OPERATIONAL AMPLIFIERS (revised 11/05/20) 1 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 A CL ( f ) is given by A CL ( f ) = V OUT V IN = − R 2 A 0 ( f ) R 1 A 0 ( f ) + R 1 + R 2 , where A 0 (f) is the open loop gain which can be approximated by the form A 0 ( f ) = A 0 1 + j f f C O . 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 5 th page of the data sheet below with A 0 = 2×10 5 (=106 dB) and f C O = 5 Hz . Note that as long as R 1 A 0 (f) remains very large compared to (R 1 +R 2 ), A CL ( f ) reduces to the expected inverting amp gain: –R 2 /R 1 . However, this assumption is no longer true at sufficiently high frequencies. Substituting the expression for A 0 (f) into A CL ( f ) (with some algebraic effort) yields A CL ( f ) = − R 2 R 1 ⋅ 1 1 + j f f C C-L , where f C C-L = f C O A 0 R 1 R 1 + R 2 ≈ f C O A 0 A CL ( f = 0) . This shows that A CL ( f ) also follows the single-pole low-pass form and that the product A CL (0) ⋅ f C CL ≈ A 0 f C O for any A CL . 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 R 1 = 1 kΩ and R 2 = 10 kΩ. Note that the V CC (+15V) and V EE (–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 V in grounded, adjust the pot on the circuit board for zero output voltage. Using sine waves from the function generator for V in (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 f C CL .