Bài giảng Electronic circuits - Chapter 5: Frequency response - Trịnh Xuân Dũng
Dr. Dung Trinh
HCMUT / 2017
Electronic Circuits
Chapter 5: Frequency Response
Dr. Dung Trinh
1
Dr. Dung Trinh
HCMUT / 2017
Outline
Introduction
Low frequency and high frequency models
Low frequency response of CS and CE Amplifier
High frequency model of MOSFET and BJT
Miller’s Theorem and Exact Analysis
HF Response of CG, Source and Emitter Followers
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Dr. Dung Trinh
HCMUT / 2017
Introduction
At lower frequencies, the magnitude of the amplifier gain falls off. This occurs
because the coupling and bypass capacitors no longer have low impedances.
The gain of the amplifier falls off at the high-frequency end. This is due to
internal capacitive effects in the BJT and in the MOSFET.
3
Dr. Dung Trinh
HCMUT / 2017
Introduction: Low-pass Circuit
푉
1
푉
ꢀ
ꢀ
In frequency domain:
푉 =
표
∙
=
1
푗휔퐶 1 + 푗휔푅퐶
푅 +
푗휔퐶
푉
1
1
표
→ 퐴푣= =
=
푓
푉 1 + 푗휔푅퐶
ꢀ
1 + 푗
풇ퟎ
ퟏ
ퟏ
풇ퟎ =
=
흉 = ퟐ흅푹푪
ퟐ흅푹푪 흉
4
Dr. Dung Trinh
HCMUT / 2017
Introduction: High-pass Circuit
푉 푅
푉
ꢀ
ꢀ
In frequency domain:
푉 =
=
1
표
1
푗휔퐶
1
푅 +
1 +
푗휔푅퐶
푉
1
표
→ 퐴푣= =
=
1
푓
푉
ꢀ
표
1 − 푗
1 − 푗
푓
휔푅퐶
ퟏ
ퟏ
풇ퟎ =
=
흉 = ퟐ흅푹푪
ퟐ흅푹푪 흉
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Dr. Dung Trinh
HCMUT / 2017
Introduction: Octave vs Decade
If f2 = 2f1, then f2 is one octave above f1.
If f2 = 10f1, then f2 is one decade above f1
푓
푓
2
2
# 표푓 표푐푡푎푣푒 = 푙표푔 = 3.32푙표푔
2 푓
10 푓
1
1
푓
2
# 표푓 푑푒푐푎푑푒 = 푙표푔
10 푓
1
Example:
2 GHz is one octave above 1 GHz
10 GHz is one decade above 1 GHz
6
Dr. Dung Trinh
HCMUT / 2017
Introduction: 3dB definition
ퟏ
3dB points are points at which the magnitude is that at mid-band
ퟐ
frequency.
Power is halved. Voltage is scaled as:
푉
푉
표
표
=
1 + 푗
2
From which:
퐴푑퐵 = 20푙표푔10 2 = 3푑퐵
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Dr. Dung Trinh
HCMUT / 2017
Introduction: Gain
Amplifier has intrinsic gain: 푨ퟎ
ퟏ
Low-pass characteristics:
풇
ퟏ+풋
풇
풉풊
풇
풋
풇
풍풐
High-pass characteristics:
풇
ퟏ+풋
풇
풍풐
풇
풋
ퟏ
풇
풍풐
Overall gain:
푨 풇 = 푨ퟎ ퟏ+풋
풇
풇
풇
ퟏ+풋
풇
풉풊
풍풐
At very high frequency, the gain becomes:
ퟐ
흎
흎
푮 = −ퟐퟎ풍풐품ퟏퟎ ퟏ +
≈ −ퟐퟎ풍풐품ퟏퟎ
흎ퟎ
흎ퟎ
Slope of curve is -20db/decade
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Dr. Dung Trinh
HCMUT / 2017
Model for general amplifying element
CC1 and CC2 are coupling capacitors (large): 휇퐹.
Cin and Cout are parasitic capacitors (small): 푝퐹.
Mid-band frequency: - Coupling capacitors are short circuits
- Parasitic capacitors are open circuits
풗풐풖풕
푨푴푩 =
풗풊풏
푹풊풏
푹푳
=
푨
푹풊풏 + 푹품 푹푳 + 푹풐풖풕
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Dr. Dung Trinh
HCMUT / 2017
Low frequency model
Low frequency model: - Coupling capacitors are present.
