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ECE 3336 Introduction to Circuits & Electronics. Set #14. MORE on Operational Amplifiers. Fall 2012, TUE&TH 5:30-7:00 pm Dr. Wanda Wosik. Basics of Operational Amplifiers Noninverting Case. We will focus on operational amplifiers, specifically on

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Ece 3336 introduction to circuits electronics
ECE 3336 Introduction to Circuits & Electronics

Set #14

MORE on Operational Amplifiers

Fall 2012,

TUE&TH 5:30-7:00 pm

Dr. Wanda Wosik

Basics of operational amplifiers noninverting case
Basics of Operational AmplifiersNoninverting Case

We will focus on operational amplifiers, specifically on

  • Ideal Operational Amplifiers, definitions and requirements for their ideal operation in noninverting configuration

  • Negative Feedback that allows for op-amp to be controlled by external elements

Solving op amp circuits
Solving Op Amp Circuits

As for inverting configuration we will have two assumptions for the analysis and design. We will again treat the op amps as ideal circuits. We will again call these assumptions golden rules.

  • The first assumption: i- = i+ = 0.results from large resistances at the inputs. Currents do not flow into the op-amp.

  • The second assumption v+≈v- deals with the output that makes the input voltages equal v+≈v-. This is realized by introducing negative feedback loop, which spans the output and the inverting input.


negative feedback loop

A note on the second assumption
A Note on the Second Assumption

The second golden rule v- = v+results in the virtual short, or the summing-point constraint. The constrain refers to the input voltages, which become the same v- = v+ if there is the negative feedback and the open loop gain Av(OL) is large.

Without negative feedback, even a small input voltage will cause saturation of the output either at V+ or V-. That depends on the sign of vin.

Negative dc

power supply







This is open loop configuration

+ dc V supply

Op amp circuits with the negative feedback loop
Op Amp Circuits with the Negative Feedback Loop

Negative feedback adds a portion of the output signal to the inverting input. Since the signs of these voltages are opposite, the negative feedback acts as if the signal applied to the input decreases.

The net result is that the output voltage can be controlled by the external elements and does not saturate.

Negative feedback

For ideal op-amps we will apply two golden rules to solve circuits


Golden Rules

1)i- = i+ = 0.

2) v- = v+. Virtual short

Op amp in the non inverting configuration
Op Amp in the Non-inverting Configuration

These comments are identical as for the inverting configuration

An op amp operates in the noninverting configuration when the input voltage is applied to the noninverting terminal.

RF is the feedback resistor

Rs is the source resistor

  • There is a negative feedback thanks to RF

  • Negative feedback gives the virtual short:v-=v+. Since v+=Vs also v-=Vs.

  • The op-amp does not draw currents iin=0A



Solving op amp in the non inverting configuration closed loop
Solving op-amp in the Non-Inverting Configuration Closed Loop

As earlier, to find vout we have to find vRF.

To find vRF we have to know current iFwhich can be calculated from is.

The current is is given by the voltage v-=Vs and Rs.

Since we have golden rules (iin=0, v+=v-)







Closed loop voltage GAIN:

Significance of the closed loop gain
Significance of the Closed Loop Gain

The negative feedback loop, combined with ideal properties of the op-amp (high open loop gain 105-107 and large input resistance) ensures that

  • the gain does not depend on the op amp

  • the gain is the determined by a ratio of two resistors connected to the op-amp.

No phase change


Voltage follower
Voltage Follower

Golden rules apply:

v+=v- and iin=0A

  • Important application of the noninverting configuration is obtained when there is no resistance in the negative feedback loop.


So, the voltage at the input is the same as the voltage at the output vout=vS.

Do we gain anything here by doing that?




We do! We have a very large input resistance of this circuit:

  • Such op-amps do not showloading effects (i.e. voltage drop due to low resistance connected to an output of a circuit).

  • They work as voltage follower but they also act as impedance buffers.

The differential amplifier
The Differential Amplifier

  • This is a combination of inverting and noninverting configuration. As earlier we have negative feedback and the op-amp is ideal.




Group and arrange:

Instrumentation amplifier ia
Instrumentation Amplifier (IA)

IA are made as integrated circuits

Now use the results from differential op-amp










Very high input resistance

Very high common-mode-rejection-ratio CMMR (goal: CMMR  for perfectly matched resistors. That results in vout≈0V for v1=v2)


The integrating circuit was used earlier

Now we add the op-amp and we get an integrator. It also constitutes a part of an analog computer

The Golden Rules are used for the op-amp

Now we integrate both sides and we have the integrator

Virtual short


The differentiating circuit was used earlier

Now we add the op-amp and we get a differentiator. It also constitutes a part of an analog computer.

The Golden Rules are used for the op-amp

Active filters
Active Filters

  • The concept of frequency dependence of the signals seen in the filters (remember that we had |H(j)|max=1 for those filters) is here combined with the signal amplification.

  • We will use here the negative feedback configuration

  • We will also use impedances instead of resistors

  • We still have the same golden rules:

    • no input currents (high Rin)

    • virtual short

Active low pass filter
Active Low-Pass Filter

The voltage gain ALP is calculated using Golden Rules


Cutoff frequency



So the cutoff frequency is also the 3dB frequency (as before)


Phase is just like for the simple filter

Negative feedback

Inverting configuration

Active High-Pass Filter

The voltage gain calculated using Golden Rules




3dB frequency


Phase is just like for the simple high pass filter

Op amp as a level shifter
Op-Amp as a Level Shifter

A useful circuit to adjust DC voltage level = to remove the DC offset from the signal

Use the superposition principle (one source at a time)





Power supply

We can design such precision voltage sources using Rp

We want this to be equal 0V

That gives Vref=1.714V


Negative feedback

Inverting configuration

Active Band-Pass Filter

The voltage gain ABP is again calculated using Golden Rules

Three characteristic frequencies

Relations between the frequencies

Magnitude of ABP


1 is the unity gain frequency

Characteristic frequencies in the band pass filters
Characteristic Frequencies in the Band-Pass Filters

The voltage gain has 3 characteristic frequencies: 1, LP and HP



Gain around LP


Gain around HP


Cancel off 0

So LP and HP are 3dB frequencies while 1 is the unity gain frequency

Bode plots for the active band pass filter
Bode Plots for the Active Band-Pass Filter

We can plot the magnitude of the voltage gain as a function of frequency

Linear scale

dB scale







Relations between the frequencies



The phase is like for simple bandpass filters



Limitations of the Op-Amps

Saturation of the voltage at the output occurs at about ±Vs.

Small signals at the input are required

Limitations of the op amps
Limitations of the Op-Amps

Frequency Response Limits refer to the voltage gain of the open loop and closed loop configuration

Open loop gain decreases very quickly with frequency

The voltage gain decreases in the closed loop configuration but the cutoff frequency increases

The gain-bandwidth product is constant K

Limitations of the op amps1
Limitations of the Op-Amps

Slew rate limitation of op-amp means that the op-amp output voltage does not respond with the same slope as the input signal

Increasing frequency means faster changing or steeper slopes at the zero crossing

Slew rate is limited by the frequency and amplitude product

As the result of limited slew there is a distortion of the output signal.