,RF Integrated Circuits
and Systems
Hooman Darabi
March 2020
1
, Course Syllabus
• RF IC Components
• RF Communication Systems
System
• RF networks
• Noise
• Distortion
• Low-noise amplifiers
• Mixers
Circuit
• Oscillators
• Power amplifiers
• Transceiver architectures
2
, Teaching Guidelines
• Slides only used as a guideline, best to use whiteboard only
• Likely not possible to cover all slides for basic RF course
• Skip the following sections:
̶ Chapter 3: Slides 41-43
̶ Chapter 5: Slides 56-57, 61, 64-67
̶ Chapter 7: Slides 108-111, 115-118
̶ Chapter 9: Slides 144-151, 157-163
• About 7-8 slides per lecture may be covered in 20-lecture
quarter-based curricula
• No material for PLLs (chapter 10). It may be covered in a
separate course.
3
, RF IC Components
• Transistors
• High frequency model good for RF (several GHz)
• Resistors
• LC circuits
• Capacitors
• Inductors
• Differential, Transformers
• Transmission lines
4
, LC Circuits
• Widely used in amplifiers, oscillators …
• The energy moves between L and C
• In lossy circuit however, energy decays eventually
+ iL(t) +
C vc(t) L C R vc(t)
- -
Ideal: lossless Practical
5
, Lossless LC Circuit: Ideal Oscillator
𝜕 2 𝑣𝐶 1
• Solve the differential equation: 𝜕𝑡 2
+ 𝑣 =0
𝐿𝐶 𝐶
• The capacitor voltage: 𝑣𝐶 𝑡 = 𝑉0 𝑐𝑜𝑠𝜔0 𝑡
1
• And its energy: 𝑊𝐶 𝑡 = 𝐶𝑉0 2 𝑐𝑜𝑠𝜔0 𝑡 2
2
1
V0 : Initial voltage 𝐿𝐶
½CV02
1
𝑊𝐶 𝑡 = 𝐶𝑉0 2 𝑐𝑜𝑠𝜔0 𝑡 2
2
1
𝑊𝐿 𝑡 = 𝐶𝑉0 2 𝑠𝑖𝑛𝜔0 𝑡 2
2
p/2 p w0t 6
, Lossy LC Circuit
𝜕 2 𝑣𝐶 1 𝜕𝑣𝐶 1
• The new differential equation: 𝜕𝑡 2
+
𝑅𝐶 𝜕𝑡
+ 𝑣 =0
𝐿𝐶 𝐶
• The Laplace-domain roots are:
𝜔0 1 jw
𝑠1,2 =− ± 𝑗𝜔0 1 − 2 = −𝛼 ± 𝑗𝜔𝑑
2𝑄 4𝑄
w0 jwd
1
𝜔0 =
𝐿𝐶
Where: 𝑅
f
s
𝑄= = 𝑅𝐶𝜔0
𝐿𝜔0 -a
𝜔0 −𝛼𝑡
• Thus: 𝑣𝐶 𝑡 = 𝑉0
𝜔𝑑
𝑒 cos(𝜔0 𝑡 + 𝜙)
𝑉0 −𝛼𝑡
𝑖𝐿 𝑡 = 𝑒 sin𝜔0 𝑡
𝐿𝜔𝑑 Assume Q >> 1
7
, Energy Balance in Low-Loss LC Circuit
• The total energy is:
1
𝑊𝑇 (𝑡) = 𝑊𝑐 𝑡 + 𝑊𝐿 𝑡 ≈ 𝐶𝑉0 2 𝑒 −2𝛼𝑡
2
½CV02
Capacitor Energy
e-2at
p/2 p
• Energy still moves between L and C, but also decays
8
, Quality Factor
𝑑𝑊𝑇 𝜔0
• The power dissipated is: 𝑝(𝑡) = −
𝑑𝑡
= 2𝛼𝑊𝑇 =
𝑄 𝑇
𝑊
Decay Rate (½CV02)(w0/Q)
e-2at
WT
Q
p/2 p
w0t
• A more physical definition of Q:
𝑊𝑇 𝑇𝑜𝑡𝑎𝑙 𝐸𝑛𝑒𝑛𝑟𝑔𝑦 𝑆𝑡𝑜𝑟𝑒𝑑
𝑄 = 𝜔0 = 𝜔0
𝑝 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑜𝑤𝑒𝑟 𝐷𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑
9
and Systems
Hooman Darabi
March 2020
1
, Course Syllabus
• RF IC Components
• RF Communication Systems
System
• RF networks
• Noise
• Distortion
• Low-noise amplifiers
• Mixers
Circuit
• Oscillators
• Power amplifiers
• Transceiver architectures
2
, Teaching Guidelines
• Slides only used as a guideline, best to use whiteboard only
• Likely not possible to cover all slides for basic RF course
• Skip the following sections:
̶ Chapter 3: Slides 41-43
̶ Chapter 5: Slides 56-57, 61, 64-67
̶ Chapter 7: Slides 108-111, 115-118
̶ Chapter 9: Slides 144-151, 157-163
• About 7-8 slides per lecture may be covered in 20-lecture
quarter-based curricula
• No material for PLLs (chapter 10). It may be covered in a
separate course.
