Op Amps Ch 2: Common Op Amp Configurations

Ch2: Common Op Amps Configurations

Op Amps Table of Contents

Unity Gain Buffer

To build a unity gain buffer, you simply connect the input to the non-inverting pin and feedback the output to the inverting pin. It’s a very simple circuit and gives you an amplifier circuit with a gain of 1. This might not seem like a very useful feature, but check out this video to learn more about this circuit:

This video describes the connections and purposes of a unity gain buffer and shows why an infinite open loop voltage gain leads to unity gain when you have negative feedback.

Unity Gain Amplifier Practice Problems

Question 1. (Click on arrow for answer)

Write the transfer function (input/output equation) for an operational amplifier with an open-loop voltage gain of 100,000, and the inverting input connected directly to its output terminal. In other words, write an equation describing the output voltage of this op-amp ( $V_{out}$ ) for any given input voltage at the noninverting input ( $V_{in(+)}$ ):

Then, once you have an equation written, solve for the over-all voltage gain ( $A_V = {V_{out} \over V_{in(+)}}$ ) of this amplifier circuit, and calculate the output voltage for a noninverting input voltage of +6 volts.

File Num: 00927

Answer

V_{out} = 100,000(V_{in(+)} - V_{out})

(I’ve left it up to you to perform the algebraic simplification here!)

A_V = {100,000 \over 100,001} = 0.99999

For an input voltage of +6 volts, the output voltage will be +5.99994 volts.

Notes

The significant point of this question is that students see the over-all voltage gain of the opamp radically attenuated from 100,000 to approximately 1. What is not so evident is just how stable this new voltage gain is, which is one of the purposes for employing negative feedback.

Question 2. (Click on arrow for answer)

How much effect will a change in the op-amp’s open-loop voltage gain have on the overall voltage gain of a negative-feedback circuit such as this?

If the open-loop gain of this operational amplifier were to change from 100,000 to 200,000, for example, how big of an effect would it have on the voltage gain as measured from the noninverting input to the output?

File Num: 02288

Answer

The different in overall voltage gain will be trivial.

Follow-up question: what advantage is there in building voltage amplifier circuits in this manner, applying negative feedback to a “core” amplifier with very high intrinsic gain?

Notes

Work with your students to calculate a few example scenarios, with the old open-loop gain versus the new open-loop gain. Have the students validate their conclusions with numbers!

Negative feedback is an extremely useful engineering principle, and one that allows us to build very precise amplifiers using imprecise components. Credit for this idea goes to Harold Black, an electrical engineer, in 1920’s. Mr. Black was looking for a way to improve the linearity and stability of amplifiers in telephone systems, and (as legend has it) the idea came to him in a flash of insight as he was commuting on a ferry boat.

An interesting historical side-note is that Black’s 1928 patent application was initially rejected on the grounds that he was trying to submit a perpetual motion device! The concept of negative feedback in an amplifier circuit was so contrary to established engineering thought at the time, that Black experienced significant resistance to the idea within the engineering community. The United States patent office, on the other hand, was inundated with fraudulent “perpetual motion” claims, and so dismissed Black’s invention at first sight.

Question 3. (Click on arrow for answer)

Complete the table of voltages for this opamp “voltage follower” circuit:

$$\vbox{\offinterlineskip \halign{\strut \vrule \quad\hfil # \ \hfil & \vrule \quad\hfil # \ \hfil \vrule \cr \noalign{\hrule}

V_{in}

V_{out}

\cr\noalign{\hrule}

0 volts & 0 volts \cr

\noalign{\hrule}+5 volts & \cr\noalign{\hrule}+10 volts & \cr\noalign{\hrule}+15 volts & \cr\noalign{\hrule}+20 volts & \cr\noalign{\hrule}-5 volts & \cr\noalign{\hrule}-10 volts & \cr\noalign{\hrule}-15 volts & \cr\noalign{\hrule}-20 volts & \cr\noalign{\hrule} } % End of \halign }$$ % End of \vbox

File Num: 02289

Answer

$$\vbox{\offinterlineskip \halign{\strut \vrule \quad\hfil # \ \hfil & \vrule \quad\hfil # \ \hfil \vrule \cr \noalign{\hrule}

V_{in}

V_{out}

\cr\noalign{\hrule}

0 volts & 0 volts \cr

\noalign{\hrule}+5 volts & +5 volts \cr\noalign{\hrule}+10 volts & +10 volts \cr\noalign{\hrule}+15 volts & +15 volts \cr\noalign{\hrule}+20 volts & +15 volts \cr\noalign{\hrule}-5 volts & -5 volts \cr\noalign{\hrule}-10 volts & -10 volts \cr\noalign{\hrule}-15 volts & -15 volts \cr\noalign{\hrule}-20 volts & -15 volts \cr\noalign{\hrule} } % End of \halign }$$ % End of \vbox

Follow-up question: the output voltage values given in this table are ideal. A real opamp would probably not be able to achieve even what is shown here, due to idiosyncrasies of these amplifier circuits. Explain what would probably be different in a real opamp circuit from what is shown here.

