Operational Amplifiers, Gain

Main Ideas and Concepts

An operational amplifier (op-amp) is an active, three-port device with two inputs—the non-inverting (+) and inverting (−) inputs—and one output. Its output responds to the voltage difference between the inputs, multiplied by the op-amp’s gain. An op-amp requires a power supply.

Ideal Op-Amp Assumptions

The following assumptions are commonly used when analyzing ideal op-amp circuits:

• Infinite open-loop voltage gain
• Infinite input impedance, so the inputs draw no current
• Zero output impedance
• Infinite bandwidth
• Zero input-offset voltage

Differential and Common-Mode Gain

• Differential gain amplifies the difference between the two input signals and should be high.
• Common-mode gain amplifies the part shared by both inputs and should be very low.
• The video gives typical practical ranges of about 100,000 to 100 million for differential gain and about (10^{-5}) for common-mode gain.

Gain and Bandwidth

Real op-amps have limitations. Typical gain-bandwidth products are about 1–20 MHz, although some video-oriented devices are faster. Increasing the gain set by the external resistors reduces the usable bandwidth. For many op-amps, the gain-versus-frequency relationship is approximately linear on a logarithmic scale.

The −3 dB bandwidth point is where the output amplitude falls to about 0.707 of its value at the reference frequency. For example:

• 1 V becomes about 0.707 V.
• 10 V becomes about 7.07 V.

Gain Configurations

Inverting Amplifier

The signal passes through an input resistor (R_i) to the inverting input. A feedback resistor (R_f) connects the output to that same input. In the lab setup, the non-inverting input is grounded.

[ \text{Gain} = -\frac{R_f}{R_i} ]

The negative sign indicates that the output is inverted relative to the input.

Non-Inverting Amplifier

The signal goes to the non-inverting input. The feedback resistor connects the output to the inverting input, while a second resistor (R_g) connects the inverting input to ground.

[ \text{Gain} = 1 + \frac{R_f}{R_g} ]

The output is in phase with the input.

Voltage Follower (Buffer)

Connecting the output directly to the inverting input produces a gain of approximately one. The buffer’s high input impedance minimizes loading on the source, while its lower output impedance allows it to drive a load more effectively.

Signal Adder

Multiple signals can enter an inverting stage through separate input resistors. The resistor values determine each signal’s contribution. A non-inverting version is also possible.

Practical Considerations

Input Offset

Real op-amps do not have infinite input impedance. In high-gain circuits, input currents can create an output offset if the reference input is grounded directly. A rule of thumb is to use a resistor to ground whose value equals the parallel combination of the gain resistors.

For this lab, the instructor says to ground the non-inverting input directly and ignore the resulting offset.

Power-Supply Decoupling

Decoupling capacitors should be placed close to the op-amp. The demonstrated setup uses a larger tantalum capacitor in parallel with a small ceramic capacitor on each supply rail.

Tantalum capacitors are polarized:

• On the +12 V rail, the positive side goes to +12 V.
• On the −12 V rail, the positive side goes to ground and the negative side goes to −12 V.

Reversing a polarized capacitor can damage it.

AD817AN Pinout

For the demonstrated AD817AN:

Pin Connection 2 Inverting input 3 Non-inverting input 4 Negative supply 6 Output 7 Positive supply

Pins 1, 5, and 8 are not used.

Lab Procedure and Measurements

Equipment and Setup

Use a breadboard, op-amp, resistors, decoupling capacitors, dual power supply, function generator, and oscilloscope.

• Connect the function generator to oscilloscope channel 1 and the op-amp output to channel 2.
• Keep the grounds common.
• The demonstrations use a 1 kHz sine wave.
• Reduce the input amplitude at higher gains to avoid saturation. The instructor uses 200 mV peak-to-peak for lower-gain tests and 100 mV peak-to-peak for higher-gain tests.

Build and Measure the Inverting Amplifier

1. Ground pin 3.
2. Connect the input through a 1 kΩ resistor to pin 2.
3. Connect a 10 kΩ feedback resistor from pin 6 to pin 2.
4. Measure the input and output amplitudes, then verify the gain and inversion.
5. For higher gain, replace the 10 kΩ feedback resistor with a 100 kΩ resistor and reduce the input amplitude.

Build and Measure the Non-Inverting Amplifier

Turn off the supply before changing the wiring.

1. Move the input from the input-resistor path to pin 3.
2. Connect the former input resistor from pin 2 to ground.
3. Measure the lower-gain configuration.
4. Replace the feedback resistor with a 100 kΩ resistor for the higher-gain test.
5. Compare the measured gains with the resistor-based calculations.

Measure Gain and Bandwidth

1. Record the gain at 1 kHz.
2. Increase the function-generator frequency until the output amplitude falls to 0.707 of its 1 kHz value.
3. Record that frequency as the bandwidth.

As gain increases, bandwidth should decrease.

Demonstrate Source Loading and Buffering

1. Set the function generator to a 1 kHz, 5 V peak-to-peak signal.
2. Connect a 150 Ω resistor from the signal to ground and measure the reduced amplitude.
3. The reduction occurs because the generator’s roughly 50 Ω series output resistance and the 150 Ω load form a voltage divider.
4. Configure the op-amp as a voltage follower by connecting pin 6 directly to pin 2 and applying the input to pin 3.
5. Place the 150 Ω load on the op-amp output and measure the signal across the load again.

The buffer should prevent the source from being significantly loaded, keeping the output close to the input amplitude.

Speakers and Sources Featured

The video features one unnamed instructor or narrator, who explains the concepts and demonstrates the breadboard setup and measurements. It also includes schematics, component illustrations, and oscilloscope demonstrations; no other speaking source is identifiable in the subtitles.