Convert AC to DC

Author Information

Name: Mohammad Hosein Assarnia
Affiliation: Department of Computer Engineering, Ferdowsi University of Mashhad
Contact: m.hosein.assarnia@gmail.com”

Chapter 1: Introduction

Definition and Importance of AC to DC Converters

AC to DC converters, also known as rectifiers, are electronic devices that convert alternating current (AC) into direct current (DC). This conversion is crucial in many electrical and electronic systems since most modern devices, such as computers, smartphones, and industrial equipment, operate on DC power. The significance of AC to DC converters extends beyond small consumer electronics to large-scale applications, including renewable energy systems, power supplies, electric vehicles, and telecommunication infrastructures.

Various Applications in Industry and Daily Life

The demand for AC to DC conversion spans across multiple fields:

3825524.jpg

Structure of the Research

Chapter 2: Fundamental Principles of AC and DC Power

Chapter 3: Power Supply Architectures and Components

Chapter 4: Rectifier Circuits and Analysis

Chapter 5: Regulation Techniques and Advanced Topologies

Chapter 6: explores the design and simulation of AC to DC converters

Chapter 7: Industrial Applications and Technological Advancements in AC to DC Converters

Chapter 8: Investigation of Challenges and Issues in AC to DC Conversion

Conclusion

Refrences

Chapter 2: Fundamental Concepts of AC and DC Power

Understanding the fundamental concepts of alternating current (AC) and direct current (DC) power is essential for analyzing and designing electrical and electronic systems. This chapter explores the physical and mathematical principles behind AC and DC power, forming a scientific foundation for the study of AC to DC converters.

Definition of Electrical Power

Electrical power is the rate at which energy is transferred over time, and it is measured in watts (W). The general formula for power is:

\(P=V×I\) thet :

$P$ : Electrical power (watts)

$V$ : Voltage (volts)

$I$ : Current (amperes)

Direct Current (DC)

In DC systems, the voltage and current remain constant over time. DC power is typically supplied by sources such as batteries and DC power supplies. A key characteristic of DC is that it delivers energy in a continuous and unidirectional flow.

Characteristics of alternating current

The typical waveform for an alternating current is a sine wave, when working with an AC power supply there are several indicators that must be taken into account:

AC.png

Advantages and disadvantages of DC power supply

Direct current, in which electricity always flows in a constant direction, has the following merits and demerits:

from PySpice.Spice.Netlist import Circuit
from PySpice.Unit import *
import matplotlib.pyplot as plt
import numpy as np

# Create a new circuit
circuit = Circuit('DC Signal')

# Define a DC voltage source
circuit.V(1, 'n1', circuit.gnd, 5@u_V)  # DC voltage of 5V

# Simulate the circuit
simulator = circuit.simulator(temperature=25, nominal_temperature=25)
analysis = simulator.operating_point()

# Extract the voltage value
voltage = float(analysis['n1'])

# Time array for plotting (0 to 10 seconds)
time = np.linspace(0, 10, 1000)
# Create an array with the DC voltage value
dc_voltage = np.full_like(time, voltage)

# Plot the DC signal
plt.figure(figsize=(10, 5))
plt.plot(time, dc_voltage, label='DC Voltage', color='blue')

# Adding labels and title
plt.title('DC Signal')
plt.xlabel('Time [s]')
plt.ylabel('Voltage [V]')
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.legend()
plt.grid(True)

# Display the plot
plt.show()

Advantages and disadvantages AC power supply

Alternating current, with its cyclic positive and negative voltage, has the following advantages and disadvantages:

import matplotlib.pyplot as plt
import numpy as np

# Time variable (0 to 2π for full cycle representation)
t = np.linspace(0, 2 * np.pi, 1000)

# Three-phase waveforms with 120-degree phase shift
V1 = np.sin(t)                       # Phase A
V2 = np.sin(t - 2 * np.pi / 3)       # Phase B (120-degree shift)
V3 = np.sin(t - 4 * np.pi / 3)       # Phase C (240-degree shift)

# Plot the waveforms
plt.figure(figsize=(10, 5))
plt.plot(t, V1, label='Phase A', color='red')
plt.plot(t, V2, label='Phase B', color='blue')
plt.plot(t, V3, label='Phase C', color='orange')

# Adding labels and title
plt.title('Three-phase AC')
plt.xlabel('Time [s]')
plt.ylabel('Voltage [V]')
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.legend()
plt.grid(True)

# Display the plot
plt.show()

Active and reactive power in AC sources

power.png

Chapter 3: Power Supply Architectures and Components

Linear vs. Switching AC/DC Power Supply

Linear AC/DC Power Supply:

A linear AC/DC power supply has a simple design. The components of a linear AC/DC power supply are transformers, rectifier and filter. By using a transformer, the alternating current (AC) input voltage is reduced to a value more suitable for the intended application. Then, the reduced AC voltage is rectified (A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction.) and turned into a direct current (DC) voltage, which is filtered in order to further improve the waveform quality. The process inside a linear DC power supply is described as below:

process.png

A huge limitation in a linear AC/DC power supply is the size of the transformer. Because the input voltage is transformed at the input, the necessary transformer would have to be very large and therefore very heavy.