- Parasitic capacitors are open circuits.
푅ꢀ푛
푗휔푅ꢀ푛퐶푐1
푣푎푏 = 풗풊풏
= 풗풊풏
1
1 + 푗휔퐶푐1 푅ꢀ푛 + 푅푔
푅ꢀ푛 + 푅푔 +
푗휔퐶푐1
푗휔퐶푐1 푅ꢀ푛 + 푅푔
푅ꢀ푛
= 풗풊풏
푅 + 푅
푔 1 + 푗휔퐶푐1 푅ꢀ푛 + 푅푔
ꢀ푛
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Dr. Dung Trinh
HCMUT / 2017
Low frequency model
1
1
푓 =
푙1
푓 =
푙2
Define:
2휋 푅표푢푡 + 푅퐿 퐶푐2
2휋 푅ꢀ푛 + 푅푔 퐶푐1
푓
푗
푗휔퐶푐1 푅ꢀ푛 + 푅푔
푅ꢀ푛
푅ꢀ푛
= 풗풊풏
푓
푙1
푣푎푏 = 풗풊풏
푓
푅ꢀ푛 + 푅
푅ꢀ푛 + 푅
푔 1 + 푗휔퐶푐1 푅ꢀ푛 + 푅푔
푔 1 + 푗
푓
푙1
푓
푗
푅퐿
푗휔퐶푐2 푅퐿 + 푅표푢푡
푅퐿
풂풃 푅퐿 + 푅
푓
푙2
푣표푢푡 = 푨풗
= 푨풗
풂풃 푅퐿 + 푅표푢푡 1 + 푗휔퐶푐2 푅퐿 + 표푢푡
푓
표푢푡 1 + 푗
푓
푙2
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Dr. Dung Trinh
HCMUT / 2017
Low frequency model
푓
푓
푗
푗
푣표푢푡
푣ꢀ푛
푅ꢀ푛
푅퐿
푓
푓
푙2
푙1
= 퐴
Overall gain:
푓
푓
푅ꢀ푛 + 푅푔 푅퐿 + 푅
표푢푡 1 + 푗 1 + 푗
푓
푓
푙2
푙1
푓
푗
푓
푗
푣표푢푡
푣ꢀ푛
푓
푓
푙2
푙1
= 푨푴푩
푓
푓
1 + 푗 1 + 푗
푓
푓
푙2
푙1
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Dr. Dung Trinh
HCMUT / 2017
High frequency model
Low frequency model: - Coupling capacitors are short.
- Parasitic capacitors are present.
푹풊풏
푹풊풏 + 푹품
푽풕풉ퟏ = 풗풊풏
Equivalent Thevenin Circuit
푹풕풉ퟏ = 푹풊풏 ∥ 푹품
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Dr. Dung Trinh
HCMUT / 2017
High frequency model
푅ꢀ푛
1
푣푎푏 = 풗풊풏
푅ꢀ푛 + 푅
푔 1 + 푗휔 푅ꢀ푛 ∥ 푅푔 퐶ꢀ푛
1
푅ꢀ푛
1
푓 =
ℎ1
where:
= 풗풊풏
2휋 푅ꢀ푛 ∥ 푅푔 퐶ꢀ푛
푓
푅ꢀ푛 + 푅
푔 1 + 푗
푓
ℎ1
푅퐿
1
푅퐿
풂풃 푅퐿 + 푅
1
푣표푢푡 = 푨풗
= 푨풗
풂풃 푅퐿 + 푅표푢푡 1 + 푗휔퐶표푢푡 푅퐿 ∥ 푅표푢푡
푓
표푢푡 1 + 푗
푓
ℎ2
1
2휋 푅표푢푡 ∥ 푅퐿 퐶표푢푡
푓 =
ℎ2
where:
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Dr. Dung Trinh
HCMUT / 2017
High frequency model
푣표푢푡
푣ꢀ푛
푅ꢀ푛
푅퐿
1
1
Overall gain:
= 푨풗풂풃
푓
푓
푅ꢀ푛 + 푅푔 푅퐿 + 푅
표푢푡 1 + 푗 1 + 푗
푓
ℎ1
푓
ℎ2
푣표푢푡
푣ꢀ푛
1
1
= 푨푴푩
푓
푓
1 + 푗 1 + 푗
푓
ℎ1
푓
ℎ2
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Dr. Dung Trinh
HCMUT / 2017
High frequency model
Example 1: Given 푅표푢푡 = 3푘Ω, 푅푔 = 200Ω, 푅ꢀ푛 = 12푘Ω , 푅퐿 = 10푘Ω, 퐶푐1 =
5휇퐹, 퐶푐2 = 1휇퐹, 퐶ꢀ푛 = 200푝퐹, 퐶표푢푡 = 40푝퐹. Compute 푓 , 푓 , 푓 , 푓 .
