# Basic principle introduction of the active smoothing circuit Dave Ross Blo

A brief introduction

1.1 Classification of the electric-wave filter; The active filter is actually a kind of amplifier with particular frequency response. It increases passive components such as some R, C,etc. and forms on the basis of operation amplifier. Usually the active filter is divided into:

Low-pass filter

High-pass filter

Band-pass filter

Band elimination filter

Characteristic curves of their range frequency is shown as in Fig. 1.

Fig. is 1 active filter of Frequency Response FR

The electric-wave filter can be formed by passive reactivity component or crystal too, is called the passive filter or crystal filter.

1.2 Use of the electric-wave filter
The electric-wave filter mainly uses the empty frequency component in the filtration signal, for example, there is a signal of relatively low frequency, among them partial discharge detector include the interference of the frequency component of some great. The filtering course is shown as in Fig. 2.

Filtering course of Fig. 2

2 active low-pass filters LPF
2.1 Main technical indicator of the low-pass filter
1 Gain to noise temperature ratio Avp of the band pass
The gain to noise temperature ratio of the band pass means the electric-wave filter is in the inner voltage gain of pass-band, as shown in Fig. 3. Inner amplitude-versus-frequency curve of LPF band pass with good characteristic is smooth, the inner voltage gain of stopband is basically zero.
2 Alpha cut frequency fp of the band pass
Its definition is the same as upper cut-off frequency of the amplifying circuit, see Fig. 3. , with calling the transition band the band pass between the stopbands, the narrower the transition band is, prove.

Amplitude-versus-frequency curve of Fig. 3 LPF

2.2 Simple low-pass active filter of first order
The circuit of the low-pass filter of first order is shown as in Fig. 4, its amplitude/frequency characteristic is shown in Fig. 5, the dash line is an ideal situation in the picture, the full line is a actual situation. The characteristic is that the circuit is simple, it is too slow that the stopband decays, selectively discrepancy.

Low-pass circuit LPF of first order of Fig. 4 Amplitude-versus-frequency curve of the first order LPF of Fig. 5

Act as f =At 0 o’clock, the capacitor can be deemed to open a way, the inner gain to noise temperature ratio of the band pass is

A brief introduction

1.1 Classification of the electric-wave filter; The active filter is actually a kind of amplifier with particular frequency response. It increases passive components such as some R, C,etc. and forms on the basis of operation amplifier. Usually the active filter is divided into:

Low-pass filter

High-pass filter

Band-pass filter

Band elimination filter

Characteristic curves of their range frequency is shown as in Fig. 1.

Fig. is 1 active filter of Frequency Response FR

The electric-wave filter can be formed by passive reactivity component or crystal too, is called the passive filter or crystal filter.

1.2 Use of the electric-wave filter
The electric-wave filter mainly uses the empty frequency component in the filtration signal, for example, there is a signal of relatively low frequency, among them include the interference of the frequency component of some great. The filtering course is shown as in Fig. 2.

Filtering course of Fig. 2

2 active low-pass filters LPF
2.1 Main technical indicator of the low-pass filter
1 Gain to noise temperature ratio Avp of the band pass
The gain to noise temperature ratio of the band pass means the electric-wave filter is in the inner voltage gain of pass-band, as shown in Fig. 3. Inner amplitude-versus-frequency curve of LPF band pass with good characteristic is smooth, the inner voltage gain of stopband is basically zero.
2 Alpha cut frequency fp of the band pass
Its definition is the same as upper cut-off frequency of the amplifying circuit, see Fig. 3. , with calling the transition measuring bridge band the band pass between the stopbands, the narrower the transition band is, prove.

Amplitude-versus-frequency curve of Fig. 3 LPF

2.2 Simple low-pass active filter of first order
The circuit of the low-pass filter of first order is shown as in Fig. 4, its amplitude/frequency characteristic is shown in Fig. 5, the dash line is an ideal situation in the picture, the full line is a actual situation. The characteristic is that the circuit is simple, it is too slow that the stopband decays, selectively discrepancy.

Low-pass circuit LPF of first order of Fig. 4 Amplitude-versus-frequency curve of the first order LPF of Fig. 5

Act as f =At 0 o’clock, the capacitor can be deemed to open a way, the inner gain to noise temperature ratio of the band pass is

The transfer function of the low-pass filter of first order is as follows
,Among them
This transfer function type sample is similar to the frequency expression of gain to noise temperature ratio of a RC low-pass link, just lack passband gain Avp this one.

2.3 Simple second order low-pass active filter
In order to make the output voltage drop for more quick speed on the high frequency section, in order to improve the filtering result, add a RC low-pass filtering link, is called the second order active smoothing circuit. It is better than the filtering result of the low-pass filter of first order. The circuit diagram of second order LPF is shown as in Fig. 6, the amplitude-versus-frequency curve is shown as in Fig. 7.