Drawing a linear AC/DC power supply using schemdraw

The code below shows a simple linear power supply:

import matplotlib.pyplot as plt
import schemdraw
import schemdraw.elements as elm
from schemdraw import dsp

with schemdraw.Drawing() as d:
    d.push()
    elm.Line()
    tr = elm.Transformer().right().label('Transformer', loc='bot').anchor('p1')
    elm.Line().length(d.unit/3).at(tr.s1)
    elm.Line().length(d.unit/2).up()
    elm.Line().right()
    rec = elm.Rectifier().anchor('N').label('Rectifier')
    d.pop()
    elm.Gap().toy(tr.p2).label(['', 'AC IN', ''])
    elm.Line().tox(tr.p1)
    elm.Line().length(d.unit/3).at(tr.s2)
    elm.Line().length(d.unit/2).down()
    elm.Line().right()
    elm.Line().toy(rec.S)
    elm.Line().length(d.unit/8).at(rec.W).left()
    lineRec = elm.Line().length(d.unit*1.3).down()
    lineOne = elm.Line().at(rec.E).right().idot()
    line = elm.Line().idot()
    lineTwo = elm.Line().length(d.unit/3).idot()
    lineThree = dsp.Square().label('Regulator')
    lineFour = elm.Line().length(d.unit/3)
    lineFive = elm.Line().length(d.unit/2).idot()
    elm.Gap().toy(lineRec.end).label(['+', 'DC OUT', '–'])
    lineFiveEnd = elm.Line().length(d.unit/2).left().dot()
    lineThreeEnd = elm.Line().tox(lineThree.S).dot()
    lineTwoEnd = elm.Line().tox(lineTwo.start).dot()
    lineEnd = elm.Line().tox(line.start).dot()
    lineOneEnd = elm.Line().tox(lineOne.start)
    elm.Line().tox(lineRec.end)
    elm.Capacitor().endpoints(lineOne.end,lineOneEnd.start).label('Filter')
    elm.Capacitor().endpoints(lineTwo.start,lineEnd.start).label('C1')
    elm.Line().endpoints(lineTwoEnd.start,lineThree.S)
    elm.Capacitor().endpoints(lineFive.start,lineFiveEnd.end).label('C2')
plt.show()

Switching AC/DC Power Supply:

New design methodology has been developed to solve many of the problems associated with linear or traditional AC/DC power supply design, including transformer size and voltage regulation. Switching power supplies are now possible thanks to the evolution of semiconductor technology, especially thanks to the creation of high-power MOSFET transistors, which can switch on and off very quickly and efficiently, even if large voltages and currents are present. A switching AC/DC power supply enables the creation of more efficient power converters, which no longer dissipate the excess power.

In switching AC power supplies, the input voltage is no longer reduced; rather, it is rectified and filtered at the input. Then the DC voltage goes through a chopper, which converts the voltage into a high-frequency pulse train. Finally, the wave goes through another rectifier and filter, which converts it back to direct current (DC) and eliminates any remaining alternating current (AC) component that may be present before reaching the output. The process is shown as below:

Although there are many different switching circuits. But the most common one used is PWM (Pulse Width Modulation). The figure is a basic block diagram of the PWM switching regulator. It maintains the voltage level in a closed-loop form:

switches.png

Smaller transformers and increased voltage regulator efficiency in switching AC/DC power supplies are the reason why we can now convert a 220V¬RMS AC voltage to a 5V DC voltage with a power converter that can fit in the palm of your hand.

main components used in rectifier circuits

1. Transformer

Function: Steps up or steps down the AC voltage to match the needs of the circuit

Working Principle:

Uses electromagnetic induction to change voltage without altering the frequency

Often includes a center tap in full-wave rectifiers to allow more efficient conversion

Benefits: Electrical isolation from the power source

Voltage adaptation for safety and compatibility

<img src="/assets/circuiteffort/ACTODC/photo_2025-05-01_20-19-22.jpg" alt="photo_2025-05-01_20-19-22.jpg"style="width: 50%; height: 50%; object-fit: contain;">
<img src="/assets/circuiteffort/ACTODC/1.jpg" alt="1.jpg"style="width: 50%; height: 50%; object-fit: contain;">

2. Rectifier Circuit

Function:

Converts AC voltage to pulsating DC voltage

Common Components:

Diodes for uncontrolled rectification

SCRs (Thyristors) or other controlled switches for adjustable output

Typical Types:

