E80 Lecture 4.1: Basic Electrical Measurements
Op Amps Circuits
E80 Spring 2014
E80 Lecture 4.2: Basic Electrical Measurements
Agenda: Operational Amplifier
o Recap: Non-inverting amplifier and unity gain buffer
o Inverting amplifier (multiplication)
o Summing amplifier (add and subtract)
o Differentiator and integrator
o Difference amplifier
o Instrumentation amplifier
o Transimpedance amplifier
o Active filters
2
E80 Lecture 4.3: Basic Electrical Measurements
Recap: Opamp Model
3
1 v+ = v− (2) 𝑖+= 0, 𝑖− = 0
V-
V+
V+
V-
E80 Lecture 4.4: Basic Electrical Measurements
Recap: Non-inverting Amplifier
4
• Non-inverting amplifier is designed to produce positive voltage gain
Special case:
R1=∞, Rf=0
Unity-gain buffer
𝑣0 = (1 +𝑅𝑓
𝑅1)𝑣𝑖
E80 Lecture 4.5: Basic Electrical Measurements
Inverting amplifier
5
• Inverting amplifier reverses the polarity of the input signal while amplifying (or attenuating) it
i
f
o vR
Rv
1
E80 Lecture 4.6: Basic Electrical Measurements
Summing amplifier
6
• Summing Amplifier is an op amp circuit that combines several inputs and produces an output that is the weighted sum of the inputs.
3
3
2
2
1
1
vR
Rv
R
Rv
R
Rv
fff
o
Q: Is it possible to construct a non-inverting summing amp?
E80 Lecture 4.7: Basic Electrical Measurements
Opamp Circuit With Capacitor
7
Inverting amplifier
What does this circuit do?
How is Vo related to Vi?
E80 Lecture 4.8: Basic Electrical Measurements
Opamp Circuit With Capacitor
8
Integrator circuit
What does this circuit do?
How is Vo related to Vi?
)0()(1
)(0
C
t
io vdvRC
tv
E80 Lecture 4.9: Basic Electrical Measurements
Example
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What does the output waveform look like?
E80 Lecture 4.10: Basic Electrical Measurements
Solving Differential Equation Using
Opamp Circuit
10
𝑣0 + 3𝑣0 + 2𝑣0 = 4cos (10𝑡)
RC=1 sec
E80 Lecture 4.11: Basic Electrical Measurements
Difference Amplifier
11
• Difference amplifier is a device that amplifies the difference between two inputs but rejects any signals common to the two inputs.
𝑣0 =1 + 𝑅2/𝑅11 + 𝑅3/𝑅4
𝑣2 −𝑅2𝑅1
𝑣1 𝑅1 = 𝑅2 𝑎𝑛𝑑 𝑅3 = 𝑅4
𝑣0 = 𝑣2 − 𝑣1
Special case:
E80 Lecture 4.12: Basic Electrical Measurements
Instrumentation Amplifier
E80 Lecture 4.13: Basic Electrical Measurements
Instrumentation Amplifier Application
(1) Only amplify difference
(2) Infinite Input resistance
zero Output resistance
E80 Lecture 4.14: Basic Electrical Measurements
Transimpedance amplifier for
photodiode
𝑣0 = 𝑖 ∙ 𝑅
D
R
Vbias
photon
voi
• Much easier to measure voltage than current
• Provide large amplification
E80 Lecture 4.15: Basic Electrical Measurements
Active filter
• RC and OpAmp (<1MHz, bulky inductor
in RLC filters)
• 1st order filters
– Low pass
– High pass
– Inverting
– Non-inverting
• 2nd order low pass filter
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E80 Lecture 4.16: Basic Electrical Measurements
Active Filter Example
Say Rf>Ri
𝐻 𝑗𝜔 = −𝑅𝑓/𝑅𝑖
1 + 𝑗𝜔𝑅𝑓𝐶𝑓
Low pass filter
Sketch Bode Plot
E80 Lecture 4.17: Basic Electrical Measurements
Active Filter Example
17
Non-inverting 1st order low pass active filter
𝐻 𝑗𝜔 =1 + 𝑅2/𝑅31 + 𝑗𝜔𝑅1𝐶1
E80 Lecture 4.18: Basic Electrical Measurements
Active Filter Example
18
Say Rf>Ri
𝐻 𝑗𝜔 = −𝑗𝜔𝑅𝑓𝐶𝑖
1 + 𝑗𝜔𝑅𝑖𝐶𝑖
High pass filter
Sketch Bode Plot
E80 Lecture 4.19: Basic Electrical Measurements
Active Filter Example
19
Non-inverting 1st order high pass active filter
𝐻 𝑗𝜔 =𝑗𝜔𝑅1𝐶1(1 +
𝑅2𝑅3
)
1 + 𝑗𝜔𝑅1𝐶1
E80 Lecture 4.20: Basic Electrical Measurements
Active Filter Example
20
Say R2>R1
𝐻 𝑗𝜔 =−𝑗𝜔𝑅2𝐶1
(1 + 𝑗𝜔𝑅1𝐶1)(1 + 𝑗𝜔𝑅2𝐶2)
Bandpass filter
Sketch Bode Plot
E80 Lecture 4.21: Basic Electrical Measurements
2nd order Active Filter
Sallen-Key Low Pass Filter
21
Find frequency response function of unity-gain Sallen Key
Topology
𝐻 𝑗𝜔 =1
1 + 𝑗𝜔(𝑅1+𝑅2)𝐶1 −𝜔2𝑅1𝑅2𝐶1𝐶2