Notes

A common mistake I see students new to opamps make is assuming that the output voltage will magically attain whatever value the gain equation predicts, with no regard for power supply rail voltage limits.

Another good follow-up question to ask your students is this: “How much voltage is there between the two input terminals in each of the situations described in the table?” They will find that the “golden rule” of closed-loop opamp circuits can be violated!

If students have difficulty answering the follow-up question, drop these two hints: (1) Rail-to-rail output swing and (2) Latch-up.

Question 4. (Click on arrow for answer)

This operational amplifier circuit is often referred to as a voltage buffer, because it has unity gain (0 dB) and therefore simply reproduces, or “buffers,” the input voltage:

What possible use is a circuit such as this, which offers no voltage gain or any other form of signal modification? Wouldn’t a straight piece of wire do the same thing? Explain your answers.

File Num: 03801

Answer

While this circuit offers no voltage gain, it does offer current gain and impedance transformation. Much like the common-collector (or common-drain) single transistor amplifier circuits which also had voltage gains of (near) unity, opamp buffer circuits are useful whenever one must drive a relatively “heavy” (low impedance) load with a signal coming from a “weak” (high impedance) source.

Notes

I have found that some students have difficulty with the terms “heavy” and “light” in reference to load characteristics. That a “heavy” load would have very few ohms of impedance, and a “light” load would have many ohms of impedance seems counter-intuitive to some. It all makes sense, though, once students realize the terms “heavy” and “light” refer to the amount of current drawn by the respective loads.

Ask your students to explain why the straight piece of wire fails to “buffer” the voltage signal in the same way the the opamp follower circuit does.

Question 5. (Click on arrow for answer)

For all practical purposes, how much voltage exists between the inverting and noninverting input terminals of an op-amp in a functioning negative-feedback circuit?

File Num: 00930

Answer

Zero volts

Notes

Ask your students to explain why there will be (practically) no voltage between the input terminals of an operational amplifier when it is used in a negative feedback circuit.

Question 6. (Click on arrow for answer)

Just as certain assumptions are often made for bipolar transistors in order to simplify their analysis in circuits (an ideal BJT has negligible base current, $I_C = I_E$ , constant $\beta$ , etc.), we often make assumptions about operational amplifiers so we may more easily analyze their behavior in closed-loop circuits. Identify some of these ideal opamp assumptions as they relate to the following parameters:

Magnitude of input terminal currents:
Input impedance:
Output impedance:
Input voltage range:
Output voltage range:
Differential voltage (between input terminals) with negative feedback:

File Num: 02749

Answer

Magnitude of input terminal currents: infinitesimal
Input impedance: infinite
Output impedance: infinitesimal
Input voltage range: never exceeding +V/-V
Output voltage range: never exceeding +V/-V
Differential voltage (between input terminals) with negative feedback: infinitesimal

Notes

Just in case your students are unfamiliar with the words infinite and infinitesimal, tell them they simply mean “bigger than big” and “smaller than small”, respectively.

Question 7. (Click on arrow for answer)

The purpose of this circuit is to provide a pushbutton-adjustable voltage. Pressing one button causes the output voltage to increase, while pressing the other button causes the output voltage to decrease. When neither button is pressed, the voltage remains stable:

After working just fine for quite a long while, the circuit suddenly fails: now it only outputs zero volts DC all the time.

An experienced technician first checks the power supply voltage to see if it is within normal limits, and it is. Then, the technician checks the voltage across the capacitor. Explain why this is a good test point to check, and what the results of that check would tell the technician about the nature of the fault.

File Num: 03773

Answer

Checking for voltage across the capacitor will tell the technician what voltage the op-amp follower is being “told” to reproduce at the output.

Challenge question: why do you suppose I specify a CA3130 operational amplifier for this particular circuit? What is special about this opamp that qualifies it for the task?

Notes

Knowing where to check for critical signals in a circuit is an important skill, because it usually means the difference between efficiently locating a fault and wasting time. Ask your students to explain in detail the rationale behind checking for voltage across the capacitor, and (again, in detail) what certain voltage measurements at that point would prove about the nature of the fault.

Inverting Amplifier Circuit

An inverting amplifier is one where the output is inverted, or phase shifted by 180^o compared to the input. This is another simple circuit, but a little more complicated than the unity gain buffer. See this video to learn more:

This video shows why the amplifier is called an “inverting” one and shows how to figure out the voltage gain based on the input and feedback resistor. It also includes an LTSpice simulation to demonstrate how the amplifier works.

Introduction to Inverting Op Amp Circuits