Half-Wave Rectifier: Uses only one half-cycle of AC; simple but inefficient

Full-Wave Rectifier (Center Tap or Bridge): Uses both half-cycles for higher efficiency and lower ripple

Notes:

A diode bridge uses four diodes

In controlled rectifiers, firing angle can be adjusted to regulate output voltage

<img src="/assets/circuiteffort/ACTODC/images.png" alt="images.png"style="width: 50%; height: 50%; object-fit: contain;">
<img src="/assets/circuiteffort/ACTODC/2.jpg" alt="2.jpg"style="width: 50%; height: 50%; object-fit: contain;">

3. Filter (Capacitor / Inductor)

Function: Smooths out fluctuations (ripple) in the rectified DC signal

Main Filtering Components:

Capacitor: Role: Stores and releases charge to fill voltage gaps

Effect: Significantly reduces voltage ripple

Placement: Connected in parallel with the load

Inductor: Role: Resists rapid changes in current

Effect: Smooths the DC current flow

Placement: Typically in series with the load or part of LC/π filters

Combo: Using both capacitor and inductor in LC or π-filter configurations results in better DC quality

capacitor-filter.png
<img src="/assets/circuiteffort/ACTODC/3.jpg" alt="3.jpg"style="width: 50%; height: 50%; object-fit: contain;">

4. Voltage Regulator

Role:

Stabilizes the output DC voltage to protect the load and reduce residual fluctuations.

Application: After filtering, the voltage may still fluctuate slightly or be slightly higher than required. Regulators (such as 7805 for 5V, 7812 for 12V, etc.) are responsible for keeping the DC output at a certain and stable value. In more complex systems, switching regulators are also used.

<img src="/assets/circuiteffort/ACTODC/regulator-ic-500x500.webp" alt="regulator-ic-500x500.webp"style="width: 50%; height: 50%; object-fit: contain;">
<img src="/assets/circuiteffort/ACTODC/4.jpg" alt="4.jpg"style="width: 50%; height: 50%; object-fit: contain;">

Single-Phase vs. Three-Phase Power Supplie

An alternating current (AC) power supply can either be single-phase or three-phase:

Y and Delta Three-phase configurations

There are two configurations for the transmission of power through a three-phase power supply: delta (Δ) and wye (Y) configurations, also referred to as triangle and star configurations, respectively. The main difference between these two configurations is the ability to add a neutral wire. Delta connections offer greater reliability, but Y connections can supply two different voltages: phase voltage, which is the single-phase voltage supplied to homes, and line voltage, for powering larger loads. The Delta configuration has the 3 phases connected like in a triangle. They don’t normally have a neutral cable. In Delta configuration, the phase voltage is equal to the line voltage whereas in Y configuration, the phase voltage is the line voltage divided by root 3. Wye configurations are typically used for systems where a neutral is required, such as in distribution networks for residential or commercial buildings, because they allow for both 120V and 240V outputs; Delta configurations are often used in industrial settings where high power is required, and a neutral is not necessary, such as in motors and heavy machinery.

The image below shows how a Y and Delta configurations wires are attached:

<img src="/assets/circuiteffort/ACTODC/delta.png" alt="delta.png"style="width: 50%; height: 50%; object-fit: contain;">

As mentioned before, three-phase power is not only used for transportation, but is also used to power large loads, such as electric motors or charging large batteries. This is because the parallel application of power in three-phase systems can transfer much more energy to a load, and can do so more evenly, due to the overlapping of the three phases. For example, when charging an electric vehicle (EV), the amount of power you can transfer to the battery determines how fast it charges. Single-phase chargers are plugged into the alternating current (AC) mains and converted to direct current (DC) by the car’s internal AC/DC power converter (also called an on-board charger). These chargers, are limited in power by the grid and the AC socket.

The image below shows the power transfered in Single-Phase and Three-Phase systems:

<img src="/assets/circuiteffort/ACTODC/phase.png" alt="phase.png"style="width: 50%; height: 50%; object-fit: contain;">

Y and Delta configurations example using PySpice:

This examples shows the computation of the voltage for the Y and Delta configurations. Lets use an 220 V / 50 Hz electric network. The phase voltages in Y configuration are dephased of $\frac{2\pi}{3}$ :

\(V_{L1-N} = V_{pp} cos(𝜔t)\) \(V_{L2-N} = V_{pp} cos(𝜔t-\frac{2\pi}{3})\) \(V_{L3-N} = V_{pp} cos(𝜔t-\frac{4\pi}{3})\)

We rewrite them in complex notation: \(V_{L1-N} = V_{pp} e^{jwt}\) \(V_{L2-N} = V_{pp} e^{j(wt-\frac{2\pi}{3})}\) \(V_{L3-N} = V_{pp} e^{j(wt-\frac{4\pi}{3})}\)

From these expressions, we compute the voltage in delta configuration using trigonometric identities :

\(V_{L1-L2} = V_{L1} \sqrt{3}\ e^{j\frac{\pi}{6}}\) \(V_{L2-L3} = V_{L2} \sqrt{3}\ e^{j\frac{\pi}{6}}\) \(V_{L3-L1} = V_{L3} \sqrt{3}\ e^{j\frac{\pi}{6}}\)

In comparison to the Y configuration, the voltages in delta configuration are magnified by a factor $/sqrt{3}$ and dephased of $\frac{\pi}{6}$ .

