Low-Pass Butterworth Filter Design

Low-Pass Butterworth Filter Design

NI Multisim 10

Low-Pass Butterworth Filter

R10Ω C1

0F

L10H

L20H

R20Ω

2V1

1 Vpk 1kHz 0°

0

13

Open Multisim 10 and start building the Butterworth LPF like in figure.

Press CTRL+W to open the Component Library.


we will describe the design of a simple low-pass Butterworth filter using normalized prototype circuits.

Butterworth filter has a smooth passband response and more gradual out-of-band attenuation.

The procedure for designing a filter based on a normalized prototype Step1: you determine the order of filter that will

be needed to fulfill your design requirements. Step2: list the element values that will produce a

lowpass filter of that order with a cutoff frequency of 1 radian/second, with source and load terminations of 1 Ohm connected to it. These are the normalized prototype values

Step3: Formulas are used to scale those values to the actual source and load impedances and to the actual design cutoff frequency.


Cutoff Frequency — the point at which 3dB

Fc 100 MHz

Passband Ripple— The maximum allowable ripple within the passband

R(dB) 1 dB

The frequency at which the specified passband ripple occurs.

Fr 50MHz

Out of band attenuation A (dB) 30 dB

The frequency at which the out of band attenuation must be met

FX 500 MHz

Calculate order (N) of filter Step1: The cutoff frequency Fc, out of band attenuation, AdB, and

its frequency Fx, are related to the order of the filter (n) by the following formula:

• The cutoff frequency Fc, passband attenuation, RdB, and its frequency Fr, are related to the order of the filter (n) by the following formula:

Based on the values we entered, the filter we are designing will have to be of order n = 3 to meet all specifications.

n

C

Xdb F

FA

2

1log10

nR

R

C

FF 2

1

10 110

Read prototype element values from table ---Step2:

Rs=1Ohm L1=1H C2=2F L3=1H RL=1 Ohm

R11Ω

R11Ω

L11H

L11H

C1

2F

Recall that the prototype values in the tables have been normalized with respect to frequency and termination impedance. Note that RS = RL = 1 Ohm. If you used these values to build a filter, the cutoff frequency would be 1 Hertz, and your source and load impedances would have to be 1 Ohm.

Impedance and frequency scale Step3: The next step is to de-normalize the prototype element values,

scaling them up to the desired cutoff frequency and input/output impedance. The transformation formulas that yield the appropriate values for a desired cutoff frequency and source/load resistor value

are:

Lc

n

RFC

C2

c

Ln

FRl

L2

where:C = the final capacitor value L = the final inductor value cn = low-pass prototype capacitor value from table ln = a low-pass prototype inductor value from table RL = the desired load resistor value, for impedance scaling Fc = the desired cutoff frequency 2*pi*Fc= the desired cutoff radian frequency, for frequency scaling


R150Ω C1

63.662pF

L179.577nH

L279.577nH

R250Ω

2V1

1 Vpk 1kHz 0°

XBP1

IN OUT

1

0

3

0


Phase Response

Magnitude Response

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Low-Pass Butterworth Filter Design