Analog Electronics Workshop

Filtering

March 13, 2013

A filters purpose in life

is to Obtain desired amplitude versus frequency characteristics

or

Introduce a purposeful phase-shift versus frequency response

or

Introduce a specific time-delay (delay equalizer)

Common filter applications

Band limiting filter in a

noise reduction application

Filter Types

Low-pass

High-pass

Band-pass

Band-stop, or band-reject

All-pass

Common filters employed in analog electronics

Filter Types Low-pass High-pass

Band-pass Band-stop

A low-pass filter has a single pass-band up to a cutoff

frequency, fc and the bandwidth is equal to fc

A high-pass filter has a single stop-band 0fl, and two stop-bands 0

Filter Order gain vs. frequency behavior for different low-pass filter orders

Frequency (Hz)

10 100 1k 10k 100k 1M

Gain

(dB

)

-80

-60

-40

-20

0

20

-160dB/dec

-120dB/dec

-80dB/dec

-40dB/decFilter Order

2nd

4th

6th

8th

Pass-band Stop-band

Frequency (Hz)

250.00 538.61 1.16k 2.50k

Gain

(dB

)

-12

-9

-6

-3

0

3

fC (-3dB) 1kHz

typically, one active filter stage is required for each 2nd-order function

Filter Reponses Common active low-pass filters - amplitude vs. frequency

Frequency (Hz)

100 1k 10k 100k

Ga

in (

dB

)

-80

-60

-40

-20

0

20

1kHz, 4th-order low-pass

responses, Av = +5V/V

Bessel

Butterworth

Chebyshev (2dB)

Gaussian

Linear Phase (0.5deg)

attenuation of nearly 30 dB

at 1 decade

Why Active Filters?

Inductor size, weight and cost for low frequency LC filters are often prohibitive

Magnetic coupling by inductors can be a problem

Active filters offer small size, low cost and are comprised of op-amps, resistors and capacitors

Active filter R and C values can be scaled to meet electrical or physical size needs

RS1 1k L1 225m

C1 220n

-

+ Vpas

RL1 1k

R1 2.72k R2 19.8k

-

+

IOP1

C1 10n

C2 47n

-

+ Vact

+

VG1

-

+

-

+

VCV1

RL2 1k

1kHz Passive LP

1kHz Active LP

Source

Impedance

Load

Impedance

Vact

Vpas

Passive and Active

reponses are identical

Frequency (Hz)

10 100 1k 10k 100k 1M

Gain

(dB

)

-100

-80

-60

-40

-20

0

20

Gain vs. FrequencyPassive and Active

reponses are identical

Vact

Vpas

Frequency (Hz)

10 100 1k 10k 100k 1M

Phase [

deg]

-180

-135

-90

-45

0

Phase vs. Frequency

Vact

Vpas

A comparison of a 1kHz passive and active 2nd-order, low-pass filter

-+

IOP1R1 4.64k R3 14k

C1

22

n

C2 2.2n

R2 9.31k

Vo_MFB

+

VG1

-

+

IOP1

R4 10kR3 10k

C3

10

n

R2 13.7kR1 2.1k

C2

22

n

Vo_SK

+

VG1

Two popular single op-amp active filter topologies 2nd-order implementations

Multiple Feedback (MFB) low-pass

supports common low-pass, high-pass and band-pass filter responses

inverting configuration

5 passive components + 1 op-amp per stage

low dependency on op-amp ac gain-bandwidth to assure filter response

Q and fn have low sensitivity to R and C values

maximum Q of 10 for moderate gains

Sallen-Key (SK) low-pass

supports common low-pass, high-pass and band-pass filter responses

non-inverting configuration

4-6 passive components + 1 op-amp per stage

high dependency on op-amp ac gain-bandwidth to assure filter response

Q is sensitive to R and C values

maximum Q approaches 25 for moderate gains

Active filter synthesis programs to the rescue!