Finally we rewrite them in temporal notation:

\(V_{L1-L2} = V_{pp} \sqrt{3} cos(𝜔t+\frac{\pi}{6})\) \(V_{L2-L3} = V_{pp} \sqrt{3} cos(𝜔t-\frac{\pi}{2})\) \(V_{L3-L1} = V_{pp} \sqrt{3} cos(𝜔t-\frac{7\pi}{6})\)

Now we plot the waveforms:

import math
import numpy as np
import matplotlib.pyplot as plt
from PySpice.Unit import *

frequency = 50@u_Hz
w = frequency.pulsation
period = frequency.period
rms_mono = 220
amplitude_mono = rms_mono * math.sqrt(2)

t = np.linspace(0, 3*float(period), 1000)

##Y configuration
L1 = amplitude_mono * np.cos(t*w) ##phase one
L2 = amplitude_mono * np.cos(t*w - 2*math.pi/3) ##phase two
L3 = amplitude_mono * np.cos(t*w - 4*math.pi/3) ##phase three

rms_tri = math.sqrt(3) * rms_mono
amplitude_tri = rms_tri * math.sqrt(2)

##Delta configuration
L12 = amplitude_tri * np.cos(t*w + math.pi/6)
L23 = amplitude_tri * np.cos(t*w - math.pi/2)
L31 = amplitude_tri * np.cos(t*w - 7*math.pi/6)

figure, ax = plt.subplots(figsize=(20, 10))
ax.plot(
    t, L1, t, L2, t, L3,
    t, L12, t, L23, t, L31,
    # t, L1-L2, t, L2-L3, t, L3-L1,
)
ax.grid()
ax.set_title('Three-phase electric power: Y and Delta configurations (220V Mono/400V Tri 50Hz Iran)')
ax.legend(
    ('L1-N', 'L2-N', 'L3-N',
     'L1-L2', 'L2-L3', 'L3-L1'),
    loc=(.7,.5),
)
ax.set_xlabel('t [s]')
ax.set_ylabel('[V]')
ax.axhline(y=rms_mono, color='blue')
ax.axhline(y=-rms_mono, color='blue')
ax.axhline(y=rms_tri, color='blue')
ax.axhline(y=-rms_tri, color='blue')

plt.show()

Chapter 4: Rectifier Circuits and Analysis

Half-Wave Rectifier

A half-wave rectifier converts AC to DC by blocking one half of the waveform, using a single diode, and is less efficient than a full-wave rectifier. A full-wave rectifier, such as the full bridge rectifier with four diodes, converts the entire waveform to DC, providing a smoother output.

Power Diode Rectifier

Power diodes can be used individually as below or connected together to produce a variety of rectifier circuits

<img src="/assets/circuiteffort/ACTODC/HWR_WaveForm.png" alt="HWR_WaveForm.png"style="width: 50%; height: 50%; object-fit: contain;">

In many applications, we reduce the peak voltage using a transformer before applying it to a half-wave rectifier.

<img src="/assets/circuiteffort/ACTODC/HWR_Transformer1.PNG" alt="HWR_Transformer1.PNG"style="width: 50%; height: 50%; object-fit: contain;">

During the positive half-cycle of the AC sine wave, the forward-biased diode allows current to flow, making the output voltage equal to the supply voltage minus the diode’s forward voltage. In the negative half-cycle, the reverse-biased diode blocks current, resulting in an output voltage of zero.

The DC side of the circuit is unidirectional, with the load resistor receiving an irregular voltage waveform comprising positive and zero volts. This voltage is equivalent to $ 0.318 * V_\text{max} $ or $ 0.45 * V_\text{rms} $ of the input sinusoidal waveform.

DC output value calculation

\[V_{\text{avg}} = \frac{1}{T} \int_{0}^{T} v(t) \, dt\]

For a half-wave rectified sinusoidal waveform, we need to consider the average over one period, but since the waveform is rectified, it’s zero for half the period. Thus, we compute the average over the non-zero half-cycle and then use the formula for the full period.

The waveform $ v(t) = V_{\text{max}} \sin(\omega t) $ for $0 \leq t < T/2$ and zero for $ T/2 \leq t < T $.

