ou have been tasked with the design
o
f
a boost converter whose output voltage
i
s

1
2
V
,
and whose
input voltage may vary between
6
V
and
1
2
V
.
The maximum output power
o
f
the co

Question

ou have been tasked with the design 
o
f
 ﻿a boost converter whose output voltage 
i
s
 
1
2
V
,
 ﻿and whose
input voltage may vary between 
6
V
 ﻿and 
1
2
V
.
 ﻿The maximum output power 
o
f
 ﻿the converter 
i
s
 ﻿specified
a
t
 
2
4
W
,
 ﻿and the switching frequency 
o
f
 ﻿the converter 
i
s
 ﻿set 
t
o
 
2
0
0
k
H
z
.
 ﻿The current ripple 
i
n
 ﻿the inductor
must not exceed 
1
0
%
 
o
f
 ﻿the 
D
C
 ﻿component, and the output voltage ripple must not exceed 
5
%
 
o
f
 ﻿the 
D
C
output voltage, under any operating conditions 
(
h
i
n
t
: 
a
n
 ﻿important part 
o
f
 ﻿the problem 
i
s
 ﻿finding the
worst
-
case operating condition for both current and voltage ripple
)
.
 ﻿Total losses 
i
n
 ﻿the inductor and
capacitor should not exceed 
1
W
.
Select 
a
n
 ﻿inductor and a capacitor that satisfy these requirements. Provide the datasheets 
o
f
 ﻿these
components when submitting your assignment. Show all calculations for inductor current ripple,
capacitor voltage ripple, and losses.

VIPSolutions · Accepted Answer

# Boost Converter Design

## Specifications

- **Output Voltage, $ V_{out} $:** 12 V  
- **Input Voltage Range, $ V_{in} $:** 6 V to 12 V  
- **Output Power, $ P_{out} $:** 24 W  
- **Switching Frequency, $ f_{sw} $:** 200 kHz  
- **Inductor Current Ripple:** ≤ 10% of DC inductor current  
- **Output Voltage Ripple:** ≤ 5% of output voltage (.6 V)  
- **Inductor + Capacitor Losses:** ≤ 1 W

---

## 1. Calculating Key Parameters

### 1.1. Output Current

$$
I_{out} = \frac{P_{out}}{V_{out}} = \frac{24\,W}{12\,V} = 2\,A
$$

---

### 1.2. Input Current

Minimum $ V_{in} $ (worst-case for current ripple and losses):

$$
I_{in, min} = \frac{P_{out}}{\eta \cdot V_{in, min}}
$$
Assume efficiency $ \eta \approx .9 $ initially.

$$
I_{in, min} = \frac{24}{.9 \times 6} \approx 4.44\,A
$$

---

### 1.3. Duty Cycle

$$
D = 1 - \frac{V_{in}}{V_{out}}
$$

Worst-case (lowest $ V_{in} $):

$$
D_{max} = 1 - \frac{6}{12} = .5
$$

Best-case (highest $ V_{in} $):

$$
D_{min} = 1 - \frac{12}{12} = 
$$

---

## 2. Inductor Selection

### 2.1. Inductor Current Ripple ($ \Delta I_L $)

$$
\Delta I_L = \frac{V_{in} \cdot D}{L \cdot f_{sw}}
$$

Worst-case ripple occurs at **minimum $ V_{in} $ and maximum D**.

- $ V_{in} = 6\,V $
- $ D = .5 $
- $ f_{sw} = 200\,kHz $
- Inductor DC current at this point $ I_{L,avg} = I_{in, min} = 4.44\,A $
- 10% ripple: $ \Delta I_{L, max} = .1 \times 4.44 = .444\,A $

**Solve for minimum L:**

$$
L \geq \frac{V_{in} \cdot D}{\Delta I_L \cdot f_{sw}}
= \frac{6 \times .5}{.444 \times 200,000}
= \frac{3}{88,800}
\approx 33.8\,\mu H
$$

**Choose next standard value:**  
**$ L = 47\,\mu H $** (for margin)

---

## 3. Output Capacitor Selection

### 3.1. Output Voltage Ripple ($ \Delta V_{out} $)

$$
\Delta V_{out} \leq .05 \times 12\,V = .6\,V
$$

Ripple comes from both capacitance and ESR. For ceramic capacitors, ESR is very low, so focus on capacitance.

$$
\Delta V_{out,cap} = \frac{I_{out} \cdot D}{f_{sw} \cdot C}
$$

Worst-case at highest D ($ D = .5 $), highest $ I_{out} $:

$$
\Delta V_{out,cap} = \frac{2 \times .5}{200,000 \cdot C} = \frac{1}{200,000 \cdot C}
$$

Set $ \Delta V_{out,cap} \leq .6 $:

$$
C \geq \frac{1}{200,000 \cdot .6} = \frac{1}{120,000} \approx 8.33\,\mu F
$$

**Choose margin:**  
**$ C = 22\,\mu F $** (ceramic, rated ≥16 V)

---

## 4. Loss Calculations

### 4.1. Inductor Loss

Assume DCR (DC resistance) of $ 15\,m\Omega $:

$$
P_{L} = I_{L, rms}^2 \cdot R_{L}
$$

Worst-case at $ I_{L, avg} = 4.44\,A $, ripple is small:

$$
I_{L, rms} \approx I_{L, avg} = 4.44\,A
$$
$$
P_{L} = (4.44)^2 \times .015 = .295\,W
$$

### 4.2. Capacitor Loss

For ceramic, ESR ≈ .01 Ω.

$$
I_{C,rms} \approx \frac{\Delta I_L}{2\sqrt{3}} \approx \frac{.444}{3.464} \approx .128\,A
$$
$$
P_{C} = I_{C, rms}^2 \cdot ESR = (.128)^2 \times .01 \approx .00016\,W
$$

**Total losses:**  
$$
P_{L} + P_{C} \approx .295\,W + .00016\,W \approx .3\,W < 1\,W
$$

---

## 5. Component Selection

### 5.1. Inductor

- **Value:** 47 μH
- **Current rating:** ≥5A (for margin)
- **Low DCR:** ≤15 mΩ

**Example:**  
- [Coilcraft MSS1278T-473NL](https://www.coilcraft.com/en-us/products/power/inductors/mss1278/mss1278t-473nl/)
  - Inductance: 47 μH
  - Rated current: 5.2A
  - DCR: 13.8 mΩ

### 5.2. Capacitor

- **Value:** 22 μF
- **Voltage rating:** ≥16V
- **Type:** Ceramic (X7R or better)
- **Low ESR**

**Example:**  
- [Murata GRM32ER71C226KE15L](https://datasheet.lcsc.com/szlcsc/Murata-GRM32ER71C226KE15L_C98108.pdf)
  - Capacitance: 22 μF
  - Voltage: 16 V
  - ESR:

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