<> catalogue

Chapter I ： Overall thinking
Chapter II ： circuit design
Chapter III ： Experiment and analysis
1, Time domain analysis
2, Frequency domain analysis
3,S Domain analysis
Chapter IV ： summary
Chapter V ： appendix

<> Chapter I Overall thinking

This design focuses on the fourth-order Butterworth low-pass filter , Slave circuit design , Time domain analysis , frequency analysis ,S Domain analysis starts from several aspects , Through theoretical analysis , simulation experiment , Real measurement to study and verify the properties of the whole system . Verify the impulse response, step response and zero input response of the system in time domain ; Verify the amplitude frequency curve and phase frequency curve of the system in frequency domain analysis ; stay S The stability of the system is studied by pole distribution on the field .

<> Chapter II circuit design

1, Selection of op amp chip
The cut-off frequency of this experiment is not greater than 1KHZ, Bandwidth not greater than 1MHZ, Choose a general-purpose operational amplifier chip , Finally decided to adopt LMV358 This general chip .

2, The circuit principle diagram

It can be obtained by looking up the table , The amplification factor of the primary circuit of the fourth-order Butterworth is 1.152, The second stage amplification factor is 2.235.

be R2/R1=1.152-1=0.152,R4/R3=2.235-1=1.135. Therefore, the resistance value is selected as R1=100KΩ,R2=15.2KΩ,R1=10KΩ,R1=12.35KΩ. All resistors used for filtering are 20kΩ, Capacitor adoption 0.01uf. Then resonant frequency f0=1/(2ΠRC)≈795HZ. Total gain of the circuit Av=1.152
2.235=2.57472. The following is the solution process of the system transfer function .

Chapter III ： Experiment and analysis
1, Time domain analysis
① Step response
a, theoretical analysis ：
use matlab The system function is obtained by inverse Laplace transform 1/s Time domain expression of . Then pass matlab Draw the image of the time-domain expression .
Enter command ：

Solution ：

Enter command ：

Get the waveform ：

b,multisim simulation
Generation of step signal ：

Let the frequency be small enough when designing parameters , The duty cycle is large enough , Ensure that the analog step signal .
circuit design ：

simulation result ：

It can be seen that the simulated waveform is basically correct , The voltage gain is approximately 2.574, The waveform is also similar to matlab equally .
c, Actual effect

② Impulse response
a, theoretical analysis
stay matlab input ：

Solution ：

input ：

obtain ：

b,multisim simulation
Generation of impulse signal ：

simulation result ：

It can be seen that high voltage appears at the beginning , Then there is a very low voltage , Then the oscillation decreases gradually , Consistent with theoretical analysis .
c, Actual effect

③ Sinusoidal function response
a, theoretical analysis
Enter command ：

obtain ：

b,multisim simulation
Circuit ：

result ：

It can be seen from the above two figures ,multisim Simulation results and matlab Basically consistent .
c, Actual effect

Compared with theoretical value , There is a little difference in voltage amplitude , But the overall trend is consistent .

Basically consistent with the theoretical value .
2, Frequency domain analysis
① Amplitude frequency curve
a, theoretical analysis
Enter command ：

obtain ：

It can be seen from the figure that the passband gain is 20lg(2.574)=8.21, The cut-off frequency is 5000rad/s, That is, about 795HZ. Since the two damping coefficients are specially set , Compared with the previous calculation f0=1/(2ΠRC)≈795HZ identical .
b,multisim simulation
circuit design ：
Measuring amplitude frequency curve with baud meter

result ：

It can be seen from the above figure , When the gain is 5.25dB Hour , Namely -3dB Around o'clock , The frequency is about 795HZ, This is related to matlab The calculation results of are the same .
c, Actual effect
Pictures of actual measurement part ：

measurement result ：

from matlab Draw a scatter chart ：

It can be seen from the figure , Actual measurement effect and matlab and multisim The results are roughly the same , Theoretically deceived f=795HZ Hour ,20*lg(Av)=5.21, And in the figure 5.29 close .
② Phase frequency curve
a, theoretical analysis
Enter command ：

obtain ：

It can be seen from the figure that the cut-off angular frequency is 6210rad/s, Namely 988HZ. stay 988HZ place ,ΔΨ=-223°

b,multisim simulation
circuit design ：
Measuring amplitude frequency curve with baud meter

simulation result ：

As can be seen from the above figure , Results and matlab The calculation results are basically consistent .
c, Actual effect
Pictures of actual measurement part ：

measurement result ：

use matlab Draw phase frequency curve ：

As can be seen from the above figure, in f=988HZ Hour , The corresponding phase difference is -224°, This is different from the theoretical value -223° Basically consistent .
3,S Domain analysis
Enter command ：

obtain ：

As can be seen from the above figure , Poles are on the left , So the system is stable .

<> Chapter IV ： summary

This experiment is actually a multifaceted analysis of a system with fixed components , First, consult the information and then design the circuit according to the Convention , Then calculate the transfer function of the system , Finally, the experiment is carried out around the system transfer function . Through this experimental design , Aware of the importance of theoretical knowledge . The second-order low-pass filter circuit we have done before , The concept of damping coefficient is not involved , use 20KΩ and 0.01uf The cut-off frequency of the second-order circuit constructed by the component is not 1/(2ΠRC), But by setting the damping coefficients of the first and second stages , You can make the cut-off frequency equal to 1/(2ΠRC).
Through this experiment , Learned ：
①matlab As a powerful mathematical calculation tool , Can pass matlab Calculate cut-off frequency , Draw spectrum diagram , Draw the response of various signals ,matlab It can be more used for theoretical calculation .

②multisim How to use the medium baud meter , The unit of amplitude frequency and phase frequency of baud meter is matlab of use margin The units of the image drawn by the function are consistent , however matlab If rate uses angular frequency , and multisim With HZ. Only when the start value and end value of the baud meter are set reasonably, the baud meter will display the image .

③ stay matlab In the process of calculating the cut-off frequency , Stuck margin Input parameter problem of , Finally, it is found that it must be used tf Function can only be used as a system transfer function after it is built margin Input parameters for , Even if the transfer function has been converted to include s Formula of .

④ When making circuits , The resistance used for amplification factor must be accurate , This is directly related to the frequency domain response . So in this experiment 15.2KΩ and 12.35KΩ The resistance of adopts two 0603 The encapsulated resistor is used in series , Increase accuracy .

<> Chapter V appendix

Actual circuit diagram

Boom surface

schematic diagram

Pcb chart

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