0.7V – 0V = 0.7V

ΔI = 10mA – 0A = 0.01A

Now, calculate the dynamic resistance:

rd = 0.7V / 0.01A = 70 ohms

#### Problem 2: Diode Power Dissipation

A diode is forward-biased with a voltage of 0.5V across it and passes a current of 20mA. Calculate the power dissipation in the diode.

The power dissipation (P) in the diode can be calculated using the formula:

P = V × I

V is the voltage across the diode, and I is the current flowing through it.

Given:

V = 0.5V

I = 20mA = 0.02A

Now, calculate the power dissipation:

P = 0.5V × 0.02A = 0.01W = 10mW

#### Problem 3: Diode Power Dissipation

A power resistor with a resistance of 10 ohms is connected to a voltage source of 12V. Calculate the power dissipation in the resistor.

The power dissipation in the resistor can be calculated using the formula:

P = V^2 / R

V is the voltage across the resistor, and R is the resistance.

Given:

V = 12V

R = 10 ohms

Now, calculate the power dissipation:

P = (12V)^2 / 10 ohms = 144W / 10 ohms = 14.4W

#### Problem 4: Maximum Current Handling of a Power Resistor

A power resistor has a power rating of 5W and a resistance of 20 ohms. What maximum current can this resistor handle without exceeding its power rating?

The maximum current (Imax) that the power resistor can handle without exceeding its power rating can be calculated using the formula:

Imax = √(Pmax / R)

Where Pmax is the power rating, and R is the resistance.

Given:

Pmax = 5W

R = 20 ohms

Now, calculate the maximum current:

Imax = √(5W / 20 ohms) = √(0.25A) ≈ 0.5A

Therefore, the maximum current this power resistor can handle is approximately 0.5A.

Note: When working with power resistors, it’s essential to ensure that the actual operating current is below the calculated maximum current to avoid exceeding the resistor’s power rating and causing damage to the component.

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## Control Techniques in Power Electronic Circuits

The control techniques we discussed above and used in the simulation of power electronics systems for the interconversion of AC and DC are crucial concerning devices and power electronic circuits in the PE Power Exam. Let’s have a quick look at these control techniques.

### Pulse Width Modulation (PWM) Control

Pulse Width Modulation (PWM) is a widely used control technique in power electronic circuits. It involves modulating the width of a square wave (also known as the carrier wave) to control the average voltage or current delivered to the load. PWM control allows precise regulation and efficient power conversion.

*Working*

In PWM control, a high-frequency carrier waveform is compared with a reference waveform (usually a sine wave for voltage control or a DC level for current control). The width of the carrier pulses is adjusted based on the comparison to achieve the desired output voltage or current.

*Mathematically*

The duty cycle (D) of the PWM waveform is defined as the ratio of the ON time (Ton) to the total period (T) of the carrier waveform.

Duty Cycle (D) = Ton / T

*Formulas*

**For Voltage Control:**

Average output voltage (Vout_avg) = Vdc * D,

Where Vdc is the DC voltage source, and D is the duty cycle.

**For Current Control:**

Average output current (Iout_avg) = Iin * D,

Where Iin is the input current, and D is the duty cycle.

*Sample Problem – PWM Voltage Control*

A PWM voltage control circuit is supplied by a 24V DC voltage (Vdc). The reference sine wave has a peak value of 10V. Calculate the average output voltage if the duty cycle is set to 40%.

We have

Vdc = 24V

Peak value of reference sine wave (Vref_peak) = 10V

Duty cycle (D) = 40%

Calculate the average output voltage (Vout_avg):

Vout_avg = Vdc * D

Vout_avg = 24V * 0.4

Vout_avg = 9.6V

### Voltage Control Techniques in Power Electronic Circuits

Voltage control techniques concerning devices and power electronic circuits in the PE Power exam focus on regulating the output voltage to a desired level. These techniques can be used in applications like DC-DC converters, inverters, and voltage regulators.

*Working*

Voltage control techniques involve comparing the output voltage with a reference voltage and adjusting the control signal to maintain the desired output voltage. Different control methods, such as feedback and feedforward, are used for voltage regulation.

*Mathematically*

In feedback control, the error between the reference voltage (Vref) and the measured output voltage (Vout) is used to generate a control signal. The control signal is then applied to the power electronic circuit to adjust the output voltage.

### Current Control Techniques in Power Electronic Circuits

Current control techniques concerning devices and power electronic circuits in the PE Power Exam focus on regulating the output current to a desired level. These techniques are essential in applications like motor drives, inverters, and current-limited power supplies.

*Working*

Current control techniques involve measuring and comparing the output current with a reference current. The control signal is then adjusted to maintain the desired output current level.

*Mathematical Aspect*

Similar to voltage control, current control can also use a PID controller for feedback control. The error between the reference and measured output currents is used to generate the control signal.

### Feedback Control Systems in Power Electronic Circuits

Feedback control systems in power electronic circuits play a vital role in achieving stable and precise voltage or current regulation. These systems use feedback signals to continuously adjust the control signals based on the difference between the desired and actual output.

*Working*

The output voltage or current is compared with a reference value in feedback control systems. The error signal is then fed into a controller (such as a PID controller) that generates the appropriate control signal to adjust the power electronic circuit’s operation.

*Mathematically*

The mathematical aspect of feedback control systems involves analyzing the system’s transfer function, stability, and frequency response. Control theory principles, Laplace transforms, and frequency domain analysis are applied to design and analyze these systems.

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### Conclusion

Understanding devices and power electronic circuits in the PE Power exam is paramount for power exam preparation. According to the NCEES® PE Power exam guidelines and course roadmap, a solid grasp of power electronic components, such as diodes, transistors, thyristors, and inverters, is vital for successfully tackling exam questions and practical scenarios.

For those looking to take their preparation to the next level, Study for FE provides a recognized platform offering comprehensive PE Power exam preparation courses. Explore Study for FE today to achieve your career aspirations and make a lasting impact in the world of power engineering.