How to solve the parameters of a second order regression filter

y^2=a*exp(-c*x)+b1.First, find the logarithm on both sides of the equation, and turn it into a linear (with the logarithm as a variable) to get 2lny=lna-cx+lnb, and now the problem is transformed into a solution, which can be solved with linear least squares. x=[,,y=[,,lny=log(abs(y));coef=[ones(length(y),1),ones(length(y),1),-x']\(2*lny');lna=coef(1);lnb=coef(2);c=coef(3);a=exp(lna);b=exp(lnb);

1. This has a special IC that can be used, and you can find it on the Internet.

2. In addition, split parts are used to form LED displays.

First, the audio message is converted to a DC level, and then the design is compared according to the requirements.

Then output to the LED.

It's really hard to explain all at once, so it's best to go to the hard city and check it out.

Use Multisim to design a Butterworth low-pass filter for you!

The order of the low-pass BAI filter is understood as a filter. du

The first-order low-pass zhi filter is to filter the special harmonic once;

The two-order filter is to filter the harmonics twice.

The higher the filtering order, the better the filtering effect, but the higher the filtering order, the higher the cost, because the higher the order, the more complex the circuit structure of the low-pass filter, and the more difficult it will be to deal with it.

The cut-off frequency of the low-pass filter refers to its frequency at 3dB, so you can determine its cut-off frequency by knowing its transfer function and plotting the transfer function curve.

As for the cut-off frequency, it is calculated as: f=1 2 rc

You can write the transfer function of the filter, the order of the denominator is the order of the filter, and the frequency corresponding to -3db is found on the curve of the transfer function is the cut-off frequency, generally the higher the order, the more complex the transfer function.

The book is generally divided according to the number of components, as for how to calculate the cut-off frequency of the low-pass filter, it is more complicated to say, it is recommended to find this professional book to see it.

First-order filters usually come with a resistor self.

and capacitors, the second order is the first order, and then a first order is added, as the name suggests, the third and fourth orders are also based on this principle.

The higher the order, the better the filtering effect, that is, the faster the attenuation after the cut-off frequency, as for the calculation of the cut-off frequency, it is generally f=1 2 rc

Parameter determination method:

1. Determine a capacitance value (according to the cut-off frequency, the cut-off frequency is different, and the choice of capacitance is also different) 2. Then find the r value according to the formula r=1 2*pi*fc (the value of the two-order rc is the same).

3. Next is the q value, which can be solved by the concatenation of the transfer function and the function n=2 in the Butterworth b(s) table.

q=1 3-af is solved to obtain af and then solve rf,r1 by af=1+rf r1 and the simultaneous equations of equal resistance at the two inputs of the op amp

Specifically, it's very troublesome, so let's briefly introduce it!

First, determine a capacitance value (according to the cut-off frequency, the cut-off frequency is different, the choice of capacitance is also different), and then according to the formula r=1 2*pi*fc to find the r value (the value of the two orders rc is the same), and then the q value, the transfer function and the function n=2 in the Butterworth b(s) table can be solved.

q=1 3-af is solved to obtain af and then solve rf,r1 by af=1+rf r1 and the simultaneous equations of equal resistance at the two inputs of the op amp

The first one should be the same as RB, where the capacitor is fed back to the negative end of the op amp. The negative end is used to suppress high-frequency response.

The second one is easy to understand, but it also has shortcomings, the principle of this is that two low-pass filters are connected in series, but instead of an active filter, it becomes a load, and R1 and C2 are a filter.

R2 and C1 are a filter for the first filter, but they are also a load, so the calculation of the circuit is very difficult to calculate, and the performance is not necessarily very good.

The first circuit is a little better, mainly C1

R1 plus the resistance of R2, and then C2, this constitutes a filter, the filtered signal is amplified by the op amp, and then through C1 positive feedback back, at this time, R2 and C2 are a filter circuit, and then added to the op amp amplification, so that the effect of filtering is far better than the second circuit.

Note: It is the filtered signal, to put it bluntly, it is a useful signal

Excuse me, is it okay to remove the R1 resistor? Why use two resistors? I asked.

Manual calculations are still quite complicated, you need to use Laplace transforms, if you are interested, you can refer to the analog electronic technology of Tong Shibai, which has detailed calculation methods.

The filter design process you mentioned is reversed, and the bandwidth, Q value, etc. should be set according to the needs of the system, and then the appropriate form and order of the filter should be designed and selected to achieve these goals.

Engineering is never to calculate the filter by yourself, ** e-book "Quick and Practical Design of Active Filters" or "Accurate Design Manual of Active Filters", according to the method given in the manual and ** to get the component values.

1. Write out its transfer function (s-domain).

2. Write out the amplitude frequency expression.

3. Find the corresponding frequency of the expression == as the cut-off frequency.

First, the characteristics are expressed in different ways.

1. First-order filter: The characteristics are expressed by first-order linear differential equations.

2. Second-order filter: The characteristics are expressed by second-order linear differential equations.

Second, the characteristics are different.

1. First-order filter: In addition to the characteristics of a linear continuous system in the "time domain", it can be expressed by differential equations or shock responses, and can also be expressed as a function with frequency as an independent variable.

2. Second-order filter: The left side of the equation is exactly the same as the standard form of a general second-order system, while the right side is the derivative term of the excitation source.

Third, the composition is different.

1. First-order filter: The excitation source forms a charging loop for the capacitor through a resistor, and responds to the voltage at both ends of the capacitor, which constitutes a "first-order system" described by the first-order differential equation.

2. Second-order filter: The excitation source forms a series loop through a resistor R, inductor L and capacitor C, and responds with the voltage at both ends of the resistor, which constitutes a "second-order bandpass filter" described by the second-order differential equation.

1. The characteristics are different.

First-order filter: Its characteristics are generally expressed by first-order linear differential equations.

Second-order filter: Its characteristics are expressed by second-order linear differential equations.

2. The characteristics are different.

First-order filter: Frequency response.

Second-order filter: The amplitude-frequency response is at zero frequency.

3. The application is different.

First-order filter: the circuit is the simplest, but the out-of-band transmission coefficient attenuates slowly, and is generally selected in the case where the out-of-band attenuation is not required.

Second-order filters: In addition to the fields of electronics and signal processing, an example of the application of bandpass filters is in the field of atmospheric science, where bandpass filters are used to filter weather data over the last 3 to 10-day time frames, so that only cyclones that are disturbances remain in the data domain.

The out-of-band attenuation of the simulated first-order filter is 20dB ten-octave, while the second-order is 40dB ten-octave, and the higher the order, the faster the out-of-band attenuation. It can be roughly assumed that the higher the order, the better the filtering effect, but sometimes it may be necessary to compromise on phase shift, stability, and other factors.

The higher the order, the better the filtering effect. Of course, whether it is an inductor-capacitor filter or an analog filter, the algorithm will become more complex as the order increases.