Module 5 -- Power Converters

#Basic-Electrical-Engineering #Semester-1

Index

DC-DC Converters and Duty Ratio
Buck Converter -- Step Down DC
Boost Converter -- Step Up DC
Inverters and Sinusoidal PWM
The H-Bridge — How Switching Creates AC
Sinusoidal PWM — Making a Proper Sine Wave
Single-Phase vs Three-Phase Inverters
Practice Numericals

DC-DC Converters and Duty Ratio

Everything in Unit 5 is about converting electrical power from one form to another efficiently. Two conversion problems:

DC → DC at a different voltage level (buck/boost converters) DC → AC (inverters)

Notice — this is the power electronics answer to the same problem transformers solve, but for DC. Transformers can't work on DC (no changing flux), so we need a completely different approach. That approach is switching.

The Core Idea: Switching

Instead of wasting excess voltage as heat (like a resistor would), a switching converter rapidly turns a switch ON and OFF. By controlling how long the switch stays on vs off, you control how much energy gets through — and therefore the output voltage. This is far more efficient than resistive voltage division.

The key parameter controlling this is the duty ratio (D):

D = \frac{t_{o n}}{T} = \frac{t_{o n}}{t_{o n} + t_{o f f}}

where $T$ is the total switching period. D ranges from 0 to 1 (or 0% to 100%)

Think of it like a tap that opens and closes rapidly — the duty ratio is the fraction of time the tap is open. The longer it stays open per cycle, the more water (energy) gets through.

Buck Converter -- Step Down DC

Pasted image 20260311125947.png

https://www.youtube.com/watch?v=rfChSvb8FX0

Pasted image 20260311032206.png

Job: Take a higher DC voltage in, deliver a lower DC voltage out.

Key components: A switch (transistor), a diode, an inductor, and a capacitor.

How it works conceptually:

Switch ON → input voltage drives current through the inductor to the load. The inductor stores energy.
Switch OFF → inductor releases its stored energy to keep current flowing to the load (through the diode). Output capacitor smooths the voltage.

The inductor is the hero here — it resists sudden changes in current, so it acts as an energy buffer, smoothing out the choppy switching into a steady DC output.

Output voltage:

V_{o u t} = D \times V_{i n}

Since $D < 1$ , output is always less than input — hence "buck" (step down). If $D = 0.6$ and $V_{i n} = 12 V$ then $V_{o u t} = 7.2 V$ .

Boost Converter -- Step Up DC

Pasted image 20260311130002.png

https://www.youtube.com/watch?v=9QM55r5fnUk

Pasted image 20260311032549.png

Job: Take a lower DC voltage in, deliver a higher DC voltage out.

How it works conceptually:

Switch ON → current flows through the inductor, building up a magnetic field. The diode blocks current from reaching the output, so the capacitor supplies the load alone.
Switch OFF → the inductor's collapsing magnetic field generates a voltage in addition to the supply voltage. This combined voltage charges the capacitor and supplies the load — at a higher level than the input.

The inductor here acts like a spring — you compress it (store energy) when the switch is on, then it kicks back with extra force when released.

Output voltage:

V_{o u t} = \frac{V_{i n}}{1 - D}

Since $(1 - D) < 1$ , dividing by it gives a number larger than $V_{i n}$ -- hence "boost" (step up). If $D = 0.6$ and $V_{i n} = 5 V$ , then $V_{o u t} = \frac{5}{0.4} = 12.5 V$ .

Buck vs Boost — Side by Side

	Buck Converter	Boost Converter
Function	Step down DC	Step up DC
Output Voltage	$V_{o u t} = D \cdot V_{i n}$	$V_{o u t} = \frac{V_{i n}}{1 - D}$
D effect	Higher $D \to$ Higher $v_{o u t}$	Higher $D \to$ Higher $v_{o u t}$
Analogy	Tap controlling flow	Spring storing then releasing

Note both converters increase output voltage by increasing D — the difference is just the mechanism and the direction of conversion.

Inverters and Sinusoidal PWM

https://www.youtube.com/watch?v=lHWmh0Bc83g

The Problem Inverters Solve

Buck and boost converters deal with DC→DC. But what if you have DC (like a battery or solar panel) and need AC to power normal household or industrial equipment? That's what an inverter does — DC in, AC out.

The core challenge: how do you make AC from DC using switches? You can't just flip a switch once — you need a controlled, repeating pattern that mimics a sine wave.

The H-Bridge — How Switching Creates AC

Pasted image 20260311034142.png

The fundamental inverter circuit is an H-bridge — four switches arranged so that by turning specific pairs on and off, you can force current through the load in alternating directions.

Switches S1 and S4 ON → current flows left to right through load → positive half cycle
Switches S2 and S3 ON → current flows right to left through load → negative half cycle

Alternate these pairs at the desired AC frequency (say 50 Hz) and you get a square wave AC output. That's the basic idea — but a square wave isn't a sine wave. This is where PWM comes in.

Sinusoidal PWM — Making a Proper Sine Wave

Pasted image 20260311035303.png

PWM stands for Pulse Width Modulation. The idea is elegant:

Instead of switching at a fixed duty ratio, you vary the duty ratio continuously in a pattern that follows a sine wave. Rapid pulses with varying widths — wide pulses where the sine wave should be large, narrow pulses where it should be small.

The load (especially if it has inductance, like a motor) naturally filters out the high-frequency switching and responds only to the average — which, if the pulse widths were varied sinusoidally, is a sine wave.

How it's generated: Two signals are compared:

A reference sine wave at the desired output frequency (e.g. 50 Hz) — this is what you want the output to look like
A high-frequency triangular carrier wave (e.g. 5000 Hz) — this is the switching clock

When the sine wave is above the triangular carrier → switch ON. When below → switch OFF. The result is a series of pulses whose widths naturally follow the sine shape.

Modulation Index = m = \frac{V_{r e f e r e n c e}}{V_{c a r r i e r}}

m = 1 → full sine wave output
m < 1 → reduced amplitude output
m > 1 → overmodulation, distortion begins

Single-Phase vs Three-Phase Inverters

Single-phase inverter — A single-phase inverter converts DC source voltage (from batteries or solar panels) into a 220V/110V single-phase AC output for home/office appliances. Utilizing bridge circuits, they produce a sinusoidal waveform to power single-phase loads. One H-bridge, produces one AC output. Used in small UPS systems, solar inverters for homes.

Three-phase inverter — A three-phase inverter is a power electronics device that converts DC power (from solar panels, batteries) into three-phase AC power, featuring three 120-degree phase-shifted outputs. It uses six switches (IGBTs/MOSFETs) arranged in three legs to produce high-efficiency AC power for industrial motor drives, HVDC systems, and large-scale solar installations. Three H-bridges sharing the same DC bus, each producing a sine wave shifted 120° from the others. Exactly replicating the three-phase AC system from Unit 2.

The same PWM principle applies to three-phase — just three reference sine waves, each 120° apart, compared against the same triangular carrier.

The Full Unit 5 Story Connected

DC source → need lower DC voltage → Buck converter (D controls step-down)

DC source → need higher DC voltage → Boost converter (D controls step-up)

DC source → need AC → Inverter (H-bridge switching) → shaped by Sinusoidal PWM → clean sine wave output → single or three-phase depending on application

All three are fundamentally the same idea: controlled switching doing what resistors and transformers can't — converting power efficiently without wasting it as heat.