Electronic Circuits for Mechatronics (ELCT 609)...Note that: Q1 and Q2 are matched and β is large. 𝑉 =𝐾 𝐼 𝐼 𝑉 =𝐾 𝐼 𝐼 − Course Instructor: Dr. Eman Azab Contact:

Electronic Circuits for Mechatronics

(ELCT 609)

Summer 2020 : Round II

Lecture 11: Op-amp Linear and Non-linear

Applications

Course Instructor: Dr. Eman Azab

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Op-amps: IntroductionCircuit Modeling


Contact: [email protected]

Electronic Circuits for Mechatronics ELCT 609

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mailto:[email protected]

Ideal Op-amp Operational amplifiers are

voltage amplifiers with very highgain

Differential Input/Single outputcircuit is the most famous op-amp structure

Ideal op-amp have the followingSpecs:

Infinite Differential voltagegain

Zero Common-modevoltage gain

Infinite Input Resistance

Zero Input Currents

Zero Output Resistance

Infinite Bandwidth (Gain isconstant all over thefrequency Spectrum)

𝑉𝑜𝑢𝑡 = 𝐴𝑉𝑑 𝑉1 − 𝑉2 + 𝐴𝑉𝑐𝑚𝑉1 + 𝑉2

2

𝐴𝑉𝑑 = ∞ 𝐴𝑉𝑐𝑚 = 0

𝑅𝑖𝑛 = ∞ 𝑅𝑜𝑢𝑡 = 0

𝐴𝑉𝑑 𝑠 = 𝐶𝑜𝑛𝑠𝑡.

𝑖𝑖𝑛+ = 0 𝑖𝑖𝑛− = 0




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Operational amplifiers arevoltage amplifiers with very highgain

Differential Input/Single outputcircuit is the most famous op-amp structure

Ideal op-amp have the followingSpecs:

Infinite Differential voltagegain

Zero Common-modevoltage gain

Infinite Input Resistance

Zero Input Currents

Zero Output Resistance

Infinite Bandwidth (Gain isconstant all over thefrequency Spectrum)


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Ideal Op-amp Ideal Op-amp can be modeled using the following circuit:


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𝐴𝑉𝑑 = ∞ 𝐴𝑉𝑐𝑚 = 0

𝑅𝑖𝑛 = ∞ 𝑅𝑜𝑢𝑡 = 0

𝐴𝑉𝑑 𝑠 = 𝐶𝑜𝑛𝑠𝑡.

𝑖𝑖𝑛+ = 0 𝑖𝑖𝑛− = 0Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.




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Non-ideal Op-ampCircuit Realizations of Op-amp




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Ex.: Two stage CMOS Op-amp




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Ex.: BJT 741 Op-amp




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Op-amp Applications




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Voltage Amplifier

Inverting and Non-Inverting Amplifiers

𝑣𝑂𝑣𝐼

= −𝑅2𝑅1

𝑣𝑂𝑣𝐼

= 1 +𝑅2𝑅1

Figures from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.




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Voltage Amplifier

Inverting Amplifiers

𝑣𝑂𝑣𝐼

= −𝑅2𝑅1




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Voltage Buffer

Voltage Buffer

The voltage at the input is derived at the output node

without drawing any current from the input source

𝑣𝑂𝑣𝐼

= 1

Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.




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Voltage Difference Amplifier

The circuit subtracts two voltage signals

By Applying Superposition principle between 𝑣𝐼1 and 𝑣𝐼2

By Choosing:

𝑣𝑂 = −𝑣𝐼1𝑅2𝑅1

+ 𝑣𝐼2𝑅4

𝑅4 + 𝑅31 +

𝑅2𝑅1

𝑅2𝑅1

=𝑅4𝑅3

𝑣𝑂 =𝑅2𝑅1

𝑣𝐼2 − 𝑣𝐼1




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Voltage Integrator

Inverting configuration with General Impedances

Lossless inverting Integrator

𝑉𝑂𝑉𝑖

= −𝑍2𝑍1




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Voltage Integrator

Lossy Integrator

DC Gain is defined by:

𝑣𝑂𝑣𝑖

= −

𝑅𝐹𝑅

1 + 𝑠𝐶𝑅𝐹

𝑣𝑂𝑣𝑖(0) = −

𝑅𝐹𝑅




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Voltage Differentiator

Op-amp based Differentiator

𝑣𝑂𝑣𝑖(𝑠) = −𝑠𝐶𝑅




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Voltage Weighted Summer





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Voltage Comparator


Positive Feedback is employed

The output voltage is either the high or the low voltagesupply

𝑣𝑖 < 𝑣+ 𝑣𝑂 = 𝑉𝐶𝐶

𝑣𝑖 > 𝑣+ 𝑣𝑂 = 𝑉𝑆𝑆




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Voltage Logarithmic Amplifier Non-linear logarithmic Amplifier

BJT operates in the Active Region

𝑉𝑜𝑢𝑡 = −𝑉𝐵𝐸 = −𝑉𝑇𝑙𝑛𝐼𝐶𝐼𝑜

𝐼𝐶 =𝑉𝑖𝑛𝑅1

𝑉𝑜𝑢𝑡 = −𝑉𝐵𝐸 = −𝑉𝑇𝑙𝑛𝑉𝑖𝑛𝐼𝑜𝑅1




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Voltage anti-Logarithmic Amplifier

Non-linear Anti-logarithmic Amplifier

BJT operates in the Active Region

𝑉𝑖𝑛 = −𝑉𝐵𝐸 = −𝑉𝑇𝑙𝑛𝐼𝐶𝐼𝑜

𝐼𝐶 =𝑉𝑜𝑢𝑡𝑅1

𝑉𝑜𝑢𝑡 = 𝐼𝑜𝑅1exp−𝑉𝑖𝑛𝑉𝑇




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Voltage Multiplier or Divider

𝑉𝑜𝑢𝑡 = 𝐼𝑜𝑅1exp−𝑉𝑖𝑛𝑉𝑇

𝑉𝑜𝑢𝑡 = −𝑉𝐵𝐸 = −𝑉𝑇𝑙𝑛𝑉𝑖𝑛𝐼𝑜𝑅1




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Example

For the 4127 IC showed in figure, find the output voltage (Vout) as a function in the input currents (Ix and Iy).

Using the 4127 IC and the linear/nonlinear op-amp applications, design the following functions with minimum number of op-amps and derive K, n and m as a function in the circuit parameters.

Note that: Q1 and Q2 are matched and β is large.

𝑉𝑜𝑢𝑡 = 𝐾𝐼𝑥𝐼𝑦

𝑚

𝑉𝑜𝑢𝑡 = 𝐾𝐼𝑥𝐼𝑦

𝑚−𝑛




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Example Solution

For the 4127 IC showed in figure, find the output voltage (Vout) as a function in the input currents (Ix and Iy).

Note that: Q1 and Q2 are matched and β is large.


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Documents

Electronic Circuits for Mechatronics (ELCT 609)...Note that: Q1 and Q2 are matched and β is large. 𝑉 =𝐾 𝐼 𝐼 𝑉 =𝐾 𝐼 𝐼 − Course Instructor: Dr. Eman Azab Contact: