Design of second-order RC low-pass filter for PWM wave to DC

1. Principle and Application

(1) The principle is directly quoted * atom STM32 Explain PWM turn DAC Chapter *

 

(2) When MCU in DAC When the function is not enough , But also output controllable DC level , This mode can be used to achieve the purpose ; Others are made up of PWM Controlled load device , Such as proportional valve 、 The motor , To test the equivalent current flowing through these loads , You can also use this method

2. Demand analysis

We use second order here RC Low pass filtering to achieve the purpose of current detection resistance PWM Wave equivalent DC DC level function ;

 

The circuit diagram is as follows , there PWM No MCU Direct output , But the signal processed by the push-pull amplifier circuit

 

 

R11/R12 、C3/C4 Form a second order RC wave filtering ; here R11=R12、C3=C4

3. Mathematical calculation

If we require the result of filtering to reach the detection current ±1mA, be 1 The accuracy of one bit reaches 1.5/2048=0.0007324V, Sampling resistance level range 0-1.5V

Assume the filtered signal voltage range 0-1.5V, Then the maximum value of the first harmonic 1.5*2/π=0.95496, Then the circuit should at least provide -20log(0.95496/0.0007324V)=-63dB attenuation

the PWM yes F=20KHz

If it's first order RC wave filtering , The cut-off frequency Fs Is calculated by -10*log[1+(F/Fs)^2]=-63dB, have to Fs=14Hz

If it's second order RC wave filtering , The cut-off frequency Fs Is calculated by -20*log[1+(F/Fs)^2]=-63dB, have to Fs=532Hz

Parameters RC choice ：

A second-order low-pass filter is used here ,Fs=1/2πRC, have to R=1KΩ,C=300nF（ Here is the designer's choice ）,(R11=R12=R,C3=C4=C), This RC The product is a constant value , as for R  C Select combination , It can be determined according to practical application , But there is an idea ：R or C Not too small , such as R When it's big ,C Must be smaller , At this time, due to the parasitic effect of the circuit , Resulting in a large proportion of the final equivalent capacitance increase , It will affect the filtering effect , That won't work ; Choose... In reverse R equally

First order and second-order comparison , Except for the difference in circuit ; The calculated cut-off frequency is also very different

The second-order attenuation is a little more serious than the first-order attenuation 、 But the second-order delay is small , And the first-order ripple is large

4. Circuit simulation and waveform data - Second order filter

Because the actual load operating current range ：0-1A, Therefore, the voltage range on the current resistance 0-1.5V

Parameter description ： Use here Cadence OrCAD Circuit simulation function

V1 Is the minimum output level

V2 Is the maximum output level , Actually V1-V2 Choose between to test

TD yes PWM Wave delay time

TR Is the edge rise time

TF Is the edge descent time

PW Duty cycle

PER cycle

It can be seen from the figure that the green waveform is t=3-4ms Reach stability when , Maximum 3-4ms Delay of （ according to 100% Calculation ）

Actually RC Parameter determination , According to the delay time of the output 、 Considering the ripple size ; Of course, this is just a simulation , Into the actual hardware circuit , You will find that there are still changes

In the simulation waveform , You will find that the filtered waveform will attenuate , This needs to be compensated

5. Hardware experiment waveform and data

Finally, select the parameters R=1kΩ、C=220nF The waveforms measured by the actual hardware are as follows ：

The simulation results are as follows ：

Compare the waveform , The simulation is basically consistent with the actual hardware test