Filter and Attenuator Circuit Design

1. Design of filter image parameter method The filter is a typical frequency selection circuit. In a given frequency band, it theoretically allows the signal to pass through the circuit without attenuation. This section is called other signals outside the passband. will be subject to great attenuation. The frequency band with great attenuation is called the stop band. The boundary frequency between the pass band and the stop band is called the cutoff frequency. The basic requirements for the filter are: (1) The attenuation of the signal in the pass band should be small. , the attenuation of the signal in the stop band should be large, and the attenuation characteristics of the transition from the pass band to the stop band rise sharply; (2) The characteristic impedance in the pass band should be constant to facilitate impedance matching. The classification of filters is as follows: Filter: 1. Passive filter 2. Active filter. Passive filter is further divided into: RC filter and LC filter. RC filter is further divided into: 1. Low-pass RC filter. 2 High-pass RC filter 3 Band-pass RC filter LC filter is divided into: 1 Low-pass LC filter 2 High-pass LC filter 3 Band-stop LC filter 4 Band-pass LC filter Active filter is divided into: 1 Active high-pass filter 2 Active low-pass filter 3 Active band-pass filter 4 Active band-stop filter There are currently two filter analysis and design methods: one is the image parameter analysis method, and the other is the operating parameter Analytical method (also called comprehensive method). The former is simple in design and easy to master, but the measured filter characteristics of this filter are quite different from the theoretical predetermined characteristics. It cannot achieve good impedance matching in the passband, making it difficult to meet the requirements for high accuracy of filter characteristics; the latter It is an analysis method based on network synthesis theory. It selects a selected area to find a network function that is similar to the ideal filter characteristics, and then implements the network function according to the comprehensive method. For the filter designed by this method, the measured filter characteristics are consistent with the theory. The predetermined characteristics are very close, so they are suitable for high-precision filter design requirements. 1. RC filter [see Table 1] Table 1 RC filter High-pass filter Low-pass filter Band-pass filter Multi-stage filter circuit (a) (b) (c) (d) Calculation formula three decibels fc≈1 /6.28RC fc≈1/6.28RC fL≈1/[6.28C2(RL+RB)] fH≈(RL+RB)/6.28C1RLRB One decibel fc≈1/3.2RC fc≈1/3.2RC fL≈1/ 3.2C2(RL+RB) fH≈(RL+RB)/[3.2C1RLRB The calculation example is known: fc=10kHz R=1kΩ, then the capacitance value of 3 dB is: C≈1/6.28fcR =1/6.28×10× 10 ×10 ≈0.015μF. It is known that fc=1kHZ R=3kΩ. Then the capacitance value of 3dB is: C≈1/6.28fcR =1/6.28×10×10 ×10 ≈0.015μF. It is known that: fH=200kHz, fL= 15kHz input impedance is 10, output impedance is 5kΩ ∵Input and output must have impedance matching∴ Let RL=10kΩ, RB=5kΩ, if calculated according to the 3dB formula, then C≈(RL+RB)/6.28fHRLRB=(10 +5)×10 /6.28×200×10 ×10×5×10 =240pF C2≈1/6.28×15×10 ×(10+5)10 ≈680pF Features RC filter is suitable for filtering out audio signals. For a simple filter, since the reactance of the capacitor decreases as the frequency increases, if the series arm is connected to the capacitor C and the parallel arm is connected to the resistor R, a high-pass filter is formed. The series arm of the low-pass filter is connected to the resistor R and the parallel arm is connected to the capacitor. C. Since the capacitive reactance of the capacitor decreases as the frequency increases, the high-frequency components of the signal cannot pass through the filter. fL is the lower limit cutoff frequency and fH is the upper limit cutoff frequency. Usually fH>10fL can avoid interference between combination circuits. Significant interference Since the filtering characteristics of a single-stage RC filter are slow, if you want to increase the steepness of the filtering characteristics, you can use a multi-stage RC filter. As can be seen from the figure, with each additional stage of RC filter, the decibel attenuation at the cutoff frequency The amount will increase by 16dB. Note that the units of the above formula are: R, RL, and RB are Ω, C, C1, and C2 are F, fc, fL, and fH are Hz. 2. LC filter LC filter is suitable for high-frequency signals. Filtering, which consists of an inductor L and a capacitor C. Since the inductive reactance increases as the frequency increases, and the capacitive reactance decreases as the frequency increases, the series arm of the LC low-pass filter is connected to the inductor, and the parallel arm is connected to the capacitor. High-pass filtering The L and C positions of the filter are opposite to it. Generally, there are two types of LC filters, one is the fixed K type LC filter, and the other is the m deduced type LC filter. K-type filter refers to the series arm impedance Z1 and parallel arm impedance Z2