Analyzing Second-Order Low-Pass Filter Circuit Using Multisim

1 Introduction

Multisim is an upgraded version of the electronic circuit simulation software EWB (Electronics Workbench, virtual electronic work platform) launched by Interactive Image Technologies in Canada in recent years. Multisim provides users with an integrated design experiment environment. With Multisim, circuit building, simulation analysis and result output can all be completed in an integrated menu. Its simulation methods are practical, and the components and instruments are very close to the actual situation. The Multisim component library not only has thousands of circuit components to choose from, but is also fully compatible with the components provided by PSpice, a commonly used circuit analysis software. Multisim provides a wealth of analysis functions, including transient analysis, steady-state analysis, time domain analysis, frequency domain analysis, noise analysis, distortion analysis and discrete Fourier analysis of circuits. This article uses Multisim as a working platform; it deeply analyzes the second-order low-pass filter circuit. Multisim can be used to achieve seamless data transmission from schematics to PCB wiring toolkits (such as Ultiboard of Electronics Workbench), and the interface is intuitive and easy to operate.

2 Circuit Design

Since the amplitude-frequency characteristic of the first-order low-pass filter has a decreasing rate of only -20 dB/10 f, which is too far from the ideal situation, its filtering effect is not good. In order to speed up the decreasing rate, make it closer to the ideal state, and improve the filtering effect, we often use a second-order RC active filter. The improvement measure taken is to add another RC network on the basis of the first order.

The circuit structure is shown in Figure 1. The upper part of this circuit is a common-phase proportional amplifier circuit, which consists of two resistors R1, Rf and an ideal operational amplifier. R1 and Rf are both 16 kΩ. The lower part is a second-order RC filter circuit, which consists of two resistors R2, R3 and two capacitors C1, C2. R2 and R3 are both 4 kΩ, and C1 and C2 are both 0.1 μF. The circuit is provided by an AC voltage source with an amplitude of 1 mV and adjustable frequency to provide input signals, and a resistor with a resistance of 1 kΩ is used as the load.

3 Theoretical Analysis

3.1 Frequency characteristics

The frequency characteristics of the second-order low-pass filter circuit are:

3.2 Passband voltage gain AUP

At low frequencies, the two capacitors are equivalent to an open circuit, and this circuit is a common-mode ratiometer.

3.3 Characteristic frequency f0 and passband cutoff frequency fP

4 Multisim Analysis

4.1 Virtual Oscilloscope Analysis

Select the virtual dual-trace oscilloscope in the virtual instrument column of the Multisim software, connect the A and B terminals of the oscilloscope to the input and output terminals of the circuit respectively (i.e. nodes 1 and 3 in Figure 1), and then click the simulation button to simulate and obtain the following waveform.

Figure 2 shows the input and output of the second-order low-pass filter circuit when the input signal frequency is 1 kHz and the amplitude is 1 mV. In the figure, the horizontal axis is time and the vertical axis is voltage amplitude. We choose the oscilloscope scanning frequency to be 1 ms/div. Each vertical axis grid represents 1 mV, and the output mode is Y/T mode. The large amplitude is the input signal, and the small amplitude is the output signal.

Obviously, the frequency of the output signal is consistent with the input signal, indicating that the second-order low-pass filter circuit will not change the signal frequency. It can also be seen from Figure 2 that when the input signal frequency is large (such as 1 kHz), the amplitude of the output signal is significantly smaller than the amplitude of the input signal. The theoretical calculation result under low frequency is AUP=2; that is, under low frequency, the amplitude of the output signal should be twice the input signal. Obviously, the amplification effect of the circuit is not ideal when the input signal frequency is large.

The input frequency is adjusted to 800 Hz, 600 Hz, 400 Hz, 300 Hz, 200 Hz, 150 Hz, and 1 Hz. The output voltage Uo1=2 mV, i.e. AUP=2, is obtained from the virtual oscilloscope when the input frequency is 1 Hz, which is consistent with the theoretical calculated value. When the input frequency is 150 Hz, Uo2=1.5 mV. At this time, Uo2 is closest to the output voltage UP=0.707Uo1=1.414 mV at the cutoff. This shows that the cutoff frequency fP is close to 150 Hz.

