This document discusses capacitor design and analysis. Section 4 describes the electrical characteristics of capacitors, including impedance formulas. Section 6 analyzes quality factor Q and its relationship to equivalent series resistance ESR and equivalent series inductance ESL. Section 8 covers various capacitor properties like target impedance, anti-resonance, ESR effects, quality factors for different capacitor types, and parasitic elements. The document provides technical details on capacitor modeling and design considerations for high frequency applications.

2. 1 .................................................................... - 1 -
2 ................................................................................ - 1 -
3 ............................................................................ - 2 -
4 .................................................................................... - 3 -
4.1 .............................................. - 3 -
4.2 ...................................................... - 4 -
5 ............................................................................................ - 5 -
6 .................................................................................... - 8 -
7 ...................................................................................... - 10 -
8 .................................................................. - 12 -
8.1 Target Impedance .......................................... - 12 -
8.2 ............................................................................ - 13 -
8.3 ........................................................................ - 15 -
8.4 Anti-Resonance ...................... - 16 -
8.5 ESR Anti-Resonance ...................................... - 17 -
8.6 .................................................................... - 18 -
8.7 ................................................................................ - 20 -
8.8 ................................................................................ - 21 -
9 .......................................................................................................... - 24 -

3. 1
2
-1-

4. 3
-2-

5. KHz
600 800
1GHz
PCB
4
4.1
-3-

6. 1
I
I0 A
IC
C
B
1
I0
Ic 0
I0
Ic 0
dV
I =C 1
dt
C
4.2
1 2 AB
AB
AB AB
-4-

7. I
I0 A
IC
C
B
2
3
A
Z
B
3
∆V = Z ∆ I 2
AB AB
2 Z 2
5
-5-

8. 4 SPICE ESR
ESL C
4
4
1 ⎛ 1 ⎞
Z = ESR + j 2π fESL + = ESR + j ⎜ 2π fESL − ⎟ 3
j 2π fC ⎝ 2π fC ⎠
1
2π fESL 2π fESL
2π fC
1
2π fC
1 1
f0 = 2π fESL = 0
2π ESL C 2π fC
5 0805
0.1uF
-6-

9. 5
AVX
ESL nH ESR
0402 0.4 0.06
0603 0.5 0.098
0805 0.6 0.079
1206 1 0.12
1210 0.9 0.12
1812 1.4 0.203
2220 1.6 0.285
RLC Q
UC=I*1/ωC=U/ωCR=QU Q=1/ωCR I
UL=ωLI=ωL*U/R=QU Q=ωL/R UC=UL Q=1/ωCR=ωL/R
U UC/U= I*1/ωC /RI=1/ωCR=Q
U UL/U=ωLI/RI=ωL/R=Q
-7-

10. 6 Q
Q
I/I0 ω ω0
6 I/I0 ω ω0
Q Q1>Q2>Q3 ω ω0
I/I0 1 Q
Q Q
ESL
ESR Q
6
2
2
-8-

11. ⎡ ⎛ 4h ⎞ ⎤
L = 5.08h ⎢ln ⎜ ⎟ + 1⎥
⎣ ⎝ d ⎠ ⎦
L nH h d
63mil 1.6
8mil
⎡ ⎛ 4 × 0.063 ⎞ ⎤
L = 5.08 × 0.063 ⎢ln ⎜ ⎟ + 1⎥ = 1.4242 nH
⎣ ⎝ 0.008 ⎠ ⎦
0805 0.01uF
C=0.01uF ESL=0.6
nH Lmount=1.5nH
1 1
f0 = = = 64.975MHz
2π ESL C 2π 0.6nH × 0.01uF
0.6+1.5=2.1nH
3nH
1 1
f0 = = = 34.73MHz
2π L C 2π 2.1nH × 0.01uF
-9-

12. 7
7 NOT
GATE Input Q1 Q2 Q4
Q3 Output
7
8
0
3.3V 2V 1 0.8V 0
0.8V 2V
0 1
8
Vcc GND Vcc
GND
8
- 10 -

13. 8
9
9 VCC
9
- 11 -

14. 8
8.1 Target Impedance
Target Impedance
VDD × Ripple ∆VDD
X MAX = = 4
∆I MAX ∆I MAX
VDD 5V 3.3V 1.8V 1.26V 1.2V
Ripple 2.5%
- 12 -

15. ∆I MAX
1
2
8.2
ESL ESR
Target Impedance
30pF 2ns 0V 3.3V
dV 3.3V
I =C = 30 pF × = 49.5mA 5
dt 2ns
36 36*49.5mA=1.782A
3.3*2.5%=82.5 mV
C=I*dt/dv=1.782A*2ns/0.0825V=43.2nF
2ns
1.782A 82.5 mV 82.5 mV
- 13 -

16. 82.5 mV
1.2V
2.5% 600mA
VDD × Ripple 1.2 ∗ 0.025
X MAX = = = 50mΩ
∆I MAX 0.6
DC kHz DC 100kHz
100kHz 100kHz
2.5% 100kHz
2.5%
bulk
1
ZC =
2π fC
f
100kHz
1
C= = 31.831 uF
2π fX MAX
bulk
Z C = 2π f × ESL
f ESL 5nH
X MAX
f max = = 1.6MHz 100kHz
2π ESL
- 14 -

17. 1.6MHz 1.6MHz
1.6MHz
500MHz
2π f × Lmax ≤ X MAX
X MAX
Lmax ≤ = 0.016 nH
2π × 500MHz
AVX 0402 0.4nH
0.6nH 1 nH
0.16 nH 1/0.016=62.5
63 0402
1.6MHz
1
C= = 1.9894 uF
2π × 1.6MHz × X MAX
1.9894/63=0.0316 uF
1 31.831 uF 63 0.0316 uF
Target Impedance
8.3
63 0.0316 uF ESL 1 nH
0.159 nH ESL 1.9908 uF
- 15 -

18. 10
10
V
0.1uF
8.4 Anti-Resonance
11
11
- 16 -

19. LC LC L C
12
12 12
a 10
b Anti-Resonance
PCB
EMI
8.5 ESR Anti-Resonance
Anti-Resonance 12
LC ESR
ESR X2
Z= + X
2 2 ESR
- 17 -

20. ESR
8.6
Q
3 4 3 4
0.47 0.22 0.1
10 0.1 0.01 0.001
- 18 -

21. 13 2 680uF 7 2.2uF
0805 13 0.22uF 0603 26 0.022uF 0402
680uF
V 2.2uF 0.22uF 0.022uF
500kHz 150MHz 33 500MHz
110
13
NP0 ESR
Q
ESL
- 19 -

22. 8.7
f λ
2R
j 2π f
I = Ae c
A R C
λ 4 π 180
0
λ 4
λ 4 0 λ 50
0.001uF 1.6nH
125.8MHz 7.95ps
166ps/inch 47.9 47.9/50=0.958 2.4
2.4 2.4
- 20 -

23. 8.8
14
10
14
680pF
- 21 -

24. -> -> -> -> -> ->
-> -> 15
15
16
16
- 22 -

25. 0402 20mil
17
17
18
18
- 23 -

26. 9
PLL
DLL
- 24 -