푙1 푙2 ℎ1 ℎ2
1
푓 =
= 2.61 퐻푧
= 12.2 퐻푧
푙1
2휋 × 12200 × 5 × 10−6
1
푓 =
푙2
2휋 × 13000 × 1 × 10−6
1
푓 =
= 4.05 푀퐻푧
= 1.72 푀퐻푧
ℎ1
2휋 × 12000 ∥ 200 × 2 × 10−10
1
푓 =
ℎ2
2휋 × 10000 ∥ 3000 × 4 × 10−11
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Dr. Dung Trinh
HCMUT / 2017
LF Response of CE Amplifier
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Dr. Dung Trinh
HCMUT / 2017
LF Response of CE Amplifier
Considering the Effect of Each of the Three Capacitors Separately
Case 1: Consider 푪푪ퟏ, short circuit 푪푬 and 푪푪ퟐ
푅퐵 ∥ 푟
휋
푉 = 푽풔풊품
휋
1
풔퐶푐1
푅퐵 ∥ 푟 + 푅푠ꢀꢁ +
휋
풔 = 풋흎
푉 = −품풎푽흅 푹푪 ∥ 푹푳
표
푉
푅퐵 ∥ 푟
휋
표
= −
×
품풎 푹푪 ∥ 푹푳
푉
푠ꢀꢁ
푅퐵 ∥ 푟 + 푅푠ꢀꢁ
휋
푠
1
푠 +
퐶푐1 푅퐵 ∥ 푟 + 푅푠ꢀꢁ
휋
1
푅퐵 ∥ 푟
휋
푓 =
푃1
푨푴푩 = −
품풎 푹푪 ∥ 푹푳
2휋퐶푐1 푅퐵 ∥ 푟 + 푅푠ꢀꢁ
푅퐵 ∥ 푟 + 푅푠ꢀꢁ
휋
휋
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Dr. Dung Trinh
HCMUT / 2017
LF Response of CE Amplifier
Considering the Effect of Each of the Three Capacitors Separately
Case 2: Consider 푪푬, short circuit 푪푪ퟏ and 푪푪ퟐ
푅퐵
퐼푏 = 푽
1
풔풊품 푅퐵 + 푅푠ꢀꢁ
1
풔퐶퐸
푅퐵 ∥ 푅푠ꢀꢁ + 훽 + 1 푟 +
푒
풔 = 풋흎
푉 = −휷푰풃 푹푪 ∥ 푹푳
표
푉
푅퐵
휷 푹푪 ∥ 푹푳
표
= −
×
푉
푠ꢀꢁ
푅퐵 + 푅푠ꢀꢁ
푅퐵 ∥ 푅푠ꢀꢁ + 훽 + 1 푟
푒
푠
1
푠 +
푅퐵 ∥ 푅푠ꢀꢁ
퐶퐸 푟 +
푒
훽 + 1
1
푓 =
푃2
푅퐵 ∥ 푅푠ꢀꢁ
2휋퐶퐸 푟 +
푒
훽 + 1
19
Dr. Dung Trinh
HCMUT / 2017
LF Response of CE Amplifier
Considering the Effect of Each of the Three Capacitors Separately
Case 3: Consider 푪푪ퟐ, short circuit 푪푬 and 푪푪ퟏ
푅퐵 ∥ 푟
휋
푉 = 푽풔풊품
휋
푅퐵 ∥ 푟 + 푅푠ꢀꢁ
휋
풔 = 풋흎
푹푪
푉 = −품풎푽흅
표
푹푳
ퟏ
풔푪ퟐ
푹푪 +
+ 푹푳
푉
푅퐵 ∥ 푟
표
휋
= −
×
품풎 푹푪 ∥ 푹푳
푉
푠ꢀꢁ
푅퐵 ∥ 푟 + 푅푠ꢀꢁ
휋
푠
1
푠 +
퐶푐2 푅퐶 + 푅퐿
1
푓 =
푃3
2휋퐶푐2 푅퐶 + 푅퐿
20
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