KuenziFilter.pdf

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Wir schaffen Wissen heute fr morgen

Paul Scherrer Institut

10.05.2014

Ren Knzi

Filter Design - Passive Power Filters

CERN ccelerator School !"#$% &a'en% Swit(erlan'


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Suitable Filter Structures

R. Knzi Power Filter Design CAS 2014 10.05.2014 2


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Suitable Filter Structures



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H-Bridge



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H-Bridge with CM filter



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2nd order filter - Transferfunction


1

1

1

1

R

C

s 1

LCRC s L C C s

RCs 1

1

1

with

3rd order PT

(1)

1st order PD


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1

1

1

3rd order PT in itsnormalized form:

(2)


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By expanding (2) and comparing the coefficients with (1) we get:

1

1

(3a)

(3b)

(3c)

The 3 independent equations (3a.3c) contain 5 unknowns (L1, C1, RD, CD and0). Therefore we have the choice to select 2 of them and the remaining 3 depend

on that selection.


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2nd order filter - Selection of 0


For a given frequency

B well in the blocking area (

B >>

0) we can define thedesired attenuation GB. In the blocking area the highest order terms of both the nu-merator and denominator in equation (1) dominate, therefore (1) can be simplified to:

! 1

(4)


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2nd order filter - Definition of L1


For cost reasons L1 shouldbe as small as possible,but a too small inductancewill result in an excessive

ripple current!

The DC-voltage across C1 is m*VDC. When the IGBT is on, the current in L1 increases

and the peak-peak ripple current

IL1 can be calculated:

"# $%#

$& "' "' "' 1 (

)*# ( + $%#

$& ( 1

,- "

' 1 (

"' 1 ( (

,-

"' ./0

,- )*#

Maximum 0.25for m = 0.5

(5)


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2nd order filter - Definition of L1


Alternative approach to determine L1:

*#2345567255

2345567255

0 8 ,345567

2345567255

0 8 ,345567 *#2345567255(6)


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2nd order filter Calcualting filter elements


Substitute (3a) in (3c) and we receive:

Selection: L1 and 0 Selection: C1 and 0 Selection: L1 and C1

Solve (3b) for CD:

Solve (3a) for RD:

(7a) (7b) (7c)

(8)

(9)


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2nd order filter Example 1


DC-link voltage: 200V DC-link current: 500A IL1 50App. C1 must be 22mF (because of high ripple current)

Design a 2nd order filter for all three given optimization methods and compare the results.


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Select L1 to meet the ripplecurrent requirement:

Select C1:

Calculate the remaining

filter elements

(6)

(7c, 8, 9)

2345567255

0 8 ,345567 *#2345567255

0.. ./19 "::

0 8 9..; .

00(?


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x3 x5 x8

Results:


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Maximum amplitude of resonance:Butterworth 4.5 dBBessel 3.1 dBCritical damping 2.3 dB

Frequency, for -3 dB attenuation:Butterworth 74 Hz

Bessel 67 HzCritical damping 59 Hz

Attenuation: -28dB @ 300Hz


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DC-link voltage: 120V fs = 20kHz IOut_max = 500A IL1 50App.

Attentuation: GB = 250 @

B = 2*

*20kHz

Same premises asfor example 3

Design a 2nd order filter for all three given optimization methods and compare the results.


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"' ./0

,- )*#

10." ./0

0.>@ .< 9.=>


Select 0 to meet theattenuation requirement:


filter elements

(5)

(7a, 8, 9)

(4)

d


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x3 x5 x8

Results:

2 d d fil E l 2


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Maximum amplitude of resonance:Butterworth 4.5 dBBessel 3.1 dB

Critical damping 2.3 dB

Frequency, for -3 dB attenuation:Butterworth 1.5 kHz

Bessel 1.4 kHzCritical damping 1.2 kHz

Attenuation: -48dB @ 20kHz

4th d filt T f f ti


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4th order filter - Transferfunction


1

1

1

1

1

1

1

1

4th d filt T f f ti


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1

A B

1

1

AA B

B

1

B

A

with

1st order PD

5th order PT

(10)

4th d filt T f f ti


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5th order PT in its normalized form:

(11) 1

1 1

1

Optimisation methods:

4th order filter Transferfunction


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1

A A

B

B

1

By expanding (11) and comparing the coefficients with (10) we get:

B

B

A

A

(12a)

(12b)

(12c)

(12d)

(12e)

4th order filter selection of and L


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4th order filter selection of 0 and L1


The 5 independent equations (12a.12e) contain 7 unknowns (L1, C1, L2, C2, RD, CDand 0). Therefore we have the choice to select 2 of them (0 and L1) the remaining 5depend on that selection.

For a given frequency B well in the blocking area (B >> 0) we can define thedesired attenuation GB. In the blocking area the highest order terms of both the

numerator and denominator in equation (10) dominate, therefore (10) can besimplified to:

A

A A

B

B

B

B

D(13)

! B 1

Select L1 according to ripple current requirements with (5) or (6)

4th order filter Calculating filter elements


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4th order filter Calculating filter elements


By solving the equation system (12a12e) we get:

B

B

A

A

B A

BA 1

A

BA

A

A

B A

with

(14a)

(14b)

(14c)

(14d)

(14e)

4th order filter Example 3


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Design a 4th order filter for all three given optimization methods and compare the results.

DC-link voltage: 120V

fs = 20kHz IOut_max = 500A IL1 50App. Attentuation: GB = 250 @ B = 2**20kHz

Same premises asfor example 2



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"' ./0

,- )*#

10." ./0

0.>@ .< 9.=>


Select 0 to meet theattenuation requirement:

D


filter elements

(5)

(14a.e)

(13)



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4 order filter Example 3


Results:



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4 order filter Example 3


Maximum amplitude of resonance:Butterworth 8.6 dBBessel 5.4 dB

Critical damping 3.8 dB

Frequency, for -3 dB attenuation:Butterworth 5.5 kHz

Bessel 5.0 kHzCritical damping 3.9 kHz

Attenuation: -48dB @ 20kHz

Comparison of different filter designs


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+64%

+42%



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Practical Aspects - Wiring


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Practical Aspects Wiring

Effect of a 0.5m longwire 16mm2 (wiring of C1and C2)

Skin Effect Skin depth in Cu @

20kHz: 0.5mm

Reduces the effective

cross section to 6.3 mm2

Wire resistance @20kHz: 1.4m

Wire inductance is

approx. 0.5H


To be avoided !

Practical Aspects low inductive setup


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Practical Aspects low inductive setup


C1

L1

L2

C2

RD

CD

Life time of electrolytic capacitors


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y p


The useful life time of an electrolytic capacitor depends verymuch on the ripple current and the ambient temperature.

Nominal ripple current at nominal frequency (100Hz) and nominal capacitor temperature (85C).

17.4A in our example


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Life time of electrolytic capacitors


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y p


Determine the allowed ripple

current for a desired usefullife and Ta:

For 25000h (3 years)

and Ta = 50C,2.6 * 23.5A = 61A

For 250000h (30years)and Ta = 50C

0.85 * 23.5A = 20A

The useful life time dramatically decreases at higher ambient temperatures!


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References

U. Tietze, Ch. Schenk; Halbleiter-Schaltungs-Technik, 12. Auflage, Pages 815ff

Epcos, Datasheet, Capacitors with screwterminals Type B43564, B43584, November2012


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KuenziFilter.pdf