Lab Report 7

.pdf

School

University Of Connecticut *

*We aren’t endorsed by this school

Course

2001

Subject

Electrical Engineering

Date

Dec 6, 2023

Type

pdf

Pages

Uploaded by UltraPowerPenguin28

Experiment Number 7: Active Filter Circuits Christopher Otis ECE 2001, 11/9/2023 Abstract This lab report uses both theoretical analysis and real-world experimentation to investigate the properties of second-order active filters constructed with operational amplifiers (op amps). This experiment aims to provide a thorough understanding of active filter circuits and their behavior, with a particular emphasis on second-order designs. In addition, we will examine and model the operation of these active filter circuits using the simulation program PSpice. The importance of op amps in determining filter characteristics is highlighted in the report, which goes into detail about the theoretical foundations of second-order active filters and their transfer functions. Additionally, building active filter circuits, determining their performance parameters, and comparing the outcomes to theoretical predictions make up the experimental portion of the study. This study improves our capacity to effectively design and analyze these circuits and provides insightful information about the behavior of active filters in real-world scenarios. Introduction Active filters play a vital role in determining how a circuit or system responds to frequencies, making them indispensable parts of contemporary electronics. We explore the realm of active filters in this lab experiment, concentrating on second-order designs made with operational amplifiers (op amps). To achieve particular filtering characteristics, active filters combine passive components like resistors and capacitors with active components like op amps. This experiment's main goals are to learn about the theoretical underpinnings of second-order active filters and their transfer functions as well as to acquire hands-on experience in circuit design and analysis. Our goal in doing this is to comprehend the connection between theoretical projections and actual performance. We'll use PSpice, a potent simulation tool, to simulate and project the behavior of our active filter circuits in order to make our analysis easier. We will examine the fundamentals of active filters, the role that operational amplifiers play in them, and the vital variables that control their functionality—such as cutoff frequency, gain, and bandwidth—during this lab. This research attempts to provide us with a thorough understanding of second-order active filters and the resources required to efficiently design and assess these circuits by fusing theoretical knowledge with hands-on experimentation. These abilities lay the groundwork for more complex electronic circuit design and are crucial for any engineer or electronics enthusiast looking to use filtering solutions in a variety of applications. Theory In this experiment, we explore the world of second-order active filters, which are electronic circuits made to precisely control a signal's frequency response. Comparing these filters to their first-order counterparts, the roll-off is steeper and the selectivity is improved. Operational amplifiers, or op amps, are the core component of these circuits because they are high-gain, differential amplifiers. To obtain the desired filter response, op amps are configured as voltage followers, integrators, or differentiators. Voltage gain (A) is infinite in ideal op amps.

Resistors (R) and capacitors (C), two passive parts, are essential in determining the filter's properties. The cutoff frequency (fc) and quality factor (Q) of the filter are determined by the values of R and C. Understanding the behavior of the filter depends critically on the transfer function (H(s)), which expresses the relationship between input and output signals in the frequency domain mathematically. Figure 1.1 shows some basic low and high pass active filter setups. Figure 1.1 - High/Low pass example The two main filter types that are the subject of this experiment are the second-order high-pass filter, which suppresses low-frequency signals while permitting high-frequency ones, and the second-order low-pass filter, which attenuates high-frequency signals while permitting low-frequency ones. For both filter types, the cutoff frequency (fc) is a crucial parameter. The active filter's gain (A), which is crucial for boosting or attenuating signals inside the filter, is based on how the op amp and feedback network are configured. A = -Rf / Rin is the formula that can be used to calculate gain (A). The cutoff frequency can be visualized in the figure 1.2 below. Figure 1.2 - Cutoff frequency visual Through this research, we hope to learn more about how these parts interact to affect the transfer function, gain, and frequency response of circuits with second-order active filters. When using simulation tools like PSpice for practical applications and efficient circuit design, this knowledge is essential.

Experimental Procedures This is a very straightforward and simple lab procedure to follow for this experiment. There is a preparation section of the experiment and an experimental section. The preparation for this experiment starts with building the circuit shown in figure 2.1 in PSpice. Once it has been built, plot the amplitude response for the filter. The resistors will each have a value of 1k ohms and the capacitance will be valued at 15 nF. Lastly the cutoff frequency needs to be determined. Figure 2.1 - Sallen and Key low pass filter The same steps are repeated from before for the next circuit. This circuit can be seen in figure 2.2 below. As stated before the resistors will each have a value of 1k ohms and the capacitance will be valued at 15 nF. Determine if this circuit exhibits true high pass behavior after PSpice is used to plot the amplitude response as it was done previously. Figure 2.2 - Sallen and Key high pass filter The last part of the preparation for this lab is to calculate the capacitance and both resistance values for the third circuit. There are three formulas that will be used to calculate these values. The circuit can be visualized in figure 2.3. The formulas that need to be used can be seen in figure 2.4 below. All three of the values that are calculated need to obtain a center frequency of 12 kHz +/- 10% and a quality factor of 0.4 +/- 10%. Lastly as done for the previous two circuits use PSpice to plot the amplitude response.

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