Modern filter synthesis programs make filter development fast and easy to use; no calculations, tables, or nomograms required

They may provide low-pass, high-pass, band-pass, band-reject and all-pass responses

Active filter synthesis programs such as FilterPro V3.1 and Webench Active Filter Designer (beta) are available for free, from Texas Instruments

All you need to provide are the filter pass-band and stop-band requirements, and gain requirements

The programs automatically determine the filter order required to meet the stop-band requirements

FilterPro provides Sallen-Key (SK), Multiple Feedback (MFB) and differential MFB topologies; the Webench program features the SK and MFB

Commercially available programs such as Filter Wiz Pro provide additional, multi-amplifier topologies suitable for low sensitivity, and/or high-gain, high-Q filters

The operational-amplifier gain-bandwidth requirements

TI s FilterPro calculates each filter sections Gain-Bandwidth Product (GBW) from:

GBWsection = G fn Q 100

where: G is the section closed-loop gain (V/V) fn is the section natural frequency

Q is stage quality factor (Q = 1/2) 100 (40 dB) is a loop gain factor

The operational-amplifier gain-bandwidth requirement an example of the FilterPro estimation

FilterPros GBW estimation for the worst-case stage yields:

GBW = G fn Q 100

GBW = (2V/V)(10kHz)(8.82)(100) = 17.64MHz

vs. 16.94 MHz from the precise determination see Appendix for details

Let FilterPro estimate the minimum GBW for a 5th-order, 10 kHz (fc) low-pass

filter having a Chebyshev response, 2 V/V gain and a 3 dB pass-band ripple

Operational amplifier gain-bandwidth effects the Sallen-Key topology

The operational amplifier gain-bandwidth (GBW) affects the

close-in response

It also affects the ultimate attenuation at high frequency

-

++

U2 OPA340

-

+ Vo

R5 5.11k R6 931

C3 22n

C4 2.4n

R7 2.49k R8 22.6k

+

VG1

+

VS1 5

+

VS2 2.5

Sallen-Key - Butterworth 10 kHz,

2nd-order low-pass, Av = +10 V/V

T

Frequency (Hz)

1k 10k 100k 1M 10M

Ga

in (

dB

)

-60

-40

-20

0

20

40

OPA170 GBW 1.2MHz

OPA314 GBW 2.7 MHz

OPA340 GBW 5.5 MHz

OPA140 GBW 11 MHz

Op-amp fH Hz dB

OPA170 90 k -21.8

OPA314 110 k -23.5

OPA340 260k -38.1

OPA140 428 k -44.3

FilterPro GBW 7.1 MHz

Operational amplifier gain-bandwidth effects the Multiple Feedback (MFB) topology

The MFB shows much less GBW dependency than the SK

Close-in response shows little effect

Insufficient GBW affects the roll-off at high frequencies

The lowest GBW device (1.2 MHz) produces a gain deviation about 50-60

dB down on the response

A GBW 7 MHz for this example provides near ideal roll-off

+

VS1 2.5

+

VS2 2.5

R1 1.13k R2 1.02k

C1 22n+

VG1

C2 1n

R3 11.3k

-

+

Vo

-

++

U1 OPA340

Multiple Feedback - Butterworth 10 kHz,

2nd-order low-pass, Av = +10 V/V

T

Frequency (Hz)

1k 10k 100k 1M 10M

Ga

in (

dB

)

-80

-60

-40

-20

0

20

40

OPA170 GBW 1.2 MHz

OPA314 GBW 2.7 MHz

OPA340 GBW 5.5 MHz

OPA140 GBW 11 MHz

Achieving optimum active filter performance Capacitors

Use quality C0G or film dielectric for low

distortion

Type C0G has a low temperature

coefficient (20 ppm)