Second order low-pass circuit LPF of Fig. 6 Second order low-pass circuit amplitude-versus-frequency curve of Fig. 7

1 Gain to noise temperature ratio of the band pass
Act as f =At 0 o’clock, every capacitor can be deemed to open a way, the inner gain to noise temperature ratio of the band pass is

2 Transfer function of the second order low-pass active filter
Can be written out according to Fig. 8-2.06

Usually have, unite and set up three above type solving, get the transfer function of the electric-wave filter

3Alpha cut frequency of the band pass
Change s into j, make 0 =2 f0 =1/RC Can have

Act as f =Fp hour, the mould of the aboving denominator

Solve alpha cut frequency:

Compared with ideal second order Bode diagram, after exceeding f0, amplitude/frequency characteristic drop with speed of 40 dB/dec, faster than the decline of first order. But in the alpha cut frequency fp of the band pass It is not quick enough that the amplitude/frequency characteristic drops between f0.

2.4 Second order voltage-controlled type low-pass active filter
1 Second order voltage-controlled type LPF
The second order voltage-controlled type low-pass active filter is shown as in Fig. 8. A capacitor C1 among them was earthy originally, change to receive the Ausgang now. Obviously, the changing to connect of C1 does not influence the gain to noise temperature ratio of the band pass.

Amplitude/frequency characteristic of the second order voltage-controlled type LPF picture 9 second order voltage-controlled type LPF of Fig. 8

2 Transfer function of second order voltage-controlled type LPF

As to the node N, can list the following equations

Unite and set up three above type solving, get the transfer function of LPF

It shows that aboving, the gain to noise temperature ratio of band pass of this electric-wave filter should be smaller than 3, could ensure circuit stable operation.

3 Frequency response
Can write out the expression of frequency response by transfer function

Act as f =F0 hour, aboving all right abbreviation is

Define the Q factor q-factor of the active filter as f =F0 diploid mould of voltage amplification of hour compares with gain to noise temperature ratio of the band pass

The above-mentioned two types show, act as 2

2.5 Second order against the low-pass active filter of the facies pattern
It is shown as in Fig. 8-2.10 against the facies pattern LPF that second order, it adds a knot of RC low-pass circuit to form in the input end of the integrating device of proportion of oppisite phase. It is shown as in Fig. 8-2.11 against the improved circuit of the facies pattern LPF that second order.

It is feedbacked against the facies pattern second order LPF that Fig. 10 is multi-channel against the second order LPF picture 11 of the facies pattern
Knowing by Fig. 11

As to the node N, can list the following equations

Transfer function is

Frequency response is

In the above-mentioned all types

3 active high-pass filters HPF
The circuit diagram of the second order voltage-controlled type active high-pass filter is shown as 13.12 pictures

Second order voltage-controlled type second order voltage-controlled type HPF frequency character of HPF picture 13 of Fig. 12
1 Gain to noise temperature ratio of the band pass

2 Transfer function

3 Frequency response
Order ,Can obtain the Frequency Response FR expression

Therefore the frequency response characteristic drawn is shown as in Fig. 13.
Conclusion: Act as f <<F0 hour, the slope of the amplitude-versus-frequency curve is 40 dB/dec; When Avp is greater than or equal to 3, the circuit is autoexcited.

4 active band-pass filters BPF And band elimination filter BEF
Active band-pass filter BPF The circuit is shown as in Fig. 14. Active band elimination filter BEF The circuit is shown as in Fig. 15.
The band-pass filter was made up by low-pass RC link and high pass RC link. Set up the lower cut-off frequency of high pass as less than low-pass upper cut-off frequency. It is a band elimination filter on the contrary.

Second order voltage-controlled type BPF picture 15 second order voltage-controlled type BEF of Fig. 14

If you want to win strain wave property, generally need higher order. The design of the electric-wave filter calculates it is very troublesome, can rely on curve and relevant computer aided design softwares of engineering calculation while needing.
The example 1: Require fc of second order voltage-controlled type LPF =400Hz, q-factor is 0.7, tries asking the resistance, capacitance value in the circuit of Fig. 16.

Fig. 16 second order voltage-controlled type LPF

Solve: According to fc, chooses C, and then ask R.
1. The capacity of C is difficult to exceed 1uF. Because the high-capacity capacitor is bulky, costly, should try hard to avoid using.
Fetch C =0.1 UF, 1k<R<1MO

Calculate R =3979, fetches R =3.9k

2. Ask R1 and Rf, because f according to q-factor =Fc hour Q =1/3-Avp =0.7 ,Then Avp =1.57 . According to the relation between Avp, R1, Rf, two input ends of integrated operational amplifier connect the symmetrical condition 1Rf/R1 of the resistance =Avp =1.57,R1 //Rf=RR=2R . Solve and have: Tagged