The average value over the period is:

\[V_{\text{avg}} = \frac{1}{T} \int_{0}^{T} v(t) \, dt\]

Since $ v(t) = V_{\text{max}} \sin(\omega t) $ from $0$ to $T/2$ and $0$ from $T/2$ to $T$:

\[V_{\text{avg}} = \frac{1}{T} \left( \int_{0}^{T/2} V_{\text{max}} \sin(\omega t) \, dt \right)\]

Compute the integral:

\[\int_{0}^{T/2} V_{\text{max}} \sin(\omega t) \, dt = \frac{V_{\text{max}}}{\omega} \left[ -\cos(\omega t) \right]_{0}^{T/2}\]

Substituting the limits:

\[\frac{V_{\text{max}}}{\omega} \left[ -\cos\left(\frac{\omega T}{2}\right) + \cos(0) \right]\]

Since $\cos\left(\frac{\omega T}{2}\right) = \cos(\pi) = -1$ and $\cos(0) = 1$:

\[\frac{V_{\text{max}}}{\omega} \left[ -(-1) + 1 \right] = \frac{V_{\text{max}}}{\omega} \cdot 2\]

Therefore:

\[\frac{1}{T} \cdot \frac{V_{\text{max}} \cdot 2}{\omega}\]

Since $\omega = \frac{2\pi}{T}$:

\[\frac{1}{T} \cdot \frac{2 V_{\text{max}} T}{2 \pi} = \frac{2 V_{\text{max}}}{2 \pi} = \frac{V_{\text{max}}}{\pi}\]

So, the correct average value $ V_{\text{avg}} $ is:

\[V_{\text{DC}} =V_{\text{avg}} = \frac{V_{\text{max}}}{\pi}=0.318V_{\text{max}}\]

also we write $ V_{\text{rms}} $ in terms of $ V_{\text{max}} $:

\[V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}\]

Express $ V_{\text{max}} $ in terms of $ V_{\text{DC}} $:

Given $ V_{\text{DC}} = \frac{V_{\text{max}}}{\pi} $,

\[V_{\text{max}} = \pi \times V_{\text{DC}}\]

Substitute $ V_{\text{max}} $ into the $ V_{\text{rms}} $ formula:

\[V_{\text{rms}} = \frac{\pi \times V_{\text{DC}}}{\sqrt{2}}\]

Simplify the expression:

\[V_{\text{rms}} = \pi \times \frac{V_{\text{DC}}}{\sqrt{2}}\]

So,

\[V_{\text{DC}} \approx 0.45 \times V_{\text{rms}}\]

Reminder: To find $ V_{\text{rms}} $ of the input sinusoidal signal over one period, and then relate it to $ V_{\text{DC}} $, we should calculate the RMS value for the entire period of the input signal.

RMS value of the input sinusoidal signal:

The input sinusoidal signal $ v(t) = V_{\text{max}} \sin(\omega t) $ over one period $ T $ has the RMS value:

\[V_{\text{rms}} = \sqrt{\frac{1}{T} \int_0^T \left(V_{\text{max}} \sin(\omega t)\right)^2 \, dt}\] \[V_{\text{rms}} = V_{\text{max}} \sqrt{\frac{1}{T} \int_0^T \sin^2(\omega t) \, dt}\]

Using the identity $ \sin^2(x) = \frac{1 - \cos(2x)}{2} $:

\[\sin^2(\omega t) = \frac{1 - \cos(2\omega t)}{2}\]

Thus,

\[V_{\text{rms}} = V_{\text{max}} \sqrt{\frac{1}{T} \int_0^T \frac{1 - \cos(2\omega t)}{2} \, dt}\] \[V_{\text{rms}} = V_{\text{max}} \sqrt{\frac{1}{T} \cdot \frac{1}{2} \int_0^T (1 - \cos(2\omega t)) \, dt}\]

The integral of $ 1 $ over $ 0 $ to $ T $ is $ T $, and the integral of $ \cos(2\omega t) $ over one period $ T $ is zero:

\[\int_0^T 1 \, dt = T\] \[\int_0^T \cos(2\omega t) \, dt = 0\]

So,

\[V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}\]

Full-wave rectifier

Full Wave Rectifier

Power diodes can be connected to form a full wave rectifier, converting AC voltage into DC voltage for power supplies. This rectifier uses four diodes to convert both halves of each AC waveform cycle into a DC signal. While smoothing capacitors can reduce ripple for low-power applications, a full wave rectifier is more efficient for higher power needs, utilizing every half-cycle of the input voltage.

