Design and simulation of analog filter based on Matlab

0 Introduction

The theory and design method of analog filters based on Laplace transform have been developed quite maturely, and there are several typical filters for people to choose from, such as Butterworth filter, Chebyshev filter, etc. However, the selection and calculation of circuit component parameters for filter implementation is a tedious task. Here, a method based on Matlab to program circuit parameter calculation is proposed, and the purpose of optimizing circuit parameters is achieved through effect simulation, and the program has extended functions.

1 Analog filter design process

The design indicators of analog low-pass filters are ap, Ωp, as, Ωs, where Ωp and Ωs are the passband cutoff frequency and the stopband cutoff frequency respectively; ap is the maximum attenuation coefficient in the passband Ω; as is the minimum attenuation coefficient in the stopband Ω≥Ωs. ap and Ωs are generally expressed in dB. Here, it is hoped that the amplitude square function meets the given technical indicators ap, Ωp, as, Ωs.

(1) Butterworth filter

The square of the amplitude-frequency characteristic modulus is:

Where: N is the order of the filter; wc is the filter cutoff frequency.

(2) Chebyshev filter

Where: ε determines the ripple parameter of the fluctuation size in the passband; TN is the first kind of Chebyshev polynomial:

The T-type circuit and ∏-type circuit of the LC one-port network correspond to different continued fraction expansion forms of the Ha(s) function. When designing, first find the normalized low-pass component value, and then invert the actual value of the circuit component.

2 Analog circuit design and simulation using Matlab programming

(1) Design example of passive single-port analog filter

Technical indicators:

Allowable fluctuations in the passband: -1 dB, O≤Ω≤2 π×104 rad／s;

Stopband attenuation: ≤-15 dB, 2 π×2×104 rad／s≤Ω<+∞:

The source internal resistance Rs and the load resistance RL are equal, both of which are 600 Ω.

Matlab language is used to program and calculate the circuit element parameters of Butterworth T-type and ∏-type circuit diagrams as shown in Figure 1. Figure 2 shows the circuit element parameters of Chebyshev T-type and ∏-type circuit diagrams.

Figure 3 is a Matlab simulation diagram of the output voltage amplitude-frequency characteristics of the designed Butterworth T-type and ∏-type circuit diagrams. Figure 4 is a Matlab simulation diagram of the amplitude-frequency characteristics of the Chebyshev output circuit.

Figure 3 shows that the curve is decreasing in a modulated manner. As the angular frequency Ω increases, the curve approaches zero, and the designed Butterworth circuit meets the parameter requirements; Figure 4 shows that the curve changes unevenly, and the amplitude changes in Ω<Ωc in a certain proportion, and it decreases monotonically in the section of Ω>Ωc. The amplitude-frequency characteristic of the Chebyshev circuit has a narrower transition characteristic than that of the Butterworth circuit.

(2) Program Description

3 Conclusion

This paper uses the deconvolution method to extract the coefficients of a polynomial expressed as a continued fraction, and programs the design of T-type and ∏-type Kaul circuits, reducing the labor burden of tedious calculations. The program is easy to expand, and the simulation results show that the designed circuit meets the technical indicators and the program is correct.