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Measurements of op-amp circuit parameters such as open or closed-loop frequency response, or output impedance as a function of frequency, over a reasonably broad range of frequencies, can be tedious and very challenging for undergraduate students to accomplish using signal generators and oscilloscopes. In fact, measurements of total harmonic distortion (measure of op-amp linearity), with and without resistive load, are almost impossible to make in the time domain with conventional oscilloscopes. Of greater concern is that the time-domain methods for measuring frequency domain characteristics of an op-amp do not present a “real-time” visualization for students. This problem can even mask important operational limitations such as op-amp slewrate nonlinearities for higher frequency sinusoidal inputs. This paper presents some of the successful measurement methodologies that our students use at the U.S. Coast Guard Academy in a junior-level Linear Circuits laboratory. As part of this lab, students use the Agilent 35670 Dynamic Signal Analyzer (DSA) to measure some of the specifications of an inverting amplifier op-amp (μA741) circuit. They use averaging on the measurement data to minimize the impact of noise in the measurements of the μA741circuit. Here we present typical measurement results, along with informal student feedback that suggests to us that the “real-time” nature of a DSA frequency domain presentation (that looks almost exactly like Matlab TM and MultiSim TM predictions) really does reinforce student learning. The lab procedure consists of four steps: (1) Students set the DSA to measure the open-loop frequency response of the op-amp over two different frequency ranges. (2) Students then measure the closed-loop frequency response of an inverting amplifier for two different gain settings. (3) Students measure the output impedance of an inverting amplifier circuit as a function of frequency. (4) Finally, they compare the Total Harmonic Distortion (THD) at the output and differential input, for unloaded and resistive load conditions. Frequency response measurements are compared with theoretical expectations from Matlab TM and with MultiSim TM AC analysis simulations, thereby solidifying the frequency domain presentation of real-world opamp characteristics. Introduction Measuring Operational Amplifier (op-amp) parameters can represent one of the most challenging laboratories for undergraduate students. For the most part, many of these challenges stem from the fact that classical time-domain methods for measuring op-amp “frequency domain P ge 25919.2 parameters” can be cumbersome, and typically do not present a “real-time” visualization for the student. Parameters such as gain-bandwidth product, open and closed loop frequency responses, and Total Harmonic Distortion (THD) at the op-amp output and differential input (under loaded and unloaded conditions) are inherently easier to interpret, compute, and visualize in the frequency domain. Some of the early ideas for considering the effects of design with “real-world” op-amps originated with Peterson, Hartnett, and Gross at the U.S. Coast Guard Academy 1 , however the authors focused primarily on the theoretical analysis and did not discuss measurement methodologies. Classic references such as Schaumann and Van Valkenburg 2 and Van Valkenberg 3 also discuss the idea of “one-pole roll-off” and “two-pole roll-off” real-world opamp models, but present no measurements or methodologies. In this paper we introduce successful measurement of op-amp parameters that our undergraduate students achieve at the U.S. Coast Guard Academy in a junior-level Linear Circuits laboratory. Students use Agilent 35670A Dynamic Signal Analyzers (DSA’s) to measure the open-loop and closed-loop frequency responses, output resistance, and THD (at output and inverting input) of an inverting amplifier circuit using a μA741 op-amp. From their DSA measurements of frequency response, THD, and output resistance, students learn that even a low-cost μA741 opamp can behave as an “ideal amplifier” in a circuit, if one operates the amplifier within the gainbandwidth product, slew rate, and output current limitations of the selected op-amp. All frequency response measurements are then verified with theoretical expectations from Matlab TM and MultiSim TM AC analysis simulations. Laboratory Procedures The lab procedure consists of four steps: (1) Students set the DSA to measure the open-loop frequency response of the op-amp over two different frequency ranges. (2) Students then measure the closed-loop frequency response of an inverting amplifier for two different gain settings. (3) Students measure the output impedance of an inverting amplifier circuit as a function of frequency. (4) Finally, students measure the total harmonic distortion at Vand Vout for a (clean) sinusoidal input, for loaded and unloaded inverting amplifier configurations. In the first step, students are instructed to build the circuit shown in Figure 1 using a A741 opamp. After verifying proper operation, they begin measuring the A741 op-amp open loop frequency response; that is the transfer function of the op-amp itself from the inverting terminal Vto Vout. The general idea in this measurement is to provide the circuit input with a periodic chirp waveform, from the “source output” of the DSA, over the frequency range of interest. Connecting Channel#1 of the DSA to Vand Channel#2 of the DSA to Vout of the circuit, coupled with selecting a “frequency response” measurement, yields a measurement of open-loop magnitude response for the student. P ge 25919.3 Figure 1. Op-amp circuit used to measure open loop frequency response of μA741 op-amp. One might ask why it would matter what circuit our students use if we are interested in an openloop frequency response measurement (i.e. from Vto Vout). The short answer is that an op-amp circuit is considerably more stable with negative feedback, so it is often much easier to measure open-loop characteristics operating within a closed loop system. The longer answer regarding why this particular circuit is used is perhaps more subtle. One might initially be tempted to have students simply use an inverting amplifier circuit such as one shown in Figure 2. In this circuit, assuming a periodic chirp input (which is spectrally flat), and taking a closer look at the voltage V(the op-amp inverting input) as a function of frequency, we realize that the amplitudes of the low frequency components are extremely small compared to the higher frequency components. As a result, the A/D range for Channel #1 on the DSA would be dominated by high frequency components, and low frequency (low amplitude) measurements of V(which form the denominator of the open-loop frequency response) would render open-loop frequency response measurements extremely challenging for students to make. Figure 2. Typical inverting amplifier configuration (showing a linear gain of -10). R3

Measurement of Op-Amp Parameters Using Vector Signal Analyzers in Undergraduate Linear Circuits Laboratory