<img src="/assets/circuiteffort/ACTODC/BriedgePoleDiode_Rectfier.PNG" alt="BriedgePoleDiode_Rectfier.PNG"style="width: 50%; height: 50%; object-fit: contain;">

How its work

The Positive Half-cycle

<img src="/assets/circuiteffort/ACTODC/BridgePositiveHalfCycle.PNG" alt="BridgePositiveHalfCycle.PNG"style="width: 50%; height: 50%; object-fit: contain;">

The Negative Half-cycle

<img src="/assets/circuiteffort/ACTODC/NegativeBridge.PNG" alt="NegativeBridge.PNG"style="width: 50%; height: 50%; object-fit: contain;">

Advantages and Circuit Operation

A full wave rectifier produces a higher average DC output voltage with less ripple compared to a half wave rectifier, resulting in a smoother output waveform. Such as Half Wave Rectifier, can reach to:

Full Wave Rectifier

A full-wave rectifier converts the entire AC waveform into DC, providing a smoother and more efficient output compared to a half-wave rectifier. It utilizes four diodes to rectify both halves of the AC cycle, resulting in a higher average DC output with reduced ripple.

Power Diode Rectifier

Power diodes can be configured into various rectifier circuits. A common design is the full-wave rectifier, using a center-tapped transformer and two diodes to handle both half-cycles of the input waveform. This configuration doubles the frequency of the output signal, resulting in a smoother DC output.

DC Output Value Calculation

For a full-wave rectifier, the average DC output voltage $V_{\text{DC}}$ is given by:

\[V_{\text{DC}} = \frac{2 V_{\text{max}}}{\pi}\]

where $ V_{\text{max}} $ is the peak value of the AC signal. This result shows that the DC output voltage is higher and smoother compared to a half-wave rectifier.

The circuit uses two diodes and a center-tapped transformer, allowing each diode to conduct during opposite half-cycles. This configuration doubles the output frequency, making the full wave rectifier 100% efficient. The consistent current direction through the load resistor during both half-cycles ensures a continuous DC output.

<img src="/assets/circuiteffort/ACTODC/FullWaveTransformer.PNG" alt="FullWaveTransformer.PNG"style="width: 50%; height: 50%; object-fit: contain;">

Full Wave Rectifier with Smoothing Capacitor

Capacitors smooth the full-wave rectifier output, reducing peak-to-peak ripple for a more stable voltage.

Ripple Factor of a Half-Wave Rectifier

Ripple is the residual AC component in the output of a half-wave rectifier that causes the DC waveform to pulsate. The ripple factor $ \gamma $ quantifies this unwanted AC component and is obtained as:

\[\gamma = \frac{\text{RMS value of the AC component}}{\text{DC component value}} = \frac{V_{r(\text{rms})}}{V_{dc}}.\] \[\gamma = \sqrt{\frac{V_{rms}^2}{V_{dc}^2} - 1}.\]

Proof: Here, $ V_{r(\text{rms})} $ represents the RMS value of the AC component, and $ V_{dc} $ is the DC component of the output.

To determine $ V_{r(\text{rms})} $, we start by expressing the output voltage of the half-wave rectifier as:

\[V_o(t) = V_{ac} + V_{dc},\]

where $ V_{ac} $ is the AC component remaining after rectification. The RMS value of the AC component can be calculated using:

\[V_{r(\text{rms})} = \left( \frac{1}{T} \int_0^T V_{ac}^2 \, dt \right)^{1/2}.\]

We can also write $ V_{r(\text{rms})} $ as:

\[V_{r(\text{rms})}^2 = \frac{1}{T} \int_0^T (V_o - V_{dc})^2 \, dt.\]

Expanding the square and integrating, we get:

\[V_{r(\text{rms})}^2 = \frac{1}{T} \int_0^T (V_o^2 - 2V_o V_{dc} + V_{dc}^2) \, dt.\]

This simplifies to:

\[V_{r(\text{rms})}^2 = \frac{1}{T} \int_0^T V_o^2 \, dt - \frac{2V_{dc}}{T} \int_0^T V_o \, dt + V_{dc}^2.\]

Since $ \frac{1}{T} \int_0^T V_o \, dt = V_{dc} $, we have:

\[V_{r(\text{rms})}^2 = V_{rms}^2 - V_{dc}^2,\]

where $ V_{rms} $ is the RMS value of the entire voltage signal.

