The design method of active filter can be roughly summarized into two categories: cascade method and analog method.
According to the requirements of technical indicators, find out the transfer function that can be physically realized (usually can be found in the ready-made active filter materials and manuals), and decompose it into the product of low-order functions (mainly second-order functions). The low-order functions are realized by active circuits and then cascaded together to realize the original transfer function. Circuits that implement low-order functions are generally called basic sections, and there are many typical second-order basic section circuits for designers to choose from. According to the number of amplifiers used in the basic section, it can be divided into single amplifier circuit, double amplifier circuit, three amplifier circuit, and four amplifier circuit. Figure 1 shows several basic section examples. The cascade method design process is relatively simple, the circuit characteristic adjustment is easy, the realized circuit is relatively economical, it is a commonly used method.
First design an LC filter that can meet the technical index requirements as a design prototype, and then use an active circuit to simulate it. This method can be divided into component simulation method and functional simulation method, and the prototype is mostly based on the LC ladder type filter with double-terminal termination resistor. Generally, the analog method requires more components than the cascade method.
When designing an active filter, generally follow the following design steps.
1. Design of transfer function
According to the requirements of filter characteristics, design a certain type of n-order transfer function, which can be decomposed into several low-order (such as first-order, second-order or third-order) transfer function product form.
When designing low-pass, high-pass, band-pass, and band-stop filters, the frequency normalization method is usually used, and the low-pass prototype transfer function is first designed. If you need to design a low-pass filter, you can transform the low-pass prototype transfer function into a low-pass target transfer function: if you need to design a high-pass filter, you can transform the number passed by the low-pass prototype into a high-pass target transfer function; if you need to design In the case of a band-pass filter, the low-pass prototype transfer function can be transformed into a band-pass target transfer function; if the design of a band-stop filter is required, the number passed by the low-pass prototype can be transformed into a band-stop target transfer function.
2, circuit design
According to the design requirements of each low-order transfer function, design and calculate the basic section of the active filter circuit. First select the circuit form, and then design and calculate the corresponding component parameter values according to the designed transfer function. According to the design requirements, specific requirements are put forward for each circuit component.
3, circuit assembly and debugging
First design and assemble each low-order filter circuit, and then cascade each low-order circuit to form the entire filter circuit. Then carry on the corresponding adjustment and performance test to the whole filter circuit, and examine the design result.
Design a low-pass filter circuit, requiring its cut-off frequency F0 to be 10 kHz, Q=0.707, passband gain H=10, f is far greater than fo, the attenuation rate is not less than 40dB/10 frequency band, cutoff frequency and gain The error of etc. is required to be within ±10%.
1. First select the circuit form, and determine the order n of the filter according to the design requirements.
(1) From the attenuation rate requirement -20xndB/decade frequency≥40dB/decade frequency range, calculate n=2
(2) According to the requirements of the subject, choose the infinite gain multiple feedback low-pass active filter circuit form.
2. Design the specific values of the corresponding components in the circuit according to the requirements of the transfer function.
(1) Select the value of capacitor C and resistor R according to the characteristic frequency fo of the filter.
The size of the capacitor C generally does not exceed 1uF, and the value of the resistance R is in the order of kQ. Table 1 provides the reference comparison table for the selection of cut-off frequency fo and capacitance value.
(1) Select C2, set the value of capacitor C2 to 1 nanofarad, and get the values of C1, R1, R2, and R3.
3. If there is a sensitivity requirement, further limit the error and stability of the component parameter value according to the sensitivity.