RF Integrated Circuits and Systems Hooman Darabi March 2020
1
Circuit
System
Course Syllabus • RF IC Components • RF Communication Systems • RF networks • Noise • Distortion • Low-noise amplifiers • Mixers • 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
-
Ideal: lossless
R
vc(t) -
Practical 5
Lossless LC Circuit: Ideal Oscillator 𝜕 2 𝑣𝐶 1 + 𝑣 =0 𝜕𝑡 2 𝐿𝐶 𝐶
• Solve the differential equation: 𝑣 𝑡 = 𝑉 𝑐𝑜𝑠𝜔 𝑡 • The capacitor voltage: 𝐶
• And its energy:
0
0
1 𝑊𝐶 𝑡 = 𝐶𝑉0 2 𝑐𝑜𝑠𝜔0 𝑡 2 2 1
𝐿𝐶
V0 : Initial voltage ½CV02 𝑊𝐶 𝑡 =
1 𝐶𝑉0 2 𝑐𝑜𝑠𝜔0 𝑡 2 2
1 𝑊𝐿 𝑡 = 𝐶𝑉0 2 𝑠𝑖𝑛𝜔0 𝑡 2 2
p/2
p
w0t
6
Lossy LC Circuit • The new differential equation: • The Laplace-domain roots are:
𝜕 2 𝑣𝐶 1 𝜕𝑣𝐶 1 + + 𝑣 =0 𝜕𝑡 2 𝑅𝐶 𝜕𝑡 𝐿𝐶 𝐶
𝜔0 1 𝑠1,2 = − ± 𝑗𝜔0 1 − 2 = −𝛼 ± 𝑗𝜔𝑑 2𝑄 4𝑄 𝜔0 =
Where:
• Thus:
𝑖𝐿 𝑡 =
jwd
w0
1
𝐿𝐶 𝑅 𝑄= = 𝑅𝐶𝜔0 𝐿𝜔0
𝑣𝐶 𝑡 = 𝑉0
jw
f
s
-a
𝜔0 −𝛼𝑡 𝑒 cos(𝜔0 𝑡 + 𝜙) 𝜔𝑑
𝑉0 −𝛼𝑡 𝑒 sin𝜔0 𝑡 𝐿𝜔𝑑
Assume Q >> 1 7
Energy Balance in Low-Loss LC Circuit • The total energy is: 𝑊𝑇 (𝑡) = 𝑊𝑐 𝑡 + 𝑊𝐿 𝑡 ≈
1 𝐶𝑉0 2 𝑒 −2𝛼𝑡 2
Capacitor Energy
½CV02
e-2at
p/2
p
• Energy still moves between L and C, but also decays 8
Quality Factor • The power dissipated is:
𝑝(𝑡) = −
𝑑𝑊𝑇 𝜔0 = 2𝛼𝑊𝑇 = 𝑊 𝑑𝑡 𝑄 𝑇
e-2at
WT
Decay Rate
(½CV02)(w0/Q)
p/2
Q p
w0t
• A more physical definition of Q: 𝑊𝑇 𝑇𝑜𝑡𝑎𝑙 𝐸𝑛𝑒𝑛𝑟𝑔𝑦 𝑆𝑡𝑜𝑟𝑒𝑑 𝑄 = 𝜔0 = 𝜔0 𝑝 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑜𝑤𝑒𝑟 𝐷𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 9
More Practical Q Definition • Practical inductors/capacitors have series loss 1 𝑟 − 𝑗𝐿𝜔 1 1 = = + • Since: 1 𝑟 + 𝑗𝐿𝜔 𝑟 + (𝐿𝜔 ) 𝑟(𝑄 + 1) 0
0
2
0
2
2
𝑗𝐿𝜔0 (1 +
𝑄2
)
L
@ r
• In general:
𝑄=
L
R=rQ2
• The circuits below are equivalent (at one frequency)
𝑅 𝐿𝜔0 = 𝐿𝜔0 𝑟
1 1 1 ≈ + 𝑄 𝑄𝐿 𝑄𝐶
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