Analysis of second-order low-pass filter circuit with Multisim

Multisim is an advanced version of the electronic circuit simulation software EWB (Electronics Workbench), developed by Interactive Image Technologies from Canada. It offers a fully integrated design and analysis environment, allowing users to build circuits, perform simulations, and generate results all within a single intuitive interface. The simulation techniques are practical and closely resemble real-world scenarios, with a vast library of components that are fully compatible with PSpice, one of the most widely used circuit analysis tools. Multisim supports a wide range of analyses, including transient, steady-state, time-domain, frequency-domain, noise, distortion, and discrete Fourier analysis. In this paper, Multisim is used as the primary platform for analyzing a second-order low-pass filter circuit. Additionally, it allows seamless data transfer between schematic designs and PCB layout tools like Ultiboard, offering an easy-to-use and efficient workflow. 2. Circuit Design The amplitude-frequency response of a first-order low-pass filter decreases at a rate of -20 dB per decade, which is not sufficient for achieving an ideal filtering performance. To enhance the roll-off rate and improve the filtering effect, a second-order RC active filter is commonly used. This is achieved by adding an additional RC network to the first-order configuration. The circuit structure is shown in Figure 1. The upper section consists of an operational amplifier-based non-inverting amplifier, made up of resistors R1 and Rf, both set at 16 kΩ. The lower part is a second-order RC filter composed of two resistors (R2 and R3) and two capacitors (C1 and C2), each with values of 4 kΩ and 0.1 μF respectively. An AC voltage source with an adjustable amplitude of 1 mV and a 1 kΩ internal resistance provides the input signal. 3. Theoretical Analysis 3.1 Frequency Characteristics The frequency response of the second-order low-pass filter is characterized by its ability to pass low-frequency signals while attenuating higher frequencies. 3.2 Passband Voltage Gain (AUP) At low frequencies, the capacitors act as open circuits, making the circuit function similarly to a comparator. The gain is calculated as: $$ A_{UP} = 1 + \frac{R_f}{R_1} = 2 $$ 3.3 Characteristic Frequency (f₀) and Passband Cutoff Frequency (fₚ) The characteristic frequency and cutoff frequency can be determined using the following formulas: $$ f_0 = \frac{1}{2\pi\sqrt{R_2 R_3 C_1 C_2}} $$ $$ f_P = \frac{1}{2\pi\sqrt{R_2 C_1}} $$ 4. Multisim Analysis 4.1 Virtual Oscilloscope Analysis Using the virtual dual-trace oscilloscope in Multisim, the input and output signals of the second-order low-pass filter were observed. When the input frequency was 1 kHz, the output signal showed a significant reduction in amplitude, confirming the filter’s behavior. At 1 Hz, the output voltage was 2 mV, matching the theoretical gain of 2. As the frequency increased, the output amplitude decreased, indicating the filter's effectiveness. 4.2 AC Analysis To obtain precise frequency characteristics, AC analysis was performed. The results showed that the passband gain remained stable at around 6.02 dB (equivalent to a voltage gain of 2). The cutoff frequency was found to be approximately 148.5 Hz, consistent with theoretical predictions. 4.3 Parameter Sweep Analysis By varying component values such as C1, C2, R1, R2, R3, and Rf, the impact on the circuit's performance was studied. For example, decreasing C1 increased the cutoff frequency, widening the passband, while changes in R1 and Rf affected the gain without altering the frequency response. 5. Conclusion The simulation results obtained from Multisim closely matched the theoretical calculations, demonstrating its reliability and accuracy. As a powerful tool for both circuit design and education, Multisim enhances the teaching of electronics through interactive, real-time simulations. Its flexibility and ease of use make it an essential resource in modern electronics education, enriching both classroom instruction and student learning experiences.

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