Engineering 43
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Engineering 43. Chp 6.4 RC OpAmps Ckts. Bruce Mayer, PE Registered Electrical & Mechanical Engineer [email protected] RC OpAmp Circuits. Introduce Two Very Important Practical Circuits Based On Operational Amplifiers Recall the OpAmp. The “Ideal” Model That we Use R O = 0

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Bruce mayer pe registered electrical mechanical engineer bmayer chabotcollege

Engineering 43

Chp 6.4RC OpAmps Ckts

Bruce Mayer, PE

Registered Electrical & Mechanical [email protected]


Rc opamp circuits

RC OpAmp Circuits

  • Introduce Two Very Important Practical Circuits Based On Operational Amplifiers

  • Recall the OpAmp

  • The “Ideal” Model That we Use

    • RO = 0

    • Ri = ∞

    • Av = ∞

  • Consequences of Ideality

    • RO = 0  vO = Av(v+−v−)

    • Ri = ∞  i+ = i− = 0

    • Av = ∞  v+ = v−


Rc opamp ckt integrator

=

v

0

+

RC OpAmp Ckt  Integrator

  • KCL At v- node

  • By Ideal OpAmp

    • Ri = ∞  i+ = i- = 0

    • Av = ∞  v+ = v- = 0


Rc opamp integrator cont

RC OpAmp Integrator cont

  • Separating the Variables and Integrating Yields the Solution for vo(t)

  • By the Ideal OpAmp Assumptions

  • Thus the Output is a (negative) SCALED TIME INTEGRAL of the input Signal

  • A simple Differential Eqn


Rc opamp ckt differentiator

KVL

=

v

0

+

RC OpAmp Ckt  Differentiator

  • By Ideal OpAmp

    • v- = GND = 0V

    • i- = 0

  • KCL at v-

  • Now the KVL


Rc opamp differentiator cont

RC OpAmp Differentiator cont.

  • Recall the Capacitor Integral Law

  • Recall Ideal OpAmp Assumptions

    • Ri = ∞  i+ = i- = 0

    • Av = ∞  v+ = v- = 0

  • Then the KCL

  • Thus the KVL

  • Taking the Time Derivative of the above


Rc opamp differentiator cont1

RC OpAmp Differentiator cont

  • Examination of this Eqn Reveals That if R1 were ZERO, Then vO would be Proportional to the TIME DERIVATIVE of the input Signal

    • in Practice An Ideal Differentiator Amplifies Electrical Noise And Does Not Operate

    • The Resistor R1 Introduces A Filtering Action.

      • Its Value Is Kept As Small As Possible To Approximate A Differentiator

  • In the Previous Differential Eqn use KCL to sub vO for i1

    • Using


Aside electrical noise

ALL electrical signals are corrupted by external, uncontrollable and often unmeasurable, signals. These undesired signals are referred to as NOISE

Signal

Signal

Noise

Noise

Aside → Electrical Noise

  • The Signal-To-Noise Ratio

  • Use an Ideal Differentiator

  • Simple Model For A Noisy 1V, 60Hz Sinusoid Corrupted With One MicroVolt of 1GHz Interference

  • The SN is Degraded Due to Hi-Frequency Noise


Class exercise ideal differen

Class Exercise  Ideal Differen.

  • Let’s Turn on the Lites for 10 minutes for YOU to Differentiate

  • Given the IDEAL Differentiator Ckt and INPUT Signal

  • Find vo(t) over 0-10 ms

  • Given Input v1(t)

    • SAWTOOTH Wave

  • Recall the Differentiator Eqn

R1 = 0; Ideal ckt


Rc opamp differentiator ex

RC OpAmp Differentiator Ex.

  • The Slope from 0-5 mS

  • Given Input v1(t)

  • For the Ideal Differentiator

  • Units Analysis


Rc opamp differentiator cont2

RC OpAmp Differentiator cont.

  • Derivative Scalar PreFactor

  • A Similar Analysis for 5-10 mS yields the Complete vO

OutPut

InPut

  • Apply the Prefactor Against the INput Signal Time-Derivative (slope)


Rc opamp integrator example

RC OpAmp Integrator Example

  • For the Ideal Integrator

  • Given Input v1(t)

    • SQUARE Wave

  • Units Analysis Again


Rc opamp integrator ex cont

RC OpAmp Integrator Ex. cont.

  • 0<t<0.1 S

    • v1(t) = 20 mV (Const)

  • The Integration PreFactor

  • 0.1t<0.2 S

    • v1(t) = –20 mV (Const)

  • Next Calculate the Area Under the Curve to Determine the Voltage Level At the Break Points

  • Integrate In Similar Fashion over

    • 0.2t<0.3 S

    • 0.3t<0.4 S


Rc opamp integrator ex cont 1

RC OpAmp Integrator Ex. cont.1

  • Apply the 1000/S PreFactor and Plot Piece-Wise


Practical example

Practical Example

  • Simple Circuit Model For a Dynamic Random Access Memory Cell (DRAM)

  • Note How Undesired Current Leakage is Modeled as an I-Src

  • Also Note the TINY Value of the Cell-State Capacitance (50x10-15 F)


Practical example cont

Practical Example cont

  • During a WRITE Cycle the Cell Cap is Charged to 3V for a Logic-1

    • Thus The TIME PERIOD that the cell can HOLD the Logic-1 value

  • The Criteria for a Logic “1”

    • Vcell >1.5 V

  • Now Recall that V = Q/C

    • Or in terms of Current

  • Now Can Calculate the DRAM “Refresh Rate”


Practical example cont 2

Practical Example cont.2

  • Consider the Cell at the Beginning of a READ Operation

  • When the Switch is Connected Have Caps in Parallel

  • Then The Output

  • Calc the Change in VI/O at the READ


Design example

Design an OpAmp ckt to implement in HARDWARE this Math Relation

Design Example

  • Examine the Reln to find an

Integrator

Adder


Design example1

The Proposed Solution

Design Example

  • The by Ideal OpAmps & KCL & KVL &Superposition


Design example2

Design Example

  • The Ckt Eqn

  • Then the Design Eqns

  • This means that we, as ckt designers, get to PICK 3 values

  • For 1st Cut Choose

    • C = 20 μF

    • R1 = 100 kΩ

    • R4 = 20 kΩ

  • TWO Eqns in FIVE unknowns


Design example3

In the Design Eqns

Design Example

20μ

20k

20k

100k

10k

  • If the voltages are <10V, then all currents should be the in mA range, which should prevent over-heating

  • Then the DESIGN


Whiteboard work

WhiteBoard Work

  • Let’s Work These Probs

80k

choose C such that

Find Energy Stored on Cx


Appendix

APPENDIX

IC GROUND BOUNCE


Bruce mayer pe registered electrical mechanical engineer bmayer chabotcollege

LEARNING EXAMPLE

FLIP CHIP MOUNTING

IC WITH WIREBONDS TO THE OUTSIDE

GOAL: REDUCE INDUCTANCE IN

THE WIRING AND REDUCE THE

“GROUND BOUNCE” EFFECT

A SIMPLE MODEL CAN BE USED TO

DESCRIBE GROUND BOUNCE


Bruce mayer pe registered electrical mechanical engineer bmayer chabotcollege

MODELING THE GROUND BOUNCE EFFECT

IF ALL GATES IN A CHIP ARE CONNECTED TO A SINGLE GROUND THE CURRENT

CAN BE QUITE HIGH AND THE BOUNCE MAY BECOME UNACCEPTABLE

USE SEVERAL GROUND CONNECTIONS (BALLS) AND ALLOCATE A FRACTION OF

THE GATES TO EACH BALL


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