Negative feedback amplifiers - I
In this lecture we will discuss:
Negative feedback amplifier
• Desensitization
Seven design steps
• Overview
• First 5 steps consider:
• Feedback
• Gain
Reading instructions: Pages 553-593
Modern Electronics: F10 - feedback amplifiers - I
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Negative feedback amplifier
𝑆𝑜 = 𝑎𝑆𝑒
𝑆𝑓𝑏 = 𝑓𝑆𝑜
𝑆𝑒 = 𝑆𝑖 -𝑆𝑓𝑏 =𝑆𝑖 -𝑓𝑆𝑜
𝑆𝑜 = 𝑎𝑆𝑖 -𝑎f𝑆𝑜
Modern Electronics: F10 - feedback amplifiers - I
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Negative feedback amplifier
𝑆𝑜 = 𝑎𝑆𝑒
𝑆𝑓𝑏 = 𝑓𝑆𝑜
𝑆𝑒 = 𝑆𝑖 -𝑆𝑓𝑏 =𝑆𝑖 -𝑓𝑆𝑜
𝑆𝑜 = 𝑎𝑆𝑖 -𝑎f𝑆𝑜
The feedback determines the transfer function, the closed loop gain:
𝑆𝑜
𝑆𝑖
=𝐴=
𝑎
1+𝑎𝑓
1
𝑓
→ ,𝑎 → ∞
(T=af called loop gain)
The gain stage amplifies the error signal
The more gain a, the smaller errors may be corrected
Distortion is decreased since the errors of the non-linear gain stage are
corrected through the linear feedback
Modern Electronics: F10 - feedback amplifiers - I
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Desensitization
Common source/emitter voltage gain
𝐴𝑉 ~𝑔𝑚 𝑅𝐿
Bipolar: 𝑔𝑚
=
MOSFET: 𝑔𝑚
𝑞𝐼𝐶
𝑘𝑇
=
𝑊
2𝐼𝐷 𝜇𝐶𝑜𝑥
𝐿
Absolute gain depends on
• Load
• Biasing
• Temperature
• Device parameters
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Design steps
1. Identify source and load, asymptotic gain
2. Implement negative feedback, estimate the acquired gain
3. Design first gain stage, consider noise
4. Design last stage, consider distortion
5. Add gain stages to meet the acquired performance
6. Optimize bandwidth, move poles
• Stability, phase margin
• Maximum bandwidth
7. Design biasing
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Step 1, Identify source and load
• Voltage source -> large input impedance and feedback inserted in series
• Current source -> small input impedance and feedback inserted in shunt
• Voltage load -> small output impedance and feedback measured in shunt
• Current load -> large output impedance and feedback measured in series
𝑉 → 𝑉, 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟, 𝑉 𝑉
𝑉 → 𝐼, 𝑇𝑟𝑎𝑛𝑠𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟, [𝐼 𝑉]
Four combinations
𝐼 → 𝑉, 𝑇𝑟𝑎𝑛𝑠𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟, 𝑉 𝐼
𝐼 → 𝐼, 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟, 𝐼 𝐼
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Voltage amplifier
+
+
RL VL
a
-
RS
vS
-
+
vfb
-
R1
+
-
R2
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Two-port gain stage – three terminal devices
Gain stages implemented with one common terminal
• The gain stage may not short-circuit the feedback stage
• The gain stage must support negative feedback
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Common source/emitter
- Negative transfer
- No local feedback
- Almost always present in negative feedback amplifiers
+
-
-
+
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Transconductance Amplifier: Loop gain
a
id
RS
𝑖
Gain 𝑎 = 𝑣𝑑
+
v1
r0
gm·v1
-
1
Feedback 𝑓 =
vS
𝑣1
𝑖𝑑 𝑣𝑠 =0
RI
f
RL
Loop gain, 𝑇 = 𝑎𝑓
1 −𝑎𝑓
Closed-loop gain 𝐴𝑡 = 𝑓 1−𝑎𝑓
Negative feedback amplifier -> 𝑎𝑓 negative
Let us only characterize the DC loop gain today and add frequency response on next
lecture
Modern Electronics: F10 - feedback amplifiers - I
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Example 1
Single stage transconductance amplifier
CS
iL
RS
vS
RL
R1
Modern Electronics: F10 - feedback amplifiers - I
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Common gate/base
- Positive transfer
- Local feedback
- Rules-of-thumb:
• Never used as single amplifier stage
• Never used as input or output stage
+
+
-
-
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Common drain/collector
- Positive transfer
- Local feedback
- Rules-of-thumb:
• Never used as single amplifier stage
• Never used as input stage
+
+
-
-
Modern Electronics: F10 - feedback amplifiers - I
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Differential common source stage
+
Negative transfer
No local feedback
”Real two-port”
- +
-
+
+
IBIAS
Cgd
+
v1
Cgs / 2
Cgd
gm·v1/2
2·r0
vo
+
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Example 2
Two stage voltage amplifier, diff input and cs output
Diff. CS
-
+
+
+
RL VL
-
RS
vS
R1
R2
Modern Electronics: F10 - feedback amplifiers - I
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Transconductance amplifier
+
+
iL
a
-
RS
vS
-
RL
+
vfb
-
R1
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Transresistance amplifier
+
iS
RS
+
RL VL
a
-
+
-
-
ifb
R2
Modern Electronics: F10 - feedback amplifiers - I
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Current amplifier
+
iS
+
RS
iL
a
-
-
RL
ifb
R2
R1
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Example of frequency dependency
Single stage transconductance amplifier
CS
iL
RS
vS
RL
R1
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