DC-DC Converter Design Based on Roll Number 98

A Comprehensive Buck Converter Design with a Critical Parameter Constraint

Highlights

Critical Parameter and Topology: The design is anchored on a critical parameter set to 98; here, we use a switching frequency of 98 kHz as our basis while alternatively also showcasing the possibility of fixing the inductance to 98 μH.
Systematic Computation: All converter components are computed using essential formulas for a buck (step-down) converter, ensuring the design meets the specified output requirements while maintaining design margins.
Signal and Circuit Representation: The design includes a detailed circuit diagram, calculated component values, accompanying timing diagrams, and simulation considerations.

1. Converter Circuit Overview

1.1. Chosen Topology: Buck Converter

The buck converter is a common DC-DC converter used for efficiently stepping down voltage. In this design, one critical parameter is fixed based on the roll number 98. We demonstrate two options:

The switching frequency is set to 98 kHz.
Alternatively, the inductance value can be chosen as 98 μH.

For our demonstration, we illustrate the design using the switching frequency constraint of 98 kHz while noting that similar techniques apply if the critical parameter is set on the inductance.

1.2. Circuit Diagram

A typical buck converter circuit contains the following components:

An input voltage source (Vin).
A controlled switch (usually a MOSFET) driven by a PWM signal.
A diode for freewheeling current when the switch is OFF.
An inductor (L) used for energy storage and current shaping.
An output capacitor (C) for voltage filtering.
A load resistor (R) representing the output load.

The schematic diagram of the buck converter is illustrated below:


       Vin
        │
        │
        ├─────────┐
        │         │
        │      [SW]  ← Controlled Switch (MOSFET)
        │         │
        │         └───── L ─────┐
        │                      │
        │                   [ Diode ]
        │                      │
        │                      C
        │                      │
        └──────────────────────┴──→ Vout → R (Load)

2. Computation of Component Values

2.1. Design Specifications and Assumptions

The design parameters chosen are as follows. We will use the roll number 98 to set the switching frequency as 98 kHz (or, in an alternative approach, fix the inductance to 98 μH). For this design, we assume:

Parameter	Value	Unit	Description
Vin	12	V	Input voltage (chosen for a low voltage application)
Vout	5	V	Desired regulated output voltage
Iout	1	A	Load current, providing baseline design currents
fs	98	kHz	Switching frequency, fixed by the roll number as the critical design parameter

In the alternative method, one could choose the inductance to be 98 μH and modify the other parameters accordingly. In our current synthesis, we will use fs = 98 kHz as the guiding design constraint.

2.2. Duty Cycle (D)

In an ideal buck converter, the output voltage is related to the input voltage by the duty cycle (D):

Formula: D = Vout / Vin

Substituting the values:

D = 5 V / 12 V ≈ 0.4167, or approximately 41.67%

2.3. Calculation of the Inductor Value (L)

The inductor is designed to limit the current ripple (ΔIL) in the circuit. A typical design target is to set the ripple current as a percentage of the output current; here, we assume 20% of Iout:

ΔIL = 0.2 × 1 A = 0.2 A

Inductor Value Formula:
L = (Vin – Vout) × D / (fs × ΔIL)

Calculation:

L = (12 V – 5 V) × 0.4167 / (98,000 Hz × 0.2 A)

L = 7 V × 0.4167 / 19,600 ≈ 2.9169 V / 19,600 ≈ 0.000149 H or 149 µH

In a practical implementation, component tolerances may lead us to choose a standard inductor value near this calculated result.

2.4. Calculation of the Output Capacitor (C)

The output capacitor helps smooth the output voltage by reducing voltage ripple (ΔVout). Let us assume the output voltage ripple is limited to 1% of Vout:

ΔVout = 0.01 × 5 V = 0.05 V

Capacitor Value Formula:
C = Iout × D / (fs × ΔVout)

Calculation:

C = 1 A × 0.4167 / (98,000 Hz × 0.05 V) ≈ 0.4167 / 4,900 ≈ 0.0000851 F or 85.1 µF

Due to component tolerances and non-ideal behaviors (such as equivalent series resistance, ESR), designers often select a higher standard capacitor value. For instance, a capacitor value of 100 µF might be chosen in practice.

2.5. Switch and Diode Selection Criteria

The controlled switch, typically a MOSFET, must handle the input voltage (Vin) and the maximum current of the circuit. Similarly, the freewheeling diode must withstand a reverse voltage equal to at least Vin and conduct the inductor current when the switch is off.

For our low-voltage design, the following ratings are advisable:

MOSFET: Voltage rating above 12 V, current rating above 1 A, and with fast switching characteristics.
Diode: Reverse voltage at least 12 V and current rating above the inductor’s peak current, typically 1.2 A or more to account for margin.

3. Signal Waveforms

3.1. PWM Signal for the Switch

With a switching frequency (fs) fixed at 98 kHz, the switch is driven by a PWM signal with the calculated duty cycle. The PWM signal is a square waveform that is high for approximately 41.67% of the period and low for the remaining 58.33%.