We found that it was difficult to obtain the accurate value of fP through virtual oscilloscope analysis alone, and it was also impossible to intuitively see the impact of the frequency of the input signal on the circuit amplification performance. Therefore, we used AC analysis in Multisim to accurately observe the input and output characteristics of the circuit.

4.2 AC Analysis

Stop Multisim simulation analysis (Multisim simulation analysis and AC analysis cannot be performed at the same time), select AC Analysis in the simulate item in the main menu bar. Set the parameters as follows: start frequency is 1 Hz, end frequency is 10 MHz, scan mode uses decimal, vertical axis is in dB, select output node in Output variables (i.e. node 3 in Figure 1), and then click simulate to perform simulation analysis, and obtain the amplitude-frequency characteristic curve of the circuit as shown in Figure 3.

4.2.1 Measurement of passband voltage gain AUP

It can be seen from the characteristic curve that the frequency change has little effect on AUP at low frequencies, and AUP decreases sharply with increasing frequency at high frequencies. At high frequencies, the output voltage is close to 0. From the dialog box, it can be seen that the maximum value of the ordinate is 6.020 4 dB, that is, AUP=2, which is consistent with the theoretical calculated value.

4.2.2 Measurement of passband cutoff frequency fP

fP is the frequency corresponding to the vertical coordinate dropping 3 dB from the maximum value (6.020 4 dB), that is, the frequency corresponding to the vertical coordinate of 3.020 4 dB. Move the ruler on the right side of Figure 3 to the vicinity of 3.020 4 dB, select a part to zoom in; then move the ruler precisely to the vertical coordinate of 3.020 4 dB, and the horizontal coordinate obtained is 148.495 2 Hz, that is, fP=148.495 2 Hz. This is basically consistent with the theoretical calculation.

4.3 Parameter sweep analysis

When the parameters of a component change, the parameter sweep analysis function in Multisim can be used to obtain the changes in the input and output characteristics of the circuit.

In the main menu bar, select parameter sweep in Analysis from the simulate item. The parameter settings are as follows (taking C1 as an example): select capacitor device in the device item, select C1 as the component name, select capacitance as the parameter, and use three values ​​for capacitance: le-006F, le-007F, and le-008F. Click the more option, select AC Analysis, and then select node 3 as the output node. Click simulate to simulate and obtain the amplitude-frequency characteristic curve of the circuit when C1 takes the above three different values ​​(as shown in Figure 4).

In Figure 4, the three curves correspond to capacitances of le-006F, le-007F, and le-008F from bottom to top, and the corresponding cutoff frequencies are 35.550 Hz, 148.493 7 Hz, and 193.375 6 Hz, respectively. Obviously, the reduction of C1 causes the cutoff frequency of the circuit to increase and the passband to become wider. However, the change of C1 has little effect on the voltage gain.

Using a similar method, we get the following effects of C2, R1, R2, R3 and Rf on circuit performance: The reduction of C2, R2 and R3 will increase the cutoff frequency of the circuit and widen the passband. However, the changes of C2, R2 and R3 have little effect on the voltage gain. R1 is inversely proportional to the output voltage amplitude, and Rf is proportional to the output voltage amplitude, but the changes of R1 and Rf do not affect the frequency characteristics of the circuit.

5 Conclusion

From the above analysis, it can be seen that the simulation analysis results in Multisim are very close to the theoretical calculation results. Multisim is not only a software specially used for electronic circuit design and simulation, but also a very excellent electronic technology teaching tool. The application of Multisim in classroom teaching has enriched the content of multimedia-assisted teaching of electronic technology, which is a leap in the development of educational technology. With its functional features such as development, flexibility, richness, vividness, real-time interactivity and high efficiency, Multisim has greatly enriched the teaching methods of electronic circuits, expanded the breadth and depth of teaching content, and provided another effective means to improve the quality of electronic technology teaching.