3
, RF IC Components
• Transistors
• High frequency model good for RF (several GHz)
• Resistors
• LC circuits
• Capacitors
• Inductors
• Differential, Transformers
• Transmission lines
4
, LC Circuits
• Widely used in amplifiers, oscillators …
• The energy moves between L and C
• In lossy circuit however, energy decays eventually
+ iL(t) +
C vc(t) L C R vc(t)
- -
Ideal: lossless Practical
5
, Lossless LC Circuit: Ideal Oscillator
𝜕 2 𝑣𝐶 1
• Solve the differential equation: 𝜕𝑡 2
+ 𝑣 =0
𝐿𝐶 𝐶
• The capacitor voltage: 𝑣𝐶 𝑡 = 𝑉0 𝑐𝑜𝑠𝜔0 𝑡
1
• And its energy: 𝑊𝐶 𝑡 = 𝐶𝑉0 2 𝑐𝑜𝑠𝜔0 𝑡 2
2
1
V0 : Initial voltage 𝐿𝐶
½CV02
1
𝑊𝐶 𝑡 = 𝐶𝑉0 2 𝑐𝑜𝑠𝜔0 𝑡 2
2
1
𝑊𝐿 𝑡 = 𝐶𝑉0 2 𝑠𝑖𝑛𝜔0 𝑡 2
2
p/2 p w0t 6
, Lossy LC Circuit
𝜕 2 𝑣𝐶 1 𝜕𝑣𝐶 1
• The new differential equation: 𝜕𝑡 2
+
𝑅𝐶 𝜕𝑡
+ 𝑣 =0
𝐿𝐶 𝐶
• The Laplace-domain roots are:
𝜔0 1 jw
𝑠1,2 =− ± 𝑗𝜔0 1 − 2 = −𝛼 ± 𝑗𝜔𝑑
2𝑄 4𝑄
w0 jwd
1
𝜔0 =
𝐿𝐶
Where: 𝑅
f
s
𝑄= = 𝑅𝐶𝜔0
𝐿𝜔0 -a
𝜔0 −𝛼𝑡
• Thus: 𝑣𝐶 𝑡 = 𝑉0
𝜔𝑑
𝑒 cos(𝜔0 𝑡 + 𝜙)
𝑉0 −𝛼𝑡
𝑖𝐿 𝑡 = 𝑒 sin𝜔0 𝑡
𝐿𝜔𝑑 Assume Q >> 1
7
, Energy Balance in Low-Loss LC Circuit
• The total energy is:
1
𝑊𝑇 (𝑡) = 𝑊𝑐 𝑡 + 𝑊𝐿 𝑡 ≈ 𝐶𝑉0 2 𝑒 −2𝛼𝑡
2
½CV02
Capacitor Energy
e-2at
p/2 p
• Energy still moves between L and C, but also decays
8
, Quality Factor
𝑑𝑊𝑇 𝜔0
• The power dissipated is: 𝑝(𝑡) = −
𝑑𝑡
= 2𝛼𝑊𝑇 =
𝑄 𝑇
𝑊
Decay Rate (½CV02)(w0/Q)
e-2at
WT
Q
p/2 p
w0t
• A more physical definition of Q:
𝑊𝑇 𝑇𝑜𝑡𝑎𝑙 𝐸𝑛𝑒𝑛𝑟𝑔𝑦 𝑆𝑡𝑜𝑟𝑒𝑑
𝑄 = 𝜔0 = 𝜔0
𝑝 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑜𝑤𝑒𝑟 𝐷𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑
9