Therefore, the ripple factor $ \gamma $ can be written as:

\[\gamma = \sqrt{\frac{V_{rms}^2}{V_{dc}^2} - 1}.\]

For Half Wave Rectifier

Substituting the values for $ V_{dc} $ and $ V_{rms} $, we find:

\[\gamma = \sqrt{\frac{V_m^2 / 2 \cdot \pi}{V_m / \pi}^2 - 1} = \sqrt{\left(\frac{\pi}{2}\right)^2 - 1} \approx 1.21.\]

Ripple Factor of a Full-Wave Rectifier

The ripple factor ($ \gamma $) for a full-wave rectifier is defined as:

\[\gamma = \frac{V_{r(\text{rms})}}{V_{dc}} = \sqrt{\frac{V_{rms}^2}{V_{dc}^2} - 1},\]

where $ V_{r(\text{rms})} $ is the RMS value of the AC component, and $ V_{dc} $ is the DC component. For a full-wave rectifier, the ripple factor simplifies to:

\[\gamma = \sqrt{\left(\frac{\pi}{2\sqrt{2}}\right)^2 - 1} \approx 0.48.\]

Voltage multiplier

A voltage multiplier is an electrical circuit that converts AC electrical power from a lower voltage to a higher DC voltage, typically using a network of capacitors and diodes. Voltage multipliers can be used to generate a few volts for electronic appliances, to millions of volts.

Example $ V_o $ of four times the peak of the AC input voltage $ V_i $

<img src="/assets/circuiteffort/ACTODC/VoltageMultiplier_4Vmax_ACSignal.PNG" alt="VoltageMultiplier_4Vmax_ACSignal.PNG"style="width: 50%; height: 50%; object-fit: contain;">

Chapter 5: Regulation Techniques and Advanced Topologies

Regulators

After rectification, the DC output can be further stabilized using regulators, which are primarily of two types:

Linear regulator

A simple transistor regulator maintains a relatively constant output voltage (Uout) despite changes in input voltage (Uin) and load resistance (RL), provided Uin exceeds Uout sufficiently and the transistor’s power capacity isn’t exceeded. The stabilizer’s output voltage equals the Zener diode voltage minus the transistor’s base-emitter voltage (UZ − UBE), with UBE typically around 0.7 V for silicon transistors. If Uout drops due to external factors, UBE increases, activating the transistor further to boost the load voltage. Rv supplies bias current to both the Zener diode and transistor, with its value affecting input voltage requirements and regulator efficiency. Lower Rv values increase diode power dissipation and worsen regulator performance.

Linear Regulator Schematic

Regulator with a differential amplifier

The stability of the output voltage can be enhanced by using a differential amplifier, such as an operational amplifier. It adjusts the transistor current based on input voltage discrepancies, allowing for an adjustable output voltage via a voltage divider.

Linear Regulator with Differential Amplifier

LM-series integrated circuits

Example of linear regulator is LM317: Adjustable 1.5 A positive voltage regulator (1.25 V-37 V)

LM317 Linear Regulator

Protective Diode

Diode protector to limit the emitter–base voltage

Diode Protector for Emitter-Base Voltage

Diodes can be used to limit the input of OPAMP to 0.7V

Op-Amp Input Protection with Diodes

POLARITY INSURANCE

Polarity Insurance Circuit

Relay with Diode Circuit

A relay circuit consists of three key components: switches, a relay coil, and a diode. The switches ensure reliable electrical contact without bounce, while the relay coil controls the switching between open and closed states. The diode provides transient voltage suppression, protecting the switching circuitry from voltage spikes caused by the relay’s activation and deactivation.

Basic Relay with Diode Circuit

Chapter 6: explores the design and simulation of AC to DC converters

import matplotlib.pyplot as plt
import schemdraw
import schemdraw.elements as elm
from schemdraw import dsp

with schemdraw.Drawing() as d:
    d.push()
    elm.Line()
    tr = elm.Transformer().right().label('Transformer', loc='bot').anchor('p1')
    elm.Line().length(d.unit/3).at(tr.s1)
    elm.Line().length(d.unit/2).up()
    elm.Line().right()
    rec = elm.Rectifier().anchor('N').label('Rectifier')
    d.pop()
    elm.Gap().toy(tr.p2).label(['', 'AC IN', ''])
    elm.Line().tox(tr.p1)
    elm.Line().length(d.unit/3).at(tr.s2)
    elm.Line().length(d.unit/2).down()
    elm.Line().right()
    elm.Line().toy(rec.S)
    elm.Line().length(d.unit/8).at(rec.W).left()
    lineRec = elm.Line().length(d.unit*1.3).down()
    lineOne = elm.Line().at(rec.E).right().idot()
    line = elm.Line().idot()
    lineTwo = elm.Line().length(d.unit/3)
    lineThree = dsp.Square().label('Regulator')
    lineFour = elm.Line().length(d.unit/3)
    lineFive = elm.Line().length(d.unit/2)
    elm.Gap().toy(lineRec.end).label(['+', 'DC OUT', '–'])
    lineFiveEnd = elm.Line().length(d.unit/2).left()
    lineThreeEnd = elm.Line().tox(lineThree.S)
    lineTwoEnd = elm.Line().tox(lineTwo.start)
    lineEnd = elm.Line().tox(line.start).dot()
    lineOneEnd = elm.Line().tox(lineOne.start)
    elm.Line().tox(lineRec.end)
    elm.Capacitor().endpoints(lineOne.end,lineOneEnd.start).label('Filter')
    
    elm.Line().endpoints(lineTwoEnd.start,lineThree.S)
    


    
plt.show()
Basic Relay with Diode Circuit

Chapter 7: Industrial Applications and Technological Advancements in AC to DC Converters

AC to DC converters are not only fundamental in small electronic circuits but also play a vital role in many industrial systems. Their ability to convert alternating current (AC) to direct current (DC) makes them essential in power systems, manufacturing processes, and modern technologies.

