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ECE 3336 Introduction to Circuits & Electronics

MORE on Operational Amplifiers

Spring 2015,TUE&TH 5:30-7:00 pmDr. Wanda Wosik

Set #14

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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

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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.

iin=0A• 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

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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.

Inverting Input

Noninverting Input

+ dc V supply

Output

NO NEGATIVE FEEDBACK yet

This is open loop configuration

Negative dc power supply

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Op Amp Circuits with the Negative Feedback Loop

Golden Rules

1) i- = i+ = 0.

2) v- = v+. Virtual short

Negative feedback

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.

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

ideal

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Op Amp in the Non-inverting Configuration

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

RF is the feedback resistorRs 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

These comments are identical as for the inverting configuration

ideal

Av(OL)≈∞

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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 iF which can be calculated from is. The current is is given by the voltage v-=Vs and Rs.

ideal

v+=vSAv(OL)≈∞

0A

0A

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

Closed loop voltage GAIN:

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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 ideal

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Voltage Follower

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

ideal

VS

VS

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 show loading 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.

RF=0ΩGolden rules apply:

v+=v- and iin=0A

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The Differential Amplifier

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

op-amp is ideal. i2=-i1

v-=v+

iin=0

Group and arrange:

Rearrange

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Instrumentation Amplifier (IA)

iR1

v2

v1

iin=0

iin=0iin=0

Now use the results from differential op-amp with vout1 and vout2 replacing original

v1 and v2

vout2

vout1

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

IA are made as integrated circuits

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Integrator

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

Virtual short

The integrating circuit was used earlier

Now we integrate both sides and we have the integrator

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Differentiator

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

The differentiating circuit was used earlier

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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

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Active Low-Pass Filter

0V

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

Phase is just like for the simple filter

The voltage gain ALP is calculated using Golden Rules

Amplification

Cutoff frequencyAmplification

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Active High-Pass Filter

Phase is just like for the simple high pass filter

The voltage gain calculated using Golden Rules

Negative feedbackInverting configuration

cutoff

3dB frequency

Phase:

Amplification

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Op-Amp as a Level Shifter

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

inverting noninverting

220kΩ

10kΩ

We want this to be equal 0VThat gives Vref=1.714V

We can design such precision voltage sources using Rp

Potentiometer

Power supply

Use the superposition principle (one source at a time)

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Active Band-Pass FilterThe voltage gain ABP is again calculated using Golden Rules

Magnitude of ABP

Negative feedbackInverting configuration

1 is the unity gain frequency

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Relations between the frequencies

Three characteristic frequencies

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Characteristic Frequencies in the Band-Pass Filters

Cancel off 0 -3dB

-3dB

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

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

Gain around LP

Gain around HP

=0 =0

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Bode Plots for the Active Band-Pass Filter

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LP HP

LP HP1

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

Relations between the frequencies

The phase is like for simple bandpass filters LP HP

Linear scale dB scale

45°

-45°

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Limitations of the Op-Amps

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

Small signals at the input are required

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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 increasesThe gain-bandwidth product is constant K

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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.