Lower tolerance, 1-2%, assures more

accurate response

Higher order filters require ever lower

tolerances for

accurate response

Resistors

Use quality, low tolerance resistors

1 % and 0.1% reduce filter sensitivity

Lower tolerance assures more accurate response

Low temperature coefficient reduces response change with

temperature

Higher order filters require ever lower tolerances for accurate

response

Operational Amplifier

Use required GBW - especially for the Sallen-Key

Be sure to consider the amplifier noise

High Zo effects can distort response

Higher amplifier current often equates to lower Zo and wider GBW

Consider dc specifications especially bias current

Signal source

Zs 0

An op-amp driver with low closed-

loop gain often

provides a low

source impedance

FilterPro Simulation Measurement

16

FilterPro

1. Select Lowpass

2. Next

FilterPro

1. Check Set Fixed

2. Next

FilterPro

1. Select

Butterworth

2. Next

FilterPro

1. Finish

FilterPro 1. Change Res Tol to 1%

2. Change Cap Tol to 5%

3. Notice Min GBW

Circuit Response

FilterPro 1. Repeat process, but change Topology to Sallen-Key

FilterPro

Circuit Response

1. Be sure to change R and C tolerances

2. Notice Min GBW for op amp

TINA Exercise-OPA2170 MFB

V+

V-

V+ 15

V- 15

V+

V-

R4 11.3k R5 5.76k

+Vin

Vout

C8 39n

C7 10n

R3 11.3k

-

++

U1 OPA170

FilterPro

TINA Exercise-OPA2170 MFB

Analysis->AC Analysis->AC Transfer Char

TINA Exercise-OPA2170 MFB

T

Frequency (Hz)

10 100 1k 10k 100k

Gain

(dB

)

-60

-40

-20

0

TINA Exercise-Filtering T

Frequency (Hz)

10 100 1k 10k 100k

Gain

(dB

)

-60

-40

-20

0

OPA170-MFB

OPA170-SK

OPA241-MFB

OPA241-SK

NI myDAQ Exercise-Filtering

Populate U1 with OPA2170

Set J7 & J8 to MFB

V+

V-

R4 11.3k R5 5.76k

J8

+

AO(0)J7

AI(1)

C8 39n

C7 10n

R3 11.3k

-

++

U1 OPA170

S-K

S-K

MFB

MFB

12

3

1

23

NI myDAQ Exercise-Filtering

Launch Bode Start Frequency=10Hz

Stop Frequency=20kHz

Steps=10

Peak Amplitude=2.00

Run

OPA2170 MFB TINA Results Lab Results

T

Frequency (Hz)

10 100 1k 10k 100k

Gain

(dB

)

-60

-40

-20

0

NI myDAQ Exercise-Filtering

Set J7 & J8 to SK

V+

V-

R1 7.87k R2 14.7k

C5 10n

C6 22n

J8

+

AO(0)

J7

AI(1)-

++

U1 OPA170

MFB

S-KMFB

S-K

12

3

1

23

FilterPro

OPA2170 Sallen-Key TINA Results Lab Results

T

Frequency (Hz)

10 100 1k 10k 100k

Gain

(dB

)

-60

-40

-20

0

OPA2241 Sallen-Key

Replace OPA2170 with OPA2241

TINA Results Lab Results T

Frequency (Hz)

10 100 1k 10k 100k

Gain

(dB

)

-40

-20

0

OPA2241 MFB

Set J7 & J8 to MFB

TINA Results Lab Results T

Frequency (Hz)

10 100 1k 10k 100k

Gain

(dB

)

-60

-40

-20

0

NI myDAQ Exercise-Filtering

TINA Results Lab Results

OPA2241 GBW=35kHz

OPA2170 GBW=1.2MHz

T

OPA2241-SK

OPA2241-MFB

OPA2170-SK

OPA2170-MFB

Frequency (Hz)

10 100 1k 10k 100k

Gain

(dB

)

-60

-40

-20

0

OPA2170-MFB

OPA2170-SK

OPA2241-MFB

OPA2241-SK

FilterPro

Further Reading

Successful application of Active Filters

By Thomas Kuehl

Senior Applications Engineer

and

John Caldwell

Applications Engineer

Precision Analog Linear ProductsTexas Instruments Tucson, Arizona

Backup/Extra