Industrial Applications

Consumer Electronics and Telecommunications: Nearly all modern electronic devices – from computers to smartphones – require DC voltage, which is supplied through AC/DC power converters.

Automotive Industry: Electric and hybrid vehicles use AC to DC converters for charging batteries and powering internal electronic systems.

Control Systems and Automation: In industrial automation, devices like PLCs, sensors, and motor drives operate on DC power. Converters provide stable voltage for these control systems.

Industrial Power Supplies: Switch-mode power supplies (SMPS) in industrial applications rely on efficient AC to DC conversion for high-performance and energy-saving operations.

Technological Advancements

Recent technological developments have significantly improved the performance of AC to DC converters:

Advanced Semiconductor Materials (SiC, GaN) : These materials are used to build faster and more efficient power devices with lower losses.

High-Efficiency and Compact Designs : Modern converters are designed to be smaller, lighter, and more efficient, using advanced topologies and control methods.

Digital Control and Smart Features : Integration of microcontrollers and digital signal processing allows for smarter and more precise regulation of output voltage and current.

Chapter 8: Investigation of Challenges and Issues in AC to DC Conversion

While AC to DC converters are essential in various applications, their design and operation face several challenges. These issues range from technical and design-related problems to efficiency concerns and safety risks.

Technical Challenges

Ripple Voltage:

Even after rectification, the output DC voltage is not completely smooth. Ripple can cause instability or malfunction in sensitive electronic circuits.

Voltage Drop in Diodes:

Every diode has a forward voltage drop (typically ~0.7V for silicon diodes), which reduces the overall efficiency, especially in low-voltage applications.

Heat Loss:

Power components such as regulators and diodes produce heat, and without proper thermal management, performance may degrade or components may fail.

Design and Economic Challenges

Size and Weight at High Power Levels:

High-power converters require large components like transformers or capacitors, increasing the size and weight of the system.

Cost of Advanced Components:

While using modern semiconductors like GaN or SiC improves performance, it significantly raises the design and production costs.

Complex Control Requirements:

Smart or digital AC/DC converters often require precise control algorithms and microcontrollers, making the system more complex to design and maintain.

Conclusion

The conversion of alternating current to direct current represents a cornerstone of modern electrical engineering, enabling the operation of countless electronic devices and industrial systems. This research has systematically examined the fundamental principles, operational mechanisms, and practical applications of AC to DC power conversion.

The comprehensive analysis revealed distinct advantages and disadvantages of both AC and DC power supplies, highlighting their complementary roles in electrical systems. The investigation of linear versus switching conversion methods demonstrated the superior practicality of switching techniques, particularly in terms of transformer size optimization and overall efficiency.

Furthermore, the exploration of three-phase power systems, including Y and Delta configurations, underscored their significant advantage in power transmission capacity compared to single-phase systems. The detailed examination of rectifier circuits, voltage regulation techniques, and component selection criteria provides valuable insights for practical implementation.

Looking forward, the field of AC to DC conversion continues to evolve with emerging technologies and innovative approaches. Future research directions should focus on developing advanced semiconductor materials, intelligent control algorithms, and integrated power management solutions to address ongoing challenges in efficiency, thermal management, and system miniaturization.

In essence, this research contributes to a deeper understanding of power conversion technologies and their critical role in bridging the gap between AC power distribution networks and DC-powered applications, ultimately supporting the advancement of more efficient and sustainable electrical systems.

Refrences:

https://www.sciencefacts.net/direct-current.html https://www.monolithicpower.com/en/learning/resources/ac-dc-power-supply-basics https://www.matsusada.com/column/dc_and_ac.html https://eshop.se.com/in/blog/post/difference-between-active-power-reactive-power-and-apparent-power.html https://en.wikipedia.org/wiki/Rectifier https://pyspice.fabrice-salvaire.fr/releases/v1.4/examples/electricity/three-phase.html https://www.build-electronic-circuits.com/linear-power-supply/ https://www.eleccircuit.com/what-switching-power-supply-how-does-it-work/ https://youtu.be/jsBn2r94BDA https://youtu.be/JXJaRPXPwjQ https://www.rohm.com/electronics-basics/ac-dc-converters/acdc_what1

*اصلاح فرمت عکس ها- فارسی -انگلیسی - ادرس دهی -فهم مطالب*\