CHAPTER 9

Basics of

Operational

Amplifiers

OBJECTIVESDescribe and Analyze:

• Op-Amp Basics

• Feedback

• Inverting Amplifiers

• Non-Inverting Amplifiers

• Comparators

• Troubleshooting

IntroductionOp-Amps have:

• Differential Inputs: (+) & (-)• High “Open Loop” Gain: AOL > 100,000

(Open-loop means without feedback. More on that later.)

• High Input Impedance: Zin > 1 Meg• Low Output Impedance: Zout 0

Introduction Some Facts about Op-Amps:

• Op-amps are the most commonly used linear ICs.• An IC package can have 1, 2, 4, or more op-amps.• Op-amps come in many varieties based on

parameters such as bandwidth, cost, and transistor type (BJT, JFET, MOSFET).

Op-Amp Basics

Analysis can be based on two approximations:• No current flows into or out of the input pins• The voltage across the input pins is zero

Op-Amp Basics

The front-end of an Op-Amp is a differential amplifier

Voltage Follower

Simplest circuit, illustrates use of negative feedback

Non-Inverting Amplifier

Av = 1 + (Rf / Ri)

Non-Inverting Amp Gain equation derived as follows:

• Vin applied to (+) input means V(+) = Vin• zero difference across inputs implies V(-) = V(+) • V(-) = V(+) implies V(-) = Vin• Iin = 0 implies V(-) = Vin = [Ri / (Ri + Rf)] Vout• which leads to Vin / Vout = Ri / (Ri + Rf) • which leads to Vout / Vin = Av = (Ri + Rf) / Ri• which is the same as Av = 1 + Rf / Ri

Non-Inverting Amp An example calculation:

a) Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k

b) Find voltage at (-) input

• Av = 1 + Rf / Ri = 1 + 10k / 5k = 1 + 2 = 3• Vout = Av Vin = 3 1V = 3 Volts DC• V(-) = V(+) = 1 Volt DC

Negative Feedback

Negative feedback reduces gain to a useable value

Negative Feedback Besides setting the gain, negative feedback provides performance improvements such as:

• Makes Zin higher• Makes Zout lower• Increases the usable bandwidth• Reduces distortion in the op-amp

Negative Feedback

It looks complicated, but actually it’s not

Negative Feedback We can analyze negative feedback as follows:• Some of the output is fed back to the input:

Vfb = B Vout where 0 < B < 1• The signal that gets to the op-amp is the applied

input plus the feedback: Vx = Vin + Vfb = Vin + B Vout

• But the output is the open-loop gain of the op-amp times the signal that gets to the input: Vout = AOL Vx = AOL (Vin + B Vout)

• Now we can find closed-loop gain: ACL = Vout / Vinas we will see on the next slide.

Negative Feedback Start with Vout = AOL (Vin + B Vout)

Then Vout = AOL Vin + AOL B Vout

Then Vout – B AOL Vout = AOL Vin

Then (1 - B AOL ) Vout = AOL Vin

Then Vout = [AOL / (1 - B AOL ) ] VinThen Vout / Vin = ACL = AOL / (1 - B AOL )

Where ACL is the closed-loop gain

Now, if B AOL >> 1 (which is usually the case)

then ACL 1 / B where B is set by a resistor ratio.

The Inverting Amplifier

Av = - (Rf / Ri) where minus means 180O phase shift

The Inverting Amp Gain equation derived as follows:• Vin applied to (-) input through Ri • zero difference across inputs implies V(-) = V(+) • (+) input grounded implies V(-) 0

(-) input is a “virtual ground”• which leads to Iin = Vin / Ri and If = Vout / Rf• no current into (-) input implies If = Iin• so Vout / Rf = Vin / Rin and Vout / Vin = Rf / Rin • If Vin makes Iin flow in, Vout must make If flow out.

So Vout has opposite polarity of Vin: Av = -Rf / Ri

The Inverting Amp An example calculation:

Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k

• Av = - Rf / Ri = - (10k / 5k) = - 2 • Vout = Av Vin = -2 1V = -2 Volts DC

Comparators

Very small V between inputs gives a binary output

Comparators Some Facts about Comparators:• Comparator output is high or low depending on which input

has the higher voltage applied to it.• An open-loop op-amp can be used as a comparator.• Open-loop op-amps go into saturation, and they take a

relatively long time to get out of saturation.• The output can “chatter” (oscillate high / low) when inputs are

equal. Chatter can be cured with hysteresis.• There are ICs designed to be comparators. They are better at

the job than op-amps.

Troubleshooting• Check the power rails: +VCC and –VCC

• Check if the output is in saturation (usually, saturation is not a good thing).

• Check the input voltages, knowing that voltage across inputs is supposed to be virtually zero.

• Check that polarity (phase) of output is the same as input for a non-inverting amplifier.

• Check that polarity (phase) of output is the opposite input for an inverting amplifier.

• Check signal levels based on gains (look at the resistor ratios of the feedback loops).