OPERATIONAL AMPLIFIERS (revised 11/05/20)

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EXPERIMENT 9: LINEAR OP-AMP CIRCUITS In this experiment we will examine the properties of operational amplifier circuits with various feedback networks. Circuits which perform four basic linear mathematical operations — addition, subtraction, integration, and differentiation — will be studied. We will use a model µA741, operational amplifier. This is a general purpose, integrated-circuit op-amp with detailed specifications listed in the appendix to this experiment. The op-amp requires a ±15 V power source. We will use a small power supply that provides these voltages plus a zero to ±5 V variable DC output. The op-amp will supply a maximum output current of about 25 mA and has typical offset currents of about 20 nA. This implies that resistors in the range 1 kΩ to 100 kΩ should be used. All of this information and more, including circuit suggestions, is shown on the component data sheet included at the end of the lab. Note that as with most integrated circuits, the first two characters “µA” identify the manufacturer, and “741” is the relevant portion of the part number. The LM741, OP741, or AD741 would be closely equivalent parts made by other companies. In most cases these can be freely substituted, but you should check the manufacturers’ data sheets to be sure for parameters critical to your application.

Use a scope for all measurements.

Part 1 — Failure of A ! infinity approximation at high frequencies:

(a) For this inverting amplifier circuit, show that the closed-loop gain ACL ( f ) is given by

ACL ( f ) =VOUTVIN

=−R2A0 ( f )

R1A0 ( f )+ R1 + R2, where A0(f) is the open loop

gain which can be approximated by the form A0 ( f ) =A0

1+ j ffCO

.

This is the single-pole low-pass form and is a good description of the log-log plot of the open-loop gain curve shown on the 5th page of the data sheet below with A0 = 2×105 (=106 dB) and fCO = 5 Hz . Note that as long as R1A0(f) remains very large compared to (R1+R2), ACL ( f ) reduces to the expected inverting amp gain: –R2/R1. However, this assumption is no longer true at sufficiently high frequencies. Substituting the expression for A0(f) into ACL ( f ) (with some algebraic effort) yields

ACL ( f ) =−R2R1

⋅1

1+ j ffCC-L

, where fCC-L = fCOA0R1

R1 + R2≈

fCOA0ACL ( f = 0)

. This shows that ACL ( f ) also

follows the single-pole low-pass form and that the product ACL (0) ⋅ fCCL ≈ A0 fCO for any ACL . This product is called the “gain-bandwidth product” of the op-amp (often referred to as just “bandwidth” in data sheets).

(b) Construct the inverting amplifier shown below with R1 = 1 kΩ and R2 = 10 kΩ. Note that the VCC

(+15V) and VEE (–15V) pins must be connected to the small white power supply and the supply ground connected to your circuit ground even though this is not conventionally shown on the schematic diagram. With Vin grounded, adjust the pot on the circuit board for zero output voltage. Using sine waves from the function generator for Vin (with the amplitude set for 0.01 V p-p), make a rough plot of the amplitude and phase of the gain A(f) over the range 100 Hz ≤ f ≤ 1 MHz. Take just enough points to show that it follows a single-pole low-pass response and find fCCL .

OPERATIONAL AMPLIFIERS (revised 11/05/20)

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Part 2 — Output saturation voltage: Set f = 1 kHz. Increase the amplitude of vin until vout exhibits saturation at both positive and negative

voltages. Sketch or print screen and determine the saturation voltages. Compare with the data sheet values (called “output voltage swing”).

Part 3 — Slew rate limitations: (a) The slew rate of the amplifier is defined as the maximum rate of change of the output

voltage. Switch the input to square waves and set f = 10 kHz. Adjust the amplitude to obtain a peak-to-peak output voltage of 10 Volts. Measure the slew rate by observing dvout/dt and compare your result to the typical value listed in the data sheet.

(b) Suppose you want to use the amplifier to produce a sine wave output with an amplitude of 10 Volts peak-to-peak. What is the maximum frequency you can use before the output wave begins to be distorted by the finite slew rate of the amplifier? (SinceV (t) = 5sin(2π ft) , calculate the peak value of dV/dt, set it equal to the slew rate from the data sheet, and solve for f.) Switch the input to sine waves and observe what happens when you exceed that frequency (by quite a bit to make the distortion obvious). Sketch the input and output waveforms.

(c) Now can you explain why you had to use such a small voltage when measuring ACL ( f ) ?

Part 4 (this is optional — skip and come back if you have time): (a) Set up the differentiator circuit shown below with C = 100 nF and R = 2 kΩ. For the input use a 2 Volt peak-to-peak, f = 1 kHz triangle wave. Sketch the input and output waves and measure the magnitude of vout. Compare your measured value with the expected result, vout = − RC x dvin/dt. Also, measure and tabulate the values of vout (no sketches required) for f = 2 kHz with C = 100 nF, and for f =2 kHz with C= 50 nF.

(b) Switch the input waveform to square wave and sketch vin and vout. Explain why vout looks the way it does. (Consider the square wave as a Fourier series sum of sine waves.)

Part 5: (a) Set up the integrator circuit shown below, with C = 100 nF, RF = 200 kΩ, and R = 10 kΩ. Use a 2 Volt peak-to-peak, f = 1 kHz square wave for vin. Sketch the input and output wave forms and determine the magnitude of vout. Compare your measurement with the expected result out inv (1/ RC) v dt= − × ∫ .

(b) Observe what happens to the output voltage as you make RF larger and smaller. What happens when RF is removed (=∞)? Explain why we need to have a feedback resistor in any integrating circuit.

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