Time Period Calculation: The period T is the reciprocal of the switching frequency:

T = 1/fs = 1/98,000 ≈ 10.2 µs

Thus, the switch is ON for about 4.25 µs and OFF for about 5.95 µs.

3.2. Inductor Current Waveform

The inductor current in a buck converter is characterized by a triangular ripple superimposed on an average DC level. When the switch is on, the inductor current ramps upward; when the switch is off, the current ramps downward due to the freewheeling diode conduction.

The calculated ripple (ΔIL) is approximately 0.2 A, meaning the inductor current will oscillate ±0.1 A around its average value of 1 A.

A simplified timing diagram for the inductor current is as follows:


       Inductor Current (IL)
         /\      /\      /\
        /  \    /  \    /  \
       /    \__/    \__/    \

The average inductor current equals the load current, while the peak-to-peak ripple is limited by the design.

3.3. Output Voltage Waveform

The output voltage (Vout) should ideally remain at a steady DC level of 5 V with minimal ripple. The output capacitor filters the ripple caused by the switching action. In our design, the output ripple is constrained to roughly 0.05 V, resulting in a clean DC voltage.


       Vout (5V DC)
        ────────|¯|───────|¯|───────

In practice, oscilloscope traces of Vout will reveal a small high-frequency ripple superimposed on the DC output voltage.

4. Alternative Design Approach

4.1. Fixing Inductance as the Critical Parameter

Alternatively, the critical parameter may be chosen as the inductor value, fixed at 98 μH according to the roll number. In this scenario, the switching frequency and other parameters will be recalculated to ensure that the design meets the required performance targets.

For example, let’s consider the following alternate specifications:

Parameter	Value	Unit	Description
Vin	24	V	Input voltage
Vout	12	V	Desired output voltage
Iout	~4.17	A	Output current for a 50W load
L	98	µH	Critical parameter set by roll number
fs	Typically, 100 kHz or higher	-	Chosen to manage ripple and switching losses

With L fixed at 98 μH, the designer would then use:

ΔIL = (Vin – Vout) × D / (L × fs) and adjust fs and D to achieve the desired output, ensuring consistent performance while the inductor value remains anchored by the roll number.

4.2. Signal Considerations in the Alternative Approach

The signal waveforms will remain similar in nature—PWM for the switching element, a triangular ripple for the inductor current, and filtered DC on the output. However, the amplitude and timing of these signals might adjust slightly owing to the changes in frequency and duty cycle that accompany the fixed inductance constraint. Designers must use simulation tools such as SPICE, MATLAB/Simulink, or equivalent to validate these signals and adjust component ratings.

5. Practical Considerations & Simulation

5.1. Component Selection and Safety Margins

When designing a real-world converter, component selection must account for non-ideal factors such as switching losses, parasitic resistances, and temperature variations. It is recommended to choose:

A MOSFET with a voltage rating 20-30% above Vin and sufficient current handling capability.
A diode with a reverse voltage rating comfortably above Vin and capable of fast recovery.
An inductor with a core material that minimizes losses at high frequency, with a saturation current rating above the peak current.
A low-ESR capacitor to better manage the transient response and ripple filtering.

5.2. Simulation and Testing

Prior to hardware implementation, simulation can help predict performance metrics. Tools like MATLAB/Simulink or SPICE allow designers to:

Validate the calculated duty cycle, ripple currents, and voltage ripple through waveform visualization.
Examine transient responses and stability under load variations.
Iterate on component values in a controlled environment to optimize performance.

A typical simulation would involve setting up the buck converter model, running a transient analysis, and comparing the simulated waveforms with the theoretical predictions discussed above.

Conclusion

This design example demonstrates a comprehensive approach to constructing a buck converter with a critical design parameter derived from the roll number 98. By fixing the switching frequency at 98 kHz (or alternatively, the inductor at 98 μH), the remaining parameters such as duty cycle, inductor value, and output capacitor are computed to meet the desired electrical outputs. In our primary design, with Vin = 12 V, Vout = 5 V, Iout = 1 A, and a calculated duty cycle of approximately 41.67%, component values were derived leading to an inductor value of roughly 149 µH and a capacitor of about 85 µF.

Design considerations include careful component selection to manage real-world issues such as parasitic effects, ensuring a converter that functions reliably under various conditions. Additionally, simulation plays a pivotal role in validating the theoretical calculations and optimizing the design prior to fabrication.

Both design approaches—anchoring the switching frequency at 98 kHz or fixing the inductance to 98 μH—are valid, and the choice may depend on specific application requirements and component availability. The synthesized design herein provides a structured framework that meets academic assignment requirements while illustrating the practical integration of theory and engineering practice.

References

DC-DC Converter Design Basics (Part 1): Buck Converters - Electronic Design
How to Design a DC-DC Converter: A Comprehensive Guide - WehoPower
DC-to-DC Converter Testing Guidelines - Keysight
Building a DC-DC Power Supply - Analog Devices